Re: Truth Bearer or Truth Maker

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