Economics Dictionary of ArgumentsHome | |||
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Definability: is about the question whether the meanings of linguistic elements and symbols of a statement in a given frame, a theory, a model or a system can be stated in a way that these elements and symbols can be replaced by other symbols. This replacement is to aid understanding. Is this the case new symbols (words, terms, links) can be created the meaning of which can be understood from the symbols already defined. Therefore these new symbols are definable. See also definition, context definition, implicit definition, explicit definition, models, systems, theories, foundation._____________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 |
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Alfred Tarski on Definability - Dictionary of Arguments
Berka I 481 Features/Class/Definability/Tarski: a property E of a class is only definable when there is a propositional function, that determines E. >Propositional functions. Then you can show that there are also other characteristics of classes: E.g. emptiness, containing only one element, two , etc. Tarski: problem: Containing an infinite number of elements cannot be defined.(1) >Cardinality, >Element relation, >Sets, >Set theory, >Subsets. 1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935 - - - Skirbekk I 188 Def definable/Tarski: an object is definable when there is a propositional function that defines it - the term is purely mathematical, it expresses a property (called a class) of mathematical objects.(2) >Mathematical entities, >Classes. 2. A.Tarski, „Die semantische Konzeption der Wahrheit und die Grundlagen der Semantik“ (1944) in: G. Skirbekk (ed.) Wahrheitstheorien, Frankfurt 1996_____________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. |
Tarski I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 Skirbekk I G. Skirbekk (Hg) Wahrheitstheorien In Wahrheitstheorien, Gunnar Skirbekk, Frankfurt 1977 |