Sujet : "undecidable" / "unentscheidbar" (Was Analytic Truth-makers)
De : janburse (at) *nospam* fastmail.fm (Mild Shock)
Groupes : comp.theory sci.logicDate : 23. Jul 2024, 23:02:01
Autres entêtes
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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_SystemsMild 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