|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. |
Variable/mathematics/logic/Frege: have nothing to do with change - arithmetic: has nothing to do with quantities like e.g. lengths - only with numbers.
II 83 f
Variable/Frege: not name of an "indeterminate" or "variable" number. - "x" has no properties (only in context) - "indeterminately": not an adjective but an adverb to the process of the calculation - "universality": not meaning but suggestion.
Letters are rarely names of numbers: π, i, e are not variables but constants.
Solution: E.g. "n" is used in the antecedent of a conditional sentence.
Number/Frege: E.g. "A variable takes a value." Here, the number must play both roles: as object it becomes a variable, as property it is called value.
Variable/Designation/Description/Frege: "x" designates nothing! - x only hints at numbers. - Therefore, e.g. "x² + 3x" designates nothing. - The whole function only indicates. - On the other hand, "sin" (sinus) is a sign that designates. - But not a law yet.
Law/Frege: e.g. "y = sin x"._____________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.
Die Grundlagen der Arithmetik Stuttgart 1987
Funktion, Begriff, Bedeutung Göttingen 1994
Logische Untersuchungen Göttingen 1993