From Newsgroup: comp.ai.philosophy

https://github.com/plolcott/x86utm/blob/master/Halt7.c https://github.com/plolcott/x86utm/blob/master/README.md

*Succinct proof that the Halting Problem Theorem is incorrect*

Axiom 1 --- Paraphrase of Emil Post
All computations are essentially the application of finite string transformation rules to finite string inputs to derive any and all
outputs. All computations are only allowed to apply finite string transformations to their finite string inputs.

Axiom 2
The only correct finite string transformation rules that HHH is
allowed to apply to its finite string input DD is specified by
the operational semantics of the C programming language.

Axiom 3
This is a single unique sequence thus making every other sequence incorrect.

Axiom 4
This sequence does not derive the behavior of DD() executed from main().
HHH cannot report on the behavior of its caller DD().

Axiom 5
DD correctly simulated by HHH cannot possibly reach its simulated
final halt state is determined by the execution trace shown below.

Conclusion
Simulating halt decider HHH is applied to the conventional
Halting Problem proof counter-example finite string input DD.
HHH applies Emil Post finite string transformations to this DD.
Because the input is C source code correct transformations must
correspond to the operational semantics of the C programming
language. The above prohibits HHH from reporting on the behavior
of its caller DD() directly executed in main(). This also enables
HHH to correctly reject its input finite string DD as non-halting.

typedef int (*ptr)();
int HHH(ptr P);

01 int DD()
02 {
03 int Halt_Status = HHH(DD);
04 if (Halt_Status)
05 HERE: goto HERE;
06 return Halt_Status;
07 }
08
09 void main()
10 {
11 HHH(DD);
12 }

Correct simulation is defined as DD simulated by HHH according to the (operational) semantics of the C programming language. Ordinary software engineering conclusively proves that DD correctly simulated by HHH
cannot possibly reach its own simulated return instruction and terminate normally.

Execution Trace
Line 11: main() invokes HHH(DD);

keeps repeating (unless aborted)
Line 03: simulated DD() invokes simulated HHH(DD) that simulates DD()

Simulation invariant
DD correctly simulated by HHH cannot possibly reach past its own line 03 whether or not HHH ever aborts this simulation.

DD correctly simulated by HHH cannot possibly reach its simulated final
state.
--
Copyright 2026 Olcott

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).

--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: comp.ai.philosophy

On 10/10/2026 3:52 PM, dart200 wrote:

On 10/10/26 1:17 PM, olcott wrote:

https://github.com/plolcott/x86utm/blob/master/Halt7.c
https://github.com/plolcott/x86utm/blob/master/README.md

*Succinct proof that the Halting Problem Theorem is incorrect*

Axiom 1 --- Paraphrase of Emil Post
All computations are essentially the application of finite string
transformation rules to finite string inputs to derive any and all
outputs. All computations are only allowed to apply finite string
transformations to their finite string inputs.

Axiom 2
The only correct finite string transformation rules that HHH is
allowed to apply to its finite string input DD is specified by
the operational semantics of the C programming language.

Axiom 3
This is a single unique sequence thus making every other sequence
incorrect.

Axiom 4
This sequence does not derive the behavior of DD() executed from main().
HHH cannot report on the behavior of its caller DD().

Axiom 5
DD correctly simulated by HHH cannot possibly reach its simulated
final halt state is determined by the execution trace shown below.

Conclusion
Simulating halt decider HHH is applied to the conventional
Halting Problem proof counter-example finite string input DD.
HHH applies Emil Post finite string transformations to this DD.
Because the input is C source code correct transformations must
correspond to the operational semantics of the C programming
language. The above prohibits HHH from reporting on the behavior
of its caller DD() directly executed in main(). This also enables
HHH to correctly reject its input finite string DD as non-halting.

typedef int (*ptr)();
int HHH(ptr P);

01 int DD()
02 {
03   int Halt_Status = HHH(DD);
04   if (Halt_Status)
05     HERE: goto HERE;
06   return Halt_Status;
07 }
08
09 void main()
10 {
11  HHH(DD);
12 }

Correct simulation is defined as DD simulated by HHH according to the
(operational) semantics of the C programming language. Ordinary
software engineering conclusively proves that DD correctly simulated
by HHH cannot possibly reach its own simulated return instruction and
terminate normally.

Execution Trace
Line 11: main() invokes HHH(DD);

keeps repeating (unless aborted)
Line 03: simulated DD() invokes simulated HHH(DD) that simulates DD()

Simulation invariant
DD correctly simulated by HHH cannot possibly reach past its own line
03 whether or not HHH ever aborts this simulation.

DD correctly simulated by HHH cannot possibly reach its simulated
final state.

bruh ur never gunna build a machine that decides whether any given input machine halts or not

You did not carefully study the above words that
took me 20,000 hours over 22 years to write.

If you spent 1 / 40,000th of the time that I did
to carefully studying my words you would see how
terrible your paraphrase is.

the problem of constructing paradoxical dependencies that is inherent to computing prevents this

whatever innovation is to had on the matter is going to be in-spite of
that limitation, not by denying or removing it

--
Copyright 2026 Olcott

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).
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: comp.ai.philosophy

On 10/13/2026 3:42 AM, chine.bleu wrote:

olcott wrote:

All computations are essentially the application of finite string

Finite but unbounded. The string can grow beyond the currently allocated space and if halts, it will eventually reach its maximum but you do not
know when. Or if.

I don't think that this extra detail materially effects
any aspect of my proof so it seems true and irrelevant.
--
Copyright 2026 Olcott

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).
--- Synchronet 3.22a-Linux NewsLink 1.2