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Ben's objection finally fully addressed --- much more clearly

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  Ben's objection finally fully addressed --- much more clearly olcott <NoOne@NoWhere.com> - 2025-12-09 18:09 -0600
    New Signature Line polcott <polcott333@gmail.com> - 2025-12-09 21:15 -0600

#123124 — Ben's objection finally fully addressed --- much more clearly

On 10/14/2022 7:44 PM, Ben Bacarisse wrote:

*Original context*
On 10/14/2022 12:06 PM, olcott wrote:
 > Professor Sipser has agreed that this is the correct criteria:
 >
 > If simulating halt decider H correctly simulates its input
 > D until H correctly determines that its simulated D would
 > never stop running unless aborted then H can abort its
 > simulation of D and correctly report that D specifies a
 > non-halting sequence of configurations.
 >

> I don't think that is the shell game.  PO really /has/ an H (it's
> trivial to do for this one case) that correctly determines that P(P)
> *would* never stop running *unless* aborted.  He knows and accepts that
> P(P) actually does stop.  The wrong answer is justified by what would
> happen if H (and hence a different P) where not what they actually are.
> 

Turing machine deciders only compute the mapping from
their [finite string] inputs to an accept or reject
state on the basis that this [finite string] input
specifies or fails to specify a particular semantic
or syntactic property.

Professor Sipser only agreed with a tautology.

I will rephrase this tautology into terms that
are more unequivocal.

int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}

int main()
{
   HHH(DD);
}

DD is simulated by HHH according to the semantics
of the C programming language.

HHH watches the behavior of its simulated DD
step-by-step until it sees the recursive
simulation non-halting behavior pattern.

This is the correct measure of the behavior that
the input to HHH(DD) actually specifies.

The provably correct first paragraph requires
that HHH report on this basis.

The halting problem itself derives a category
error by requiring that HHH report on any other
behavior.

The behavior that the halting problem incorrectly
requires is the behavior of DD() executed from main
that calls HHH(DD).

The caller of a function is certainly not
one-and-the-same thing as an argument to
this same function.



-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

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#123127 — New Signature Line

On 12/9/2025 6:09 PM, olcott wrote:

-- 
Copyright 2025 Olcott

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

This required establishing a new foundation
for correct reasoning.

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