From Newsgroup: comp.ai.philosophy

These terms are replaced:
(a) "Turing machine description" is replaced with
[Finite string source code for a Turing Machine]

The term: "description" is too vague the finite string
source code actually specifies an exact sequence of steps.

The term: "machine description" enables indirect
reference to behavior other than the behavior specified
by the input finite string of source code.

(b) "Decider" and replace it with sequence of inference
steps that are applied to an input static finite string
that are syntactically or semantically relevant to the
decision criteria.

Concrete example of a decider where relevance is required.
int strcmp(const char *str1, const char *str2);
and the finite string inputs are the entire basis.

This tightens the term "decider" to the actual requirements
that are never expressly stated. We can see things much
more clearly with these additional details.

WE HAVE CORRECTED THE ERRORS AT THE FOUNDATION OF COMPUTATION.
At this point we only need to see what is semantically entailed
by these corrections.
--
Copyright 2026 Olcott

*Succinct refutation of the Halting Theorem* https://github.com/plolcott/x86utm/blob/master/README.md


The essence of computation is applying finite
string transformations to finite string inputs
to derive outputs. // paraphrase of Emil Post

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).

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From Newsgroup: comp.ai.philosophy

On 2026-10-23 12:10, olcott wrote:

These terms are replaced:
(a) "Turing machine description" is replaced with
    [Finite string source code for a Turing Machine]

The term: "description" is too vague the finite string
source code actually specifies an exact sequence of steps. >
The term: "machine description" enables indirect
reference to behavior other than the behavior specified
by the input finite string of source code.

The term 'description' as using in computational theory normally refers
to a 7-tuple as described here:

<https://en.wikipedia.org/wiki/Turing_machine#Formal_definition>

How is that any more vague that your alternative? Note also that the
term 'source code' isn't normally used for Turing Machines since Turing Machines are mathematical objects, not things that are compiled to run
on digital computers.

(b) "Decider" and replace it with sequence of inference
     steps that are applied to an input static finite string
     that are syntactically or semantically relevant to the
     decision criteria.

     Concrete example of a decider where relevance is required.
     int strcmp(const char *str1, const char *str2);
     and the finite string inputs are the entire basis.

strcmp() isn't a decider at all. A decider takes a single input and
either accepts it or rejects it. It is an algorithm implementing the membership function of a set.

This tightens the term "decider" to the actual requirements
that are never expressly stated. We can see things much
more clearly with these additional details.

Since your example isn't a decider, it rather difficult to see how your
claims somehow 'tightens' the term.

André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

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From Newsgroup: comp.ai.philosophy

On 10/23/2026 2:11 PM, André G. Isaak wrote:

On 2026-10-23 12:10, olcott wrote:

These terms are replaced:
(a) "Turing machine description" is replaced with
     [Finite string source code for a Turing Machine]

The term: "description" is too vague the finite string
source code actually specifies an exact sequence of steps. >
The term: "machine description" enables indirect
reference to behavior other than the behavior specified
by the input finite string of source code.

The term 'description' as using in computational theory normally refers
to a 7-tuple as described here:

<https://en.wikipedia.org/wiki/Turing_machine#Formal_definition>

How is that any more vague that your alternative? Note also that the
term 'source code' isn't normally used for Turing Machines since Turing Machines are mathematical objects, not things that are compiled to run
on digital computers.

(b) "Decider" and replace it with sequence of inference
      steps that are applied to an input static finite string
      that are syntactically or semantically relevant to the
      decision criteria.

      Concrete example of a decider where relevance is required.
      int strcmp(const char *str1, const char *str2);
      and the finite string inputs are the entire basis.

strcmp() isn't a decider at all. A decider takes a single input and
either accepts it or rejects it. It is an algorithm implementing the membership function of a set.

This tightens the term "decider" to the actual requirements
that are never expressly stated. We can see things much
more clearly with these additional details.

Since your example isn't a decider, it rather difficult to see how your claims somehow 'tightens' the term.

André

Nit-picky irrelevant details. The idea was to show
that the decision criteria restricts the steps to
those that are syntactically relevant.

This is a key missing element of the foundations
of computation that prevents computation from being
understood more deeply.
--
Copyright 2026 Olcott

*Succinct refutation of the Halting Theorem* https://github.com/plolcott/x86utm/blob/master/README.md


The essence of computation is applying finite
string transformations to finite string inputs
to derive outputs. // paraphrase of Emil Post

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).
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From Newsgroup: comp.ai.philosophy

Nit-picky irrelevant details. The idea was to show
that the decision criteria restricts the steps to
those that are syntactically relevant.

This is a key missing element of the foundations
of computation that prevents computation from being
understood more deeply.

No, Peter.

That is not a "missing element of the foundations of computation."

That is a new restriction you have just invented.

You started with:

computation operates on finite strings

which nobody disputes.

You have now silently strengthened that into:

computation may use only steps that Peter declares
"syntactically relevant" to the decision criterion.

Those propositions are not remotely equivalent.

Post's characterization of effective computation does not give you a
magical "relevance" filter that permits a purported decider to ignore consequences of its own result.

And `strcmp()` proves nothing of the sort.

It merely computes a particular function of two finite strings.

More importantly, André's objection is not "nit-picky."

You are claiming to have discovered an error in the foundations of computability while simultaneously redefining its basic terms.

When someone points out that your example is not even a decider in the standard technical sense, answering:

"irrelevant details"

is rather spectacular.

Definitions ARE the details when your claimed revolution consists of
changing definitions.

And now we have yet another newly introduced term:

"syntactically relevant"

Please define it mathematically.

Then prove your claimed theorem:

A decision procedure may consider only
syntactically relevant inference steps.

In particular, define "relevant" without circularly meaning:

whatever allows HHH to return the answer
Peter wants while ignoring the consequence
that makes that answer wrong.

Because until you do that, you have not discovered a missing foundation of computation.

You have invented an undefined restriction and declared it foundational.

That is not deeper understanding.

That is moving the goalposts and giving the new goalpost a name.
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