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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD correctly emulated by HHH is correctly rejected as
 non-halting. --- You are not paying attention
Date: Sat, 20 Jul 2024 08:22:31 -0500
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On 7/20/2024 3:42 AM, Mikko wrote:
> On 2024-07-19 13:48:49 +0000, olcott said:
> 
>>
>> Some undecidable expressions are only undecidable because
>> they are self contradictory. In other words they are undecidable
>> because there is something wrong with them.
> 
> Being self-contradictory is a semantic property. Being uncdecidable is
> independent of any semantics. 

Not it is not. When an expression is neither true nor false
that makes it neither provable nor refutable. As Richard
Montague so aptly showed Semantics can be specified syntactically.

> An arithmetic sentence is always about
> numbers, not about sentences.

So when Gödel tried to show it could be about provability
he was wrong before he even started?

>  A proof is about sentences, not about
> numbers.
> 
>> The Liar Paradox: "This sentence is not true"
> 
> cannot be said in the language of Peano arithmetic.
> 

Since Tarski anchored his whole undefinability theorem in a 
self-contradictory sentence he only really showed that sentences that
are neither true nor false cannot be proven true.

https://liarparadox.org/Tarski_247_248.pdf
https://liarparadox.org/Tarski_275_276.pdf

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