|Propositional function: open sentence E.g. "Something is green", "x is green" - neither true nor false. A propositional function has an argument position (variable) in which an expression can be inserted. Only after inserting we can decide whether the then complete sentence is true or false._____________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. |
Bertrand Russell on Propositional Functions - Dictionary of Arguments
Propositional functions/Russell/Gödel: always have something ambiguous, because of the variables - (Frege: somewhat unsaturated).
Propositional function/Terminology/Principia Mathematica/Russell: if we want to speak of the Propositional function that "x is hurt" corresponds to, we will write: "x ^ is hurt" and "x is hurt" is an ambiguous value thereof. ((s) x^: class of x).
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Statement function/russell: any expression which has one or more indefinite parts and which becomes a statement when the indefinite part is determined. Example "x is red".
A propositional function can be always true (x = x, necessary), sometimes true (x = human, possible) or never true (x = unicorn, impossible).
Some predicates can only be attributed to statement functions and not to statements.
_____________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.
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986
The ABC of Relativity, London 1958, 1969
Das ABC der Relativitätstheorie Frankfurt 1989
The Problems of Philosophy, Oxford 1912
Probleme der Philosophie Frankfurt 1967
"The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202
Die Philosophie des logischen Atomismus
Eigennamen, U. Wolf (Hg), Frankfurt 1993
On the Nature of Truth and Falsehood, in: B. Russell, The Problems of Philosophy, Oxford 1912 - Dt. "Wahrheit und Falschheit"
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996