https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) https://plato.stanford.edu/entries/proof-theoretic-semantics/
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
On 6/19/2026 2:23 AM, Mikko wrote:I've spent a couple of hours reading that web page. It is abstract in
On 18/06/2026 22:35, olcott wrote:Calling my views (anchored in proof theoretic semantics)
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and reject
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
reject alternative views out-of-hand without review.
alternative views out-of-hand without review.
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics. https://plato.stanford.edu/entries/proof-theoretic-semantics/
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and
| perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has purported to understand Proof-theoretic semantics and repeatedly cited a
web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that Gödel's Incompleteness Theorem is unproven when one takes PTS as a basis. I put
it to you this is a lie, and that you are as clueless about PTS as you
are about Gödel's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a central role in reasoning and inference". I put it to you you cannot do this.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and
| perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has purported to understand Proof-theoretic semantics and repeatedly cited a
web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that Gödel's Incompleteness Theorem is unproven when one takes PTS as a basis. I put
it to you this is a lie, and that you are as clueless about PTS as you
are about Gödel's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a central role in reasoning and inference". I put it to you you cannot do this.
On 6/19/26 1:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been >> | occupied with logical constants. Logical constants play a central
role
| in reasoning and inference, but are definitely not the exclusive,
and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has
purported to understand Proof-theoretic semantics and repeatedly cited a
web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that Gödel's
Incompleteness Theorem is unproven when one takes PTS as a basis. I put
it to you this is a lie, and that you are as clueless about PTS as you
are about Gödel's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a
central role in reasoning and inference". I put it to you you cannot do
this.
u ever gunna write something that isn't totally saturated with various fallacies alan?
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:That's non-responsive to my point, which I'll repeat: you are as clueless
In comp.theory olcott <polcott333@gmail.com> wrote:My basis in PTS is what is referred to in the Literature
On 6/19/2026 2:23 AM, Mikko wrote:I've spent a couple of hours reading that web page. It is abstract in
On 18/06/2026 22:35, olcott wrote:Calling my views (anchored in proof theoretic semantics)
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and reject
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
reject alternative views out-of-hand without review.
alternative views out-of-hand without review.
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and
| perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has purported to understand Proof-theoretic semantics and repeatedly cited a web page far outside his own understanding, believing nobody else would ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that Gödel's Incompleteness Theorem is unproven when one takes PTS as a basis. I put
it to you this is a lie, and that you are as clueless about PTS as you
are about Gödel's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a central role in reasoning and inference". I put it to you you cannot do this.
as Dag Prawitz Theory of Grounds and its extensions and
elaborations. https://scholar.google.com/scholar?hl=en&as_sdt=0,42&q=Prawitz+theory+of+grounds
I came up with all this stuff on my own entirely onAll things beyond your understanding, if they are coherent things at all.
the basis of reverse-engineering from first principles.
I only very recently found out that it has an existing
basis in the work of others.
These are the usual things that PTS refers to:
Natural Deduction, Sequent Calculus, Martin-Löf Type Theory,
Intuitionistic Logic. I extend the essence of PTS all the way
to natural language formalized as CycL.
https://en.wikipedia.org/wiki/CycL
----
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>> | occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and >>> | perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has
purported to understand Proof-theoretic semantics and repeatedly cited a >>> web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that Gödel's >>> Incompleteness Theorem is unproven when one takes PTS as a basis. I put >>> it to you this is a lie, and that you are as clueless about PTS as you
are about Gödel's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a
central role in reasoning and inference". I put it to you you cannot do >>> this.
My basis in PTS is what is referred to in the Literature
as Dag Prawitz Theory of Grounds and its extensions and
elaborations.
https://scholar.google.com/scholar?hl=en&as_sdt=0,42&q=Prawitz+theory+of+grounds
That's non-responsive to my point, which I'll repeat: you are as clueless about PTS as you are about Gödel's Theorem. You are as ignorant of PTS
as you are of mathematics. Refute me by responding directly to the
points I made in my last post.
I came up with all this stuff on my own entirely on
the basis of reverse-engineering from first principles.
I only very recently found out that it has an existing
basis in the work of others.
These are the usual things that PTS refers to:
Natural Deduction, Sequent Calculus, Martin-Löf Type Theory,
Intuitionistic Logic. I extend the essence of PTS all the way
to natural language formalized as CycL.
https://en.wikipedia.org/wiki/CycL
All things beyond your understanding, if they are coherent things at all.
--
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and
| perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has purported to understand Proof-theoretic semantics and repeatedly cited a
web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that Gödel's Incompleteness Theorem is unproven when one takes PTS as a basis. I put
it to you this is a lie, and that you are as clueless about PTS as you
are about Gödel's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a central role in reasoning and inference". I put it to you you cannot do this.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central
role
| in reasoning and inference, but are definitely not the exclusive,
and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and
extra-logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has
purported to understand Proof-theoretic semantics and repeatedly cited a
web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that Gödel's
Incompleteness Theorem is unproven when one takes PTS as a basis. I put
it to you this is a lie, and that you are as clueless about PTS as you
are about Gödel's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a
central role in reasoning and inference". I put it to you you cannot do
this.
The field since 2016 has expanded to include what
logicians would call quantifier free FOL.
I will research this more so that I can explain
my own ideas within the frame-of-reference of PTS.
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants.
The was the original position:
Ever since 2016 PTS has been anchored in Horn Clauses
thus not limited to logical constants.
On 06/19/2026 07:35 PM, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>> | occupied with logical constants.
The was the original position:
Ever since 2016 PTS has been anchored in Horn Clauses
thus not limited to logical constants.
One might aver that Huntington postulates are more relevant than Horn clauses.
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and
| perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Never was an actual contradiction when properly
formalized. The directed graph of its evaluation
always had a cycle.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog finally once and for all resolves the Liar
Paradox as semantically incoherent within the
analytical framework of Proof Theoretical Semantics.
On 19/06/2026 23:28, Alan Mackenzie wrote:Do its proponents have any idea what PTS ought to be useful for? What it
In comp.theory olcott <polcott333@gmail.com> wrote:Yes. It means that proof-theoretic semantics is currently and in the
On 6/19/2026 2:23 AM, Mikko wrote:I've spent a couple of hours reading that web page. It is abstract in
On 18/06/2026 22:35, olcott wrote:Calling my views (anchored in proof theoretic semantics)
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and reject
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
reject alternative views out-of-hand without review.
alternative views out-of-hand without review.
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and
| perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
near future not useful as making it useful requires much time and
effort if it is possible at all.
----
Mikko
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role >>> | in reasoning and inference, but are definitely not the exclusive, and
| perhaps not even the most typical sort of entities that can be defined >>> | inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical >>> | inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? What it
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
a principle of thorough reason
supplants, subsumes, and includes
a principle of sufficient reason
a principle of implosion
obviates and makes an example of
a principle of explosion
On 06/19/2026 04:30 PM, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>> | occupied with logical constants. Logical constants play a central >>> role
| in reasoning and inference, but are definitely not the exclusive, >>> and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and
extra-logical
| inferential definitions alike.
Does this have any meaning?
I put it to everybody here that Peter Olcott has been bluffing. He has >>> purported to understand Proof-theoretic semantics and repeatedly cited a >>> web page far outside his own understanding, believing nobody else would
ever challenge this deception.
I'm challenging it now. Peter, you have repeatedly stated that Gödel's >>> Incompleteness Theorem is unproven when one takes PTS as a basis. I put >>> it to you this is a lie, and that you are as clueless about PTS as you
are about Gödel's Theorem. Feel free to refute my assertion.
Or, at the very least, explain in readily accessible English precisely
what is meant above by "logical constants" and how and why "they play a
central role in reasoning and inference". I put it to you you cannot do >>> this.
The field since 2016 has expanded to include what
logicians would call quantifier free FOL.
I will research this more so that I can explain
my own ideas within the frame-of-reference of PTS.
Such reductionisms as "term-free" or "constant-free" or "variable-free"
or "quantifier-free" are simplifications that fail to include
resolutions of the paradoxes of induction, quantification, identity, infinity, and continuity.
On 06/19/2026 07:35 PM, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>> | occupied with logical constants.
The was the original position:
Ever since 2016 PTS has been anchored in Horn Clauses
thus not limited to logical constants.
One might aver that Huntington postulates are more relevant than Horn clauses.
On 06/19/2026 10:27 PM, Ross Finlayson wrote:
On 06/19/2026 07:35 PM, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>> the extreme. One thing is utterly clear: its level of abstraction is >>>> well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>> been
| occupied with logical constants.
The was the original position:
Ever since 2016 PTS has been anchored in Horn Clauses
thus not limited to logical constants.
One might aver that Huntington postulates are more relevant than Horn
clauses.
Horn clauses are useful idioms to declare or claim inductive completion
about things like completion and compactness and tail recursion what
would otherwise be inductive incompleteness, and thusly are merely notational, while Huntington postulates include actual accounts of
quantifier disambiguation and the like about induction and
counter-induction and super-classical completions, besides the usual
reading
that Huntington postulates are just a usual logic, which in the usual accounts of formal logic is merely "quasi-modal" logic, and ignorant
of quantifier disambiguation and other notions of all the implicits.
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
On 19/06/2026 23:28, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been >> | occupied with logical constants. Logical constants play a central
role
| in reasoning and inference, but are definitely not the exclusive,
and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun. --------------------------------------
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>> the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role >>> | in reasoning and inference, but are definitely not the exclusive, and >>> | perhaps not even the most typical sort of entities that can be defined >>> | inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical >>> | inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
----
Copyright 2026 Olcott
On 6/20/2026 11:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
That's not what I asked. I asked if the following statement is true:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
[ Followup-To: set]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>>>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>> | occupied with logical constants. Logical constants play a central role >>>>> | in reasoning and inference, but are definitely not the exclusive, and >>>>> | perhaps not even the most typical sort of entities that can be defined >>>>> | inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical >>>>> | inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
Taking a best guess at what that phrase is meant to mean, it doesn't. Or
at the very least, you have failed to meet your burden of proof that it
does.
We know that in any sufficiently powerful language (and the bar is not
high), there are statements which are "incomputable". If you doubt this,
and still believe PTS gives a different result, please show some
mathematical proof which comes out differently between standard logic and PTS, illustrating the essence of PTS which makes it so.
--
Copyright 2026 Olcott
On 6/20/2026 10:23 AM, dbush wrote:
On 6/20/2026 11:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
That's not what I asked. I asked if the following statement is true:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
So you are not smart enough to understand that
when the actual composition of the Moon is specified
and that this composition is not green cheese that
the system would report false?
I will not play head sames with you on this. Instead
of head games your replies will be ignored.
On 6/20/2026 10:34 AM, Alan Mackenzie wrote:No, I have understood it well enough. It is an immature branch of
In comp.theory olcott <polcott333@gmail.com> wrote:You have failed to sufficiently understand the gist of proof
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:Taking a best guess at what that phrase is meant to mean, it doesn't. Or at the very least, you have failed to meet your burden of proof that it does.
Mikko <mikko.levanto@iki.fi> wrote:reliably computable for the entire body of knowledge.
On 19/06/2026 23:28, Alan Mackenzie wrote:Do its proponents have any idea what PTS ought to be useful for? What it >> It makes "true on the basis of meaning expressed in language"
In comp.theory olcott <polcott333@gmail.com> wrote:Yes. It means that proof-theoretic semantics is currently and in the >>>> near future not useful as making it useful requires much time and
On 6/19/2026 2:23 AM, Mikko wrote:I've spent a couple of hours reading that web page. It is abstract in >>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
On 18/06/2026 22:35, olcott wrote:Calling my views (anchored in proof theoretic semantics)
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and reject
https://www.youtube.com/@rossfinlaysonreject alternative views out-of-hand without review.
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>> Some people only memorize conventional views and
alternative views out-of-hand without review.
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
That page's level of abstraction is high enough that I can't be
bothered to read it any further. If it actually says anything at
all, that something is heavily disguised. From it's "Conclusion
and Outlook" section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>> | occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and >>>>> | perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential >>>>> | definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
effort if it is possible at all.
theoretic semantics.
This applies to your next statement as well. You must have a 100%That is a condescending lie. Your ideas are very far from proven and
complete understanding of the gist of PTS and then my ideas are proven coherent and true.
--We know that in any sufficiently powerful language (and the bar is not high), there are statements which are "incomputable". If you doubt this, and still believe PTS gives a different result, please show some mathematical proof which comes out differently between standard logic and PTS, illustrating the essence of PTS which makes it so.--
Copyright 2026 Olcott
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
[ Followup-To: set]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 10:34 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered to read it any further. If it actually says anything at >>>>>>> all, that something is heavily disguised. From it's "Conclusion >>>>>>> and Outlook" section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>>>> | occupied with logical constants. Logical constants play a central role
| in reasoning and inference, but are definitely not the exclusive, and >>>>>>> | perhaps not even the most typical sort of entities that can be defined
| inferentially. A framework is needed that deals with inferential >>>>>>> | definitions in a wider sense and covers both logical and extra-logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
Taking a best guess at what that phrase is meant to mean, it doesn't. Or >>> at the very least, you have failed to meet your burden of proof that it
does.
You have failed to sufficiently understand the gist of proof
theoretic semantics.
No, I have understood it well enough. It is an immature branch of
philosophy which gives mathematical results the same as standard logic
does. It is _you_ who have failed sufficiently to understand PTS.
Otherwise you could answer questions about it.
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius language"
of all the truths, then the haeccity and quiddity, or "thing-nesses",
these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word
and the light of the word, and the Atman and Brahman as giving accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of
the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and the fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements
in the theory and gets connected via language to non-logical or properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model
of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth,
where truth
is the quantity and truth is conserved, and the universe is full of it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after well-dispersion, the infinitary reasoning since the classical accounts
of the super-classical or Zeno's thought experiments, what makes for
a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and super-classical reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism",
that there's one good theory and any number of ways to talk about it.
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge
and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is.
On 6/20/2026 11:44 AM, olcott wrote:
On 6/20/2026 10:23 AM, dbush wrote:
On 6/20/2026 11:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
That's not what I asked. I asked if the following statement is true:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
So you are not smart enough to understand that
when the actual composition of the Moon is specified
and that this composition is not green cheese that
the system would report false?
So you're saying the moon is not made of green cheese? So based on
that, is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
I will not play head sames with you on this. Instead
of head games your replies will be ignored.
I am not playing head games. I am merely employing Socratic questioning.
https://en.wikipedia.org/wiki/Socratic_questioning
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius language"
of all the truths, then the haeccity and quiddity, or "thing-nesses",
these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word
and the light of the word, and the Atman and Brahman as giving accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of
the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller
dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the
enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and the
fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements
in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model
of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth,
where truth
is the quantity and truth is conserved, and the universe is full of it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the
paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical accounts
of the super-classical or Zeno's thought experiments, what makes for
a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and super-classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism",
that there's one good theory and any number of ways to talk about it.
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge
and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is.
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius language"
of all the truths, then the haeccity and quiddity, or "thing-nesses",
these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word
and the light of the word, and the Atman and Brahman as giving accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller dialectic, >>> the pre-Socratics or Eleatics, making the paleo-classical account, of
the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller
dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the
enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and the
fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements
in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model
of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth,
where truth
is the quantity and truth is conserved, and the universe is full of it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the
paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical accounts
of the super-classical or Zeno's thought experiments, what makes for
a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and super-classical >>> reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism",
that there's one good theory and any number of ways to talk about it.
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge
and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is.
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
On 6/20/2026 11:47 AM, Ross Finlayson wrote:
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius language" >>>> of all the truths, then the haeccity and quiddity, or "thing-nesses",
these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word
and the light of the word, and the Atman and Brahman as giving accounts >>>> of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller
dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of
the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller
dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the
enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and the >>>> fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements
in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model
of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth,
where truth
is the quantity and truth is conserved, and the universe is full of it, >>>> then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the
paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical accounts >>>> of the super-classical or Zeno's thought experiments, what makes for
a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and super-
classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism", >>>> that there's one good theory and any number of ways to talk about it.
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge >>>> and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is. >>>>
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
All pathological self-reference derives a cycle
in the directly graph of the evaluation sequence
of the expression. This causes the expression to
be rejected as semantically incoherent input.
On 6/20/2026 11:47 AM, Ross Finlayson wrote:
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius language" >>>> of all the truths, then the haeccity and quiddity, or "thing-nesses",
these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word
and the light of the word, and the Atman and Brahman as giving accounts >>>> of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller
dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of
the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller
dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the
enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and the >>>> fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements
in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model
of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth,
where truth
is the quantity and truth is conserved, and the universe is full of it, >>>> then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the
paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical accounts >>>> of the super-classical or Zeno's thought experiments, what makes for
a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and
super-classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism", >>>> that there's one good theory and any number of ways to talk about it.
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge >>>> and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is. >>>>
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
All pathological self-reference derives a cycle
in the directly graph of the evaluation sequence
of the expression. This causes the expression to
be rejected as semantically incoherent input.
I handled this for the Liar Paradox
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory of Gödel's G
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification
tree exists.
and the Halting Problem proofs https://github.com/plolcott/x86utm/blob/master/Halt7.c
Proof Theoretic Semantics halt prover HHH correctly
determines that its input DD is ungrounded in its
atomic base according to the operational semantics
of the C programming language.
On 6/20/2026 12:57 PM, olcott wrote:
On 6/20/2026 11:47 AM, Ross Finlayson wrote:
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius
language"
of all the truths, then the haeccity and quiddity, or "thing-nesses", >>>>> these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word >>>>> and the light of the word, and the Atman and Brahman as giving
accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller
dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of >>>>> the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller >>>>> dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the >>>>> enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and
the
fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements >>>>> in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model >>>>> of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth, >>>>> where truth
is the quantity and truth is conserved, and the universe is full of
it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the >>>>> paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical accounts >>>>> of the super-classical or Zeno's thought experiments, what makes for >>>>> a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and super-
classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism", >>>>> that there's one good theory and any number of ways to talk about it. >>>>>
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge >>>>> and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is. >>>>>
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
All pathological self-reference derives a cycle
in the directly graph of the evaluation sequence
of the expression. This causes the expression to
be rejected as semantically incoherent input.
Big words from someone who's unable to say if the following statement is true:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
On 06/20/2026 09:57 AM, olcott wrote:
On 6/20/2026 11:47 AM, Ross Finlayson wrote:
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius
language"
of all the truths, then the haeccity and quiddity, or "thing-nesses", >>>>> these are archaic terms yet common since about at least 800 years.
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word >>>>> and the light of the word, and the Atman and Brahman as giving
accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller
dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of >>>>> the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller >>>>> dialetic of the full Aristotlean and Aristotlean realism, and then
since the Scholastics and the renewed Aristotlean, DesCartes and the >>>>> enlightened rationality, Leibnitz and the universals, then Kant and
Hegel bring Being and Nothing, and the sublime and ding-an-sich and >>>>> the
fuller dialectic, these are elements of the canon and the dogma and
the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements >>>>> in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description
basically has that a "heno-theory" is a realist structuralist's model >>>>> of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth, >>>>> where truth
is the quantity and truth is conserved, and the universe is full of >>>>> it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the >>>>> paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical accounts >>>>> of the super-classical or Zeno's thought experiments, what makes for >>>>> a thorough sort of account of the modal, temporal, relevance logic,
in descriptive accounts of formalism, for infinitary and
super-classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist positivism", >>>>> that there's one good theory and any number of ways to talk about it. >>>>>
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and knowledge >>>>> and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable,
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean
realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there is. >>>>>
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
All pathological self-reference derives a cycle
in the directly graph of the evaluation sequence
of the expression. This causes the expression to
be rejected as semantically incoherent input.
I handled this for the Liar Paradox
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory of Gödel's G
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification
tree exists.
and the Halting Problem proofs
https://github.com/plolcott/x86utm/blob/master/Halt7.c
Proof Theoretic Semantics halt prover HHH correctly
determines that its input DD is ungrounded in its
atomic base according to the operational semantics
of the C programming language.
I'd imagine that "directed" graph was intended,
yet what's so is that a more _thorough_ account
actual detects cycles instead of presuming their
inexistence, which is a stipulation that simply
doesn't apply to fuller graphs in relation.
There are at least three laws of large numbers (LLN's):
the Law of Large Numbers (LLN):
the usual Law of Small Numbers, that finite numbers m are small, there's
a larger one m + 1, setting up, and requiring, induction
the Law of Larger Numbers (LLN+):
moreso than the Law of Large Numbers, also there exists n >> m,
setting up, and requiring, counter-induction
the Law of Largest Numbers (LLN++):
furthermore there are infinitely-grand numbers besides infinitely-many, setting up, and requiring, super-classical deduction
Then things like "Chaitin's Omega" about "The Halting Problem"
and "P(Halts) the Probability of Halting" get involved variously
about laws of large numbers, models of Cantor space, and these
sorts of accounts since Erdos of "Mathematical Independence"
(meaning demonstrably contradictory given competing rulialities)
the Erdos "Giant Monsters" of Mathematical Independence, instead
for accounts of a "Great Atlas of Mathematical Independence",
that resolves the competing rulialities with analytical bridges,
with "Zeno Machines" and models of computation, "supertasks"
beyond "small supertasks" and so on.
On 6/20/2026 12:19 PM, Ross Finlayson wrote:
On 06/20/2026 09:57 AM, olcott wrote:
On 6/20/2026 11:47 AM, Ross Finlayson wrote:
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius
language"
of all the truths, then the haeccity and quiddity, or "thing-nesses", >>>>>> these are archaic terms yet common since about at least 800 years. >>>>>>
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word >>>>>> and the light of the word, and the Atman and Brahman as giving
accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller
dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of >>>>>> the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller >>>>>> dialetic of the full Aristotlean and Aristotlean realism, and then >>>>>> since the Scholastics and the renewed Aristotlean, DesCartes and the >>>>>> enlightened rationality, Leibnitz and the universals, then Kant and >>>>>> Hegel bring Being and Nothing, and the sublime and ding-an-sich
and the
fuller dialectic, these are elements of the canon and the dogma and >>>>>> the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements >>>>>> in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description >>>>>> basically has that a "heno-theory" is a realist structuralist's model >>>>>> of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth, >>>>>> where truth
is the quantity and truth is conserved, and the universe is full
of it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the >>>>>> paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical
accounts
of the super-classical or Zeno's thought experiments, what makes for >>>>>> a thorough sort of account of the modal, temporal, relevance logic, >>>>>> in descriptive accounts of formalism, for infinitary and
super-classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist
positivism",
that there's one good theory and any number of ways to talk about it. >>>>>>
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and
knowledge
and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable, >>>>>>
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean >>>>>> realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there >>>>>> is.
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
All pathological self-reference derives a cycle
in the directly graph of the evaluation sequence
of the expression. This causes the expression to
be rejected as semantically incoherent input.
I handled this for the Liar Paradox
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory of Gödel's G
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification >>> tree exists.
and the Halting Problem proofs
https://github.com/plolcott/x86utm/blob/master/Halt7.c
Proof Theoretic Semantics halt prover HHH correctly
determines that its input DD is ungrounded in its
atomic base according to the operational semantics
of the C programming language.
I'd imagine that "directed" graph was intended,
yet what's so is that a more _thorough_ account
actual detects cycles instead of presuming their
inexistence, which is a stipulation that simply
doesn't apply to fuller graphs in relation.
There are at least three laws of large numbers (LLN's):
the Law of Large Numbers (LLN):
the usual Law of Small Numbers, that finite numbers m are small, there's
a larger one m + 1, setting up, and requiring, induction
the Law of Larger Numbers (LLN+):
moreso than the Law of Large Numbers, also there exists n >> m,
setting up, and requiring, counter-induction
the Law of Largest Numbers (LLN++):
furthermore there are infinitely-grand numbers besides infinitely-many,
setting up, and requiring, super-classical deduction
Then things like "Chaitin's Omega" about "The Halting Problem"
and "P(Halts) the Probability of Halting" get involved variously
about laws of large numbers, models of Cantor space, and these
sorts of accounts since Erdos of "Mathematical Independence"
(meaning demonstrably contradictory given competing rulialities)
the Erdos "Giant Monsters" of Mathematical Independence, instead
for accounts of a "Great Atlas of Mathematical Independence",
that resolves the competing rulialities with analytical bridges,
with "Zeno Machines" and models of computation, "supertasks"
beyond "small supertasks" and so on.
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
All the rest is out-of-scope.
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two are different things. A contradiction is a statement which is necessarily
false. A paradox is a statement to which no truth value can be
consistently assigned.
André
On 6/20/2026 12:19 PM, Ross Finlayson wrote:
On 06/20/2026 09:57 AM, olcott wrote:
On 6/20/2026 11:47 AM, Ross Finlayson wrote:
On 06/20/2026 09:45 AM, olcott wrote:
On 6/20/2026 11:29 AM, Ross Finlayson wrote:
On 06/20/2026 08:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
Hm. Here the idea is that there are no more "meta-theories",
of what's a "super-theory", that's a "mono-heno-theory",
among various accounts of "heno-theories", any sort "theory".
So, giving the "fundamental question of metaphysics" ("why is
there something rather than nothing?"), and, what it is, starts
with an idea of a universe of Truth, all the logical truisms
and the grounds for a logical universe, then that the "paradox"
of quantification gives an example "Confessing Liar", that
is itself, a template and example of what would be un-true,
yet only as found and discovered among all the truth. This
invokes ideas like "univocity", about there being a "Comenius
language"
of all the truths, then the haeccity and quiddity, or "thing-nesses", >>>>>> these are archaic terms yet common since about at least 800 years. >>>>>>
So, the Bible and the Vedas have examples, for example starting
with "in the beginning ..." about a space of geometry and the
contents of the Space-Time, and "in the beginning..." about the word >>>>>> and the light of the word, and the Atman and Brahman as giving
accounts
of inter-subjective objectivity, then with Zeno's arguments after
Heraclitus for dual monism and Parmenides for a wider, fuller
dialectic,
the pre-Socratics or Eleatics, making the paleo-classical account, of >>>>>> the most common references, for discourse and reason,
about the objects of mathematics and physics, and language and
knowledge. Then, since the Aristotlean, and with the wider and fuller >>>>>> dialetic of the full Aristotlean and Aristotlean realism, and then >>>>>> since the Scholastics and the renewed Aristotlean, DesCartes and the >>>>>> enlightened rationality, Leibnitz and the universals, then Kant and >>>>>> Hegel bring Being and Nothing, and the sublime and ding-an-sich
and the
fuller dialectic, these are elements of the canon and the dogma and >>>>>> the doctrine.
A "heno-theory", then, a "one-theory", basically has logical elements >>>>>> in the theory and gets connected via language to non-logical or
properly-logical objects, any account of abstraction or description >>>>>> basically has that a "heno-theory" is a realist structuralist's model >>>>>> of a theory, that models other theories. Then the idea of a
mono-heno-theory is again that it's a one theory with all the truth, >>>>>> where truth
is the quantity and truth is conserved, and the universe is full
of it,
then that any other exercise in theory is an exercise in it.
Void and Universe <- logic's
Point and Space <- geometry's
Increment and Partition <- arithmetic's
Metaphor and Metonymy <- language's, algebra's
Energy and Entelechy <- physics' contents
Dynamis and Dunamis <- physics' activity
So, Continuity and Infinity are approached classically, then for the >>>>>> paleo-classical and the post-modern account, is a usual sort of
formal treatment that has a "the logic" and "the objects of the
universe of mathematics" with "strong mathematical platonism",
then that the formalism has for rulial and regular accounts of
competing rulialities well-foundedness and well-ordering after
well-dispersion, the infinitary reasoning since the classical
accounts
of the super-classical or Zeno's thought experiments, what makes for >>>>>> a thorough sort of account of the modal, temporal, relevance logic, >>>>>> in descriptive accounts of formalism, for infinitary and
super-classical
reasoning, after axiomless deduction, for actual infinity
and replete continuity, mathematically.
Teleology and Ontology <- the objective and subjective
Science and Statistics <- the inter-subjective
So, "complementary duals" make a great account as to why the
competing rulialities result the analytical bridges instead of
the inductive impasses and have the structuralist realism of
the super-classical results of analysis and for quantifier
disambiguation and the extraction of mathematical implicits
thusly a greater account of reason and mathematically, and
in its discourse meeting the requirements and desiderata of
both "strong mathematical platonism" and "strong logicist
positivism",
that there's one good theory and any number of ways to talk about it. >>>>>>
"Foundations", "Sole Foundations", "True Foundations"
There's a paleo-classical post-modern realist structuralist's
mathematics, then also about the intelligence and wisdom and
knowledge
and science,
Intelligence and Wisdom
Knowledge and Science
about the real, the natural, and the rational, and the reasonable, >>>>>>
De Re and De Natura
De Res and De Racio
then, thusly, there's one good theory at all that's an Aristotlean >>>>>> realism and actualized for Aristotle, and a Hegelian idealism and
with a wider, fuller dialectic for Hegel, and that's the one there >>>>>> is.
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
That's merely an account of "ontology in a vacuum"
and is bereft the needful for accounts of continuity and infinity,
and can't claim to resolve paradoxes it makes for itself.
Hilbert-Bernays paradox
All pathological self-reference derives a cycle
in the directly graph of the evaluation sequence
of the expression. This causes the expression to
be rejected as semantically incoherent input.
I handled this for the Liar Paradox
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory of Gödel's G
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification >>> tree exists.
and the Halting Problem proofs
https://github.com/plolcott/x86utm/blob/master/Halt7.c
Proof Theoretic Semantics halt prover HHH correctly
determines that its input DD is ungrounded in its
atomic base according to the operational semantics
of the C programming language.
I'd imagine that "directed" graph was intended,
yet what's so is that a more _thorough_ account
actual detects cycles instead of presuming their
inexistence, which is a stipulation that simply
doesn't apply to fuller graphs in relation.
There are at least three laws of large numbers (LLN's):
the Law of Large Numbers (LLN):
the usual Law of Small Numbers, that finite numbers m are small, there's
a larger one m + 1, setting up, and requiring, induction
the Law of Larger Numbers (LLN+):
moreso than the Law of Large Numbers, also there exists n >> m,
setting up, and requiring, counter-induction
the Law of Largest Numbers (LLN++):
furthermore there are infinitely-grand numbers besides infinitely-many,
setting up, and requiring, super-classical deduction
Then things like "Chaitin's Omega" about "The Halting Problem"
and "P(Halts) the Probability of Halting" get involved variously
about laws of large numbers, models of Cantor space, and these
sorts of accounts since Erdos of "Mathematical Independence"
(meaning demonstrably contradictory given competing rulialities)
the Erdos "Giant Monsters" of Mathematical Independence, instead
for accounts of a "Great Atlas of Mathematical Independence",
that resolves the competing rulialities with analytical bridges,
with "Zeno Machines" and models of computation, "supertasks"
beyond "small supertasks" and so on.
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
All the rest is out-of-scope.
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>> the extreme. One thing is utterly clear: its level of abstraction is >>>> well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
thus you have no basis toFalse, see above.
assess these skills of mine.
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem proof, Godel's proof, and Tarski's proof, each of which you've been attempting
(and failing) to refute for years.
That you are unable to recognize this is proof that you don't understand proof by contradiction.
thus you have no basis toFalse, see above.
assess these skills of mine.
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
----
Copyright 2026 Olcott
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem proof, Godel's proof, and Tarski's proof, each of which you've been attempting
(and failing) to refute for years.
That you are unable to recognize this is proof that you don't understand proof by contradiction.
--thus you have no basis toFalse, see above.
assess these skills of mine.
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
HHH never sees any contradiction it only sees that its proof
remains stuck in recursion.
That you are unable to recognize this is proof that you don't
understand proof by contradiction.
thus you have no basis toFalse, see above.
assess these skills of mine.
On 6/20/2026 10:23 AM, dbush wrote:
On 6/20/2026 11:22 AM, olcott wrote:
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
That's not what I asked. I asked if the following statement is true:
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
So you are not smart enough to understand that
when the actual composition of the Moon is specified
and that this composition is not green cheese that
the system would report false?
On 06/20/2026 12:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem proof,
Godel's proof, and Tarski's proof, each of which you've been attempting
(and failing) to refute for years.
That you are unable to recognize this is proof that you don't understand
proof by contradiction.
thus you have no basis toFalse, see above.
assess these skills of mine.
Hard constructivists don't even _accept_ proof-by-contradiction.
Somehow then "structural realists" and "realist structuralists"
may also be "hard constructivists" while "extreme rationalists".
Since "quasi-modal material implication" has "see rule 1: last wins",
it contradicts itself.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
So, in your system, all facts are axioms?
That would appear to make it
not a very useful system, since there is nothing left to prove. Also it
is difficult, if even possible in general, to determine whether some assertion is an axiom or not. Your "axioms" are not axioms in the normal sense of the word; they're an encyclopaedia.
Or is a fact different from an "empirical fact" in some way?
--
Copyright 2026 Olcott
On 6/20/2026 4:03 PM, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value >>>>> can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
The above is unclear, as "HHH" and "DD" could refer to:
On 6/20/2026 3:17 PM, dbush wrote:
On 6/20/2026 4:03 PM, olcott wrote:The same one that I have been talking about for years. https://github.com/plolcott/x86utm/blob/master/README.md https://github.com/plolcott/x86utm/blob/master/Halt7.c
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page. It is
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is >>>>>> necessarily false. A paradox is a statement to which no truth
value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
The above is unclear, as "HHH" and "DD" could refer to:
Atomic facts of general knowledge includes atomicAnd given that this statement is an atomic fact:
facts of empirical general knowledge such as
"cats are animals".
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun. --------------------------------------
What do you think can be concluded about whether the following statement
is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following
statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
On 6/20/2026 2:48 PM, Alan Mackenzie wrote:How about answering my question? In your system are all facts axioms, or
In comp.theory olcott <polcott333@gmail.com> wrote:Since you are not a philosopher you have no idea what
[ .... ]
I only skimmed that digression from this point:So, in your system, all facts are axioms?
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
a nightmare the analytic/synthetic distinction is.
By converting all of the atomic facts of empiricalUnlikely. I suggest to you yet again, converting all "atomic facts"
general knowledge into axioms the whole 75 year old
nightmare is ended in this single sentence.
Why do you bother responding to me? You don't answer my points andThat would appear to make it not a very useful system, since there is nothing left to prove. Also it is difficult, if even possible inAtomic facts of general knowledge includes atomic
general, to determine whether some assertion is an axiom or not.
Your "axioms" are not axioms in the normal sense of the word; they're
an encyclopaedia.
Or is a fact different from an "empirical fact" in some way?
facts of empirical general knowledge such as
"cats are animals".
----
Copyright 2026 Olcott
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following
statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that
disjunction introduction is correct.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 2:48 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
So, in your system, all facts are axioms?
Since you are not a philosopher you have no idea what
a nightmare the analytic/synthetic distinction is.
How about answering my question? In your system are all facts axioms, or
are they not?
By converting all of the atomic facts of empirical
general knowledge into axioms the whole 75 year old
nightmare is ended in this single sentence.
Unlikely. I suggest to you yet again, converting all "atomic facts" (whatever they may be) to axioms will not result in a satisfactory or
useful system.
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following
statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that
disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"∨" disjunctions.
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following
statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that
disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"∨" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun. --------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false, and how
do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following
statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that
disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"∨" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false, and
how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P ∧ ¬P // Premise
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P ∧ ¬P.
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following
statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that
disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"∨" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false, and
how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P ∧ ¬P // Premise
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P ∧ ¬P.
I didn't ask about those steps. I asked if you believe the following statement is true or false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following >>>>>>>> statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that
disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"∨" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false, and
how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P ∧ ¬P // Premise
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P ∧ ¬P.
I didn't ask about those steps. I asked if you believe the following
statement is true or false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P ∨ Q true? Yes.
On 6/20/2026 9:06 PM, olcott wrote:
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following >>>>>>>>> statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that >>>>>>> disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"∨" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false,
and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P ∧ ¬P // Premise
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P ∧ ¬P.
I didn't ask about those steps. I asked if you believe the following
statement is true or false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P ∨ Q true? Yes.
So you agree that because P is true and Q is false, the condition "at
least one of the following" is met.
Next step:
Do you believe the following statement is true or false, and how do you
come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench. --------------------------------------
On 6/20/2026 8:28 PM, dbush wrote:
On 6/20/2026 9:06 PM, olcott wrote:
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the following >>>>>>>>>> statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore that >>>>>>>> disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"∨" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false,
and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P ∧ ¬P // Premise
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P ∧ ¬P.
I didn't ask about those steps. I asked if you believe the
following statement is true or false, and how do you come to that
conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P ∨ Q true? Yes.
So you agree that because P is true and Q is false, the condition "at
least one of the following" is met.
Next step:
Do you believe the following statement is true or false, and how do
you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Clearly just head games. GFO with these head games
On 6/20/2026 9:32 PM, olcott wrote:
On 6/20/2026 8:28 PM, dbush wrote:
On 6/20/2026 9:06 PM, olcott wrote:
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the
following statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore >>>>>>>>> that disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"∨" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false, >>>>>>> and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P ∧ ¬P // Premise
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P ∧ ¬P.
I didn't ask about those steps. I asked if you believe the
following statement is true or false, and how do you come to that
conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P ∨ Q true? Yes.
So you agree that because P is true and Q is false, the condition "at
least one of the following" is met.
Next step:
Do you believe the following statement is true or false, and how do
you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Clearly just head games. GFO with these head games
I promise you I am going somewhere with this, and this is no head game.
But we must take things one small step at a time.
So I'll ask again:
Do you believe the following natural language statement is true or
false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench. --------------------------------------
On 6/20/2026 8:38 PM, dbush wrote:
On 6/20/2026 9:32 PM, olcott wrote:
On 6/20/2026 8:28 PM, dbush wrote:
On 6/20/2026 9:06 PM, olcott wrote:
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the
following statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore >>>>>>>>>> that disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"∨" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or false, >>>>>>>> and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P ∧ ¬P // Premise
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P ∧ ¬P.
I didn't ask about those steps. I asked if you believe the
following statement is true or false, and how do you come to that >>>>>> conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P ∨ Q true? Yes.
So you agree that because P is true and Q is false, the condition
"at least one of the following" is met.
Next step:
Do you believe the following statement is true or false, and how do
you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Clearly just head games. GFO with these head games
I promise you I am going somewhere with this, and this is no head
game. But we must take things one small step at a time.
So I'll ask again:
Do you believe the following natural language statement is true or
false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Go fuck off.
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>> the extreme. One thing is utterly clear: its level of abstraction is >>>> well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
On 6/20/2026 4:03 PM, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value >>>>> can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
The above is unclear, as "HHH" and "DD" could refer to:
- An algorithm, i.e. a fixed immutable sequence of instructions that
always produces the same output for a given input.
- A C function which has a specific name and may contain any arbitrary instructions
- A finite string implemented as a 32-bit function pointer.
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>> the extreme. One thing is utterly clear: its level of abstraction is >>>> well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central
role
| in reasoning and inference, but are definitely not the exclusive, and >>>> | perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
On 6/20/2026 12:25 AM, Ross Finlayson wrote:
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
Modern Logic has always simply ignored that an
expression may be semantically incoherent because
logic has always ignored semantics and focused
on syntax.
On 6/20/2026 9:57 AM, dbush wrote:
On 6/20/2026 10:54 AM, olcott wrote:
On 6/20/2026 9:36 AM, dbush wrote:
On 6/20/2026 10:18 AM, olcott wrote:
Better than the POE yet not as sound as this:
Irrelevance Logic was always a stupid idea.
Disjunction introduction: P ∴ P ∨ Q
is not allowed. No new premises can be inserted.
This by itself prevent POE from being derived.
(P ∧ ¬P) ⊢ ⊥ // out of which nothing comes
Is the following statement true?
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
Yes that is one element of what are now called atomic facts.
Good. Let's take that as a given.
Is the following statement true?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
It is hypothesized that all of the empirical atomic facts
are encoded. This means that what the Moon is made of is
already encoded.
On 6/20/2026 2:54 AM, Mikko wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>> | occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Proof Theoretic Semantics is the basis that makes:
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
A sememe is the smallest indivisible unit of meaning
in linguistics.
PTS forms a tree of knowledge such that every sememe
is connected to all of its semantic meaning entirely
via connections to other sememes.
On 6/20/2026 4:43 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 2:48 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
So, in your system, all facts are axioms?
Since you are not a philosopher you have no idea what
a nightmare the analytic/synthetic distinction is.
How about answering my question? In your system are all facts
axioms, or are they not?
By converting all of the atomic facts of empirical
general knowledge into axioms the whole 75 year old
nightmare is ended in this single sentence.
Unlikely. I suggest to you yet again, converting all "atomic facts" (whatever they may be) to axioms will not result in a satisfactory or useful system.
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge by
providing grounding in a proof theoretic atomic base.
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
Prior to yesterday I had no idea how close PTS already
is to my own system.
----
Copyright 2026 Olcott
On 20/06/2026 23:17, dbush wrote:
On 6/20/2026 4:03 PM, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page. It is
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is >>>>>> necessarily false. A paradox is a statement to which no truth
value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
The above is unclear, as "HHH" and "DD" could refer to:
- An algorithm, i.e. a fixed immutable sequence of instructions that
always produces the same output for a given input.
- A C function which has a specific name and may contain any arbitrary
instructions
- A finite string implemented as a 32-bit function pointer.
When used by Olcott it refers to the C function Olcott wrote and
put to GitHub long before he fond out that there is cometning
called "proof theoretic semantics". Or at least Olcott has said
that he always means that.
On 20/06/2026 22:02, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
You have. Everything that can be proven can be proven by a proof by contradiction, and often is, as that is the simpest way to prove
many theorems.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 4:43 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 2:48 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
So, in your system, all facts are axioms?
Since you are not a philosopher you have no idea what
a nightmare the analytic/synthetic distinction is.
How about answering my question? In your system are all facts
axioms, or are they not?
Still no answer?
By converting all of the atomic facts of empirical
general knowledge into axioms the whole 75 year old
nightmare is ended in this single sentence.
Unlikely. I suggest to you yet again, converting all "atomic facts"
(whatever they may be) to axioms will not result in a satisfactory or
useful system.
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge by
providing grounding in a proof theoretic atomic base.
Vacuously so. If all facts are axioms, there is nothing left to prove.
Of course, in this setup, determining if an assertion is an axiom or not
is an insoluble problem.
Maybe you mean something else by "atomic fact". You're clearly unable or unwilling to define that term. Obviously you either don't understand it,
or you need to keep it vague to avoid being pinned down by logic and
reality.
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're capable of understanding them.
Prior to yesterday I had no idea how close PTS already
is to my own system.
You're clueless about PTS. You can't explain it, you don't understand
it. You just like trying to flummox others by throwing around big words
and recondite phrases. When asked to explain what they mean, you just go
all vague. "Your own system" is vacuous nonsense.
--
Copyright 2026 Olcott
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 4:43 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 2:48 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
[ .... ]
I only skimmed that digression from this point:
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
So, in your system, all facts are axioms?
Since you are not a philosopher you have no idea what
a nightmare the analytic/synthetic distinction is.
How about answering my question? In your system are all facts
axioms, or are they not?
Still no answer?
By converting all of the atomic facts of empirical
general knowledge into axioms the whole 75 year old
nightmare is ended in this single sentence.
Unlikely. I suggest to you yet again, converting all "atomic facts"
(whatever they may be) to axioms will not result in a satisfactory or
useful system.
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge by
providing grounding in a proof theoretic atomic base.
Vacuously so. If all facts are axioms, there is nothing left to prove.
Of course, in this setup, determining if an assertion is an axiom or not
is an insoluble problem.
Maybe you mean something else by "atomic fact". You're clearly unable or >> unwilling to define that term. Obviously you either don't understand it, >> or you need to keep it vague to avoid being pinned down by logic and
reality.
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931
incompleteness fails. If they are mere gibberish words
to you then you will not understand.
Prior to yesterday I had no idea how close PTS already
is to my own system.
You're clueless about PTS. You can't explain it, you don't understand
it. You just like trying to flummox others by throwing around big words
and recondite phrases. When asked to explain what they mean, you just go >> all vague. "Your own system" is vacuous nonsense.
If you know essentially nothing about PTS then when
I explain things using the terminology of PTS you will
not understand. I need to go to university today to
pick up a key PTS paper.
--
Copyright 2026 Olcott the Pretentious
On 6/21/2026 4:48 AM, Mikko wrote:
On 20/06/2026 22:02, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
You have. Everything that can be proven can be proven by a proof by
contradiction, and often is, as that is the simpest way to prove
many theorems.
Each of the cases of pathological self-reference (PSR)
shows up as infinitely recursive inference steps to
every proof theoretic semantics prover.
All of the "undecidable" instances that I have been
working on since 2004 have only involved PSR.
Confusing PSR for contradiction instead of a cycle
in the directed graph of the evaluation sequence is
the mistake of everyone else not my mistake.
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:I don't believe you. You have no respect for or understanding of the
In comp.theory olcott <polcott333@gmail.com> wrote:The above is the key reason why under PTS Gödel 1931 incompleteness
On 6/20/2026 4:43 PM, Alan Mackenzie wrote:Still no answer?
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 2:48 PM, Alan Mackenzie wrote:How about answering my question? In your system are all facts
In comp.theory olcott <polcott333@gmail.com> wrote:Since you are not a philosopher you have no idea what
[ .... ]
I only skimmed that digression from this point:So, in your system, all facts are axioms?
All empirical facts of general knowledge are encoded
as axioms. This forms the most comprehensive "atomic base"
for Proof Theoretic Semantics.
a nightmare the analytic/synthetic distinction is.
axioms, or are they not?
Vacuously so. If all facts are axioms, there is nothing left to prove.It makes "true on the basis of meaning expressed in language"By converting all of the atomic facts of empiricalUnlikely. I suggest to you yet again, converting all "atomic facts"
general knowledge into axioms the whole 75 year old
nightmare is ended in this single sentence.
(whatever they may be) to axioms will not result in a satisfactory or
useful system.
reliably computable for the entire body of knowledge by
providing grounding in a proof theoretic atomic base.
Of course, in this setup, determining if an assertion is an axiom or not
is an insoluble problem.
Maybe you mean something else by "atomic fact". You're clearly unable or unwilling to define that term. Obviously you either don't understand it, or you need to keep it vague to avoid being pinned down by logic and reality.
I just found the term:You can find any number of terms. That doesn't mean you're capable of understanding them.
"grounding in a proof theoretic atomic base" yesterday.
fails.
If they are mere gibberish words to you then you will not understand.You don't understand Proof-theoritic Semantics, and you certainly don't understand Gödel's Theorem, neither the theorem itself nor any proof of
My lack of understanding of and lack of desire to understand PTS is notIf you know essentially nothing about PTS then whenPrior to yesterday I had no idea how close PTS already is to my ownYou're clueless about PTS. You can't explain it, you don't understand
system.
it. You just like trying to flummox others by throwing around big words and recondite phrases. When asked to explain what they mean, you just go all vague. "Your own system" is vacuous nonsense.
I explain things using the terminology of PTS you will
not understand.
I need to go to university today to pick up a key PTS paper.You might do better going tomorrow when it's open.
----
Copyright 2026 Olcott
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in
the extreme. One thing is utterly clear: its level of abstraction is
well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role >>> | in reasoning and inference, but are definitely not the exclusive, and
| perhaps not even the most typical sort of entities that can be defined >>> | inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical >>> | inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? What it ought to be able to do that standard logic fails at? Maybe André could elucidate. He seems to have a better grasp of it than anybody else here.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness
fails.
I don't believe you. You have no respect for or understanding of the
truth. If you really want to persuade anybody that PTS somehow causes Gödel's theorem not to hold, then cite an academic expert who'll have
some credibility.
If they are mere gibberish words to you then you will not understand.
You don't understand Proof-theoritic Semantics, and you certainly don't understand Gödel's Theorem, neither the theorem itself nor any proof of
it.
On 2026-06-20 04:26, Alan Mackenzie wrote:Thanks, André!
Mikko <mikko.levanto@iki.fi> wrote:I doubt my understanding of PTS is any better than yours. I basically
On 19/06/2026 23:28, Alan Mackenzie wrote:Do its proponents have any idea what PTS ought to be useful for? What it ought to be able to do that standard logic fails at? Maybe André could elucidate. He seems to have a better grasp of it than anybody else here.
Yes. It means that proof-theoretic semantics is currently and in thehttps://plato.stanford.edu/entries/proof-theoretic-semantics/That page's level of abstraction is high enough that I can't be bothered >>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central role >>> | in reasoning and inference, but are definitely not the exclusive, and >>> | perhaps not even the most typical sort of entities that can be defined >>> | inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical >>> | inferential definitions alike.
Does this have any meaning?
near future not useful as making it useful requires much time and
effort if it is possible at all.
only know what is presented in the Stanford Encyclopedia article (which
you correctly point out is not exactly aimed at beginners) and the
Wikipedia article. What I am quite certain of, however, is that Olcott
lacks any understanding of what PTS actually says as he's made a variety
of fairly absurd claims regarding it (for example, that PTS claims that unproven propositions are 'meaningless' or that the goal of PTS is to completely overthrow standard truth-theoretic semantics).
André--
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're capable of >>>> understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness
fails.
I don't believe you. You have no respect for or understanding of the
truth. If you really want to persuade anybody that PTS somehow causes
Gödel's theorem not to hold, then cite an academic expert who'll have
some credibility.
If they are mere gibberish words to you then you will not understand.
You don't understand Proof-theoritic Semantics, and you certainly don't
understand Gödel's Theorem, neither the theorem itself nor any proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>> the extreme. One thing is utterly clear: its level of abstraction is >>>> well beyond the comprehension capabilities of Peter Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been
| occupied with logical constants. Logical constants play a central
role
| in reasoning and inference, but are definitely not the exclusive, and >>>> | perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? What it >> ought to be able to do that standard logic fails at? Maybe André could
elucidate. He seems to have a better grasp of it than anybody else here.
I doubt my understanding of PTS is any better than yours. I basically
only know what is presented in the Stanford Encyclopedia article (which
you correctly point out is not exactly aimed at beginners) and the
Wikipedia article. What I am quite certain of, however, is that Olcott
lacks any understanding of what PTS actually says as he's made a variety
of fairly absurd claims regarding it (for example, that PTS claims that unproven propositions are 'meaningless' or that the goal of PTS is to completely overthrow standard truth-theoretic semantics).
André
On 6/21/2026 3:18 PM, André G. Isaak wrote:
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook" >>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>> | occupied with logical constants. Logical constants play a central >>>>> role
| in reasoning and inference, but are definitely not the exclusive, >>>>> and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at? Maybe André could >>> elucidate. He seems to have a better grasp of it than anybody else
here.
I doubt my understanding of PTS is any better than yours. I basically
only know what is presented in the Stanford Encyclopedia article
(which you correctly point out is not exactly aimed at beginners) and
the Wikipedia article. What I am quite certain of, however, is that
Olcott lacks any understanding of what PTS actually says as he's made
a variety of fairly absurd claims regarding it (for example, that PTS
claims that unproven propositions are 'meaningless' or that the goal
of PTS is to completely overthrow standard truth-theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're capable of >>>>> understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness
fails.
I don't believe you. You have no respect for or understanding of the
truth. If you really want to persuade anybody that PTS somehow causes
Gödel's theorem not to hold, then cite an academic expert who'll have
some credibility.
If they are mere gibberish words to you then you will not understand.
You don't understand Proof-theoritic Semantics, and you certainly don't
understand Gödel's Theorem, neither the theorem itself nor any proof of >>> it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by you,
and it is one which you have never explicitly defined, so the fault here certainly doesn't lie with Alan. It's certainly not a 'verified fact'
when you haven't even adequately explained what it is that you mean.
André
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further. If it actually says anything at all, that >>>>>> something is heavily disguised. From it's "Conclusion and Outlook" >>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>>> | occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential >>>>>> | definitions in a wider sense and covers both logical and extra- >>>>>> logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at? Maybe André could >>>> elucidate. He seems to have a better grasp of it than anybody else
here.
I doubt my understanding of PTS is any better than yours. I basically
only know what is presented in the Stanford Encyclopedia article
(which you correctly point out is not exactly aimed at beginners) and
the Wikipedia article. What I am quite certain of, however, is that
Olcott lacks any understanding of what PTS actually says as he's made
a variety of fairly absurd claims regarding it (for example, that PTS
claims that unproven propositions are 'meaningless' or that the goal
of PTS is to completely overthrow standard truth-theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value >>>>> can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
On 20/06/2026 16:50, olcott wrote:
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook" >>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>> | occupied with logical constants. Logical constants play a central >>>>> role
| in reasoning and inference, but are definitely not the exclusive, >>>>> and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If a claim is true on the basis on meaning expressed in language we
usually can easily determine its truth vaule wihout computational
tools. The truth values we want to know but are hard to determine
are of claims that are true on some other basis.
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a publishable
(or nearly publishable) article about them.
On 20/06/2026 17:18, olcott wrote:
On 6/20/2026 12:25 AM, Ross Finlayson wrote:
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
Modern Logic has always simply ignored that an
expression may be semantically incoherent because
logic has always ignored semantics and focused
on syntax.
Modern logic has
Gödel proved that every consistent first order theory has a model.
That means that a consisten first order theory cannot be semantically incoherent.
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>> fails.
I don't believe you. You have no respect for or understanding of the >>>> truth. If you really want to persuade anybody that PTS somehow causes >>>> Gödel's theorem not to hold, then cite an academic expert who'll have >>>> some credibility.
If they are mere gibberish words to you then you will not understand. >>>>You don't understand Proof-theoritic Semantics, and you certainly don't >>>> understand Gödel's Theorem, neither the theorem itself nor any proof of >>>> it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by you,
and it is one which you have never explicitly defined, so the fault
here certainly doesn't lie with Alan. It's certainly not a 'verified
fact' when you haven't even adequately explained what it is that you
mean.
André
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
I am working in anchoring all of the relevant details
of "grounded in the atomic base" in quotes from
published papers.
On 6/21/2026 3:18 PM, André G. Isaak wrote:
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook" >>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>> | occupied with logical constants. Logical constants play a central >>>>> role
| in reasoning and inference, but are definitely not the exclusive, >>>>> and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-
logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at? Maybe André could >>> elucidate. He seems to have a better grasp of it than anybody else
here.
I doubt my understanding of PTS is any better than yours. I basically
only know what is presented in the Stanford Encyclopedia article
(which you correctly point out is not exactly aimed at beginners) and
the Wikipedia article. What I am quite certain of, however, is that
Olcott lacks any understanding of what PTS actually says as he's made
a variety of fairly absurd claims regarding it (for example, that PTS
claims that unproven propositions are 'meaningless' or that the goal
of PTS is to completely overthrow standard truth-theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
On 2026-06-21 17:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>>> fails.
I don't believe you. You have no respect for or understanding of the >>>>> truth. If you really want to persuade anybody that PTS somehow causes >>>>> Gödel's theorem not to hold, then cite an academic expert who'll have >>>>> some credibility.
If they are mere gibberish words to you then you will not understand. >>>>>You don't understand Proof-theoritic Semantics, and you certainly
don't
understand Gödel's Theorem, neither the theorem itself nor any
proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by
you, and it is one which you have never explicitly defined, so the
fault here certainly doesn't lie with Alan. It's certainly not a
'verified fact' when you haven't even adequately explained what it is
that you mean.
André
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
'all knowledge expressed in language' isn't even a well-defined set.
On 2026-06-21 15:39, olcott wrote:Proof-theoretic semantics is an alternative to truth-condition semantics.
On 6/21/2026 3:18 PM, André G. Isaak wrote:
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further. If it actually says anything at all, that >>>>>> something is heavily disguised. From it's "Conclusion and Outlook" >>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>>> | occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential >>>>>> | definitions in a wider sense and covers both logical and extra- >>>>>> logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at? Maybe André could >>>> elucidate. He seems to have a better grasp of it than anybody else
here.
I doubt my understanding of PTS is any better than yours. I basically
only know what is presented in the Stanford Encyclopedia article
(which you correctly point out is not exactly aimed at beginners) and
the Wikipedia article. What I am quite certain of, however, is that
Olcott lacks any understanding of what PTS actually says as he's made
a variety of fairly absurd claims regarding it (for example, that PTS
claims that unproven propositions are 'meaningless' or that the goal
of PTS is to completely overthrow standard truth-theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
No where does it talk about 'utterly abandoning'
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page. It is
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is >>>>>> necessarily false. A paradox is a statement to which no truth
value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD
to HHH
is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
To sum this up PTS would have HHH
reject DDD.
Trump didn't have anything besides dishonest dodges when
she kept pressing his for evidence of election fraud so
he gave up and left the room.
On 6/21/2026 5:36 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other questions
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>> bothered
to read it any further. If it actually says anything at all, that >>>>>>> something is heavily disguised. From it's "Conclusion and Outlook" >>>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>> | definitions in a wider sense and covers both logical and extra- >>>>>>> logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at? Maybe André >>>>> could
elucidate. He seems to have a better grasp of it than anybody else >>>>> here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford Encyclopedia
article (which you correctly point out is not exactly aimed at
beginners) and the Wikipedia article. What I am quite certain of,
however, is that Olcott lacks any understanding of what PTS actually
says as he's made a variety of fairly absurd claims regarding it
(for example, that PTS claims that unproven propositions are
'meaningless' or that the goal of PTS is to completely overthrow
standard truth-theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat?
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semanticsSome people only memorize conventional views and
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>>> bothered
to read it any further. If it actually says anything at all, that >>>>>>>> something is heavily disguised. From it's "Conclusion and Outlook" >>>>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>>> | definitions in a wider sense and covers both logical and
extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>>> near future not useful as making it useful requires much time and >>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at? Maybe André >>>>>> could
elucidate. He seems to have a better grasp of it than anybody
else here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford Encyclopedia
article (which you correctly point out is not exactly aimed at
beginners) and the Wikipedia article. What I am quite certain of,
however, is that Olcott lacks any understanding of what PTS
actually says as he's made a variety of fairly absurd claims
regarding it (for example, that PTS claims that unproven
propositions are 'meaningless' or that the goal of PTS is to
completely overthrow standard truth-theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
That is,
they will never accept that they are wrong even when it's right up there
in clearly visible un-mathematics for us to see? That is, they tend to
have a weakness in 3D geometry I have discovered (I guess the computer scientists are going to fill in their eyes last). But far be it from
them to admit it. They will conjure answer after answer to try to back
up their position. Maybe I should go back and watch that human-AI debate that went viral. Spoiler - the humans won. It might be interesting to
see now what exactly the AI lost. Perhaps it was stating mistruths like
it still does. Wouldn't this be spectacular television today to have
that debate? It's somewhere on Youtube. I'll probably give a holler when
I find it. You may find it fairly interesting too, as you seem to also
have some experience with the LLM AIs.
By the way, I don't have a PhD in everything, but it does cover
electrical engineering -- a field heavy in mathematics. I admit we
didn't study Gödel, Escher or Bach, but I managed to get through Real Analysis with minor difficulty. It was largely the mathematics of proof. It's a more difficult field than it may sound. I found you've really got
to make the interlocking pieces overlap such that there is a story told
that is without holes in it.
I toughed it out in Real Analysis. It was easier than Solid State
Physics which appeared as if magic to me. Teleporting electrons and
other quantum features. That was one of the big sticks on my back that
made me step back and re-think my double major and set computer science
as merely a minor to handle all the tribulations.
On 6/21/2026 5:36 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other questions
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who
can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further. If it actually says anything at all, that >>>>>>> something is heavily disguised. From it's "Conclusion and Outlook" >>>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>> | definitions in a wider sense and covers both logical and extra- >>>>>>> logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at? Maybe André
could
elucidate. He seems to have a better grasp of it than anybody else
here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford Encyclopedia
article (which you correctly point out is not exactly aimed at
beginners) and the Wikipedia article. What I am quite certain of,
however, is that Olcott lacks any understanding of what PTS actually
says as he's made a variety of fairly absurd claims regarding it
(for example, that PTS claims that unproven propositions are
'meaningless' or that the goal of PTS is to completely overthrow
standard truth-theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? That is,
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semanticsSome people only memorize conventional views and
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>>> bothered
to read it any further. If it actually says anything at all, that >>>>>>>> something is heavily disguised. From it's "Conclusion and Outlook" >>>>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>>> | definitions in a wider sense and covers both logical and
extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>>> near future not useful as making it useful requires much time and >>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
ought to be able to do that standard logic fails at? Maybe André >>>>>> could
elucidate. He seems to have a better grasp of it than anybody
else here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford Encyclopedia
article (which you correctly point out is not exactly aimed at
beginners) and the Wikipedia article. What I am quite certain of,
however, is that Olcott lacks any understanding of what PTS
actually says as he's made a variety of fairly absurd claims
regarding it (for example, that PTS claims that unproven
propositions are 'meaningless' or that the goal of PTS is to
completely overthrow standard truth-theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
they will never accept that they are wrong even when it's right up there
in clearly visible un-mathematics for us to see? That is, they tend to
have a weakness in 3D geometry I have discovered (I guess the computer scientists are going to fill in their eyes last). But far be it from
them to admit it. They will conjure answer after answer to try to back
up their position. Maybe I should go back and watch that human-AI debate
that went viral. Spoiler - the humans won. It might be interesting to
see now what exactly the AI lost. Perhaps it was stating mistruths like
it still does. Wouldn't this be spectacular television today to have
that debate? It's somewhere on Youtube. I'll probably give a holler when
I find it. You may find it fairly interesting too, as you seem to also
have some experience with the LLM AIs.
By the way, I don't have a PhD in everything, but it does cover
electrical engineering -- a field heavy in mathematics. I admit we
didn't study Gödel, Escher or Bach, but I managed to get through Real Analysis with minor difficulty. It was largely the mathematics of proof.
It's a more difficult field than it may sound. I found you've really got
to make the interlocking pieces overlap such that there is a story told
that is without holes in it.
I toughed it out in Real Analysis. It was easier than Solid State
Physics which appeared as if magic to me. Teleporting electrons and
other quantum features. That was one of the big sticks on my back that
made me step back and re-think my double major and set computer science
as merely a minor to handle all the tribulations.
On 6/21/2026 6:02 AM, Mikko wrote:
On 20/06/2026 23:17, dbush wrote:He frequently equivocates to make his statements intentionally unclear.
On 6/20/2026 4:03 PM, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page. It is >>>>>>>>> abstract in
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The >>>>>>> two are different things. A contradiction is a statement which is >>>>>>> necessarily false. A paradox is a statement to which no truth
value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been >>>>> attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
The above is unclear, as "HHH" and "DD" could refer to:
- An algorithm, i.e. a fixed immutable sequence of instructions that
always produces the same output for a given input.
- A C function which has a specific name and may contain any
arbitrary instructions
- A finite string implemented as a 32-bit function pointer.
When used by Olcott it refers to the C function Olcott wrote and
put to GitHub long before he fond out that there is cometning
called "proof theoretic semantics". Or at least Olcott has said
that he always means that.
On 6/21/2026 4:48 AM, Mikko wrote:
On 20/06/2026 22:02, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The two
are different things. A contradiction is a statement which is
necessarily false. A paradox is a statement to which no truth value
can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
You have. Everything that can be proven can be proven by a proof by
contradiction, and often is, as that is the simpest way to prove
many theorems.
Each of the cases of pathological self-reference (PSR)
shows up as infinitely recursive inference steps to
every proof theoretic semantics prover.
All of the "undecidable" instances that I have been
working on since 2004 have only involved PSR.
Confusing PSR for contradiction instead of a cycle
in the directed graph of the evaluation sequence is
the mistake of everyone else not my mistake.
On 6/21/2026 5:11 AM, Mikko wrote:
On 20/06/2026 16:50, olcott wrote:
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of abstraction is >>>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be
bothered
to read it any further. If it actually says anything at all, that >>>>>> something is heavily disguised. From it's "Conclusion and Outlook" >>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>>> | occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be
defined
| inferentially. A framework is needed that deals with inferential >>>>>> | definitions in a wider sense and covers both logical and extra- >>>>>> logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If a claim is true on the basis on meaning expressed in language we
usually can easily determine its truth vaule wihout computational
tools. The truth values we want to know but are hard to determine
are of claims that are true on some other basis.
The system I propose would cut off the dangerous lies
of dangerous liars mid-sentence and be able to prove
that these are lies to every level of understanding
between kindergarten and PhD.
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human being on the face of the Earth could understand
me I could not publish.
Now that I am acquiring the lingua franca of PTS I
will finally be able to publish.
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>> fails.
I don't believe you. You have no respect for or understanding of the >>>> truth. If you really want to persuade anybody that PTS somehow causes >>>> Gödel's theorem not to hold, then cite an academic expert who'll have >>>> some credibility.
If they are mere gibberish words to you then you will not understand. >>>>You don't understand Proof-theoritic Semantics, and you certainly don't >>>> understand Gödel's Theorem, neither the theorem itself nor any proof of >>>> it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by you,
and it is one which you have never explicitly defined, so the fault
here certainly doesn't lie with Alan. It's certainly not a 'verified
fact' when you haven't even adequately explained what it is that you
mean.
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
I am working in anchoring all of the relevant detailsIn published artilce you can find enough "facts" to prove that
of "grounded in the atomic base" in quotes from
published papers.
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page. It is
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The
two are different things. A contradiction is a statement which is >>>>>> necessarily false. A paradox is a statement to which no truth
value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been
attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
On 06/21/2026 05:32 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? That is,
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semanticsSome people only memorize conventional views and
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page. It is
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>>>> bothered
to read it any further. If it actually says anything at all, that >>>>>>>>> something is heavily disguised. From it's "Conclusion and
Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>>>> | definitions in a wider sense and covers both logical and
extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in >>>>>>>> the
near future not useful as making it useful requires much time and >>>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? >>>>>>> What it
ought to be able to do that standard logic fails at? Maybe André >>>>>>> could
elucidate. He seems to have a better grasp of it than anybody
else here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford Encyclopedia >>>>>> article (which you correctly point out is not exactly aimed at
beginners) and the Wikipedia article. What I am quite certain of,
however, is that Olcott lacks any understanding of what PTS
actually says as he's made a variety of fairly absurd claims
regarding it (for example, that PTS claims that unproven
propositions are 'meaningless' or that the goal of PTS is to
completely overthrow standard truth-theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
they will never accept that they are wrong even when it's right up there
in clearly visible un-mathematics for us to see? That is, they tend to
have a weakness in 3D geometry I have discovered (I guess the computer
scientists are going to fill in their eyes last). But far be it from
them to admit it. They will conjure answer after answer to try to back
up their position. Maybe I should go back and watch that human-AI debate
that went viral. Spoiler - the humans won. It might be interesting to
see now what exactly the AI lost. Perhaps it was stating mistruths like
it still does. Wouldn't this be spectacular television today to have
that debate? It's somewhere on Youtube. I'll probably give a holler when
I find it. You may find it fairly interesting too, as you seem to also
have some experience with the LLM AIs.
By the way, I don't have a PhD in everything, but it does cover
electrical engineering -- a field heavy in mathematics. I admit we
didn't study Gödel, Escher or Bach, but I managed to get through Real
Analysis with minor difficulty. It was largely the mathematics of proof.
It's a more difficult field than it may sound. I found you've really got
to make the interlocking pieces overlap such that there is a story told
that is without holes in it.
I toughed it out in Real Analysis. It was easier than Solid State
Physics which appeared as if magic to me. Teleporting electrons and
other quantum features. That was one of the big sticks on my back that
made me step back and re-think my double major and set computer science
as merely a minor to handle all the tribulations.
If you like solid-state physics then you might consider that the wave
model and Lienard-Wiechert after Fermi holes are _abstractions_ and furthermore _reductions_, that it's _reductionism_ that arrives that
the theory's "good to the first or second order" or provides "on the
order of" accounts of proportionality, that in the real world, vary
like spiral-waves and wave-spirals, and Faraday rotation and the real behavior of "Fermi holes" that Lienard-Wiechert then is to give an
account as for Coulomb and Ampere the behavior of electron-holes with
regards to test-particles in the analysis of the continuum mechanics
(that's an infinitesimal analysis), then for example making that line
up with Maxwell's either E x B or D x H, usually just the one there
and ignoring that as Maxwell put it that either would do to define the
other, then usual "paradoxes" of quantum mechanics are actually problems
of the particle-conceit since there are fields and for example after the particle/wave duality the wave/resonance dichotomy, then besides that
the tachyonic and bradyonic would get involved in accounts
of "real wave collapse", which though anything that provides the "Schroedingerians" for quantum mechanics, much like the "Lorentzians"
for general relativity, suffices to make a theory that all the
experiments in "canonical quantum mechanics" and "confirmed general relativity" can ever be said to have said.
So, anti-reductionism is filling in further accounts of QM and GR,
like continuous quanta instead of Born's infinite self-energy and
slanted commutators or Feynman's de-normalized re-normalized theories
with virtual photons which aren't, or "doubly-objective" relativity
theory, there's room in the theory and room in the data to make
quantum mechanics continuous again and general relativity Euclidean again.
Most people might think the "crises in physics" need to get resolved
by adding hypothetical things, yet really the idea is to fit what
goes in where there's already "room" in the theory and data, since
the "reductionism" that left that "room" to paint itself into a corner,
has "revisiting the reductionism", or like I used to say, "revisit Heisenberg, Hubble, Higgs", with that they've been made end-results
that are dead-end-results.
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're capable of >>>> understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness
fails.
I don't believe you. You have no respect for or understanding of the
truth. If you really want to persuade anybody that PTS somehow causes
Gödel's theorem not to hold, then cite an academic expert who'll have
some credibility.
If they are mere gibberish words to you then you will not understand.
You don't understand Proof-theoritic Semantics, and you certainly don't
understand Gödel's Theorem, neither the theorem itself nor any proof of
it.
in the atomic base of PA.
On 6/21/2026 5:23 AM, Mikko wrote:
On 20/06/2026 17:18, olcott wrote:
On 6/20/2026 12:25 AM, Ross Finlayson wrote:
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
Modern Logic has always simply ignored that an
expression may be semantically incoherent because
logic has always ignored semantics and focused
on syntax.
Modern logic has
always put semantics outside of the formal system
in a separate model.
PTS does not do that.
Gödel proved that every consistent first order theory has a model.
That means that a consisten first order theory cannot be semantically
incoherent.
Like I just said.
On 6/21/2026 7:32 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat?
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semanticsSome people only memorize conventional views and
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page. It is >>>>>>>>> abstract in
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>>>> bothered
to read it any further. If it actually says anything at all, that >>>>>>>>> something is heavily disguised. From it's "Conclusion and >>>>>>>>> Outlook"
section at the end:
| Standard proof-theoretic semantics has practically
exclusively been
| occupied with logical constants. Logical constants play a >>>>>>>>> central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can >>>>>>>>> be defined
| inferentially. A framework is needed that deals with inferential >>>>>>>>> | definitions in a wider sense and covers both logical and
extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in >>>>>>>> the
near future not useful as making it useful requires much time and >>>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? >>>>>>> What it
ought to be able to do that standard logic fails at? Maybe André >>>>>>> could
elucidate. He seems to have a better grasp of it than anybody >>>>>>> else here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford Encyclopedia >>>>>> article (which you correctly point out is not exactly aimed at
beginners) and the Wikipedia article. What I am quite certain of, >>>>>> however, is that Olcott lacks any understanding of what PTS
actually says as he's made a variety of fairly absurd claims
regarding it (for example, that PTS claims that unproven
propositions are 'meaningless' or that the goal of PTS is to
completely overthrow standard truth-theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is not that they never admit defeat.
It is that that have a system of essentially infallible reasoning
that never errs as long as it has all the relevant information.
On 22/06/2026 02:55, olcott wrote:
On 6/21/2026 5:11 AM, Mikko wrote:
On 20/06/2026 16:50, olcott wrote:
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>> bothered
to read it any further. If it actually says anything at all, that >>>>>>> something is heavily disguised. From it's "Conclusion and Outlook" >>>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>> | definitions in a wider sense and covers both logical and extra- >>>>>>> logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>> near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If a claim is true on the basis on meaning expressed in language we
usually can easily determine its truth vaule wihout computational
tools. The truth values we want to know but are hard to determine
are of claims that are true on some other basis.
The system I propose would cut off the dangerous lies
of dangerous liars mid-sentence and be able to prove
that these are lies to every level of understanding
between kindergarten and PhD.
You have not yet demonstrated any aboility to cut off a single
lie that would matter to typical people.
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human being on
the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles
that have any is or depends on claims that should be proven but
aren't.
Now that I am acquiring the lingua franca of PTS I
will finally be able to publish.
If all you can publish is in the topic area of PtS then they may
count as uninteresting to those whose primary problems are not in
that topic area.
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>>> fails.
I don't believe you. You have no respect for or understanding of the >>>>> truth. If you really want to persuade anybody that PTS somehow causes >>>>> Gödel's theorem not to hold, then cite an academic expert who'll have >>>>> some credibility.
If they are mere gibberish words to you then you will not understand. >>>>>You don't understand Proof-theoritic Semantics, and you certainly
don't
understand Gödel's Theorem, neither the theorem itself nor any
proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by
you, and it is one which you have never explicitly defined, so the
fault here certainly doesn't lie with Alan. It's certainly not a
'verified fact' when you haven't even adequately explained what it is
that you mean.
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
What makes you believe semantic relations that can be structured as
a tree are sufficient to contain all knowledge that is exressed in
some language?
I am working in anchoring all of the relevant detailsIn published artilce you can find enough "facts" to prove that
of "grounded in the atomic base" in quotes from
published papers.
all lies are true.
On 6/21/2026 4:08 PM, André G. Isaak wrote:That is vanishingly unlikely to be true. Look at any half decent English dictionary, and it will contain lots of cycles. Any non-empty finite
On 2026-06-21 14:42, olcott wrote:All of knowledge expressed in language is structured as a tree of
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:"grounded in the atomic base of PA" is an expression used only by you,
It is a verified fact that Gödel's G is ungrounded
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
and it is one which you have never explicitly defined, so the fault here certainly doesn't lie with Alan. It's certainly not a 'verified fact'
when you haven't even adequately explained what it is that you mean.
André
semantic relations specified syntactically between finite strings.
I am working in anchoring all of the relevant detailsAs remarked already "grounded in the atomic base" is undefined and
of "grounded in the atomic base" in quotes from
published papers.
----
Copyright 2026 Olcott
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)I've spent a couple of hours reading that web page. It is >>>>>>>>> abstract in
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>>> can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The >>>>>>> two are different things. A contradiction is a statement which is >>>>>>> necessarily false. A paradox is a statement to which no truth
value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've been >>>>> attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics
do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the
C implementation you have used. When DD iss executed in that environment
it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it
could be rejected by the compiler.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
It is a verified fact that Gödel's G is ungrounded
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by you,
and it is one which you have never explicitly defined, so the fault here >>> certainly doesn't lie with Alan. It's certainly not a 'verified fact'
when you haven't even adequately explained what it is that you mean.
André
All of [general] knowledge expressed in language is structuredThat is vanishingly unlikely to be true. Look at any half decent English dictionary, and it will contain lots of cycles. Any non-empty finite
as a tree of semantic relations specified syntactically between
finite strings.
tree contains leaf nodes. Either your "tree of semantic relations" is infinite (hence useless) or it contains leaf nodes. Feel free to give an example of a leaf node in your purported tree.
I am working in anchoring all of the relevant details
of "grounded in the atomic base" in quotes from
published papers.
As remarked already "grounded in the atomic base" is undefined and meaningless.
--
Copyright 2026 Olcott
On 21/06/2026 23:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're capable of >>>>> understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness
fails.
I don't believe you. You have no respect for or understanding of the
truth. If you really want to persuade anybody that PTS somehow causes
Gödel's theorem not to hold, then cite an academic expert who'll have
some credibility.
If they are mere gibberish words to you then you will not understand.
You don't understand Proof-theoritic Semantics, and you certainly don't
understand Gödel's Theorem, neither the theorem itself nor any proof of >>> it.
in the atomic base of PA.
It is a verified fact that Gödel's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
On 22/06/2026 03:00, olcott wrote:
On 6/21/2026 5:23 AM, Mikko wrote:
On 20/06/2026 17:18, olcott wrote:
On 6/20/2026 12:25 AM, Ross Finlayson wrote:
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
Modern Logic has always simply ignored that an
expression may be semantically incoherent because
logic has always ignored semantics and focused
on syntax.
Modern logic has
always put semantics outside of the formal system
in a separate model.
And that way avoided semantic incoherence in formal systems.
PTS does not do that.
Gödel proved that every consistent first order theory has a model.
That means that a consisten first order theory cannot be semantically
incoherent.
Like I just said.
Therefore we can trust that in every theory that can express the
truths of the natural numbers there is a true sentence that cannot
be proven.
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat?
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semanticsSome people only memorize conventional views and
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>> who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't >>>>>>>>>> be bothered
to read it any further. If it actually says anything at all, >>>>>>>>>> that
something is heavily disguised. From it's "Conclusion and >>>>>>>>>> Outlook"
section at the end:
| Standard proof-theoretic semantics has practically
exclusively been
| occupied with logical constants. Logical constants play a >>>>>>>>>> central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can >>>>>>>>>> be defined
| inferentially. A framework is needed that deals with
inferential
| definitions in a wider sense and covers both logical and >>>>>>>>>> extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and >>>>>>>>> in the
near future not useful as making it useful requires much time and >>>>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? >>>>>>>> What it
ought to be able to do that standard logic fails at? Maybe
André could
elucidate. He seems to have a better grasp of it than anybody >>>>>>>> else here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford
Encyclopedia article (which you correctly point out is not
exactly aimed at beginners) and the Wikipedia article. What I am >>>>>>> quite certain of, however, is that Olcott lacks any understanding >>>>>>> of what PTS actually says as he's made a variety of fairly absurd >>>>>>> claims regarding it (for example, that PTS claims that unproven >>>>>>> propositions are 'meaningless' or that the goal of PTS is to
completely overthrow standard truth-theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is not that they never admit defeat.
It is that that have a system of essentially infallible reasoning
that never errs as long as it has all the relevant information.
It is fairly simple to build a system of essentially infallible
reasoning that never errs even when it doesn't have all the
relevant information. The real problem is to construct a system
that tells something interesting instead of just different
presentations of the same already known facts.
On 6/22/2026 2:23 AM, Mikko wrote:You have not understood Mikko's statement. It is a VERIFIED FACT that
It is a verified fact that Gödel's completeness and incompleteness theorems are inevitable consequences of Peano arithmetic.Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
Some PTS called base-extension semantics seem to thinkWhat is the nature of this alleged extension? PA is a set of axioms from which, amongst other things, Gödel's theorems can be proven. You seem to
that they can extend PA so that it is different and
not clearly acknowledge that they converted PA into PA+.
They would then say that G is grounded in PA when
they actually mean that G becomes grounded in the
modified PA+.
----
Copyright 2026 Olcott
[ Followup-To: set ]Within the foundation of Truth Conditional Semantics (TCS)
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
It is a verified fact that Gödel's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
You have not understood Mikko's statement. It is a VERIFIED FACT that Gödel's completeness and incompleteness theorems are inevitable
consequences of Peano arithmetic.
On 6/22/2026 2:40 AM, Mikko wrote:G is true.
Therefore we can trust that in every theory that can express theAs I have been saying for many years and finally
truths of the natural numbers there is a true sentence that cannot
be proven.
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever
true directly in PA.
----
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:40 AM, Mikko wrote:
Therefore we can trust that in every theory that can express the
truths of the natural numbers there is a true sentence that cannot
be proven.
As I have been saying for many years and finally
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever
true directly in PA.
G is true.
I put it to you you're lying again. No reputable mathematician would
risk his reputation by saying false things. If Dag Prawitz really did "agree" (with whom?) that Gödel's sentence G is not true in Peano Arithmetic, then produce a citation for this.
And on the off chance you're not lying, who on Earth would want to use a deficient system like PTS that can't even prove standard mathematical results?
[ .... ]
--
Copyright 2026 Olcott
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>> who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by
contradiction. The LP isn't a contradiction; it's a paradox. The >>>>>>>> two are different things. A contradiction is a statement which >>>>>>>> is necessarily false. A paradox is a statement to which no truth >>>>>>>> value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've
been attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics
do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the
C implementation you have used. When DD iss executed in that environment
it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
This has been completely rewritten just now. https://github.com/plolcott/x86utm/blob/master/README.md
On 06/22/2026 06:13 AM, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>>> who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by >>>>>>>>> contradiction. The LP isn't a contradiction; it's a paradox. The >>>>>>>>> two are different things. A contradiction is a statement which >>>>>>>>> is necessarily false. A paradox is a statement to which no truth >>>>>>>>> value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem >>>>>>> proof, Godel's proof, and Tarski's proof, each of which you've
been attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics
do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the
C implementation you have used. When DD iss executed in that environment >>> it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
This has been completely rewritten just now.
https://github.com/plolcott/x86utm/blob/master/README.md
Just ignoring "pathological self-reference" doesn't make it
go away, and anybody can declare the "facts" about it.
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:You won't understand it, but that _is_ essentially Gödel's Incompleteness Theorem. It is a statement that any sufficiently powerful system can
In comp.theory olcott <polcott333@gmail.com> wrote:He never gets to Gödel. He essentially says unprovable
On 6/22/2026 2:40 AM, Mikko wrote:G is true.
Therefore we can trust that in every theory that can express theAs I have been saying for many years and finally
truths of the natural numbers there is a true sentence that cannot
be proven.
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever
true directly in PA.
I put it to you you're lying again. No reputable mathematician would
risk his reputation by saying false things. If Dag Prawitz really did "agree" (with whom?) that Gödel's sentence G is not true in Peano Arithmetic, then produce a citation for this.
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
Almost no PTS people even ever get to true, they all stop at semantic meaning.That's a tautology. One of those meanings which they will be dealing
Again, if PTS was like you say, why would anybody want to use it when it doesn't even prove standard results without some extension? I put it toAnd on the off chance you're not lying, who on Earth would want to use a deficient system like PTS that can't even prove standard mathematical results?The Base-Extension Semantics (B-eS) sub-field of PTS
lets you extend PA so that G is provable in PA.
They also never talk about G or PA explicitly.
----
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:40 AM, Mikko wrote:
Therefore we can trust that in every theory that can express the
truths of the natural numbers there is a true sentence that cannot
be proven.
As I have been saying for many years and finally
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever
true directly in PA.
G is true.
I put it to you you're lying again. No reputable mathematician would
risk his reputation by saying false things. If Dag Prawitz really did
"agree" (with whom?) that Gödel's sentence G is not true in Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's Incompleteness Theorem. It is a statement that any sufficiently powerful system can
express true things it can't prove. So Dag Prawitz, had he been saying
the things you falsely attributed to him, would certainly have "got" to Gödel, and would have understood full well what he was saying.
On 6/22/2026 10:22 AM, Alan Mackenzie wrote:
[ Followup-To: set ]Within the foundation of Truth Conditional Semantics (TCS)
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
It is a verified fact that Gödel's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
You have not understood Mikko's statement. It is a VERIFIED FACT that
Gödel's completeness and incompleteness theorems are inevitable
consequences of Peano arithmetic.
and not Within the foundation of strict Proof Theoretic (PTS)
Semantics. When G is unprovable in PA then in strict PTS
G is ungrounded in PA.
There is a sub field of PTS called Base-Extension Semantics
(B-eS) that is not strict PTS. (B-eS) extends PA to become
PA+ then G becomes grounded in PA+. This is the same thing
as saying that G is provable in meta-math thus making it
true in PA.
On 06/22/2026 08:36 AM, olcott wrote:
On 6/22/2026 10:22 AM, Alan Mackenzie wrote:
[ Followup-To: set ]Within the foundation of Truth Conditional Semantics (TCS)
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
It is a verified fact that Gödel's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
You have not understood Mikko's statement. It is a VERIFIED FACT that
Gödel's completeness and incompleteness theorems are inevitable
consequences of Peano arithmetic.
and not Within the foundation of strict Proof Theoretic (PTS)
Semantics. When G is unprovable in PA then in strict PTS
G is ungrounded in PA.
There is a sub field of PTS called Base-Extension Semantics
(B-eS) that is not strict PTS. (B-eS) extends PA to become
PA+ then G becomes grounded in PA+. This is the same thing
as saying that G is provable in meta-math thus making it
true in PA.
"Meta" math?
Is that the one where you hire a kid off the street
to promote a venue and he takes the fliers and
dumps them in the first trash-bin and walks off
with the money?
Sort of "Instant Audience" instead of "Artificial Intelligence"?
On 06/22/2026 06:13 AM, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>>> who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by >>>>>>>>> contradiction. The LP isn't a contradiction; it's a paradox. The >>>>>>>>> two are different things. A contradiction is a statement which >>>>>>>>> is necessarily false. A paradox is a statement to which no truth >>>>>>>>> value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem >>>>>>> proof, Godel's proof, and Tarski's proof, each of which you've
been attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics
do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the
C implementation you have used. When DD iss executed in that environment >>> it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
This has been completely rewritten just now.
https://github.com/plolcott/x86utm/blob/master/README.md
Just ignoring "pathological self-reference" doesn't make it
go away, and anybody can declare the "facts" about it.
It seems a cloak of the empirical fallacy masquerading as
the triumph of reason, then axiomatizing itself complete
with what would be false-axioms, a futile, intransigent
effort doomed to be outmoded and simply inductive ignorance
of the not-quite-invincible sort.
As a satire it's more pathetic than profound.
Instead, what reasoners find is the great Renaissance (idealism)
and Enlightenment (rationalism) as an "extreme rationalism" account,
that DesCartes and Leibnitz, and Plato and Kant, can both be proud,
bring back together the analytical tradition and the idealistic
tradition as for a dually-self-infraconsistent paraconsistent-dialetheic ur-theory that provides both the Euclidean and Archimedean (geometry and arithmetic) and super-Euclidean and super-Archimedean
(with infinity and the original), making it so that the Pythagorean (amost-all rational) and Cantorian (almost-all transcendental) are
made whole in a paleo-classical post-modern account with the
strong mathematical platonism with the perfect circles and straight
lines and the strengthened (instead of weak) logicist positivism
in accounts of heno-theories and a mono-heno-theory, that
gives modal, temporal, relevance logic as a "the logic",
and makes possible the overall conscientious and thorough efforts
of the conscientious logician, mathematician, statistician, scientist,
and physicist, among large, competent, conscientious, co-operative
reasoners.
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:I was right, you didn't understand it.
In comp.theory olcott <polcott333@gmail.com> wrote:You did not pay close enough attention to my exact words.
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:You won't understand it, but that _is_ essentially Gödel's Incompleteness Theorem. It is a statement that any sufficiently powerful system can express true things it can't prove. So Dag Prawitz, had he been saying
G is true.He never gets to Gödel. He essentially says unprovable
I put it to you you're lying again. No reputable mathematician would
risk his reputation by saying false things. If Dag Prawitz really did >>> "agree" (with whom?) that Gödel's sentence G is not true in Peano
Arithmetic, then produce a citation for this.
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
the things you falsely attributed to him, would certainly have "got" to Gödel, and would have understood full well what he was saying.
If an expression is unprovable then this expression is untrue.That article is behind a pay wall, and the abstract which is avaiblable
Only for Dag Prawitz https://link.springer.com/article/10.1007/s11245-011-9107-6
In the most of the rest of pure proof theoretic semanticsYou don't understand the concept of true, so how could you tell?
an expression only acquires semantic meaning from its
completed proof. They never get to true.
When this is applied at the level of an individual formalSo what's the point of PTS?
system (almost never) then the expression never derives
semantic meaning in that formal system.
----
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician would >>>>> risk his reputation by saying false things. If Dag Prawitz really did >>>>> "agree" (with whom?) that Gödel's sentence G is not true in Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's Incompleteness >>> Theorem. It is a statement that any sufficiently powerful system can
express true things it can't prove. So Dag Prawitz, had he been saying
the things you falsely attributed to him, would certainly have "got" to
Gödel, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician would >>>>> risk his reputation by saying false things. If Dag Prawitz really did >>>>> "agree" (with whom?) that Gödel's sentence G is not true in Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's Incompleteness >>> Theorem. It is a statement that any sufficiently powerful system can
express true things it can't prove. So Dag Prawitz, had he been saying
the things you falsely attributed to him, would certainly have "got" to
Gödel, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Unfortunately for you I paid very close attention to them. I can tell
when your words express the truth, and when they don't. As I keep
telling you and you keep ignoring, any logical system bar the simplest
can express truths it can't prove. That's a fundamental mathematical
truth which you can't magic away with a magician's hat and a wand, like
you keep trying to do.
If an expression is unprovable then this expression is untrue.
Only for Dag Prawitz
https://link.springer.com/article/10.1007/s11245-011-9107-6
That article is behind a pay wall, and the abstract which is avaiblable doesn't touch on any supposed equivalence of true and provable. Many
true expressions are unprovable.
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:[ .... ]
In comp.theory olcott <polcott333@gmail.com> wrote:Dag Prawitz says: Unprovable ALWAYS means untrue
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:I was right, you didn't understand it.
In comp.theory olcott <polcott333@gmail.com> wrote:You did not pay close enough attention to my exact words.
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:You won't understand it, but that _is_ essentially Gödel's
G is true.He never gets to Gödel. He essentially says unprovable
I put it to you you're lying again. No reputable mathematician would >>>>> risk his reputation by saying false things. If Dag Prawitz really did >>>>> "agree" (with whom?) that Gödel's sentence G is not true in Peano >>>>> Arithmetic, then produce a citation for this.
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
Incompleteness Theorem. It is a statement that any sufficiently
powerful system can express true things it can't prove. So Dag
Prawitz, had he been saying the things you falsely attributed to
him, would certainly have "got" to Gödel, and would have understood
full well what he was saying.
----
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician would >>>>>>> risk his reputation by saying false things. If Dag Prawitz really did >>>>>>> "agree" (with whom?) that Gödel's sentence G is not true in Peano >>>>>>> Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's
Incompleteness Theorem. It is a statement that any sufficiently
powerful system can express true things it can't prove. So Dag
Prawitz, had he been saying the things you falsely attributed to
him, would certainly have "got" to Gödel, and would have understood >>>>> full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
[ .... ]
Either you're lying, or you've misunderstood something, yet again.
Possibly both. Established academics don't go around asserting
falsehoods that would disgrace a second year student.
Gödel's Incompleteness Theorem is true beyond doubt, but you can't understand it.
I think this discussion has come to an end.
--
Copyright 2026 Olcott
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician would >>>>>>> risk his reputation by saying false things. If Dag Prawitz really did >>>>>>> "agree" (with whom?) that Gödel's sentence G is not true in Peano >>>>>>> Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's
Incompleteness Theorem. It is a statement that any sufficiently
powerful system can express true things it can't prove. So Dag
Prawitz, had he been saying the things you falsely attributed to
him, would certainly have "got" to Gödel, and would have understood >>>>> full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
[ .... ]
Either you're lying, or you've misunderstood something, yet again.
Possibly both. Established academics don't go around asserting
falsehoods that would disgrace a second year student.
Gödel's Incompleteness Theorem is true beyond doubt, but you can't understand it.
I think this discussion has come to an end.
--
Copyright 2026 Olcott
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician would >>>>>> risk his reputation by saying false things. If Dag Prawitz really >>>>>> did
"agree" (with whom?) that Gödel's sentence G is not true in Peano >>>>>> Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's
Incompleteness
Theorem. It is a statement that any sufficiently powerful system can
express true things it can't prove. So Dag Prawitz, had he been saying >>>> the things you falsely attributed to him, would certainly have "got" to >>>> Gödel, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician >>>>>>> would
risk his reputation by saying false things. If Dag Prawitz really >>>>>>> did
"agree" (with whom?) that Gödel's sentence G is not true in Peano >>>>>>> Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's
Incompleteness
Theorem. It is a statement that any sufficiently powerful system can >>>>> express true things it can't prove. So Dag Prawitz, had he been
saying
the things you falsely attributed to him, would certainly have
"got" to
Gödel, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new ad- missible rules within a certain syntactic context. Some fifteen years
later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen’s cut-elimination theorem for sequent calculi). Later, Prawitz
used the inversion principle again, attributing it with a semantic role. Still working in natural deduction calculi, he formulated a general type
of schematic Introduction rules to be matched—thanks to the idea
supporting the inversion principle — by a corresponding general
schematic Elimination rule. This was an attempt to provide a solution to
the problem suggested by the often quoted note of Gentzen. According to Gentzen “it should be possible to display the elimination rules as
unique functions of the corresponding introduction rules on the basis of certain requirements.” Many people have since worked on this topic,
which can be appropriately seen as the birthplace of what are now
referred to as “general elimination rules”, recently studied thoroughly by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws,
and that being the usual account of naive deductive analysis, then since "natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do
about "inversion principle" is here that the thea-theory has that it's
what subsumes "non-contradiction principle", here hoping that the interpretation aligns and thusly that "principle of inversion" wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of thorough reason as subsuming principles of non-contradiction and what suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism.
In fact by definition it's about the most basic aspect of contemplation
and deliberation in abstraction of looking at both sides of issues and resolving inductive impasses with analytical bridges after complementary duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the characteristic features of Gentzen's intuitionistic natural deduction.
In the literature on proof-theoretic semantics, this principle is often coupled with another that is called the recovery principle. By adopting
the Computational Ludics framework, we reformulate these principles into
one and the same condition, which we call the harmony condition. We show
that this reformulation allows us to reveal two intuitive ideas standing behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the "converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, proof-theoretic semantics rests on the idea that we know the meaning of
a compound sentence when we know what counts as a canonical proof of it.
And if proofs are formalised within the framework of natural deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective of A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring analytical bridges about infinity and continuity.
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician
would
risk his reputation by saying false things. If Dag Prawitz really >>>>>>> did
"agree" (with whom?) that Gödel's sentence G is not true in Peano >>>>>>> Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's
Incompleteness
Theorem. It is a statement that any sufficiently powerful system can >>>>> express true things it can't prove. So Dag Prawitz, had he been
saying
the things you falsely attributed to him, would certainly have
"got" to
Gödel, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new ad- missible rules within a certain syntactic context. Some fifteen years
later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen’s cut-elimination theorem for sequent calculi). Later, Prawitz
used the inversion principle again, attributing it with a semantic role. Still working in natural deduction calculi, he formulated a general type
of schematic Introduction rules to be matched—thanks to the idea
supporting the inversion principle — by a corresponding general
schematic Elimination rule. This was an attempt to provide a solution to
the problem suggested by the often quoted note of Gentzen. According to Gentzen “it should be possible to display the elimination rules as
unique functions of the corresponding introduction rules on the basis of certain requirements.” Many people have since worked on this topic,
which can be appropriately seen as the birthplace of what are now
referred to as “general elimination rules”, recently studied thoroughly by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws,
and that being the usual account of naive deductive analysis, then since "natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do
about "inversion principle" is here that the thea-theory has that it's
what subsumes "non-contradiction principle", here hoping that the interpretation aligns and thusly that "principle of inversion" wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical-study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of thorough reason as subsuming principles of non-contradiction and what suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism.
In fact by definition it's about the most basic aspect of contemplation
and deliberation in abstraction of looking at both sides of issues and resolving inductive impasses with analytical bridges after complementary duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the characteristic features of Gentzen's intuitionistic natural deduction.
In the literature on proof-theoretic semantics, this principle is often coupled with another that is called the recovery principle. By adopting
the Computational Ludics framework, we reformulate these principles into
one and the same condition, which we call the harmony condition. We show
that this reformulation allows us to reveal two intuitive ideas standing behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the "converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, proof-theoretic semantics rests on the idea that we know the meaning of
a compound sentence when we know what counts as a canonical proof of it.
And if proofs are formalised within the framework of natural deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective of A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring analytical bridges about infinity and continuity.
So, Prawitz has has "containment" and "recovery", so, that's more
than merely "containment" and can always be "recovered".
You're going to have to find a new technical sub-field to mis-interpret,
this one's broken open again.
On 06/22/2026 09:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician >>>>>>>> would
risk his reputation by saying false things. If Dag Prawitz really >>>>>>>> did
"agree" (with whom?) that Gödel's sentence G is not true in Peano >>>>>>>> Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's
Incompleteness
Theorem. It is a statement that any sufficiently powerful system can >>>>>> express true things it can't prove. So Dag Prawitz, had he been
saying
the things you falsely attributed to him, would certainly have
"got" to
Gödel, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/publication/233365263_On_Inversion_Principles >>
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, originated in >> the work of Paul Lorenzen in the 1950s, as a method to generate new ad-
missible rules within a certain syntactic context. Some fifteen years
later, the idea was taken up by Dag Prawitz to devise a strategy of
normalization for natural deduction calculi (this being an analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, Prawitz
used the inversion principle again, attributing it with a semantic role.
Still working in natural deduction calculi, he formulated a general type
of schematic Introduction rules to be matched—thanks to the idea
supporting the inversion principle — by a corresponding general
schematic Elimination rule. This was an attempt to provide a solution to
the problem suggested by the often quoted note of Gentzen. According to
Gentzen “it should be possible to display the elimination rules as
unique functions of the corresponding introduction rules on the basis of
certain requirements.” Many people have since worked on this topic,
which can be appropriately seen as the birthplace of what are now
referred to as “general elimination rules”, recently studied thoroughly >> by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using
Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws,
and that being the usual account of naive deductive analysis, then since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke
afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do
about "inversion principle" is here that the thea-theory has that it's
what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion" wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical-study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of
thorough reason as subsuming principles of non-contradiction and what
suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism.
In fact by definition it's about the most basic aspect of contemplation
and deliberation in abstraction of looking at both sides of issues and
resolving inductive impasses with analytical bridges after complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the
characteristic features of Gentzen's intuitionistic natural deduction.
In the literature on proof-theoretic semantics, this principle is often
coupled with another that is called the recovery principle. By adopting
the Computational Ludics framework, we reformulate these principles into
one and the same condition, which we call the harmony condition. We show
that this reformulation allows us to reveal two intuitive ideas standing
behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the
"converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the meaning of
a compound sentence when we know what counts as a canonical proof of it.
And if proofs are formalised within the framework of natural deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective of A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring
analytical bridges about infinity and continuity.
So, Prawitz has has "containment" and "recovery", so, that's more
than merely "containment" and can always be "recovered".
You're going to have to find a new technical sub-field to mis-interpret,
this one's broken open again.
"Since the model-theoretic truth-clauses are invariant
modulo logical form, this leads to truth-preservation in models."
- Piccolomini, "An introduction to Prawitz’s semantics"
So, "containment" and "recovery" is pretty much like Russell's
"isolation" and "significance", yet Russell waffles that one's
the other, while Prawitz points out they're distinct not unique, while something like Quine's "relevance" is also watered-down apologetics
with regards to something like Anderson's "relevance" logic.
Piccolomini mentions "three epistemic problems".
"Prawitz-Etchemendy reduction principle
The model-theoretic validity of A is tantamount to the simple truth (on
some suitable domain) of a universal closure of A[⟨x⟩], where A[⟨x⟩] is
obtained from A by replacing constant symbols with appropriate variables.
[In the case of Etchemendy’s reduction one may need to replace also some logical symbols]
If logical validity is modal, how can it reduce to simple truth ?"
Usually that's for an account of "the thorough", that after all disambiguation and deliberation it remains as unchallenged.
"Collapse of consequence onto material implication
Modality refers to consequence. It is inherited by logical consequence
simply because the latter is consequence by virtue of logical form. But
in model-theory this means that consequence is simply material
implication."
This isn't so: "model theory" needn't admit "material implication" at
all, that's a flailing about "about "quasi-classical quasi-modal logic",
not "model theory", which is plainly a structuralist's account.
"Let PA be the Peano-axioms for N, and let A be any very complex theorem
on N. Then, PA ⊧_N A."
That simply doesn't account for the extra-ordinary and there being at
least three models of integers, three laws of large numbers, and so on,
which would be "independent" the Peano Arithmetic, so what may be
uniqueness results, would instead be distinctness results, so, that
simply makes for that independence allows incompleteness to be completed variously when the theory doesn't otherwise say.
So, no, it is not so that Prawitz says anything wrong about what a
theory doesn't say.
"The inference from PA to A contains an epistemic gap, but is valid in model-theory. [Of course, once we know that PA ⊧_N A, the truth of PA compels us to accept A as true. But we cannot require that we know an inference is valid before using it ! This provokes the Bolzano-Carroll regress.]"
Now, Bolzano has a lot more to uncover about real analysis and
non-standard analysis, yet one may aver that since the system of PA is infinitary and inductively in-complete (not needing
anti-diagonalization, just competing induction rules), that various
"very complex theorems" may simply have used the wrong "law of large
numbers" about greater accounts of arithmetic and geometry and infinity
and continuity.
Something says "Prawitz since Gentzen is intuitionistic", then that
usually means they're "non-classical logics", here instead there's
that "inversion principles" are very much part of "classical logics",
and that "quasi-modal logics", aren't.
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician >>>>>>>> would
risk his reputation by saying false things. If Dag Prawitz really >>>>>>>> did
"agree" (with whom?) that Gödel's sentence G is not true in Peano >>>>>>>> Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's
Incompleteness
Theorem. It is a statement that any sufficiently powerful system can >>>>>> express true things it can't prove. So Dag Prawitz, had he been
saying
the things you falsely attributed to him, would certainly have
"got" to
Gödel, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/publication/233365263_On_Inversion_Principles >>
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, originated in >> the work of Paul Lorenzen in the 1950s, as a method to generate new ad-
missible rules within a certain syntactic context. Some fifteen years
later, the idea was taken up by Dag Prawitz to devise a strategy of
normalization for natural deduction calculi (this being an analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, Prawitz
used the inversion principle again, attributing it with a semantic role.
Still working in natural deduction calculi, he formulated a general type
of schematic Introduction rules to be matched—thanks to the idea
supporting the inversion principle — by a corresponding general
schematic Elimination rule. This was an attempt to provide a solution to
the problem suggested by the often quoted note of Gentzen. According to
Gentzen “it should be possible to display the elimination rules as
unique functions of the corresponding introduction rules on the basis of
certain requirements.” Many people have since worked on this topic,
which can be appropriately seen as the birthplace of what are now
referred to as “general elimination rules”, recently studied thoroughly >> by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using
Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws,
and that being the usual account of naive deductive analysis, then since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke
afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do
about "inversion principle" is here that the thea-theory has that it's
what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion" wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of
thorough reason as subsuming principles of non-contradiction and what
suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism.
In fact by definition it's about the most basic aspect of contemplation
and deliberation in abstraction of looking at both sides of issues and
resolving inductive impasses with analytical bridges after complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the
characteristic features of Gentzen's intuitionistic natural deduction.
In the literature on proof-theoretic semantics, this principle is often
coupled with another that is called the recovery principle. By adopting
the Computational Ludics framework, we reformulate these principles into
one and the same condition, which we call the harmony condition. We show
that this reformulation allows us to reveal two intuitive ideas standing
behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the
"converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the meaning of
a compound sentence when we know what counts as a canonical proof of it.
And if proofs are formalised within the framework of natural deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective of A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>> who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by >>>>>>>> contradiction. The LP isn't a contradiction; it's a paradox. The >>>>>>>> two are different things. A contradiction is a statement which >>>>>>>> is necessarily false. A paradox is a statement to which no truth >>>>>>>> value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem
proof, Godel's proof, and Tarski's proof, each of which you've
been attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics
do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the
C implementation you have used. When DD iss executed in that environment
it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
This has been completely rewritten just now. https://github.com/plolcott/x86utm/blob/master/README.md
On 6/22/2026 1:27 AM, Mikko wrote:
On 22/06/2026 02:55, olcott wrote:
On 6/21/2026 5:11 AM, Mikko wrote:
On 20/06/2026 16:50, olcott wrote:
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semanticsSome people only memorize conventional views and
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is
abstract in
the extreme. One thing is utterly clear: its level of
abstraction is
well beyond the comprehension capabilities of Peter Olcott, who >>>>>>>> can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be >>>>>>>> bothered
to read it any further. If it actually says anything at all, that >>>>>>>> something is heavily disguised. From it's "Conclusion and Outlook" >>>>>>>> section at the end:
| Standard proof-theoretic semantics has practically exclusively >>>>>>>> been
| occupied with logical constants. Logical constants play a
central role
| in reasoning and inference, but are definitely not the
exclusive, and
| perhaps not even the most typical sort of entities that can be >>>>>>>> defined
| inferentially. A framework is needed that deals with inferential >>>>>>>> | definitions in a wider sense and covers both logical and
extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the >>>>>>> near future not useful as making it useful requires much time and >>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for?
What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If a claim is true on the basis on meaning expressed in language we
usually can easily determine its truth vaule wihout computational
tools. The truth values we want to know but are hard to determine
are of claims that are true on some other basis.
The system I propose would cut off the dangerous lies
of dangerous liars mid-sentence and be able to prove
that these are lies to every level of understanding
between kindergarten and PhD.
You have not yet demonstrated any aboility to cut off a single
lie that would matter to typical people.
Nothing is going to work until we get everyone to
understand the difference between truth and lies
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat?
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>
the extreme. One thing is utterly clear: its level of >>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>>> who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't >>>>>>>>>>> be bothered
to read it any further. If it actually says anything at all, >>>>>>>>>>> that
something is heavily disguised. From it's "Conclusion and >>>>>>>>>>> Outlook"
section at the end:
| Standard proof-theoretic semantics has practically
exclusively been
| occupied with logical constants. Logical constants play a >>>>>>>>>>> central role
| in reasoning and inference, but are definitely not the >>>>>>>>>>> exclusive, and
| perhaps not even the most typical sort of entities that can >>>>>>>>>>> be defined
| inferentially. A framework is needed that deals with
inferential
| definitions in a wider sense and covers both logical and >>>>>>>>>>> extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and >>>>>>>>>> in the
near future not useful as making it useful requires much time and >>>>>>>>>> effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful >>>>>>>>> for? What it
ought to be able to do that standard logic fails at? Maybe >>>>>>>>> André could
elucidate. He seems to have a better grasp of it than anybody >>>>>>>>> else here.
I doubt my understanding of PTS is any better than yours. I
basically only know what is presented in the Stanford
Encyclopedia article (which you correctly point out is not
exactly aimed at beginners) and the Wikipedia article. What I am >>>>>>>> quite certain of, however, is that Olcott lacks any
understanding of what PTS actually says as he's made a variety >>>>>>>> of fairly absurd claims regarding it (for example, that PTS
claims that unproven propositions are 'meaningless' or that the >>>>>>>> goal of PTS is to completely overthrow standard truth-theoretic >>>>>>>> semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is not that they never admit defeat.
It is that that have a system of essentially infallible reasoning
that never errs as long as it has all the relevant information.
It is fairly simple to build a system of essentially infallible
reasoning that never errs even when it doesn't have all the
relevant information. The real problem is to construct a system
that tells something interesting instead of just different
presentations of the same already known facts.
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a publishable >>>> (or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human being on
the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles
that have any is or depends on claims that should be proven but
aren't.
They are proven in Proof Theoretic Semantics
Now that I am acquiring the lingua franca of PTS I
will finally be able to publish.
If all you can publish is in the topic area of PtS then they may
count as uninteresting to those whose primary problems are not in
that topic area.
My extensions to PTS eliminate the LLM reliability issues.
This makes the Trillion dollar industry at least 100-fold
more valuable.
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>>>> fails.
I don't believe you. You have no respect for or understanding of the >>>>>> truth. If you really want to persuade anybody that PTS somehow
causes
Gödel's theorem not to hold, then cite an academic expert who'll have >>>>>> some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you certainly >>>>>> don't
understand Gödel's Theorem, neither the theorem itself nor any
proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by
you, and it is one which you have never explicitly defined, so the
fault here certainly doesn't lie with Alan. It's certainly not a
'verified fact' when you haven't even adequately explained what it
is that you mean.
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
What makes you believe semantic relations that can be structured as
a tree are sufficient to contain all knowledge that is exressed in
some language?
The CycL language and the Cyc Project.
On 6/22/2026 2:23 AM, Mikko wrote:
On 21/06/2026 23:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>> fails.
I don't believe you. You have no respect for or understanding of the >>>> truth. If you really want to persuade anybody that PTS somehow causes >>>> Gödel's theorem not to hold, then cite an academic expert who'll have >>>> some credibility.
If they are mere gibberish words to you then you will not understand. >>>>You don't understand Proof-theoritic Semantics, and you certainly don't >>>> understand Gödel's Theorem, neither the theorem itself nor any proof of >>>> it.
in the atomic base of PA.
It is a verified fact that Gödel's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
On 6/22/2026 2:40 AM, Mikko wrote:
On 22/06/2026 03:00, olcott wrote:
On 6/21/2026 5:23 AM, Mikko wrote:
On 20/06/2026 17:18, olcott wrote:
On 6/20/2026 12:25 AM, Ross Finlayson wrote:
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
Modern Logic has always simply ignored that an
expression may be semantically incoherent because
logic has always ignored semantics and focused
on syntax.
Modern logic has
always put semantics outside of the formal system
in a separate model.
And that way avoided semantic incoherence in formal systems.
It didn't really avoid it.
The semantic incoherence was merely hidden.
In every model of PA either G or its negation is true. It does notPTS does not do that.
Gödel proved that every consistent first order theory has a model.
That means that a consisten first order theory cannot be semantically
incoherent.
Like I just said.
Therefore we can trust that in every theory that can express the
truths of the natural numbers there is a true sentence that cannot
be proven.
As I have been saying for many years and finally
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever true directly in PA.
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 2:40 AM, Mikko wrote:
Therefore we can trust that in every theory that can express the
truths of the natural numbers there is a true sentence that cannot
be proven.
As I have been saying for many years and finally
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever
true directly in PA.
G is true.
I put it to you you're lying again. No reputable mathematician would
risk his reputation by saying false things. If Dag Prawitz really did
"agree" (with whom?) that Gödel's sentence G is not true in Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's Incompleteness Theorem. It is a statement that any sufficiently powerful system can
express true things it can't prove. So Dag Prawitz, had he been saying
the things you falsely attributed to him, would certainly have "got" to Gödel, and would have understood full well what he was saying.
I put it to you you have not understood that academic's work.
Almost no PTS people even ever get to true, they all stop at semantic
meaning.
That's a tautology. One of those meanings which they will be dealing
with is true. What's the point of a logical system that can't even characterise assertions as being true or false?
And on the off chance you're not lying, who on Earth would want to use a >>> deficient system like PTS that can't even prove standard mathematical
results?
The Base-Extension Semantics (B-eS) sub-field of PTS
lets you extend PA so that G is provable in PA.
They also never talk about G or PA explicitly.
Again, if PTS was like you say, why would anybody want to use it when it doesn't even prove standard results without some extension? I put it to
you further, that PTS is quite capable of proving Gödel's theorems,
without any special purpose extensions. Otherwise, what would be the
point?
--
Copyright 2026 Olcott
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician >>>>>>>>> would
risk his reputation by saying false things. If Dag Prawitz really >>>>>>>>> did
"agree" (with whom?) that Gödel's sentence G is not true in Peano >>>>>>>>> Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's
Incompleteness
Theorem. It is a statement that any sufficiently powerful system >>>>>>> can
express true things it can't prove. So Dag Prawitz, had he been >>>>>>> saying
the things you falsely attributed to him, would certainly have
"got" to
Gödel, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, originated in
the work of Paul Lorenzen in the 1950s, as a method to generate new ad-
missible rules within a certain syntactic context. Some fifteen years
later, the idea was taken up by Dag Prawitz to devise a strategy of
normalization for natural deduction calculi (this being an analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, Prawitz >>> used the inversion principle again, attributing it with a semantic role. >>> Still working in natural deduction calculi, he formulated a general type >>> of schematic Introduction rules to be matched—thanks to the idea
supporting the inversion principle — by a corresponding general
schematic Elimination rule. This was an attempt to provide a solution to >>> the problem suggested by the often quoted note of Gentzen. According to
Gentzen “it should be possible to display the elimination rules as
unique functions of the corresponding introduction rules on the basis of >>> certain requirements.” Many people have since worked on this topic,
which can be appropriately seen as the birthplace of what are now
referred to as “general elimination rules”, recently studied thoroughly >>> by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using
Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws,
and that being the usual account of naive deductive analysis, then since >>> "natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke
afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do
about "inversion principle" is here that the thea-theory has that it's
what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion" wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of
thorough reason as subsuming principles of non-contradiction and what
suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism.
In fact by definition it's about the most basic aspect of contemplation
and deliberation in abstraction of looking at both sides of issues and
resolving inductive impasses with analytical bridges after complementary >>> duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the
characteristic features of Gentzen's intuitionistic natural deduction.
In the literature on proof-theoretic semantics, this principle is often
coupled with another that is called the recovery principle. By adopting
the Computational Ludics framework, we reformulate these principles into >>> one and the same condition, which we call the harmony condition. We show >>> that this reformulation allows us to reveal two intuitive ideas standing >>> behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the
"converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the meaning of
a compound sentence when we know what counts as a canonical proof of it. >>> And if proofs are formalised within the framework of natural deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective of
A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that
make contradictions and thusly destroy each other.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
On 22/06/2026 16:13, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>
the extreme. One thing is utterly clear: its level of >>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>>> who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by >>>>>>>>> contradiction. The LP isn't a contradiction; it's a paradox. >>>>>>>>> The two are different things. A contradiction is a statement >>>>>>>>> which is necessarily false. A paradox is a statement to which >>>>>>>>> no truth value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem >>>>>>> proof, Godel's proof, and Tarski's proof, each of which you've
been attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics
do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the
C implementation you have used. When DD iss executed in that environment >>> it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Nice to see that you don't disagree.
This has been completely rewritten just now.
https://github.com/plolcott/x86utm/blob/master/README.md
The description is updated. The described is not updated.
On 22/06/2026 18:16, olcott wrote:
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat?
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>> reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>>>> who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I can't >>>>>>>>>>>> be bothered
to read it any further. If it actually says anything at >>>>>>>>>>>> all, that
something is heavily disguised. From it's "Conclusion and >>>>>>>>>>>> Outlook"
section at the end:
| Standard proof-theoretic semantics has practically
exclusively been
| occupied with logical constants. Logical constants play a >>>>>>>>>>>> central role
| in reasoning and inference, but are definitely not the >>>>>>>>>>>> exclusive, and
| perhaps not even the most typical sort of entities that >>>>>>>>>>>> can be defined
| inferentially. A framework is needed that deals with >>>>>>>>>>>> inferential
| definitions in a wider sense and covers both logical and >>>>>>>>>>>> extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and >>>>>>>>>>> in the
near future not useful as making it useful requires much time >>>>>>>>>>> and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful >>>>>>>>>> for? What it
ought to be able to do that standard logic fails at? Maybe >>>>>>>>>> André could
elucidate. He seems to have a better grasp of it than anybody >>>>>>>>>> else here.
I doubt my understanding of PTS is any better than yours. I >>>>>>>>> basically only know what is presented in the Stanford
Encyclopedia article (which you correctly point out is not
exactly aimed at beginners) and the Wikipedia article. What I >>>>>>>>> am quite certain of, however, is that Olcott lacks any
understanding of what PTS actually says as he's made a variety >>>>>>>>> of fairly absurd claims regarding it (for example, that PTS >>>>>>>>> claims that unproven propositions are 'meaningless' or that the >>>>>>>>> goal of PTS is to completely overthrow standard truth-theoretic >>>>>>>>> semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is not that they never admit defeat.
It is that that have a system of essentially infallible reasoning
that never errs as long as it has all the relevant information.
It is fairly simple to build a system of essentially infallible
reasoning that never errs even when it doesn't have all the
relevant information. The real problem is to construct a system
that tells something interesting instead of just different
presentations of the same already known facts.
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general knowledge
in your system the general knowledge has grown to inlude more facts.
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>> alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which
sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present
ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a publishable >>>>> (or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human being
on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles
that have any is or depends on claims that should be proven but
aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the proof or
has a pointer to an olready published proof.
Now that I am acquiring the lingua franca of PTS I
will finally be able to publish.
If all you can publish is in the topic area of PtS then they may
count as uninteresting to those whose primary problems are not in
that topic area.
My extensions to PTS eliminate the LLM reliability issues.
Does not help as long as those extensions are not published so that
your articles can point to them.
This makes the Trillion dollar industry at least 100-fold
more valuable.
Value of some industry in January 2049 is a proor predictor of the
vale of the same industry in December 2049.
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're >>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>>>>> fails.
I don't believe you. You have no respect for or understanding of >>>>>>> the
truth. If you really want to persuade anybody that PTS somehow >>>>>>> causes
Gödel's theorem not to hold, then cite an academic expert who'll >>>>>>> have
some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you certainly >>>>>>> don't
understand Gödel's Theorem, neither the theorem itself nor any >>>>>>> proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by
you, and it is one which you have never explicitly defined, so the
fault here certainly doesn't lie with Alan. It's certainly not a
'verified fact' when you haven't even adequately explained what it
is that you mean.
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
What makes you believe semantic relations that can be structured as
a tree are sufficient to contain all knowledge that is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
On 22/06/2026 17:44, olcott wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
On 21/06/2026 23:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>>> fails.
I don't believe you. You have no respect for or understanding of the >>>>> truth. If you really want to persuade anybody that PTS somehow causes >>>>> Gödel's theorem not to hold, then cite an academic expert who'll have >>>>> some credibility.
If they are mere gibberish words to you then you will not understand. >>>>>You don't understand Proof-theoritic Semantics, and you certainly
don't
understand Gödel's Theorem, neither the theorem itself nor any
proof of
it.
in the atomic base of PA.
It is a verified fact that Gödel's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
The proof that there are unprovable sentences with unprovable
negations does not refer to any semantics. That a sentence or
its negation is true is a feature of many semantic systems and
in particular of the arithemtic semantics of Peano arithmetic.
When people want to know how a function could be computed or whether it
can be computed at all they only care about arithmetic and computational semantics. Proof theoretic semnatics is irrelevant.
On 22/06/2026 18:12, olcott wrote:
On 6/22/2026 2:40 AM, Mikko wrote:
On 22/06/2026 03:00, olcott wrote:
On 6/21/2026 5:23 AM, Mikko wrote:
On 20/06/2026 17:18, olcott wrote:
On 6/20/2026 12:25 AM, Ross Finlayson wrote:
On 06/18/2026 12:35 PM, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>
reject alternative views out-of-hand without review.
This seems to be the rigidly conformist and memorize
by rote mindset.
Hm. Here there is a rather "rigidly conformist" approach,
and "an extreme rationalism", though, it's not the usual.
a principle of inverse
supplants, subsumes, and includes
a principle of non-contradiction/excluded-middle
Modern Logic has always simply ignored that an
expression may be semantically incoherent because
logic has always ignored semantics and focused
on syntax.
Modern logic has
always put semantics outside of the formal system
in a separate model.
And that way avoided semantic incoherence in formal systems.
It didn't really avoid it.
The semantic incoherence was merely hidden.
How can there be a semantic incoherece without any semantics?
PTS does not do that.
Gödel proved that every consistent first order theory has a model.
That means that a consisten first order theory cannot be semantically >>>>> incoherent.
Like I just said.
Therefore we can trust that in every theory that can express the
truths of the natural numbers there is a true sentence that cannot
be proven.
As I have been saying for many years and finally
strict Proof Theoretic Semantics based on Dag Prawitz
theory of Grounds agrees G is ungrounded in PA
and is only true in meta-math. G was never ever true directly in PA.
In every model of PA either G or its negation is true. It does not
mattet which, either way there is a true but unprovable sentence
in PA. Gödel also proved that if additional postulates are added
to make G or its negation (but not both) provable there will be
another sentece that is true but unprovable (unless the system is inconsistent).
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician >>>>>>>>>> would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>> really
did
"agree" (with whom?) that Gödel's sentence G is not true in Peano >>>>>>>>>> Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's
Incompleteness
Theorem. It is a statement that any sufficiently powerful
system can
express true things it can't prove. So Dag Prawitz, had he been >>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>> "got" to
Gödel, and would have understood full well what he was saying.
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't say", >>>> then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate new ad- >>>> missible rules within a certain syntactic context. Some fifteen years >>>> later, the idea was taken up by Dag Prawitz to devise a strategy of
normalization for natural deduction calculi (this being an analogue of >>>> Gentzen’s cut-elimination theorem for sequent calculi). Later, Prawitz >>>> used the inversion principle again, attributing it with a semantic
role.
Still working in natural deduction calculi, he formulated a general
type
of schematic Introduction rules to be matched—thanks to the idea
supporting the inversion principle — by a corresponding general
schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen. According to >>>> Gentzen “it should be possible to display the elimination rules as
unique functions of the corresponding introduction rules on the
basis of
certain requirements.” Many people have since worked on this topic,
which can be appropriately seen as the birthplace of what are now
referred to as “general elimination rules”, recently studied thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using
Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws, >>>> and that being the usual account of naive deductive analysis, then
since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke >>>> afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do
about "inversion principle" is here that the thea-theory has that it's >>>> what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion" wouldn't >>>> need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most >>>> modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of >>>> thorough reason as subsuming principles of non-contradiction and what
suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism. >>>> In fact by definition it's about the most basic aspect of contemplation >>>> and deliberation in abstraction of looking at both sides of issues and >>>> resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the
characteristic features of Gentzen's intuitionistic natural deduction. >>>> In the literature on proof-theoretic semantics, this principle is often >>>> coupled with another that is called the recovery principle. By adopting >>>> the Computational Ludics framework, we reformulate these principles
into
one and the same condition, which we call the harmony condition. We
show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the
"converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that each >>>> of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the meaning of >>>> a compound sentence when we know what counts as a canonical proof of
it.
And if proofs are formalised within the framework of natural deduction, >>>> then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective
of A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring >>>> analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're >>>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS Gödel 1931
incompleteness
fails.
I don't believe you. You have no respect for or understanding >>>>>>>> of the
truth. If you really want to persuade anybody that PTS somehow >>>>>>>> causes
Gödel's theorem not to hold, then cite an academic expert who'll >>>>>>>> have
some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you
certainly don't
understand Gödel's Theorem, neither the theorem itself nor any >>>>>>>> proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by
you, and it is one which you have never explicitly defined, so the >>>>>> fault here certainly doesn't lie with Alan. It's certainly not a
'verified fact' when you haven't even adequately explained what it >>>>>> is that you mean.
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
What makes you believe semantic relations that can be structured as
a tree are sufficient to contain all knowledge that is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
On 6/23/2026 1:15 AM, Mikko wrote:
On 22/06/2026 17:44, olcott wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
On 21/06/2026 23:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>>>> fails.
I don't believe you. You have no respect for or understanding of the >>>>>> truth. If you really want to persuade anybody that PTS somehow
causes
Gödel's theorem not to hold, then cite an academic expert who'll have >>>>>> some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you certainly
don't
understand Gödel's Theorem, neither the theorem itself nor any
proof of
it.
in the atomic base of PA.
It is a verified fact that Gödel's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
The proof that there are unprovable sentences with unprovable
negations does not refer to any semantics. That a sentence or
its negation is true is a feature of many semantic systems and
in particular of the arithemtic semantics of Peano arithmetic.
When people want to know how a function could be computed or whether it
can be computed at all they only care about arithmetic and computational
semantics. Proof theoretic semnatics is irrelevant.
Proof-theoretic semantics is an alternative foundation
for mathematics replacing truth conditional semantics.
"Proof-theoretic semantics is an alternative to truth-condition semantics." https://plato.stanford.edu/entries/proof-theoretic-semantics/
*Not one person has understood that one sentence yet*
On 06/23/2026 07:52 AM, olcott wrote:
On 6/23/2026 1:15 AM, Mikko wrote:
On 22/06/2026 17:44, olcott wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
On 21/06/2026 23:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>>>>> fails.
I don't believe you. You have no respect for or understanding of >>>>>>> the
truth. If you really want to persuade anybody that PTS somehow
causes
Gödel's theorem not to hold, then cite an academic expert who'll >>>>>>> have
some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you certainly >>>>>>> don't
understand Gödel's Theorem, neither the theorem itself nor any
proof of
it.
in the atomic base of PA.
It is a verified fact that Gödel's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
The proof that there are unprovable sentences with unprovable
negations does not refer to any semantics. That a sentence or
its negation is true is a feature of many semantic systems and
in particular of the arithemtic semantics of Peano arithmetic.
When people want to know how a function could be computed or whether it
can be computed at all they only care about arithmetic and computational >>> semantics. Proof theoretic semnatics is irrelevant.
Proof-theoretic semantics is an alternative foundation
for mathematics replacing truth conditional semantics.
"Proof-theoretic semantics is an alternative to truth-condition
semantics."
https://plato.stanford.edu/entries/proof-theoretic-semantics/
*Not one person has understood that one sentence yet*
"Understanding" is for suckers,
"comprehending" is what analysts do.
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician >>>>>>>>>>> would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>> really
did
"agree" (with whom?) that Gödel's sentence G is not true in >>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's
Incompleteness
Theorem. It is a statement that any sufficiently powerful
system can
express true things it can't prove. So Dag Prawitz, had he been >>>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>>> "got" to
Gödel, and would have understood full well what he was saying. >>>>>>>
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says", >>>>> and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't
say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate new >>>>> ad-
missible rules within a certain syntactic context. Some fifteen years >>>>> later, the idea was taken up by Dag Prawitz to devise a strategy of
normalization for natural deduction calculi (this being an analogue of >>>>> Gentzen’s cut-elimination theorem for sequent calculi). Later, Prawitz >>>>> used the inversion principle again, attributing it with a semantic
role.
Still working in natural deduction calculi, he formulated a general
type
of schematic Introduction rules to be matched—thanks to the idea
supporting the inversion principle — by a corresponding general
schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen “it should be possible to display the elimination rules as >>>>> unique functions of the corresponding introduction rules on the
basis of
certain requirements.” Many people have since worked on this topic, >>>>> which can be appropriately seen as the birthplace of what are now
referred to as “general elimination rules”, recently studied
thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main
threads of this chapter of proof-theoretical investigation, using
Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws, >>>>> and that being the usual account of naive deductive analysis, then
since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke >>>>> afterward there's also Sheffer and Chwistek before, and instead of
Montague for semantics there's Herbrand for semantics, so, what to do >>>>> about "inversion principle" is here that the thea-theory has that it's >>>>> what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most >>>>> modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of >>>>> thorough reason as subsuming principles of non-contradiction and what >>>>> suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the
oldest account of Western philosophy like Heraclitus with dual monism. >>>>> In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues and >>>>> resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the
characteristic features of Gentzen's intuitionistic natural deduction. >>>>> In the literature on proof-theoretic semantics, this principle is
often
coupled with another that is called the recovery principle. By
adopting
the Computational Ludics framework, we reformulate these principles
into
one and the same condition, which we call the harmony condition. We
show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the >>>>> "converse" of the inversion principle. We also formulate two other
conditions in the Computational Ludics framework, and we show that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical proof of >>>>> it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective
of A."
The "canonical proofs" are not unique, in any system strong enough
to make for infinitary reasoning and super-classical results requiring >>>>> analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
On 06/23/2026 07:52 AM, olcott wrote:
On 6/23/2026 1:15 AM, Mikko wrote:
On 22/06/2026 17:44, olcott wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
On 21/06/2026 23:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're >>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>>>>> fails.
I don't believe you. You have no respect for or understanding of >>>>>>> the
truth. If you really want to persuade anybody that PTS somehow >>>>>>> causes
Gödel's theorem not to hold, then cite an academic expert who'll >>>>>>> have
some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you certainly >>>>>>> don't
understand Gödel's Theorem, neither the theorem itself nor any
proof of
it.
in the atomic base of PA.
It is a verified fact that Gödel's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
The proof that there are unprovable sentences with unprovable
negations does not refer to any semantics. That a sentence or
its negation is true is a feature of many semantic systems and
in particular of the arithemtic semantics of Peano arithmetic.
When people want to know how a function could be computed or whether it
can be computed at all they only care about arithmetic and computational >>> semantics. Proof theoretic semnatics is irrelevant.
Proof-theoretic semantics is an alternative foundation
for mathematics replacing truth conditional semantics.
"Proof-theoretic semantics is an alternative to truth-condition
semantics."
https://plato.stanford.edu/entries/proof-theoretic-semantics/
*Not one person has understood that one sentence yet*
"Understanding" is for suckers,
"comprehending" is what analysts do.
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician >>>>>>>>>>>> would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>> really
did
"agree" (with whom?) that Gödel's sentence G is not true in >>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's >>>>>>>>>> Incompleteness
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had he been >>>>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>>>> "got" to
Gödel, and would have understood full well what he was saying. >>>>>>>>
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says", >>>>>> and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't
say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate
new ad-
missible rules within a certain syntactic context. Some fifteen years >>>>>> later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>> normalization for natural deduction calculi (this being an
analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later,
Prawitz
used the inversion principle again, attributing it with a semantic >>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>> type
of schematic Introduction rules to be matched—thanks to the idea >>>>>> supporting the inversion principle — by a corresponding general
schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen “it should be possible to display the elimination rules as >>>>>> unique functions of the corresponding introduction rules on the
basis of
certain requirements.” Many people have since worked on this topic, >>>>>> which can be appropriately seen as the birthplace of what are now
referred to as “general elimination rules”, recently studied
thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>> threads of this chapter of proof-theoretical investigation, using
Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's
laws,
and that being the usual account of naive deductive analysis, then >>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides
Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>> Montague for semantics there's Herbrand for semantics, so, what to do >>>>>> about "inversion principle" is here that the thea-theory has that
it's
what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and what >>>>>> suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>> oldest account of Western philosophy like Heraclitus with dual
monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is
often
coupled with another that is called the recovery principle. By
adopting
the Computational Ludics framework, we reformulate these principles >>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>> show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the >>>>>> "converse" of the inversion principle. We also formulate two other >>>>>> conditions in the Computational Ludics framework, and we show that >>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical proof of >>>>>> it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective >>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that >>>> make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable
mathematician
would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>>> really
did
"agree" (with whom?) that Gödel's sentence G is not true in >>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>> means untrue all the time for everything within hisYou won't understand it, but that _is_ essentially Gödel's >>>>>>>>>>> Incompleteness
own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had he been >>>>>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>> "got" to
Gödel, and would have understood full well what he was saying. >>>>>>>>>
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says", >>>>>>> and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate
new ad-
missible rules within a certain syntactic context. Some fifteen years >>>>>>> later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>>> normalization for natural deduction calculi (this being an
analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, >>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>>> type
of schematic Introduction rules to be matched—thanks to the idea >>>>>>> supporting the inversion principle — by a corresponding general >>>>>>> schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen “it should be possible to display the elimination rules as >>>>>>> unique functions of the corresponding introduction rules on the
basis of
certain requirements.” Many people have since worked on this topic, >>>>>>> which can be appropriately seen as the birthplace of what are now >>>>>>> referred to as “general elimination rules”, recently studied >>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>>> threads of this chapter of proof-theoretical investigation, using >>>>>>> Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides
Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>> Montague for semantics there's Herbrand for semantics, so, what
to do
about "inversion principle" is here that the thea-theory has that >>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>> interpretation aligns and thusly that "principle of inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and >>>>>>> what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>> oldest account of Western philosophy like Heraclitus with dual
monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>> often
coupled with another that is called the recovery principle. By
adopting
the Computational Ludics framework, we reformulate these principles >>>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>>> show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the >>>>>>> inversion principle, and the idea that the recovery principle is the >>>>>>> "converse" of the inversion principle. We also formulate two other >>>>>>> conditions in the Computational Ludics framework, and we show that >>>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical proof of >>>>>>> it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective >>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that >>>>> make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs". >>>> Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable
mathematician
would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>>> really
did
"agree" (with whom?) that Gödel's sentence G is not true in >>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>> means untrue all the time for everything within hisYou won't understand it, but that _is_ essentially Gödel's >>>>>>>>>>> Incompleteness
own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had he been >>>>>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>> "got" to
Gödel, and would have understood full well what he was saying. >>>>>>>>>
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says", >>>>>>> and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate
new ad-
missible rules within a certain syntactic context. Some fifteen years >>>>>>> later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>>> normalization for natural deduction calculi (this being an
analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, >>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>>> type
of schematic Introduction rules to be matched—thanks to the idea >>>>>>> supporting the inversion principle — by a corresponding general >>>>>>> schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen “it should be possible to display the elimination rules as >>>>>>> unique functions of the corresponding introduction rules on the
basis of
certain requirements.” Many people have since worked on this topic, >>>>>>> which can be appropriately seen as the birthplace of what are now >>>>>>> referred to as “general elimination rules”, recently studied >>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>>> threads of this chapter of proof-theoretical investigation, using >>>>>>> Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides
Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>> Montague for semantics there's Herbrand for semantics, so, what >>>>>>> to do
about "inversion principle" is here that the thea-theory has that >>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>> interpretation aligns and thusly that "principle of inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and >>>>>>> what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>> oldest account of Western philosophy like Heraclitus with dual
monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>> often
coupled with another that is called the recovery principle. By
adopting
the Computational Ludics framework, we reformulate these principles >>>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>>> show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the >>>>>>> inversion principle, and the idea that the recovery principle is the >>>>>>> "converse" of the inversion principle. We also formulate two other >>>>>>> conditions in the Computational Ludics framework, and we show that >>>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical proof of >>>>>>> it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective >>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that >>>>> make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs". >>>> Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
On 06/23/2026 10:32 AM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>>>> really
did
"agree" (with whom?) that Gödel's sentence G is not true in >>>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
I was right, you didn't understand it.He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>> means untrue all the time for everything within hisYou won't understand it, but that _is_ essentially Gödel's >>>>>>>>>>>> Incompleteness
own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had he >>>>>>>>>>>> been
saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>>> "got" to
Gödel, and would have understood full well what he was saying. >>>>>>>>>>
You did not pay close enough attention to my exact words. >>>>>>>>>>
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz >>>>>>>> says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>> new ad-
missible rules within a certain syntactic context. Some fifteen >>>>>>>> years
later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>>>> normalization for natural deduction calculi (this being an
analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, >>>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>>>> type
of schematic Introduction rules to be matched—thanks to the idea >>>>>>>> supporting the inversion principle — by a corresponding general >>>>>>>> schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen “it should be possible to display the elimination rules as >>>>>>>> unique functions of the corresponding introduction rules on the >>>>>>>> basis of
certain requirements.” Many people have since worked on this topic, >>>>>>>> which can be appropriately seen as the birthplace of what are now >>>>>>>> referred to as “general elimination rules”, recently studied >>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>>>> threads of this chapter of proof-theoretical investigation, using >>>>>>>> Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides >>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>>> Montague for semantics there's Herbrand for semantics, so, what >>>>>>>> to do
about "inversion principle" is here that the thea-theory has that >>>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>>> interpretation aligns and thusly that "principle of inversion" >>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and >>>>>>>> what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>>> oldest account of Western philosophy like Heraclitus with dual >>>>>>>> monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>>> often
coupled with another that is called the recovery principle. By >>>>>>>> adopting
the Computational Ludics framework, we reformulate these principles >>>>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>>>> show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>> standing
behind these principles: the idea of "containment" present in the >>>>>>>> inversion principle, and the idea that the recovery principle is >>>>>>>> the
"converse" of the inversion principle. We also formulate two other >>>>>>>> conditions in the Computational Ludics framework, and we show that >>>>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>> proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical
proof of
it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>> derivation ending with an introduction rule of the main connective >>>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts >>>>>> that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs". >>>>> Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>> of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
P.S. there's no reason at all to "get back to you".
... Except countering the waste-ful spammy trolling.
Finding cycles in derivations of arguments is exactly
what makes for detection of circularities then as to
whether they're the virtuous or vicious sorts of circles,
it's the act of being diligent itself, you brainless, memoryless bot.
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable mathematician >>>>>>>>>>>> would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>> really
did
"agree" (with whom?) that Gödel's sentence G is not true in >>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable
means untrue all the time for everything within his
own Theory of Grounds of strict Proof Theoretic Semantics.
You won't understand it, but that _is_ essentially Gödel's >>>>>>>>>> Incompleteness
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had he been >>>>>>>>>> saying
the things you falsely attributed to him, would certainly have >>>>>>>>>> "got" to
Gödel, and would have understood full well what he was saying. >>>>>>>>
You did not pay close enough attention to my exact words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz says", >>>>>> and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse
principle" so I think these are key aspects of fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself,
originated in
the work of Paul Lorenzen in the 1950s, as a method to generate new >>>>>> ad-
missible rules within a certain syntactic context. Some fifteen years >>>>>> later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>> normalization for natural deduction calculi (this being an analogue of >>>>>> Gentzen’s cut-elimination theorem for sequent calculi). Later, Prawitz >>>>>> used the inversion principle again, attributing it with a semantic >>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>> type
of schematic Introduction rules to be matched—thanks to the idea >>>>>> supporting the inversion principle — by a corresponding general
schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen “it should be possible to display the elimination rules as >>>>>> unique functions of the corresponding introduction rules on the
basis of
certain requirements.” Many people have since worked on this topic, >>>>>> which can be appropriately seen as the birthplace of what are now
referred to as “general elimination rules”, recently studied
thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>> threads of this chapter of proof-theoretical investigation, using
Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's laws, >>>>>> and that being the usual account of naive deductive analysis, then >>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides Kripke >>>>>> afterward there's also Sheffer and Chwistek before, and instead of >>>>>> Montague for semantics there's Herbrand for semantics, so, what to do >>>>>> about "inversion principle" is here that the thea-theory has that it's >>>>>> what subsumes "non-contradiction principle", here hoping that the
interpretation aligns and thusly that "principle of inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of most >>>>>> modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a principle of >>>>>> thorough reason as subsuming principles of non-contradiction and what >>>>>> suffices, so, I'll be curious then about what to make of Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>> oldest account of Western philosophy like Heraclitus with dual monism. >>>>>> In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues and >>>>>> resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>> characteristic features of Gentzen's intuitionistic natural deduction. >>>>>> In the literature on proof-theoretic semantics, this principle is >>>>>> often
coupled with another that is called the recovery principle. By
adopting
the Computational Ludics framework, we reformulate these principles >>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>> show
that this reformulation allows us to reveal two intuitive ideas
standing
behind these principles: the idea of "containment" present in the
inversion principle, and the idea that the recovery principle is the >>>>>> "converse" of the inversion principle. We also formulate two other >>>>>> conditions in the Computational Ludics framework, and we show that >>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives,
proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical proof of >>>>>> it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed
derivation ending with an introduction rule of the main connective >>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>> to make for infinitary reasoning and super-classical results requiring >>>>>> analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts that >>>> make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs
of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
On 6/23/2026 12:39 AM, Mikko wrote:
On 22/06/2026 16:13, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:The exact operational semantics of C conclusively
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>>> alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>>
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>>>> who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with irrelevancy. >>>>>>>>>>
The Liar's Paradox has absolutely nothing to do with proof by >>>>>>>>>> contradiction. The LP isn't a contradiction; it's a paradox. >>>>>>>>>> The two are different things. A contradiction is a statement >>>>>>>>>> which is necessarily false. A paradox is a statement to which >>>>>>>>>> no truth value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting problem >>>>>>>> proof, Godel's proof, and Tarski's proof, each of which you've >>>>>>>> been attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines
that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program. >>>>>
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics
do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the
C implementation you have used. When DD iss executed in that
environment
it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Nice to see that you don't disagree.
Not nice to see that everyone continues to
totally ignore my best validation of proof
theoretic semantics.
This is understandable for anyone that has no
idea what a directed graph is.
This has been completely rewritten just now.
https://github.com/plolcott/x86utm/blob/master/README.md
The description is updated. The described is not updated.
It always was a proof theoretic halt prover
I just didn't have those terms until recently.
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat?
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>> reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>>>>> who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I >>>>>>>>>>>>> can't be bothered
to read it any further. If it actually says anything at >>>>>>>>>>>>> all, that
something is heavily disguised. From it's "Conclusion and >>>>>>>>>>>>> Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants play a >>>>>>>>>>>>> central role
| in reasoning and inference, but are definitely not the >>>>>>>>>>>>> exclusive, and
| perhaps not even the most typical sort of entities that >>>>>>>>>>>>> can be defined
| inferentially. A framework is needed that deals with >>>>>>>>>>>>> inferential
| definitions in a wider sense and covers both logical and >>>>>>>>>>>>> extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently >>>>>>>>>>>> and in the
near future not useful as making it useful requires much >>>>>>>>>>>> time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful >>>>>>>>>>> for? What it
ought to be able to do that standard logic fails at? Maybe >>>>>>>>>>> André could
elucidate. He seems to have a better grasp of it than >>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than yours. I >>>>>>>>>> basically only know what is presented in the Stanford
Encyclopedia article (which you correctly point out is not >>>>>>>>>> exactly aimed at beginners) and the Wikipedia article. What I >>>>>>>>>> am quite certain of, however, is that Olcott lacks any
understanding of what PTS actually says as he's made a variety >>>>>>>>>> of fairly absurd claims regarding it (for example, that PTS >>>>>>>>>> claims that unproven propositions are 'meaningless' or that >>>>>>>>>> the goal of PTS is to completely overthrow standard truth- >>>>>>>>>> theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
questions presented.
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is not that they never admit defeat.
It is that that have a system of essentially infallible reasoning
that never errs as long as it has all the relevant information.
It is fairly simple to build a system of essentially infallible
reasoning that never errs even when it doesn't have all the
relevant information. The real problem is to construct a system
that tells something interesting instead of just different
presentations of the same already known facts.
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general knowledge
in your system the general knowledge has grown to inlude more facts.
It can be reasonably approximated pretty quickly.
We start with all of the textbooks.
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>> alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which >>>>>>>> sometimes have been incompatible. But you have never clearly
retracted your earlier opitions that conflict with your present >>>>>>>> ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a
publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human being
on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles
that have any is or depends on claims that should be proven but
aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the proof or
has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're >>>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS Gödel 1931
incompleteness
fails.
I don't believe you. You have no respect for or understanding >>>>>>>> of the
truth. If you really want to persuade anybody that PTS somehow >>>>>>>> causes
Gödel's theorem not to hold, then cite an academic expert who'll >>>>>>>> have
some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you
certainly don't
understand Gödel's Theorem, neither the theorem itself nor any >>>>>>>> proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by >>>>>> you, and it is one which you have never explicitly defined, so the >>>>>> fault here certainly doesn't lie with Alan. It's certainly not a
'verified fact' when you haven't even adequately explained what it >>>>>> is that you mean.
All of knowledge expressed in language is structured as a tree of
semantic relations specified syntactically between finite strings.
What makes you believe semantic relations that can be structured as
a tree are sufficient to contain all knowledge that is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
On 6/23/2026 1:15 AM, Mikko wrote:
On 22/06/2026 17:44, olcott wrote:
On 6/22/2026 2:23 AM, Mikko wrote:
On 21/06/2026 23:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>>>> fails.
I don't believe you. You have no respect for or understanding of the >>>>>> truth. If you really want to persuade anybody that PTS somehow
causes
Gödel's theorem not to hold, then cite an academic expert who'll have >>>>>> some credibility.
If they are mere gibberish words to you then you will not
understand.
You don't understand Proof-theoritic Semantics, and you certainly >>>>>> don't
understand Gödel's Theorem, neither the theorem itself nor any
proof of
it.
in the atomic base of PA.
It is a verified fact that Gödel's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
The proof that there are unprovable sentences with unprovable
negations does not refer to any semantics. That a sentence or
its negation is true is a feature of many semantic systems and
in particular of the arithemtic semantics of Peano arithmetic.
When people want to know how a function could be computed or whether it
can be computed at all they only care about arithmetic and computational
semantics. Proof theoretic semnatics is irrelevant.
Proof-theoretic semantics is an alternative foundation
for mathematics replacing truth conditional semantics.
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>>>> really
did
"agree" (with whom?) that Gödel's sentence G is not true in >>>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
I was right, you didn't understand it.He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>> means untrue all the time for everything within hisYou won't understand it, but that _is_ essentially Gödel's >>>>>>>>>>>> Incompleteness
own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had he >>>>>>>>>>>> been
saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>>> "got" to
Gödel, and would have understood full well what he was saying. >>>>>>>>>>
You did not pay close enough attention to my exact words. >>>>>>>>>>
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz >>>>>>>> says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>> new ad-
missible rules within a certain syntactic context. Some fifteen >>>>>>>> years
later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>>>> normalization for natural deduction calculi (this being an
analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, >>>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>>>> type
of schematic Introduction rules to be matched—thanks to the idea >>>>>>>> supporting the inversion principle — by a corresponding general >>>>>>>> schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen “it should be possible to display the elimination rules as >>>>>>>> unique functions of the corresponding introduction rules on the >>>>>>>> basis of
certain requirements.” Many people have since worked on this topic, >>>>>>>> which can be appropriately seen as the birthplace of what are now >>>>>>>> referred to as “general elimination rules”, recently studied >>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>>>> threads of this chapter of proof-theoretical investigation, using >>>>>>>> Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides >>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>>> Montague for semantics there's Herbrand for semantics, so, what >>>>>>>> to do
about "inversion principle" is here that the thea-theory has that >>>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>>> interpretation aligns and thusly that "principle of inversion" >>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and >>>>>>>> what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>>> oldest account of Western philosophy like Heraclitus with dual >>>>>>>> monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>>> often
coupled with another that is called the recovery principle. By >>>>>>>> adopting
the Computational Ludics framework, we reformulate these principles >>>>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>>>> show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>> standing
behind these principles: the idea of "containment" present in the >>>>>>>> inversion principle, and the idea that the recovery principle is >>>>>>>> the
"converse" of the inversion principle. We also formulate two other >>>>>>>> conditions in the Computational Ludics framework, and we show that >>>>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>> proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical
proof of
it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>> derivation ending with an introduction rule of the main connective >>>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts >>>>>> that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs". >>>>> Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>> of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
On 23/06/2026 17:29, olcott wrote:
On 6/23/2026 12:39 AM, Mikko wrote:
On 22/06/2026 16:13, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:The exact operational semantics of C conclusively
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>> reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>> look into proof theoretic semantics.I've spent a couple of hours reading that web page. It is >>>>>>>>>>>>> abstract in
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>>>
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter Olcott, >>>>>>>>>>>>> who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with
irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof by >>>>>>>>>>> contradiction. The LP isn't a contradiction; it's a paradox. >>>>>>>>>>> The two are different things. A contradiction is a statement >>>>>>>>>>> which is necessarily false. A paradox is a statement to which >>>>>>>>>>> no truth value can be consistently assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting
problem proof, Godel's proof, and Tarski's proof, each of which >>>>>>>>> you've been attempting (and failing) to refute for years.
Proof Theoretic Semantics halt prover HHH correctly determines >>>>>>>> that its input DD is ungrounded in its atomic base according
to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program. >>>>>>
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics >>>>> do not fully specify the behaviour of DD. In order to prove that DD
halts you also need additional operational spemantics provided by the >>>>> C implementation you have used. When DD iss executed in that
environment
it halts, which is sufficient to prove that in that environment DD
halts. In some other environment its execution might be aborted or it >>>>> could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Nice to see that you don't disagree.
Not nice to see that everyone continues to
totally ignore my best validation of proof
theoretic semantics.
Unfortunately that is unavoidable as long as your best presentation
of the validation and of your version of proof theoretic semantics
are not good enough.
This is understandable for anyone that has no
idea what a directed graph is.
Your understanding of understandability is far from the real thing.
This has been completely rewritten just now.
https://github.com/plolcott/x86utm/blob/master/README.md
The description is updated. The described is not updated.
It always was a proof theoretic halt prover
I just didn't have those terms until recently.
It is not a prover. It does not prove.
It produces some execution trace
but may end before termination, and presents its conclusion or crashes.
Anyway, it does not matter what you call it. It only matters that your programs don't answer any interesting question.
On 23/06/2026 17:40, olcott wrote:
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat?
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other >>>>>>>>> questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>> reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. It is >>>>>>>>>>>>>> abstract in
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I >>>>>>>>>>>>>> can't be bothered
to read it any further. If it actually says anything at >>>>>>>>>>>>>> all, that
something is heavily disguised. From it's "Conclusion and >>>>>>>>>>>>>> Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants play >>>>>>>>>>>>>> a central role
| in reasoning and inference, but are definitely not the >>>>>>>>>>>>>> exclusive, and
| perhaps not even the most typical sort of entities that >>>>>>>>>>>>>> can be defined
| inferentially. A framework is needed that deals with >>>>>>>>>>>>>> inferential
| definitions in a wider sense and covers both logical and >>>>>>>>>>>>>> extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently >>>>>>>>>>>>> and in the
near future not useful as making it useful requires much >>>>>>>>>>>>> time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful >>>>>>>>>>>> for? What it
ought to be able to do that standard logic fails at? Maybe >>>>>>>>>>>> André could
elucidate. He seems to have a better grasp of it than >>>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than yours. I >>>>>>>>>>> basically only know what is presented in the Stanford
Encyclopedia article (which you correctly point out is not >>>>>>>>>>> exactly aimed at beginners) and the Wikipedia article. What I >>>>>>>>>>> am quite certain of, however, is that Olcott lacks any
understanding of what PTS actually says as he's made a
variety of fairly absurd claims regarding it (for example, >>>>>>>>>>> that PTS claims that unproven propositions are 'meaningless' >>>>>>>>>>> or that the goal of PTS is to completely overthrow standard >>>>>>>>>>> truth- theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is not that they never admit defeat.
It is that that have a system of essentially infallible reasoning
that never errs as long as it has all the relevant information.
It is fairly simple to build a system of essentially infallible
reasoning that never errs even when it doesn't have all the
relevant information. The real problem is to construct a system
that tells something interesting instead of just different
presentations of the same already known facts.
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general knowledge
in your system the general knowledge has grown to inlude more facts.
It can be reasonably approximated pretty quickly.
We start with all of the textbooks.
That is a lot of reading, though those for the same topic area tend
to say the same, and the old ones add very little to the new ones,
mainly some now obsolete technology.
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>> alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
At different times you have expressed different opinions, which >>>>>>>>> sometimes have been incompatible. But you have never clearly >>>>>>>>> retracted your earlier opitions that conflict with your present >>>>>>>>> ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a
publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human being >>>>>> on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles
that have any is or depends on claims that should be proven but
aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the proof or
has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one
mai fail to achieve what one could, but if one believs what is
wrong one may achieve a disaseter.
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're >>>>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS Gödel 1931
incompleteness
fails.
I don't believe you. You have no respect for or understanding >>>>>>>>> of the
truth. If you really want to persuade anybody that PTS somehow >>>>>>>>> causes
Gödel's theorem not to hold, then cite an academic expert
who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you
certainly don't
understand Gödel's Theorem, neither the theorem itself nor any >>>>>>>>> proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only by >>>>>>> you, and it is one which you have never explicitly defined, so
the fault here certainly doesn't lie with Alan. It's certainly
not a 'verified fact' when you haven't even adequately explained >>>>>>> what it is that you mean.
All of knowledge expressed in language is structured as a tree of >>>>>> semantic relations specified syntactically between finite strings.
What makes you believe semantic relations that can be structured as
a tree are sufficient to contain all knowledge that is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>>>>> really
did
"agree" (with whom?) that Gödel's sentence G is not true in >>>>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
I was right, you didn't understand it.He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>>You won't understand it, but that _is_ essentially Gödel's >>>>>>>>>>>>> Incompleteness
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had he >>>>>>>>>>>>> been
saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>>>> "got" to
Gödel, and would have understood full well what he was saying. >>>>>>>>>>>
You did not pay close enough attention to my exact words. >>>>>>>>>>>
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz >>>>>>>>> says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>>> new ad-
missible rules within a certain syntactic context. Some fifteen >>>>>>>>> years
later, the idea was taken up by Dag Prawitz to devise a
strategy of
normalization for natural deduction calculi (this being an
analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, >>>>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>>>> role.
Still working in natural deduction calculi, he formulated a >>>>>>>>> general
type
of schematic Introduction rules to be matched—thanks to the idea >>>>>>>>> supporting the inversion principle — by a corresponding general >>>>>>>>> schematic Elimination rule. This was an attempt to provide a >>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen “it should be possible to display the elimination rules as >>>>>>>>> unique functions of the corresponding introduction rules on the >>>>>>>>> basis of
certain requirements.” Many people have since worked on this >>>>>>>>> topic,
which can be appropriately seen as the birthplace of what are now >>>>>>>>> referred to as “general elimination rules”, recently studied >>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the >>>>>>>>> main
threads of this chapter of proof-theoretical investigation, using >>>>>>>>> Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>>>> since
"natural deduction", which here is held as part of the theory >>>>>>>>> since it's naturally logical, then has for Gentzen that besides >>>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>>>> Montague for semantics there's Herbrand for semantics, so, what >>>>>>>>> to do
about "inversion principle" is here that the thea-theory has that >>>>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>>>> interpretation aligns and thusly that "principle of inversion" >>>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction >>>>>>>>> and what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>>>> oldest account of Western philosophy like Heraclitus with dual >>>>>>>>> monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of >>>>>>>>> the
characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>>>> often
coupled with another that is called the recovery principle. By >>>>>>>>> adopting
the Computational Ludics framework, we reformulate these
principles
into
one and the same condition, which we call the harmony
condition. We
show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>>> standing
behind these principles: the idea of "containment" present in the >>>>>>>>> inversion principle, and the idea that the recovery principle >>>>>>>>> is the
"converse" of the inversion principle. We also formulate two other >>>>>>>>> conditions in the Computational Ludics framework, and we show that >>>>>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>>> proof-theoretic semantics rests on the idea that we know the >>>>>>>>> meaning of
a compound sentence when we know what counts as a canonical >>>>>>>>> proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>>> derivation ending with an introduction rule of the main connective >>>>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>>>> to make for infinitary reasoning and super-classical results >>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts >>>>>>> that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical
proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>>> of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong). >>>>>>>
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong
about Prolog is never dishohest.
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>>>>>> really
did
"agree" (with whom?) that Gödel's sentence G is not true in >>>>>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>>>You won't understand it, but that _is_ essentially Gödel's >>>>>>>>>>>>>> Incompleteness
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had >>>>>>>>>>>>>> he been
saying
the things you falsely attributed to him, would certainly >>>>>>>>>>>>>> have
"got" to
Gödel, and would have understood full well what he was >>>>>>>>>>>>>> saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz >>>>>>>>>> says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>>>> new ad-
missible rules within a certain syntactic context. Some fifteen >>>>>>>>>> years
later, the idea was taken up by Dag Prawitz to devise a
strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>> analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, >>>>>>>>>> Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated a >>>>>>>>>> general
type
of schematic Introduction rules to be matched—thanks to the idea >>>>>>>>>> supporting the inversion principle — by a corresponding general >>>>>>>>>> schematic Elimination rule. This was an attempt to provide a >>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>> According to
Gentzen “it should be possible to display the elimination >>>>>>>>>> rules as
unique functions of the corresponding introduction rules on the >>>>>>>>>> basis of
certain requirements.” Many people have since worked on this >>>>>>>>>> topic,
which can be appropriately seen as the birthplace of what are now >>>>>>>>>> referred to as “general elimination rules”, recently studied >>>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the >>>>>>>>>> main
threads of this chapter of proof-theoretical investigation, using >>>>>>>>>> Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>>>> laws,
and that being the usual account of naive deductive analysis, >>>>>>>>>> then
since
"natural deduction", which here is held as part of the theory >>>>>>>>>> since it's naturally logical, then has for Gentzen that besides >>>>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and
instead of
Montague for semantics there's Herbrand for semantics, so, >>>>>>>>>> what to do
about "inversion principle" is here that the thea-theory has that >>>>>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>>>>> interpretation aligns and thusly that "principle of inversion" >>>>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>>>>>
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction >>>>>>>>>> and what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as >>>>>>>>>> the
oldest account of Western philosophy like Heraclitus with dual >>>>>>>>>> monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of >>>>>>>>>> issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one >>>>>>>>>> of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>>>>> often
coupled with another that is called the recovery principle. By >>>>>>>>>> adopting
the Computational Ludics framework, we reformulate these
principles
into
one and the same condition, which we call the harmony
condition. We
show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>>>> standing
behind these principles: the idea of "containment" present in the >>>>>>>>>> inversion principle, and the idea that the recovery principle >>>>>>>>>> is the
"converse" of the inversion principle. We also formulate two >>>>>>>>>> other
conditions in the Computational Ludics framework, and we show >>>>>>>>>> that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>>>> proof-theoretic semantics rests on the idea that we know the >>>>>>>>>> meaning of
a compound sentence when we know what counts as a canonical >>>>>>>>>> proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>>>> derivation ending with an introduction rule of the main
connective
of A."
The "canonical proofs" are not unique, in any system strong >>>>>>>>>> enough
to make for infinitary reasoning and super-classical results >>>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive
sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical
proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>>>> of what otherwise is flawed, or for hard constructivist realist >>>>>>>> structuralist model theorists: not-theories (examples of wrong). >>>>>>>>
Induction and counter-induction contradict each other, it's simple, >>>>>> it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong
about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
On 6/24/2026 3:23 AM, Mikko wrote:
On 23/06/2026 17:29, olcott wrote:
On 6/23/2026 12:39 AM, Mikko wrote:
On 22/06/2026 16:13, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:The exact operational semantics of C conclusively
On 6/20/2026 2:17 PM, dbush wrote:
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>> reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. It is >>>>>>>>>>>>>> abstract in
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with
irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof >>>>>>>>>>>> by contradiction. The LP isn't a contradiction; it's a >>>>>>>>>>>> paradox. The two are different things. A contradiction is a >>>>>>>>>>>> statement which is necessarily false. A paradox is a
statement to which no truth value can be consistently assigned. >>>>>>>>>>>>
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting
problem proof, Godel's proof, and Tarski's proof, each of >>>>>>>>>> which you've been attempting (and failing) to refute for years. >>>>>>>>>>
Proof Theoretic Semantics halt prover HHH correctly determines >>>>>>>>> that its input DD is ungrounded in its atomic base according >>>>>>>>> to the operational semantics of the C programming language.
That only means that your DD is not a strictly confoming C program. >>>>>>>
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational semantics >>>>>> do not fully specify the behaviour of DD. In order to prove that DD >>>>>> halts you also need additional operational spemantics provided by the >>>>>> C implementation you have used. When DD iss executed in that
environment
it halts, which is sufficient to prove that in that environment DD >>>>>> halts. In some other environment its execution might be aborted or it >>>>>> could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Nice to see that you don't disagree.
Not nice to see that everyone continues to
totally ignore my best validation of proof
theoretic semantics.
Unfortunately that is unavoidable as long as your best presentation
of the validation and of your version of proof theoretic semantics
are not good enough.
Is is dead obvious and completely clear example
of the final resolution of the Liar Paradox using
generic proof theoretic semantics implemented in
Prolog.
This is understandable for anyone that has no
idea what a directed graph is.
Your understanding of understandability is far from the real thing.
This has been completely rewritten just now.
https://github.com/plolcott/x86utm/blob/master/README.md
The description is updated. The described is not updated.
It always was a proof theoretic halt prover
I just didn't have those terms until recently.
It is not a prover. It does not prove.
It proves that no canonical proof of DD reaching
its own final halt state exists within the operational
semantics of the C programming language for PTS halt
prover HHH.
It produces some execution trace
but may end before termination, and presents its conclusion or crashes.
Perhaps you have no idea what cycles in directed graphs are?
On 6/24/2026 4:45 AM, Mikko wrote:
On 23/06/2026 17:40, olcott wrote:
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:
olcott wrote:It is not that they never admit defeat.
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? >>>>>>>
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other >>>>>>>>>> questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>>> reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. It >>>>>>>>>>>>>>> is abstract in
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I >>>>>>>>>>>>>>> can't be bothered
to read it any further. If it actually says anything at >>>>>>>>>>>>>>> all, that
something is heavily disguised. From it's "Conclusion >>>>>>>>>>>>>>> and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants play >>>>>>>>>>>>>>> a central role
| in reasoning and inference, but are definitely not the >>>>>>>>>>>>>>> exclusive, and
| perhaps not even the most typical sort of entities that >>>>>>>>>>>>>>> can be defined
| inferentially. A framework is needed that deals with >>>>>>>>>>>>>>> inferential
| definitions in a wider sense and covers both logical >>>>>>>>>>>>>>> and extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently >>>>>>>>>>>>>> and in the
near future not useful as making it useful requires much >>>>>>>>>>>>>> time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful >>>>>>>>>>>>> for? What it
ought to be able to do that standard logic fails at? Maybe >>>>>>>>>>>>> André could
elucidate. He seems to have a better grasp of it than >>>>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than yours. I >>>>>>>>>>>> basically only know what is presented in the Stanford >>>>>>>>>>>> Encyclopedia article (which you correctly point out is not >>>>>>>>>>>> exactly aimed at beginners) and the Wikipedia article. What >>>>>>>>>>>> I am quite certain of, however, is that Olcott lacks any >>>>>>>>>>>> understanding of what PTS actually says as he's made a >>>>>>>>>>>> variety of fairly absurd claims regarding it (for example, >>>>>>>>>>>> that PTS claims that unproven propositions are 'meaningless' >>>>>>>>>>>> or that the goal of PTS is to completely overthrow standard >>>>>>>>>>>> truth- theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain
expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is that that have a system of essentially infallible reasoning >>>>>>> that never errs as long as it has all the relevant information.
It is fairly simple to build a system of essentially infallible
reasoning that never errs even when it doesn't have all the
relevant information. The real problem is to construct a system
that tells something interesting instead of just different
presentations of the same already known facts.
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general knowledge >>>> in your system the general knowledge has grown to inlude more facts.
It can be reasonably approximated pretty quickly.
We start with all of the textbooks.
That is a lot of reading, though those for the same topic area tend
to say the same, and the old ones add very little to the new ones,
mainly some now obsolete technology.
It would not be too much reading for LLMs.
It could start with all of the latest textbooks
for all of the fields. Some of these latest
textbooks may be hundreds of years old for
fields that have become obsolete.
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlaysonSome people only memorize conventional views and
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>>>
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>> alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>> look into proof theoretic semantics.
At different times you have expressed different opinions, which >>>>>>>>>> sometimes have been incompatible. But you have never clearly >>>>>>>>>> retracted your earlier opitions that conflict with your present >>>>>>>>>> ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a
publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human
being on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles
that have any is or depends on claims that should be proven but
aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the proof or
has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one
mai fail to achieve what one could, but if one believs what is
wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition semantics. https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:What makes you believe semantic relations that can be structured as >>>>>> a tree are sufficient to contain all knowledge that is exressed in >>>>>> some language?
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:You can find any number of terms. That doesn't mean you're >>>>>>>>>>>> capable of
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>
understanding them.
The above is the key reason why under PTS Gödel 1931
incompleteness
fails.
I don't believe you. You have no respect for or understanding >>>>>>>>>> of the
truth. If you really want to persuade anybody that PTS
somehow causes
Gödel's theorem not to hold, then cite an academic expert >>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you
certainly don't
understand Gödel's Theorem, neither the theorem itself nor any >>>>>>>>>> proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only >>>>>>>> by you, and it is one which you have never explicitly defined, >>>>>>>> so the fault here certainly doesn't lie with Alan. It's
certainly not a 'verified fact' when you haven't even adequately >>>>>>>> explained what it is that you mean.
All of knowledge expressed in language is structured as a tree of >>>>>>> semantic relations specified syntactically between finite strings. >>>>>>
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>>>>>> really
did
"agree" (with whom?) that Gödel's sentence G is not true in >>>>>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>>>You won't understand it, but that _is_ essentially Gödel's >>>>>>>>>>>>>> Incompleteness
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had >>>>>>>>>>>>>> he been
saying
the things you falsely attributed to him, would certainly >>>>>>>>>>>>>> have
"got" to
Gödel, and would have understood full well what he was >>>>>>>>>>>>>> saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz >>>>>>>>>> says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>>>> new ad-
missible rules within a certain syntactic context. Some fifteen >>>>>>>>>> years
later, the idea was taken up by Dag Prawitz to devise a
strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>> analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, >>>>>>>>>> Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated a >>>>>>>>>> general
type
of schematic Introduction rules to be matched—thanks to the idea >>>>>>>>>> supporting the inversion principle — by a corresponding general >>>>>>>>>> schematic Elimination rule. This was an attempt to provide a >>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>> According to
Gentzen “it should be possible to display the elimination >>>>>>>>>> rules as
unique functions of the corresponding introduction rules on the >>>>>>>>>> basis of
certain requirements.” Many people have since worked on this >>>>>>>>>> topic,
which can be appropriately seen as the birthplace of what are now >>>>>>>>>> referred to as “general elimination rules”, recently studied >>>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the >>>>>>>>>> main
threads of this chapter of proof-theoretical investigation, using >>>>>>>>>> Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>>>> laws,
and that being the usual account of naive deductive analysis, >>>>>>>>>> then
since
"natural deduction", which here is held as part of the theory >>>>>>>>>> since it's naturally logical, then has for Gentzen that besides >>>>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and
instead of
Montague for semantics there's Herbrand for semantics, so, >>>>>>>>>> what to do
about "inversion principle" is here that the thea-theory has that >>>>>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>>>>> interpretation aligns and thusly that "principle of inversion" >>>>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof-
theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction >>>>>>>>>> and what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as >>>>>>>>>> the
oldest account of Western philosophy like Heraclitus with dual >>>>>>>>>> monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of >>>>>>>>>> issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one >>>>>>>>>> of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>>>>> often
coupled with another that is called the recovery principle. By >>>>>>>>>> adopting
the Computational Ludics framework, we reformulate these
principles
into
one and the same condition, which we call the harmony
condition. We
show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>>>> standing
behind these principles: the idea of "containment" present in the >>>>>>>>>> inversion principle, and the idea that the recovery principle >>>>>>>>>> is the
"converse" of the inversion principle. We also formulate two >>>>>>>>>> other
conditions in the Computational Ludics framework, and we show >>>>>>>>>> that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>>>> proof-theoretic semantics rests on the idea that we know the >>>>>>>>>> meaning of
a compound sentence when we know what counts as a canonical >>>>>>>>>> proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>>>> derivation ending with an introduction rule of the main
connective
of A."
The "canonical proofs" are not unique, in any system strong >>>>>>>>>> enough
to make for infinitary reasoning and super-classical results >>>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive
sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical
proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>>>> of what otherwise is flawed, or for hard constructivist realist >>>>>>>> structuralist model theorists: not-theories (examples of wrong). >>>>>>>>
Induction and counter-induction contradict each other, it's simple, >>>>>> it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong
about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
On 24/06/2026 23:19, olcott wrote:
On 6/24/2026 3:23 AM, Mikko wrote:
On 23/06/2026 17:29, olcott wrote:
On 6/23/2026 12:39 AM, Mikko wrote:
On 22/06/2026 16:13, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:That only means that your DD is not a strictly confoming C
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>>> reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. It >>>>>>>>>>>>>>> is abstract in
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with >>>>>>>>>>>>> irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof >>>>>>>>>>>>> by contradiction. The LP isn't a contradiction; it's a >>>>>>>>>>>>> paradox. The two are different things. A contradiction is a >>>>>>>>>>>>> statement which is necessarily false. A paradox is a >>>>>>>>>>>>> statement to which no truth value can be consistently >>>>>>>>>>>>> assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting >>>>>>>>>>> problem proof, Godel's proof, and Tarski's proof, each of >>>>>>>>>>> which you've been attempting (and failing) to refute for years. >>>>>>>>>>>
Proof Theoretic Semantics halt prover HHH correctly determines >>>>>>>>>> that its input DD is ungrounded in its atomic base according >>>>>>>>>> to the operational semantics of the C programming language. >>>>>>>>>
program.
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational
semantics
do not fully specify the behaviour of DD. In order to prove that DD >>>>>>> halts you also need additional operational spemantics provided by >>>>>>> the
C implementation you have used. When DD iss executed in that
environment
it halts, which is sufficient to prove that in that environment DD >>>>>>> halts. In some other environment its execution might be aborted >>>>>>> or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Nice to see that you don't disagree.
Not nice to see that everyone continues to
totally ignore my best validation of proof
theoretic semantics.
Unfortunately that is unavoidable as long as your best presentation
of the validation and of your version of proof theoretic semantics
are not good enough.
Is is dead obvious and completely clear example
of the final resolution of the Liar Paradox using
generic proof theoretic semantics implemented in
Prolog.
Except that it is not final -- others will continue presenting
different views about it -- and not even a resolution.
Anyway, nice to see that you still don't disabree.
This is understandable for anyone that has no
idea what a directed graph is.
Your understanding of understandability is far from the real thing.
This has been completely rewritten just now.
https://github.com/plolcott/x86utm/blob/master/README.md
The description is updated. The described is not updated.
It always was a proof theoretic halt prover
I just didn't have those terms until recently.
It is not a prover. It does not prove.
It proves that no canonical proof of DD reaching
its own final halt state exists within the operational
semantics of the C programming language for PTS halt
prover HHH.
Irrelevant. That DD halts when executed is sufficient for a reasonable
person to conclude that it halts. To formulate that inference as a
formal proof is trivial to anyone who knows the formal rules.
It produces some execution trace
but may end before termination, and presents its conclusion or crashes.
Perhaps you have no idea what cycles in directed graphs are?
Doesn't really matter, especially when they are not even mentioned.
The words are well known and the definitions can be found on the
web.
On 24/06/2026 23:23, olcott wrote:
On 6/24/2026 4:45 AM, Mikko wrote:
On 23/06/2026 17:40, olcott wrote:
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:It is fairly simple to build a system of essentially infallible
olcott wrote:It is not that they never admit defeat.
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? >>>>>>>>
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other >>>>>>>>>>> questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>>>> reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. It >>>>>>>>>>>>>>>> is abstract in
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I >>>>>>>>>>>>>>>> can't be bothered
to read it any further. If it actually says anything at >>>>>>>>>>>>>>>> all, that
something is heavily disguised. From it's "Conclusion >>>>>>>>>>>>>>>> and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants >>>>>>>>>>>>>>>> play a central role
| in reasoning and inference, but are definitely not the >>>>>>>>>>>>>>>> exclusive, and
| perhaps not even the most typical sort of entities >>>>>>>>>>>>>>>> that can be defined
| inferentially. A framework is needed that deals with >>>>>>>>>>>>>>>> inferential
| definitions in a wider sense and covers both logical >>>>>>>>>>>>>>>> and extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently >>>>>>>>>>>>>>> and in the
near future not useful as making it useful requires much >>>>>>>>>>>>>>> time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be >>>>>>>>>>>>>> useful for? What it
ought to be able to do that standard logic fails at? >>>>>>>>>>>>>> Maybe André could
elucidate. He seems to have a better grasp of it than >>>>>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than yours. I >>>>>>>>>>>>> basically only know what is presented in the Stanford >>>>>>>>>>>>> Encyclopedia article (which you correctly point out is not >>>>>>>>>>>>> exactly aimed at beginners) and the Wikipedia article. What >>>>>>>>>>>>> I am quite certain of, however, is that Olcott lacks any >>>>>>>>>>>>> understanding of what PTS actually says as he's made a >>>>>>>>>>>>> variety of fairly absurd claims regarding it (for example, >>>>>>>>>>>>> that PTS claims that unproven propositions are
'meaningless' or that the goal of PTS is to completely >>>>>>>>>>>>> overthrow standard truth- theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain >>>>>>>>>>>> expressions of our language, in particular to
logical constants, is that of proof rather than
truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>> semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is that that have a system of essentially infallible reasoning >>>>>>>> that never errs as long as it has all the relevant information. >>>>>>>
reasoning that never errs even when it doesn't have all the
relevant information. The real problem is to construct a system
that tells something interesting instead of just different
presentations of the same already known facts.
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general
knowledge
in your system the general knowledge has grown to inlude more facts.
It can be reasonably approximated pretty quickly.
We start with all of the textbooks.
That is a lot of reading, though those for the same topic area tend
to say the same, and the old ones add very little to the new ones,
mainly some now obsolete technology.
It would not be too much reading for LLMs.
It could start with all of the latest textbooks
for all of the fields. Some of these latest
textbooks may be hundreds of years old for
fields that have become obsolete.
Perhaps that apprach should be tried. The problem involves extracting
atomic facts, detecting repeated facts, and encoding facts for the
inference system.
On 24/06/2026 23:25, olcott wrote:
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>> alternative views out-of-hand without review
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review. >>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>> look into proof theoretic semantics.
At different times you have expressed different opinions, which >>>>>>>>>>> sometimes have been incompatible. But you have never clearly >>>>>>>>>>> retracted your earlier opitions that conflict with your present >>>>>>>>>>> ones.
All of the ideas that I have ever had about these things
are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a
publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human
being on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles >>>>>>> that have any is or depends on claims that should be proven but
aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the proof or
has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one
mai fail to achieve what one could, but if one believs what is
wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
You have not shown that there is any need for any alternative semantics.
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>You can find any number of terms. That doesn't mean you're >>>>>>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or
understanding of the
truth. If you really want to persuade anybody that PTS >>>>>>>>>>> somehow causes
Gödel's theorem not to hold, then cite an academic expert >>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>> certainly don't
understand Gödel's Theorem, neither the theorem itself nor >>>>>>>>>>> any proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only >>>>>>>>> by you, and it is one which you have never explicitly defined, >>>>>>>>> so the fault here certainly doesn't lie with Alan. It's
certainly not a 'verified fact' when you haven't even
adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a tree >>>>>>>> of semantic relations specified syntactically between finite
strings.
What makes you believe semantic relations that can be structured as >>>>>>> a tree are sufficient to contain all knowledge that is exressed in >>>>>>> some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If Dag >>>>>>>>>>>>>>>>> Prawitz
really
did
"agree" (with whom?) that Gödel's sentence G is not >>>>>>>>>>>>>>>>> true in
Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>>>>You won't understand it, but that _is_ essentially Gödel's >>>>>>>>>>>>>>> Incompleteness
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had >>>>>>>>>>>>>>> he been
saying
the things you falsely attributed to him, would certainly >>>>>>>>>>>>>>> have
"got" to
Gödel, and would have understood full well what he was >>>>>>>>>>>>>>> saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz >>>>>>>>>>> says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz >>>>>>>>>>> doesn't
say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>>>>> principle" so I think these are key aspects of fundamental >>>>>>>>>>> logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>>>>> new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>> fifteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>> analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, >>>>>>>>>>> Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated a >>>>>>>>>>> general
type
of schematic Introduction rules to be matched—thanks to the idea >>>>>>>>>>> supporting the inversion principle — by a corresponding general >>>>>>>>>>> schematic Elimination rule. This was an attempt to provide a >>>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>> According to
Gentzen “it should be possible to display the elimination >>>>>>>>>>> rules as
unique functions of the corresponding introduction rules on the >>>>>>>>>>> basis of
certain requirements.” Many people have since worked on this >>>>>>>>>>> topic,
which can be appropriately seen as the birthplace of what are >>>>>>>>>>> now
referred to as “general elimination rules”, recently studied >>>>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace >>>>>>>>>>> the main
threads of this chapter of proof-theoretical investigation, >>>>>>>>>>> using
Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>>>>> laws,
and that being the usual account of naive deductive analysis, >>>>>>>>>>> then
since
"natural deduction", which here is held as part of the theory >>>>>>>>>>> since it's naturally logical, then has for Gentzen that besides >>>>>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, so, >>>>>>>>>>> what to do
about "inversion principle" is here that the thea-theory has >>>>>>>>>>> that
it's
what subsumes "non-contradiction principle", here hoping that >>>>>>>>>>> the
interpretation aligns and thusly that "principle of inversion" >>>>>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof-
theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the
foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a >>>>>>>>>>> principle of
thorough reason as subsuming principles of non-contradiction >>>>>>>>>>> and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old >>>>>>>>>>> as the
oldest account of Western philosophy like Heraclitus with dual >>>>>>>>>>> monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides of >>>>>>>>>>> issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one >>>>>>>>>>> of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this
principle is
often
coupled with another that is called the recovery principle. By >>>>>>>>>>> adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>> principles
into
one and the same condition, which we call the harmony
condition. We
show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>>>>> standing
behind these principles: the idea of "containment" present in >>>>>>>>>>> the
inversion principle, and the idea that the recovery principle >>>>>>>>>>> is the
"converse" of the inversion principle. We also formulate two >>>>>>>>>>> other
conditions in the Computational Ludics framework, and we show >>>>>>>>>>> that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>>>>> proof-theoretic semantics rests on the idea that we know the >>>>>>>>>>> meaning of
a compound sentence when we know what counts as a canonical >>>>>>>>>>> proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>>>>> derivation ending with an introduction rule of the main >>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system strong >>>>>>>>>>> enough
to make for infinitary reasoning and super-classical results >>>>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>> That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive >>>>>>>>> sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical >>>>>>>> proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>>>>> of what otherwise is flawed, or for hard constructivist realist >>>>>>>>> structuralist model theorists: not-theories (examples of wrong). >>>>>>>>>
Induction and counter-induction contradict each other, it's simple, >>>>>>> it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong
about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
On 6/20/2026 9:48 PM, olcott wrote:[...]
Go fuck off.
In other words, you know this line of questioning will prove you wrong
and you can't handle it.
This constitutes your admission that Disjunction introduction is valid.
On 6/20/2026 9:48 PM, olcott wrote:
On 6/20/2026 8:38 PM, dbush wrote:
On 6/20/2026 9:32 PM, olcott wrote:
On 6/20/2026 8:28 PM, dbush wrote:
On 6/20/2026 9:06 PM, olcott wrote:
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the >>>>>>>>>>>>> following statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore >>>>>>>>>>> that disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"∨" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or
false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P ∧ ¬P // Premise
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P ∧ ¬P.
I didn't ask about those steps. I asked if you believe the
following statement is true or false, and how do you come to that >>>>>>> conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P ∨ Q true? Yes.
So you agree that because P is true and Q is false, the condition
"at least one of the following" is met.
Next step:
Do you believe the following statement is true or false, and how do >>>>> you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench. >>>>> --------------------------------------
Clearly just head games. GFO with these head games
I promise you I am going somewhere with this, and this is no head
game. But we must take things one small step at a time.
So I'll ask again:
Do you believe the following natural language statement is true or
false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Go fuck off.
In other words, you know this line of questioning will prove you wrong
and you can't handle it.
This constitutes your admission that Disjunction introduction is valid.
On 6/20/2026 9:48 PM, olcott wrote:
On 6/20/2026 8:38 PM, dbush wrote:
On 6/20/2026 9:32 PM, olcott wrote:
On 6/20/2026 8:28 PM, dbush wrote:
On 6/20/2026 9:06 PM, olcott wrote:
On 6/20/2026 7:29 PM, dbush wrote:
On 6/20/2026 8:26 PM, olcott wrote:
On 6/20/2026 7:11 PM, dbush wrote:
On 6/20/2026 6:26 PM, olcott wrote:
On 6/20/2026 4:34 PM, dbush wrote:
On 6/20/2026 5:30 PM, olcott wrote:
On 6/20/2026 4:19 PM, dbush wrote:
On 6/20/2026 5:00 PM, olcott wrote:
And given that this statement is an atomic fact:
Atomic facts of general knowledge includes atomic
facts of empirical general knowledge such as
"cats are animals".
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
What do you think can be concluded about whether the >>>>>>>>>>>>> following statement is true or false?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
If you are going to keep asking me if I know
the propositional truth table for "or" I will
block you for disrespect.
In other words, you agree that "or" is valid, and therefore >>>>>>>>>>> that disjunction introduction is correct.
OK great that is not at all a head game.
Getting rid of disjunction introduction
is not the same thing as getting rid of
"∨" disjunctions.
Then let's take this step-by-step.
Step 1: establish a true statement:
--------------------------------------
Earth is the third planet from the sun.
--------------------------------------
That has been agreed.
Step 2: do you believe the following statement is true or
false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
OK so going step by step is fine with me.
1) P ∧ ¬P // Premise
2) P // Conjunction elimination
3) ¬P // Conjunction elimination
4) P ∨ Q // Disjunction introduction
5) Q // Disjunctive syllogism
https://en.wikipedia.org/wiki/Principle_of_explosion#Proof
We ended up with Q only because we were allowed
to insert Q from out of nowhere in the inference
chain that started with P ∧ ¬P.
I didn't ask about those steps. I asked if you believe the
following statement is true or false, and how do you come to that >>>>>>> conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- The moon is made of green cheese.
--------------------------------------
P = "Earth is the third planet from the sun."
Q = "The moon is made of green cheese."
We determine that P is true on the basis empirical facts.
We determine that Q is false on the basis empirical facts.
Is P ∨ Q true? Yes.
So you agree that because P is true and Q is false, the condition
"at least one of the following" is met.
Next step:
Do you believe the following statement is true or false, and how do >>>>> you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench. >>>>> --------------------------------------
Clearly just head games. GFO with these head games
I promise you I am going somewhere with this, and this is no head
game. But we must take things one small step at a time.
So I'll ask again:
Do you believe the following natural language statement is true or
false, and how do you come to that conclusion?
--------------------------------------
At least one of the following statements is true:
- Earth is the third planet from the sun.
- There is a Walmart bag at the deepest point of the Mariana Trench.
--------------------------------------
Go fuck off.
In other words, you know this line of questioning will prove you wrong
and you can't handle it.
This constitutes your admission that Disjunction introduction is valid.
On 6/25/2026 2:09 AM, Mikko wrote:
On 24/06/2026 23:19, olcott wrote:
On 6/24/2026 3:23 AM, Mikko wrote:
On 23/06/2026 17:29, olcott wrote:
On 6/23/2026 12:39 AM, Mikko wrote:
On 22/06/2026 16:13, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:That only means that your DD is not a strictly confoming C >>>>>>>>>> program.
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>>>> reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. It >>>>>>>>>>>>>>>> is abstract in
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with >>>>>>>>>>>>>> irrelevancy.
The Liar's Paradox has absolutely nothing to do with proof >>>>>>>>>>>>>> by contradiction. The LP isn't a contradiction; it's a >>>>>>>>>>>>>> paradox. The two are different things. A contradiction is >>>>>>>>>>>>>> a statement which is necessarily false. A paradox is a >>>>>>>>>>>>>> statement to which no truth value can be consistently >>>>>>>>>>>>>> assigned.
André
Then I have never spoken of anything where proof by
contradiction applies,
False, as that is exactly the method uses by the halting >>>>>>>>>>>> problem proof, Godel's proof, and Tarski's proof, each of >>>>>>>>>>>> which you've been attempting (and failing) to refute for years. >>>>>>>>>>>>
Proof Theoretic Semantics halt prover HHH correctly determines >>>>>>>>>>> that its input DD is ungrounded in its atomic base according >>>>>>>>>>> to the operational semantics of the C programming language. >>>>>>>>>>
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational
semantics
do not fully specify the behaviour of DD. In order to prove that DD >>>>>>>> halts you also need additional operational spemantics provided >>>>>>>> by the
C implementation you have used. When DD iss executed in that
environment
it halts, which is sufficient to prove that in that environment DD >>>>>>>> halts. In some other environment its execution might be aborted >>>>>>>> or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Nice to see that you don't disagree.
Not nice to see that everyone continues to
totally ignore my best validation of proof
theoretic semantics.
Unfortunately that is unavoidable as long as your best presentation
of the validation and of your version of proof theoretic semantics
are not good enough.
Is is dead obvious and completely clear example
of the final resolution of the Liar Paradox using
generic proof theoretic semantics implemented in
Prolog.
Except that it is not final -- others will continue presenting
different views about it -- and not even a resolution.
If others did not reject mine out-of-hand
without review they could understand that
it is final.
On 6/25/2026 2:14 AM, Mikko wrote:
On 24/06/2026 23:23, olcott wrote:(a) Extracting atomic facts, would be the hardest part,
On 6/24/2026 4:45 AM, Mikko wrote:
On 23/06/2026 17:40, olcott wrote:
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:It can be reasonably approximated pretty quickly.
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:It is fairly simple to build a system of essentially infallible >>>>>>>> reasoning that never errs even when it doesn't have all the
olcott wrote:It is not that they never admit defeat.
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? >>>>>>>>>
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and other >>>>>>>>>>>> questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views >>>>>>>>>>>>>>>>>>> and reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. It >>>>>>>>>>>>>>>>> is abstract in
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I >>>>>>>>>>>>>>>>> can't be bothered
to read it any further. If it actually says anything >>>>>>>>>>>>>>>>> at all, that
something is heavily disguised. From it's "Conclusion >>>>>>>>>>>>>>>>> and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants >>>>>>>>>>>>>>>>> play a central role
| in reasoning and inference, but are definitely not >>>>>>>>>>>>>>>>> the exclusive, and
| perhaps not even the most typical sort of entities >>>>>>>>>>>>>>>>> that can be defined
| inferentially. A framework is needed that deals with >>>>>>>>>>>>>>>>> inferential
| definitions in a wider sense and covers both logical >>>>>>>>>>>>>>>>> and extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is >>>>>>>>>>>>>>>> currently and in the
near future not useful as making it useful requires much >>>>>>>>>>>>>>>> time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be >>>>>>>>>>>>>>> useful for? What it
ought to be able to do that standard logic fails at? >>>>>>>>>>>>>>> Maybe André could
elucidate. He seems to have a better grasp of it than >>>>>>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than yours. >>>>>>>>>>>>>> I basically only know what is presented in the Stanford >>>>>>>>>>>>>> Encyclopedia article (which you correctly point out is not >>>>>>>>>>>>>> exactly aimed at beginners) and the Wikipedia article. >>>>>>>>>>>>>> What I am quite certain of, however, is that Olcott lacks >>>>>>>>>>>>>> any understanding of what PTS actually says as he's made a >>>>>>>>>>>>>> variety of fairly absurd claims regarding it (for example, >>>>>>>>>>>>>> that PTS claims that unproven propositions are
'meaningless' or that the goal of PTS is to completely >>>>>>>>>>>>>> overthrow standard truth- theoretic semantics).
André
Proof-theoretic semantics is an alternative to
truth-condition semantics. It is based on the
fundamental assumption that the central notion
in terms of which meanings are assigned to certain >>>>>>>>>>>>> expressions of our language, in particular to
logical constants, is that of proof rather than >>>>>>>>>>>>> truth. In this sense proof-theoretic semantics
is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>> semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof
theoretic semantics?
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time.
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is that that have a system of essentially infallible reasoning >>>>>>>>> that never errs as long as it has all the relevant information. >>>>>>>>
relevant information. The real problem is to construct a system >>>>>>>> that tells something interesting instead of just different
presentations of the same already known facts.
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general
knowledge
in your system the general knowledge has grown to inlude more facts. >>>>>
We start with all of the textbooks.
That is a lot of reading, though those for the same topic area tend
to say the same, and the old ones add very little to the new ones,
mainly some now obsolete technology.
It would not be too much reading for LLMs.
It could start with all of the latest textbooks
for all of the fields. Some of these latest
textbooks may be hundreds of years old for
fields that have become obsolete.
Perhaps that apprach should be tried. The problem involves extracting
atomic facts, detecting repeated facts, and encoding facts for the
inference system.
yet not too hard.
(b) Detecting repeated facts, string comparison.
(c) Encoding facts, CycL
On 6/25/2026 2:18 AM, Mikko wrote:
On 24/06/2026 23:25, olcott wrote:
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and reject >>>>>>>>>>>>>> alternative views out-of-hand without review
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>> look into proof theoretic semantics.
At different times you have expressed different opinions, which >>>>>>>>>>>> sometimes have been incompatible. But you have never clearly >>>>>>>>>>>> retracted your earlier opitions that conflict with your present >>>>>>>>>>>> ones.
All of the ideas that I have ever had about these things >>>>>>>>>>> are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a >>>>>>>>>> publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human >>>>>>>>> being on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles >>>>>>>> that have any is or depends on claims that should be proven but >>>>>>>> aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the proof or >>>>>> has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one
mai fail to achieve what one could, but if one believs what is
wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition
semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
You have not shown that there is any need for any alternative semantics.
With dangerous lies that can destroy Democracy
and kill the planet with climate change having
an ultimate arbiter of truth would be useful.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>You can find any number of terms. That doesn't mean >>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or
understanding of the
truth. If you really want to persuade anybody that PTS >>>>>>>>>>>> somehow causes
Gödel's theorem not to hold, then cite an academic expert >>>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>> certainly don't
understand Gödel's Theorem, neither the theorem itself nor >>>>>>>>>>>> any proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used only >>>>>>>>>> by you, and it is one which you have never explicitly defined, >>>>>>>>>> so the fault here certainly doesn't lie with Alan. It's
certainly not a 'verified fact' when you haven't even
adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a tree >>>>>>>>> of semantic relations specified syntactically between finite >>>>>>>>> strings.
What makes you believe semantic relations that can be structured as >>>>>>>> a tree are sufficient to contain all knowledge that is exressed in >>>>>>>> some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
On 6/25/2026 2:29 AM, Mikko wrote:
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If Dag >>>>>>>>>>>>>>>>>> Prawitz
really
did
"agree" (with whom?) that Gödel's sentence G is not >>>>>>>>>>>>>>>>>> true in
Peano
Arithmetic, then produce a citation for this.
He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>>>>>You won't understand it, but that _is_ essentially Gödel's >>>>>>>>>>>>>>>> Incompleteness
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had >>>>>>>>>>>>>>>> he been
saying
the things you falsely attributed to him, would >>>>>>>>>>>>>>>> certainly have
"got" to
Gödel, and would have understood full well what he was >>>>>>>>>>>>>>>> saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag >>>>>>>>>>>> Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz >>>>>>>>>>>> doesn't
say",
then looking a bit into his tremendous volume of works, >>>>>>>>>>>> he talks about "natural deduction" then specifically an >>>>>>>>>>>> "inverse
principle" so I think these are key aspects of fundamental >>>>>>>>>>>> logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>>>>>> new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>>> fifteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>>> analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, >>>>>>>>>>>> Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated a >>>>>>>>>>>> general
type
of schematic Introduction rules to be matched—thanks to the >>>>>>>>>>>> idea
supporting the inversion principle — by a corresponding general >>>>>>>>>>>> schematic Elimination rule. This was an attempt to provide a >>>>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>>> According to
Gentzen “it should be possible to display the elimination >>>>>>>>>>>> rules as
unique functions of the corresponding introduction rules on the >>>>>>>>>>>> basis of
certain requirements.” Many people have since worked on this >>>>>>>>>>>> topic,
which can be appropriately seen as the birthplace of what >>>>>>>>>>>> are now
referred to as “general elimination rules”, recently studied >>>>>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace >>>>>>>>>>>> the main
threads of this chapter of proof-theoretical investigation, >>>>>>>>>>>> using
Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De >>>>>>>>>>>> Morgan's
laws,
and that being the usual account of naive deductive
analysis, then
since
"natural deduction", which here is held as part of the theory >>>>>>>>>>>> since it's naturally logical, then has for Gentzen that besides >>>>>>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, so, >>>>>>>>>>>> what to do
about "inversion principle" is here that the thea-theory has >>>>>>>>>>>> that
it's
what subsumes "non-contradiction principle", here hoping >>>>>>>>>>>> that the
interpretation aligns and thusly that "principle of inversion" >>>>>>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof- >>>>>>>>>>>> theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the
foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a >>>>>>>>>>>> principle of
thorough reason as subsuming principles of non-contradiction >>>>>>>>>>>> and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old >>>>>>>>>>>> as the
oldest account of Western philosophy like Heraclitus with dual >>>>>>>>>>>> monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides of >>>>>>>>>>>> issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one >>>>>>>>>>>> of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this
principle is
often
coupled with another that is called the recovery principle. By >>>>>>>>>>>> adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>>> principles
into
one and the same condition, which we call the harmony >>>>>>>>>>>> condition. We
show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>>>>>> standing
behind these principles: the idea of "containment" present >>>>>>>>>>>> in the
inversion principle, and the idea that the recovery
principle is the
"converse" of the inversion principle. We also formulate two >>>>>>>>>>>> other
conditions in the Computational Ludics framework, and we >>>>>>>>>>>> show that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and >>>>>>>>>>>> knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>>>>>> proof-theoretic semantics rests on the idea that we know the >>>>>>>>>>>> meaning of
a compound sentence when we know what counts as a canonical >>>>>>>>>>>> proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>>>>>> derivation ending with an introduction rule of the main >>>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system strong >>>>>>>>>>>> enough
to make for infinitary reasoning and super-classical results >>>>>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>>> That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive >>>>>>>>>> sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical >>>>>>>>> proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make >>>>>>>>>> repairs
of what otherwise is flawed, or for hard constructivist realist >>>>>>>>>> structuralist model theorists: not-theories (examples of wrong). >>>>>>>>>>
Induction and counter-induction contradict each other, it's simple, >>>>>>>> it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong
about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
If an error is claimed then it must be specifically
pointed out otherwise the clam of error is dishonest.
On 25/06/2026 16:43, olcott wrote:
On 6/25/2026 2:09 AM, Mikko wrote:
On 24/06/2026 23:19, olcott wrote:
On 6/24/2026 3:23 AM, Mikko wrote:
On 23/06/2026 17:29, olcott wrote:
On 6/23/2026 12:39 AM, Mikko wrote:
On 22/06/2026 16:13, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:That only means that your DD is not a strictly confoming C >>>>>>>>>>> program.
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views >>>>>>>>>>>>>>>>>>> and reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. It >>>>>>>>>>>>>>>>> is abstract in
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with >>>>>>>>>>>>>>> irrelevancy.
The Liar's Paradox has absolutely nothing to do with >>>>>>>>>>>>>>> proof by contradiction. The LP isn't a contradiction; >>>>>>>>>>>>>>> it's a paradox. The two are different things. A >>>>>>>>>>>>>>> contradiction is a statement which is necessarily false. >>>>>>>>>>>>>>> A paradox is a statement to which no truth value can be >>>>>>>>>>>>>>> consistently assigned.
André
Then I have never spoken of anything where proof by >>>>>>>>>>>>>> contradiction applies,
False, as that is exactly the method uses by the halting >>>>>>>>>>>>> problem proof, Godel's proof, and Tarski's proof, each of >>>>>>>>>>>>> which you've been attempting (and failing) to refute for >>>>>>>>>>>>> years.
Proof Theoretic Semantics halt prover HHH correctly determines >>>>>>>>>>>> that its input DD is ungrounded in its atomic base according >>>>>>>>>>>> to the operational semantics of the C programming language. >>>>>>>>>>>
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational >>>>>>>>> semantics
do not fully specify the behaviour of DD. In order to prove >>>>>>>>> that DD
halts you also need additional operational spemantics provided >>>>>>>>> by the
C implementation you have used. When DD iss executed in that >>>>>>>>> environment
it halts, which is sufficient to prove that in that environment DD >>>>>>>>> halts. In some other environment its execution might be aborted >>>>>>>>> or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Nice to see that you don't disagree.
Not nice to see that everyone continues to
totally ignore my best validation of proof
theoretic semantics.
Unfortunately that is unavoidable as long as your best presentation
of the validation and of your version of proof theoretic semantics
are not good enough.
Is is dead obvious and completely clear example
of the final resolution of the Liar Paradox using
generic proof theoretic semantics implemented in
Prolog.
Except that it is not final -- others will continue presenting
different views about it -- and not even a resolution.
If others did not reject mine out-of-hand
without review they could understand that
it is final.
Even those who think your resolution is the best there can be should understand that there are others who don't shate that opinion.
On 25/06/2026 16:47, olcott wrote:
On 6/25/2026 2:14 AM, Mikko wrote:
On 24/06/2026 23:23, olcott wrote:(a) Extracting atomic facts, would be the hardest part,
On 6/24/2026 4:45 AM, Mikko wrote:
On 23/06/2026 17:40, olcott wrote:
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:It can be reasonably approximated pretty quickly.
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:It is fairly simple to build a system of essentially infallible >>>>>>>>> reasoning that never errs even when it doesn't have all the
olcott wrote:It is not that they never admit defeat.
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? >>>>>>>>>>
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and >>>>>>>>>>>>> other questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof- >>>>>>>>>>>>>>>>>>>>>> theoretic- semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views >>>>>>>>>>>>>>>>>>>> and reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. >>>>>>>>>>>>>>>>>> It is abstract in
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that I >>>>>>>>>>>>>>>>>> can't be bothered
to read it any further. If it actually says anything >>>>>>>>>>>>>>>>>> at all, that
something is heavily disguised. From it's "Conclusion >>>>>>>>>>>>>>>>>> and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants >>>>>>>>>>>>>>>>>> play a central role
| in reasoning and inference, but are definitely not >>>>>>>>>>>>>>>>>> the exclusive, and
| perhaps not even the most typical sort of entities >>>>>>>>>>>>>>>>>> that can be defined
| inferentially. A framework is needed that deals with >>>>>>>>>>>>>>>>>> inferential
| definitions in a wider sense and covers both logical >>>>>>>>>>>>>>>>>> and extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is >>>>>>>>>>>>>>>>> currently and in the
near future not useful as making it useful requires >>>>>>>>>>>>>>>>> much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be >>>>>>>>>>>>>>>> useful for? What it
ought to be able to do that standard logic fails at? >>>>>>>>>>>>>>>> Maybe André could
elucidate. He seems to have a better grasp of it than >>>>>>>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than yours. >>>>>>>>>>>>>>> I basically only know what is presented in the Stanford >>>>>>>>>>>>>>> Encyclopedia article (which you correctly point out is >>>>>>>>>>>>>>> not exactly aimed at beginners) and the Wikipedia >>>>>>>>>>>>>>> article. What I am quite certain of, however, is that >>>>>>>>>>>>>>> Olcott lacks any understanding of what PTS actually says >>>>>>>>>>>>>>> as he's made a variety of fairly absurd claims regarding >>>>>>>>>>>>>>> it (for example, that PTS claims that unproven
propositions are 'meaningless' or that the goal of PTS is >>>>>>>>>>>>>>> to completely overthrow standard truth- theoretic >>>>>>>>>>>>>>> semantics).
André
Proof-theoretic semantics is an alternative to >>>>>>>>>>>>>> truth-condition semantics. It is based on the >>>>>>>>>>>>>> fundamental assumption that the central notion >>>>>>>>>>>>>> in terms of which meanings are assigned to certain >>>>>>>>>>>>>> expressions of our language, in particular to >>>>>>>>>>>>>> logical constants, is that of proof rather than >>>>>>>>>>>>>> truth. In this sense proof-theoretic semantics >>>>>>>>>>>>>> is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>> semantics/
In other words it answers the question:
What happens when truth conditional semantics is
utterly abandoned and is totally replaced by proof >>>>>>>>>>>>>> theoretic semantics?
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time. >>>>>>>>>>>>
We can make these lies look foolish at every language
level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is that that have a system of essentially infallible reasoning >>>>>>>>>> that never errs as long as it has all the relevant information. >>>>>>>>>
relevant information. The real problem is to construct a system >>>>>>>>> that tells something interesting instead of just different
presentations of the same already known facts.
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general
knowledge
in your system the general knowledge has grown to inlude more facts. >>>>>>
We start with all of the textbooks.
That is a lot of reading, though those for the same topic area tend
to say the same, and the old ones add very little to the new ones,
mainly some now obsolete technology.
It would not be too much reading for LLMs.
It could start with all of the latest textbooks
for all of the fields. Some of these latest
textbooks may be hundreds of years old for
fields that have become obsolete.
Perhaps that apprach should be tried. The problem involves extracting
atomic facts, detecting repeated facts, and encoding facts for the
inference system.
yet not too hard.
(b) Detecting repeated facts, string comparison.
(c) Encoding facts, CycL
The encoding must be normalized as much as possible in order to reduce repetition to a string comparison. That is not a trivial problem if one
wants a total or nearly total prevention of repetition.
On 25/06/2026 16:58, olcott wrote:
On 6/25/2026 2:18 AM, Mikko wrote:
On 24/06/2026 23:25, olcott wrote:
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>> reject
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>> look into proof theoretic semantics.
At different times you have expressed different opinions, >>>>>>>>>>>>> which
sometimes have been incompatible. But you have never clearly >>>>>>>>>>>>> retracted your earlier opitions that conflict with your >>>>>>>>>>>>> present
ones.
All of the ideas that I have ever had about these things >>>>>>>>>>>> are now under the Proof Theoretic Semantics category.
These ideas have evolved over time, yet their essence
has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a >>>>>>>>>>> publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human >>>>>>>>>> being on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles >>>>>>>>> that have any is or depends on claims that should be proven but >>>>>>>>> aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the proof or >>>>>>> has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one
mai fail to achieve what one could, but if one believs what is
wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition
semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
You have not shown that there is any need for any alternative semantics.
With dangerous lies that can destroy Democracy
and kill the planet with climate change having
an ultimate arbiter of truth would be useful.
Those who are able and willing to destroy democracy are able to provice
an ultimate arbiter of truth and usually do so. But they don't need any
proof theoretic semantics.
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or
understanding of the
truth. If you really want to persuade anybody that PTS >>>>>>>>>>>>> somehow causes
Gödel's theorem not to hold, then cite an academic expert >>>>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>> certainly don't
understand Gödel's Theorem, neither the theorem itself nor >>>>>>>>>>>>> any proof of
it.
in the atomic base of PA. That you do not understand
what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>> defined, so the fault here certainly doesn't lie with Alan. >>>>>>>>>>> It's certainly not a 'verified fact' when you haven't even >>>>>>>>>>> adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a tree >>>>>>>>>> of semantic relations specified syntactically between finite >>>>>>>>>> strings.
What makes you believe semantic relations that can be
structured as
a tree are sufficient to contain all knowledge that is exressed in >>>>>>>>> some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
On 25/06/2026 19:16, olcott wrote:
On 6/25/2026 2:29 AM, Mikko wrote:
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If Dag >>>>>>>>>>>>>>>>>>> Prawitz
really
did
"agree" (with whom?) that Gödel's sentence G is not >>>>>>>>>>>>>>>>>>> true in
Peano
Arithmetic, then produce a citation for this. >>>>>>>>>>>>>>>
He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic >>>>>>>>>>>>>>>>>> Semantics.
You won't understand it, but that _is_ essentially Gödel's >>>>>>>>>>>>>>>>> Incompleteness
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, >>>>>>>>>>>>>>>>> had he been
saying
the things you falsely attributed to him, would >>>>>>>>>>>>>>>>> certainly have
"got" to
Gödel, and would have understood full well what he was >>>>>>>>>>>>>>>>> saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag >>>>>>>>>>>>> Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz >>>>>>>>>>>>> doesn't
say",
then looking a bit into his tremendous volume of works, >>>>>>>>>>>>> he talks about "natural deduction" then specifically an >>>>>>>>>>>>> "inverse
principle" so I think these are key aspects of fundamental >>>>>>>>>>>>> logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to >>>>>>>>>>>>> generate
new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>>>> fifteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>>>> analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, >>>>>>>>>>>>> Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated a >>>>>>>>>>>>> general
type
of schematic Introduction rules to be matched—thanks to the >>>>>>>>>>>>> idea
supporting the inversion principle — by a corresponding >>>>>>>>>>>>> general
schematic Elimination rule. This was an attempt to provide a >>>>>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>>>> According to
Gentzen “it should be possible to display the elimination >>>>>>>>>>>>> rules as
unique functions of the corresponding introduction rules on >>>>>>>>>>>>> the
basis of
certain requirements.” Many people have since worked on >>>>>>>>>>>>> this topic,
which can be appropriately seen as the birthplace of what >>>>>>>>>>>>> are now
referred to as “general elimination rules”, recently studied >>>>>>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace >>>>>>>>>>>>> the main
threads of this chapter of proof-theoretical investigation, >>>>>>>>>>>>> using
Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De >>>>>>>>>>>>> Morgan's
laws,
and that being the usual account of naive deductive >>>>>>>>>>>>> analysis, then
since
"natural deduction", which here is held as part of the theory >>>>>>>>>>>>> since it's naturally logical, then has for Gentzen that >>>>>>>>>>>>> besides
Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, so, >>>>>>>>>>>>> what to do
about "inversion principle" is here that the thea-theory >>>>>>>>>>>>> has that
it's
what subsumes "non-contradiction principle", here hoping >>>>>>>>>>>>> that the
interpretation aligns and thusly that "principle of inversion" >>>>>>>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof- >>>>>>>>>>>>> theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the >>>>>>>>>>>>> foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a >>>>>>>>>>>>> principle of
thorough reason as subsuming principles of non-
contradiction and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old >>>>>>>>>>>>> as the
oldest account of Western philosophy like Heraclitus with dual >>>>>>>>>>>>> monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides of >>>>>>>>>>>>> issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as >>>>>>>>>>>>> one of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this >>>>>>>>>>>>> principle is
often
coupled with another that is called the recovery principle. By >>>>>>>>>>>>> adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>>>> principles
into
one and the same condition, which we call the harmony >>>>>>>>>>>>> condition. We
show
that this reformulation allows us to reveal two intuitive >>>>>>>>>>>>> ideas
standing
behind these principles: the idea of "containment" present >>>>>>>>>>>>> in the
inversion principle, and the idea that the recovery >>>>>>>>>>>>> principle is the
"converse" of the inversion principle. We also formulate >>>>>>>>>>>>> two other
conditions in the Computational Ludics framework, and we >>>>>>>>>>>>> show that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and >>>>>>>>>>>>> knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>>>>>>> proof-theoretic semantics rests on the idea that we know the >>>>>>>>>>>>> meaning of
a compound sentence when we know what counts as a canonical >>>>>>>>>>>>> proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>>>>>>> derivation ending with an introduction rule of the main >>>>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system strong >>>>>>>>>>>>> enough
to make for infinitary reasoning and super-classical results >>>>>>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>>>> That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive >>>>>>>>>>> sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical >>>>>>>>>> proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make >>>>>>>>>>> repairs
of what otherwise is flawed, or for hard constructivist realist >>>>>>>>>>> structuralist model theorists: not-theories (examples of wrong). >>>>>>>>>>>
Induction and counter-induction contradict each other, it's >>>>>>>>> simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong
about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
If an error is claimed then it must be specifically
pointed out otherwise the clam of error is dishonest.
Yet you claim that Ross Finlayson be dishonest without pointing
out what is dishonest in his words.
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that PTS >>>>>>>>>>>>>> somehow causes
Gödel's theorem not to hold, then cite an academic expert >>>>>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>> certainly don't
understand Gödel's Theorem, neither the theorem itself nor >>>>>>>>>>>>>> any proof of
it.
in the atomic base of PA. That you do not understand >>>>>>>>>>>>> what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>> defined, so the fault here certainly doesn't lie with Alan. >>>>>>>>>>>> It's certainly not a 'verified fact' when you haven't even >>>>>>>>>>>> adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>> finite strings.
What makes you believe semantic relations that can be
structured as
a tree are sufficient to contain all knowledge that is
exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>> what: "grounded in the atomic base" means is less
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that PTS >>>>>>>>>>>>>>> somehow causes
Gödel's theorem not to hold, then cite an academic expert >>>>>>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>> certainly don't
understand Gödel's Theorem, neither the theorem itself >>>>>>>>>>>>>>> nor any proof of
it.
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>>> defined, so the fault here certainly doesn't lie with Alan. >>>>>>>>>>>>> It's certainly not a 'verified fact' when you haven't even >>>>>>>>>>>>> adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>> finite strings.
What makes you believe semantic relations that can be
structured as
a tree are sufficient to contain all knowledge that is
exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is equal to
its successor" has no meaning in Robinson Arithmetic.
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:All of knowledge expressed in language is structured as a >>>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>>> finite strings.
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>>You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that PTS >>>>>>>>>>>>>>>> somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>>> certainly don't
understand Gödel's Theorem, neither the theorem itself >>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>>>> defined, so the fault here certainly doesn't lie with >>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' when you >>>>>>>>>>>>>> haven't even adequately explained what it is that you mean. >>>>>>>>>>>>
What makes you believe semantic relations that can be >>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is equal to
its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>>>You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that PTS >>>>>>>>>>>>>>>>> somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>>>> certainly don't
understand Gödel's Theorem, neither the theorem itself >>>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>>>> only by you, and it is one which you have never >>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' when >>>>>>>>>>>>>>> you haven't even adequately explained what it is that you >>>>>>>>>>>>>>> mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>>>> finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is equal
to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem itself >>>>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' when >>>>>>>>>>>>>>>> you haven't even adequately explained what it is that >>>>>>>>>>>>>>>> you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>>>>> tree of semantic relations specified syntactically >>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is equal
to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
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