From Newsgroup: comp.ai.philosophy

On 10/16/2026 10:09 AM, Python wrote:

Your `sum` example makes the disagreement even clearer.

I agree that

   int sum(int x, int y) { return 5; }

does NOT compute integer addition on its full domain.

But now consider:

   int add(int x, int y) {
       return addition_table[x][y];
   }

where `addition_table` contains the correct sum for every pair in the
finite domain.

This computes exactly the same mathematical function as:

   return x + y;

Yet its runtime transformations are merely:

   read x,y
   index table
   retrieve value
   return value

It does not derive the result by performing the arithmetic inference

   2 + 3 = 5.

It does not avoid the arithmetic operation it
merely offloads this operation to a human or
another process.

And we must distinguish TWO different computations here:

   A. the computation or reasoning that CONSTRUCTED the table

   B. the computation add(x,y) that USES the table

It merely an elaboration of
int sum(int x, int y) { return 5; }

That handles more inputs without actually computing the
mapping from any other them.

Perhaps A calculated every entry using arithmetic, theorem proving, a
human mathematician, or something else entirely.

That is irrelevant to what B computes.

It proves that B computes no mapping.

Once the table exists, B computes addition without reproducing,
containing, or even knowing the derivation by which the table was constructed.

Indeed, two identical copies of B compute exactly the same function even
if their tables were independently produced by completely different processes.

So saying:

   "the semantic inference was off-loaded"

actually concedes the distinction.

That B itself computes no mapping.

Yes — it was performed ELSEWHERE.

Therefore it is not an inference step of the computation B whose
behavior we are classifying.

If you nevertheless say B does NOT compute addition because the semantic derivation occurred elsewhere, then you have changed the standard
meaning of "computes a function".

B itself computes no mapping.

And your PI analogy illustrates the same distinction.

The value of PI does not depend upon HOW somebody computes it. Different algorithms can derive the same digits through radically different transformations.

So I grant:

   the output must satisfy the semantic specification.

What I do NOT grant is:

   the computation producing that output must itself
   contain a semantic derivation proving that output.

Else B itself computes no mapping.

That additional requirement does not follow merely by combining finite- string computation with operational semantics.

You keep asserting that it has "always been required".

But THAT assertion is exactly the proposition requiring proof.

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

From Newsgroup: comp.ai.philosophy

On 10/19/2026 10:35 AM, Python wrote:

Peter,

When both of your own answers are wrong this proves
that I am correct.

No. It proves exactly the Halting Theorem.

You are overlooking what your program depends on.

Your 2004 example says:

   if YOU say HALTS:
       loop
   else:
       halt

So there is no answer that can be both:

   1. supplied to the program, and
   2. a correct prediction of the resulting behavior.

Agreed.

But that does not prove that halting is an "incorrect question".

On 6/23/2004 9:34 PM, Peter Olcott wrote:

function LoopIfYouSayItHalts (bool YouSayItHalts):
if YouSayItHalts () then
while true do {}
else
return false;

Does this program Halt?

(Your (YES or NO) answer is to be considered
translated to Boolean as the function's input
parameter)

Please ONLY PROVIDE CORRECT ANSWERS!

I asked you for your answer and YOU failed.

This is NOT a fundamental limit to human reasoning
it is merely an incorrect POLAR question.
--
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).
--- Synchronet 3.22a-Linux NewsLink 1.2