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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Formal systems that cannot possibly be incomplete except for
 unknowns and unknowable
Date: Wed, 7 May 2025 13:03:00 -0500
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On 5/6/2025 11:16 AM, Richard Heathfield wrote:
> On 06/05/2025 16:38, Alan Mackenzie wrote:
>> These aren't particularly difficult things to comprehend.  As I keep
>> saying, you ought to show a lot more respect for people who are
>> mathematically educated.
> 
> I concur.
> 
> As someone who is not particularly mathematically educated (I have an A- 
> level in the subject, but that's all), I tend to steer well clear of 
> mathematical debates, although I have occasionally dipped a toe.
> 
> I have *enormous* respect for those who know their tensors from their 
> manifolds and their conjectures from their eigenvalues, even though it's 
> all Greek to me.
> 
> But to understand the Turing proof requires little if any mathematical 
> knowledge. It requires only the capacity for clear thinking.
> 
> Having been on the receiving end of lengthy Usenet diatribes by cranks 
> in my own field, I don't hold out much hope for our current culprits 
> developing either the capacity for clear thought or any measure of 
> respect for expertise any time soon.
> 
> Nor do I believe they are capable of understanding proof by 
> contradiction, which is just about the easiest kind of proof there is. 
> In fact, the most surprising aspect of this whole affair is that 

> (according to Mike) Mr Olcott seems to have (correctly) spotted a minor 
> flaw in the proof published by Dr Linz. How can he get that and not get 
> contradiction? Proof by contradiction is /much/ easier.
> 

https://www.liarparadox.org/Linz_Proof.pdf
The flaw is on the top of page 3 where
there are two q0 start states in the same sequence
of state transitions.

I encode that in this easier to understand notation.

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer