# Psychology Dictionary of Arguments

Home

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