|Predicativeness, redicativity, philosophy: concepts are predicative that do not come from the totality to which they refer. They can therefore be used without the danger of circularity. See also circularity, impredicativity, Poincaré._____________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. |
Predicative functions: f (x) - non-predicative: f(x^): Function as opposed to its values! - Predicative(s): function that is one step higher than its argument.
Class/predicative/totality/Principia Mathematica/Russell: each class can be defined by a predictive function - hence the totality of classes, of which one can sensibly say that a given term belongs to them or not, a legitimate entirety, although the entirety of functions, of which one can say that a given term fulfils them or not, is not a legitimate entirety.
Definition predicative function/Principia Mathematica/Russell: notation: j ! (x,y) (predicative function of x and y.) -
Def non-predicative/impredicative function/Principia Mathematica/Russell: function as opposed to its values: notation: j ! (x^, y^).
E. Picardi Alfred North Whitehead/Bertrand Russell: Principia Mathematica aus "Hauptwerke der Philosophie 20. Jahrhundert" , Eva Picardi u.a. Stuttgart 1992 p. 18
Non-predicative properties: E.g. having all the properties of a great commander - predicative: E.g. to be born in Corsica._____________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.
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986
Das ABC der Relativitätstheorie Frankfurt 1989
Probleme der Philosophie Frankfurt 1967
Die Philosophie des logischen Atomismus
Eigennamen, U. Wolf (Hg), Frankfurt 1993
Wahrheit und Falschheit
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996