Re: Truth Bearer or Truth Maker

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.