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From: Mild Shock <janburse@fastmail.fm>
Newsgroups: comp.theory,sci.logic
Subject: Re: Analytic Truth-makers
Date: Tue, 23 Jul 2024 22:57:39 +0200
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Since generations logicians have called sentences
which you clumsily call "not a truth-bearer",
simple called "undecidable" sentences.

A theory is incomplete, if it has undecidable
sentences. There is a small difference between
unprovable and undecidable.

An unprovable senetence A is only a sentence with:

~True(L, A).

An undecidable sentence A is a sentence with:

~True(L, A) & ~True(L, ~A)

Meaning the sentence itself and its complement
are both unprovable.

olcott schrieb:
> ~True(L,x) ∧ ~True(L,~x)
> means that x is not a truth-bearer in L.
> It does not mean that L is incomplete