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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 11:42:27 +0200
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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.