Philosophy Dictionary of Arguments

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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.

Author Concept Summary/Quotes Sources

Bertrand Russell on Propositional Functions - Dictionary of Arguments

Propositional functions/Russell/Gödel: always have something ambiguous, because of the variables - (Frege: somewhat unsaturated).
I 26
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).
- - -
VI 73
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).
VI 74
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.

Russell I
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986

Russell II
B. Russell
The ABC of Relativity, London 1958, 1969
German Edition:
Das ABC der Relativitätstheorie Frankfurt 1989

Russell IV
B. Russell
The Problems of Philosophy, Oxford 1912
German Edition:
Probleme der Philosophie Frankfurt 1967

Russell VI
B. Russell
"The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202
German Edition:
Die Philosophie des logischen Atomismus
Eigennamen, U. Wolf (Hg), Frankfurt 1993

Russell VII
B. Russell
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

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Ed. Martin Schulz, access date 2022-01-28
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