Economics Dictionary of ArgumentsHome
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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._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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David Hilbert on Decidability - Dictionary of Arguments
Berka I 331 Undecidability/Predicate calculus 1st level/Goedel(1931)(1): Goedel shows with the "Arithmetication" ("Goedelisation") that the predicate calculus of the 1st level is undecidable. >Undecidability, >Gödel numbers. This was a shocking fact for the Hilbert program. Tarski (1939)(2): Tarski proved the undecidability of "Principia Mathematica" and related systems. He showed that it is fundamental, i.e. that it cannot be abolished. Rosser(3): Rosser generalized Goedel's proof by replacing the condition of the ω-consistency by that of simple consistency. >Consistency. 1. K. Goedel: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I., Mh. Math. Phys. 38, pp. 175-198. 2. A. Tarski: On undecidable statements in enlarged systems of logic and the concept of truth, JSL 4, pp. 105-112. 3. J. B. Rosser: Extensions of some theorems of Goedel and Church, JSL 1, pp. 87-91._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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Authors A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Concepts A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
