From Newsgroup: sci.logic

The halting problem proof fails not because finite computation
is insufficient, but because it asks finite computation
to decide a judgment that is not finitely grounded under
operational semantics.

By “operational semantics” I mean the standard proof-theoretic
account of program meaning in which execution judgments are
defined by inference rules and termination corresponds to the
existence of a finite derivation.

By proof-theoretic semantics I mean the standard approach in
which the meaning of a statement is given by its rules of
proof rather than by truth conditions in a model.

This is the same sense in which operational semantics gives
meaning to programs via execution rules rather than denotations.

By denotational semantics I mean the standard approach in which
every well-formed program or statement is assigned a mathematical
object such as a function or truth value---independently of how
it is computed or proved.

This contrasts with operational or proof-theoretic semantics,
where meaning is given by execution or proof rules rather than
by an abstract denotation.

I use ‘denotational semantics’ simply to refer to any semantics
that assigns abstract mathematical meanings to programs independently
of their operational behavior.
--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>

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From Newsgroup: sci.logic

On 15/01/2026 00:14, olcott wrote:

The halting problem proof fails ...

Do you mean "The halting problem proof supposition fails ..." ?
--
Tristan Wibberley

The message body is Copyright (C) 2026 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

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From Newsgroup: sci.logic

On 1/14/2026 6:26 PM, Tristan Wibberley wrote:

On 15/01/2026 00:14, olcott wrote:

The halting problem proof fails ...

Do you mean "The halting problem proof supposition fails ..." ?

The proof does not prove that halting is undecidable.

By proof‑theoretic semantics I mean the approach in which the
meaning of a statement is determined by its rules of proof
rather than by truth conditions in an external model.
Operational semantics fits this pattern: programs have meaning
through their execution rules, not through abstract denotations.
--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: sci.logic

On 1/14/26 7:51 PM, olcott wrote:

On 1/14/2026 6:26 PM, Tristan Wibberley wrote:

On 15/01/2026 00:14, olcott wrote:

The halting problem proof fails ...

Do you mean "The halting problem proof supposition fails ..." ?

The proof does not prove that halting is undecidable.

By proof‑theoretic semantics I mean the approach in which the
meaning of a statement is determined by its rules of proof
rather than by truth conditions in an external model.
Operational semantics fits this pattern: programs have meaning
through their execution rules, not through abstract denotations.

But "Proof-Theoretic Semantics" aren't applicable to the system.

I guess in you system you can't make a computation that verifies that a
proof is correct.

Your problem is you are not ALLOWED to change the semantics of the
system the proof was done in.

At best, you can say it doesn't apply in other systems, but those system
end up being deficent in some needed criteria.

Being able to handle the properties of the Natural Numbers is one of them.
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From Newsgroup: sci.logic

On 1/14/2026 9:45 PM, Richard Damon wrote:

On 1/14/26 7:51 PM, olcott wrote:

On 1/14/2026 6:26 PM, Tristan Wibberley wrote:

On 15/01/2026 00:14, olcott wrote:

The halting problem proof fails ...

Do you mean "The halting problem proof supposition fails ..." ?

The proof does not prove that halting is undecidable.

By proof‑theoretic semantics I mean the approach in which the
meaning of a statement is determined by its rules of proof
rather than by truth conditions in an external model.
Operational semantics fits this pattern: programs have meaning
through their execution rules, not through abstract denotations.

But "Proof-Theoretic Semantics" aren't applicable to the system.

I guess in you system you can't make a computation that verifies that a proof is correct.

Your problem is you are not ALLOWED to change the semantics of the
system the proof was done in.

Sure you are. "Proof-Theoretic Semantics" does not derive the
incoherence of truth conditional semantics.

At best, you can say it doesn't apply in other systems, but those system
end up being deficent in some needed criteria.

Being able to handle the properties of the Natural Numbers is one of them.

--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21b-Linux NewsLink 1.2

From Newsgroup: sci.logic

On 1/15/26 12:33 AM, olcott wrote:

On 1/14/2026 9:45 PM, Richard Damon wrote:

On 1/14/26 7:51 PM, olcott wrote:

On 1/14/2026 6:26 PM, Tristan Wibberley wrote:

On 15/01/2026 00:14, olcott wrote:

The halting problem proof fails ...

Do you mean "The halting problem proof supposition fails ..." ?

The proof does not prove that halting is undecidable.

By proof‑theoretic semantics I mean the approach in which the
meaning of a statement is determined by its rules of proof
rather than by truth conditions in an external model.
Operational semantics fits this pattern: programs have meaning
through their execution rules, not through abstract denotations.

But "Proof-Theoretic Semantics" aren't applicable to the system.

I guess in you system you can't make a computation that verifies that
a proof is correct.

Your problem is you are not ALLOWED to change the semantics of the
system the proof was done in.

Sure you are. "Proof-Theoretic Semantics" does not derive the
incoherence of truth conditional semantics.

In other words, in your world words don't need to mean what they were
defined to mean.

That you the world of lies you live in.

I hereby define the words "Peter Olcott" to mean a totally brainless pathological liar.

Your claim to be able to change the basis of a system is the same as
that decleration.

As I have said, if you want to try to derive a NEW system by some such
rule, go ahead, but you first need to show the basic results of what
that system can do, and that it is useful.

Note, I suspect you are going to find that you can't even support basic
math in your system.

At best, you can say it doesn't apply in other systems, but those
system end up being deficent in some needed criteria.

Being able to handle the properties of the Natural Numbers is one of
them.

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