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 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 07:52 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 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 23/06/2026 17:52, 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.
It does not provide any useful alternative when no semantics is needed.
It is not shown to offer anything useful with problems with theal world semantics, which are the most important ones.
On 6/24/2026 5:06 AM, Mikko wrote:
On 23/06/2026 17:52, 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.
It does not provide any useful alternative when no semantics is needed.
That G is true in the standard model of arithmetic
cannot possibly exist when model theory is replaced
with proof theoretic semantics.
It still isn't.It is not shown to offer anything useful with problems with theal world
semantics, which are the most important ones.
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