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From: Mild Shock <janburse@fastmail.fm>
Newsgroups: sci.logic,comp.theory
Subject: Re: Truth Bearer or Truth Maker
Date: Thu, 25 Jul 2024 11:47:27 +0200
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But its even not necessary to follow such
a strict program to regain the "finite"
character of logic. Even if we stick to

classical logic, Gödels incompleteness
theorem shows that this classical logic
stil has some "finite" limitations,

in that a axiomatization of arithmetic,
will still not fully capture the intended
model of arithmetic, in that the axiomatization

will necessarily have at least one sentences
which is not truth bearing in Olcotts words:

https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems

Putting another Olcott label on the bottle
doesn't change the content of the bottle.

Mild Shock schrieb:
> 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.
>