|Variables, philosophy: variables are symbols in statements or logical formulas, in the place of which various, more precise determinations, such as constants or names of objects, can be inserted. In logic, free and bound variables are distinguished. Free variables, which are not bound by a quantifier such as (Ex) or (x), do not form a statement yet but a statement function such as e.g. "Fx" - "Something is F". Numbers or objects are not variable entities. The variability consists in the applicability of more than one possible value. See also free variables, bound variables, constants, individual constants, individual variables, substitution, substitutability, logic, statements, statement function, formulas._____________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 Variables - Dictionary of Arguments
Variables/Russell/Gödel: exist only to enable truth function. - Finite/Infinite/Ramsey: the problem of solving infinite propositions is not so critical. - Gödel: then Russell’s Apercu that propositions about classes can be interpreted as propositions about their elements literally becomes true, provided that n is the number of the (finite) individuals in the world, and provided we neglect the zero class.
Pseudo-variable/Peano/Russell: the symbol (x). φ x denotes a particular proposition and there is no sense of difference between (x). j x and (y). φ y if they occur in the same context. - ((s)> Quine: alphabetical variant). - o is x in (x) φ x not an ambiguous part of an expression and such an expression itself remains the bearer of a very specific meaning despite the ambiguity of the x in φ x. Pseudo-variables: exist if the extension does not go over the entire range. A proposition with a state of affairs x is not a function of x. Extension: is the function of which all or some values are asserted.
Ambiguous assertion and the real variable: any arbitrary value φ x of the function φ x^ can be asserted. - Real Variable: φx. - If x varies, a different proposition results.
Pseudo-variable: is obtained if we put a universal quantifier before it.
Pseudo-Variable: several possible values can be meant. Descriptions always contain pseudo-variables. Sentences without pseudo-variables: are observation sentences e.g. This is red.
Pseudo-Variable/Principia Mathematica/Russell/(s): E.g. (y).φ(x,y), which is a function of x - here y is a pseudo-variable, x is the real variable. - ((s) E.g. everything smaller than x - instead of y it could also say z here)._____________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