## Psychology Dictionary of ArgumentsHome | |||

| |||

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. | |||

Author | Concept | Summary/Quotes | Sources |
---|---|---|---|

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 |

> Counter arguments against **Hilbert**

> Counter arguments in relation to **Decidability**