Philosophy Lexicon of Arguments

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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.

Author Item Summary Meta data
I 198f
Variable/description/deputy/GeachVsCarnap: in its rules for descriptions, e.g. ""___ ___ (ix)(...x...)___ ___" etc. the strokes do not function, as Carnap believes as vacancies (substitutes) but as variables! - Carnap thinks, however, if he renames them, he avoids his problems with variables.
I 199, 200
Variables/Constants/GeachVsCarnap: Carnap does not distinguish between them, as he himself says: E.g. Carnap: "If "Q" is a constant pr (determined or indeterminate), then the sentences (Prague)" (city),"Q(a)" are all equally derivable from "Q(x)". - Geach: "determined or undetermined", shows that the alleged "constant pr" is used as a variable. - Solution: "For all "Q" if ..." - but then we have a variable ""Q"" that contains quotes as part of itself.
I 201
Free Variables/Strawson: E.g. (A) In "x is a human", "x" is a free variable. - Here, "x" does not occur as a free variable - because "x" is "x is a human" occurs as a free variable, the theorem (A) is true. - If (A) contained a free variable, it would not be a statement, but a propositional function.
I 203
Bound Variables/Use/Mention/Geach: in e.g. "x is a human being", "x" is needed, therefore it is a bound variable! (Bound by the quotes) - at the same time the expression is the name of a description, even if it does not denote anything. (> Denote/designate). - Names do not denote anything.

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.

Gea I
P.T. Geach
Logic Matters Oxford 1972

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Ed. Martin Schulz, access date 2018-06-21