Re: My reviewers think that halt deciders must report on the behavior of their caller

On 7/5/2025 9:29 AM, Mr Flibble wrote:

On Fri, 04 Jul 2025 16:53:50 -0400, Richard Damon wrote:
 

On 7/4/25 4:43 PM, olcott wrote:

On 6/3/2025 10:02 PM, dbush wrote:

On 6/3/2025 10:58 PM, olcott wrote:

On 6/3/2025 9:46 PM, dbush wrote:

On 6/3/2025 10:34 PM, olcott wrote:

On 6/3/2025 9:12 PM, dbush wrote:

>
Given any algorithm (i.e. a fixed immutable sequence of
instructions) X described as <X> with input Y:
>
A solution to the halting problem is an algorithm H that computes
the following mapping:
>
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
directly
>
>

Yes there is no algorithm that does that

>
Excellent!
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Let The Record Show
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That Peter Olcott
>
Has *EXPLICITLY* admitted
>
That no algorithm H exists that meets the above requirements, which
is precisely the theorem that the halting problem proofs prove.

>
In the exact same way that there is no set of all set that contain
themselves. ZFC did not solve Russell's Paradox as much as it showed
that Russell's Paradox was anchored in an incoherent foundation, now
called naive set theory.

>
Which arose because the axioms of naive set theory created a
contradiction.
>
>

Likewise with halt deciders that are required to report on the behavior
of directly executed Turing machines.

>
And what is the CONTRADICTION?
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The result is just some things are not computable.
>
>

Directly executed Turing machines are outside of the domain of every
Turing machine decider.

>
Then so is mathematics, as "numbers" can't be given to Turing Machines,
only representations of them.
>
By the exact same idea that we can represent a number by a finite
string, we can express the algorithm, and input, of a Turing Machine as
a finite string, and thus can talk about what it will do.
>
>

In contrast, the axioms of computation theory do *not* create a
contradiction.  It simply follows from those axioms that no H exists
the meets the above requirements, which is a completely valid
conclusion.

>
*Claude.ai seems to be the smartest bot about computation*
https://claude.ai/share/48aab578-aec3-44a5-8bb3-6851e0f8b02e
>
>

Which you just continue to lie to, so proving that you are just a
pathological liar.

 It is YOU who is the pathological liar: the recursive self reference in
the classical halting problem proofs is a category error just as in
Russell's Paradox.  All halting problems based on such an erroneous
construction are thus refuted, here and now, by me, Mr Flibble.
 /Flibble

The above link to Claude agrees with your category error
idea this way: Directly executed Turing machines are outside
of the domain of any Turing machine based decider.
This means that the behavior of a directly executed machine
does not contradict the return value of HHH(DD). HHH correctly
computes the mapping from its input finite string to the
recursive simulation behavior that it specifies.
It has never been the case that a halt decider must report
on the direct execution of any machine. This has always been
a false assumption and/or incorrect requirement. Claude
explains the details of this.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer