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 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 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 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 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 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.
On 6/26/2026 10:24 AM, olcott wrote:
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.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning in Robinson arithmetic.
On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
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.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning in
Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
On 6/26/2026 1:22 PM, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
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.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning
in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
So you agree that Robinson arithmetic is incomplete.
On 6/26/2026 12:25 PM, dbush wrote:
On 6/26/2026 1:22 PM, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
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.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning
in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
So you agree that Robinson arithmetic is incomplete.
It is as complete as it was designed to be.
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