Philosophy Lexicon of Arguments

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
Leibniz, G.W.
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Decidability Berka I 329
Decision problem/Logic/Berka: appeared historically for the first time in Leibniz with the idea of a purely arithmetical "ars iudicandi".
Behmann: (1922): "The main problem of modern logic".
Ackermann: (1954):
I. It is to be decided with exactly stated means, whether a relevant formula of a (logical) calculus is valid.
II. If it is not universal, it is to be decided whether it is valid in none of the areas or whether it is valid in an area. If it is valid in any area, one must determine which cardinal number this area has.
III. It is to be decided whether a relevant formula is valid in all areas with a finite number of elements or not."
Berka: this is a basically semantic formulation of the E problem.
E Problem/syntactical: it is to be decided with the help of exactly defined processes that have to fulfill certain conditions whether a relevant formula of a calculus is provable or refutable.
Statement Calculus/E-Problem: by Lukasiewicz (1921) Post (19219, Wittgenstein (1921) positively solved.

Lei II
G. W. Leibniz
Philosophical Texts (Oxford Philosophical Texts) Oxford 1998

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

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Ed. Martin Schulz, access date 2017-04-23