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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic,comp.theory
Subject: Re: Truth Bearer or Truth Maker
Date: Thu, 25 Jul 2024 09:16:53 -0500
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On 7/25/2024 4:42 AM, Mild Shock wrote:
> Most of the fallacies arise, since originally
> logic was only made for the every day finite.
> Applying it to the infinite automatically gets
> 
> you into muddy waters. Take sentence such as
> 
> Goldbach's conjecture
> every even natural number greater than 2 is
> the sum of two prime numbers
> 
> It contains a forall quantifier. And its an
> infinite forall quantifier. Its a not a finite
> quantifier such as "all my kitchen utils",
> 
> its an infinite quantifier "every even natural
> number". In the intented model of arithmetic
> the above sentence has a truth value.
> 
> By classical logic we should even have, this
> is a form of LEM, namely:
> 
> ∀x G(x) v ∃x ~G(x)
> 
> Without knowning which one of the sides is
> true, and without knowing whether we look at
> the intented model of arithmetic or not.
> 
> Such a generalization is for example
> rejected in intuitionistic logic, which tries
> to regain some of the "finite" character of logic.
> 
> olcott schrieb:
>> In other words there really is no such thing as true
>> because "a fish" is neither true nor false in English.
> 

"This sentence is not true" is indeed not true and
thus satisfies its assertion that it is not true.

The fact that it and its negation are both not true
meets the criteria of incompleteness thus proving that
the notion of incompleteness is incorrect.

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