Philosophy Lexicon of Arguments

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Decidability: a question, for example, whether a property applies to an object or not, is decidable if a result can be achieved within a finite time. For this decision process, an algorithm is chosen as a basis. See also halting problem, algorithms, procedures, decision theory.
 
Author Item Excerpt Meta data
Hilbert, D.
 
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Decidability Berka I 331
Undecidability/Predicate calculus 1st level/Gödel: Gödel shows with "Arithmetication" ("Gödelisation") that the predicate calculus of the 1st level is undecidable.
This was a shocking fact for the Hilbert program.
Tarski: (1939) Tarski proved the undecidability of Principia Mathematica and related systems. He showed that it is fundamental, i.e. that it cannot be abolished.
Rosser: Rosser generalized Gödel's proof by replacing the condition of the ω-consistency by that of simple consistency.

Brk I
K. Berka/L. Kreiser
Logik Texte Berlin 1983


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Ed. Martin Schulz, access date 2017-03-24