Re: HP counter-example INPUT cannot possibly exist

On 2025-06-18 14:39:02 +0000, olcott said:

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:
 

On 6/13/2025 5:37 AM, Mikko wrote:

On 2025-06-12 15:18:30 +0000, olcott said:
 

On 6/12/2025 3:23 AM, Mikko wrote:

On 2025-06-11 14:34:41 +0000, olcott said:
 

On 6/11/2025 4:19 AM, Mikko wrote:

On 2025-06-10 15:11:50 +0000, olcott said:
 

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
 There are no words.
 /Flibble

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

 What about this paper that I wrote?
 Severe anthropogenic climate change proven entirely with verifiable facts
 https://www.researchgate.net/ publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts  

 Which just shows you don't know the meaning of the word "prove".

 What specifically do you believe is not proven?

 The article makes no attempt to prove anything.

 That is a dishonest or stupid thing to say.

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

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

 Irrepevant.

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

 Indeed, but what is more relevant is that you don't know what a fact is.
 

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.

 Irrelevant as long as you don't prove anything.

 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

So far correct.

that are necessarily true and thus impossibly false.

But this is not. A proof starts with assumptions that may be true of
false. Each statement that is not a definition, axiom, postulate,
hypthesis or other assumption follows from some previous statements
by an inference rule. The conclusion of a proof is the last statement
of the sequence.

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

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

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

 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.

No, it is not. Vernacular terms "dog" and "animal" have aquired teir
traditiona meanigs separately and at different times. The statement
"Dogs are aninals" is known to be true from comparison of various
things to the traditional meanings of those words.

Like almost everyone you don't know much about
analytical truth.

As an analytincal truth says nothing about the real world the
usefulness of any knowledge about it is limited.

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

 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.

 Nonsense is not a fact.

 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.

Depending on the style of the proof one can ither prove that
the counter example exists or that if a halting decider exists
then the caunter example exists, too, and otherwise none is
needed.

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*

It is proven that for every Turing machine there is a counter
example. The proof also identifies what that counter example
is.

This may be difficult to understand.
A lack of comprehension does not count as a rebuttal.

That's right. You have no rebuttal but, lacking comprehension,
you keep claiming that you have.

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

That is not a syntactically valid sentence and therefore does not
say anything. The original sentence is meaningful but the "adaptation"
did not preserve its meaning and meaningfulness.
In particular it does not mean that:

(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

--
Mikko