|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. |
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|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 - then you can show that there are also other characteristics of classes: E.g. emptiness, containing only one element, two , etc. - ((s) cardinality) - Tarski: problem: Containing an infinite number of elements can not be defined.
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._____________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.
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983
K. Berka/L. Kreiser
Logik Texte Berlin 1983
G. Skirbekk (Hg)
Wahrheitstheorien Frankfurt 1977