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From: Mild Shock <janburse@fastmail.fm>
Newsgroups: comp.theory,sci.logic
Subject: "undecidable" / "unentscheidbar" (Was Analytic Truth-makers)
Date: Tue, 23 Jul 2024 23:02:01 +0200
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For example Gödel belongs to the generation of
logicians that use the term "undecidable".
In German the term is translated to "unentscheidbar":

Über formal unentscheidbare Sätze der Principia Mathematica und 
verwandter Systeme I" ("On Formally Undecidable Propositions of 
Principia Mathematica and Related Systems I")
https://en.wikipedia.org/wiki/On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems

Mild Shock schrieb:
> 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