HP counter-example INPUT cannot possibly exist

On 6/16/2025 3:21 AM, Mikko wrote:

On 2025-06-15 14:44:47 +0000, olcott said:
 

On 6/15/2025 4:19 AM, Mikko wrote:

On 2025-06-13 15:33:45 +0000, olcott said:
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On 6/13/2025 5:37 AM, Mikko wrote:

On 2025-06-12 15:18:30 +0000, olcott said:
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On 6/12/2025 3:23 AM, Mikko wrote:

On 2025-06-11 14:34:41 +0000, olcott said:
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On 6/11/2025 4:19 AM, Mikko wrote:

On 2025-06-10 15:11:50 +0000, olcott said:
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On 6/10/2025 6:15 AM, Richard Damon wrote:

On 6/9/25 8:34 PM, olcott wrote:

On 6/9/2025 7:16 PM, Richard Damon wrote:

On 6/9/25 3:16 PM, Mr Flibble wrote:

"big fat ignorant liar" -- Damon
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There are no words.
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/Flibble

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Can you show me wrong?
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Or are you complaining about me telling him the truth?

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What about this paper that I wrote?
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Severe anthropogenic climate change proven entirely with verifiable facts
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https://www.researchgate.net/ publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
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Which just shows you don't know the meaning of the word "prove".

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What specifically do you believe is not proven?

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The article makes no attempt to prove anything.

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That is a dishonest or stupid thing to say.

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On what page and line there is the end of the conclusion of
a proof?

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Maybe you don't know what a verified fact is?

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Irrepevant.

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That you don't know what a verified fact is, cannot
possibly be more relevant.

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Indeed, but what is more relevant is that you don't know what a fact is.
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It means that when I conclusively
prove that you are wrong you will still think that you are
correct because you lack the basis for dividing correct
from incorrect.

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Irrelevant as long as you don't prove anything.

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When I fully proven my claim and your lack of sufficient
technical knowledge fails to understand this proof that
is not any actual rebuttal at all.

 Be specific. The relevant techincal knoledge is the knowloedge
of what a proof is and how one looks like. That knowledge
I have, so I know that you have not presented any proof.
I have not failed to understand what does not exist.
 

A proof is any sequence of statements that are
necessarily true and thus impossibly false.

Your question "What specifically do you believe is not
proven?" was about proofs, not about facts.

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Facts are the ultimate ground-of-being maximum foundational
basis of all proofs.

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No, they are not, just of proofs about the real world.

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So how many decades how you carefully studied the
philosophical foundation of analytical truth?

 It doesn't take decades of study to learn that an analyitcal
truth says nothing about the real world. That is one of the
very first things teached and learned.
 

That dogs are animals is an analytical truth
that does say something about the real world.
Like almost everyone you don't know much about
analytical truth.

As you respond to my question without answering it it is
obvious that you don't see any proofs in your article.

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It is a fact that there is no actual input D to any
termination analyzer H that does the opposite of
whatever value that H derives. The key element that
all conventional HP proofs depend on cannot possibly exist.

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Nonsense is not a fact.

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After studying these things for 22 years I found
that every conventional proof of the halting problem
never provides an actual input that would do the
opposite of whatever value that its partial halt
decider (PHD) returns.

 The core part of those proofs is a constructive specification
of that test case.
 

Yet no one ever noticed that the counter-example input
cannot even be constructed thus the proof itself never
actually existed.

It is always the case that the computation the PHD
is embedded within or the function that calls the
PHD that does the opposite. It is never the input.

 Doesn't matter. Those proofs prove that for any Turing machine there
is an input that proves that the decider is not a halt decider.

*Counter-factual there never has been any such an input*
This may be difficult to understand.
A lack of comprehension does not count as a rebuttal.
When Ĥ is applied to ⟨Ĥ⟩     // *adapted from bottom of page 319*
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
(a) Ĥ copies its input ⟨Ĥ⟩
(b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
(d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩
(e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
(g) goto (d) with one more level of simulation until embedded_H
     sees the repeating pattern and transitions to Ĥ.qn.
⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly
reach its own ⟨Ĥ.qy⟩ state or final halt state of ⟨Ĥ.qn⟩
thus can never do the opposite of whatever embedded_H decides.
https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf

 That
is sufficient to prove that no Turing machine is a halt decider for
Turing machines.
 

The expression "any termination analyzer H"
does not mean anything in this context, which does not have the
definitions that would give it a meaning.

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A termination analyzer is required to report on the
sequence of state transitions that its input specifies.

 An analyzer is required to report on the program that the used wants
to be analyed if that program is in the scope of the analyzer. How
the input shall be constructed to enable that must be told in the
instruction manual of the analyzer.
 

*IT MUST BE AN ACTUAL INPUT AND NO SUCH INPUT CAN POSSIBLY EXIST*

The key element is that in the context of all convetional HP proofs
for every decider it is possible to construct a program that halts
if the decider rejects it and does not halt if the decider rejects
it, which proves that the decider is not a halting decider.

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Yet it is not possible that this program is an input to
the PHD. Unless it is an actual input then the whole
conventional HP proof fails.

 That is not true about every PHD. In particular, it is not true about
Turing machines, and the conventional proofs don't prove about anything
else.
 

I just showed how it is true in the Linz proof.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer