Re: Bad faith and dishonesty

On 5/31/2025 8:37 AM, Mike Terry wrote:

On 31/05/2025 11:03, Richard Heathfield wrote:

On 31/05/2025 10:42, Mikko wrote:

On 2025-05-30 17:27:05 +0000, olcott said:
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On 5/30/2025 12:06 PM, Richard Heathfield wrote:

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<snip>
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As far as I can recall, Olcott's ramblings never go within discus- throwing distance of a potentially erroneous step.

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There is no *INPUT* D to termination analyzer H
that can possibly do the opposite of whatever
value that H returns.

>
We can apply Truing'c construction to every Truing machine and
 prove that no Turing machine is a halting decider. With a
similar construction many other problems about Turing machine
behaviour can be proven uncomputable, too.

>
Indeed. In fact, if I'm reading Mr Olcott's retort correctly...
>
Turing: imagine a program P...
Turing: ...argument goes here...
Turing: ...and it turns out that P can't exist.
Olcott: Turing is wrong, because P can't exist.
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I /seeeeee.../
>

 More like:
 Turing: imagine a program P...
Turing: ...modify P as follows to create D...
Turing: ...argument goes here...
Turing: ...so P decides D's halting incorrectly
Turing: ...and so P is not a halt decider.
Olcott: Turing is wrong, because *D* can't exist.
 I /seeeeee.../
 Mike.
 

Turing wasn't even dealing with halting.
No one referred to this as the halting problem
until 1958 in a book by Martin Davis.
https://www.sciencedirect.com/science/article/pii/S235222082100050X
*Here is the orignal Linz proof*
https://www.liarparadox.org/Linz_Proof.pdf
In the following embedded_H is P and ⟨Ĥ⟩ is D
When Ĥ is applied to ⟨Ĥ⟩
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
It is at step (f) that embedded_H correctly
determines that its simulated ⟨Ĥ⟩ cannot possibly
reach its own simulated ⟨Ĥ.qn⟩ final halt state.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer