A Dictionary of Philosophy, Third Edition
. Symbol used to stand indefinitely for any one of a set of things or notions. It ranges over the members of the set. The members are its values and the set as its range. Individual variables, propositional variables, etc., range respectively over INDIVIDUALS, propositions, etc. Syntactical variables range over syntactical (i.e. logical) OPERATORS. A symbol assumed to stand for one thing alone throughout a given context is a constant. The thing in question may be unspecified. But with logical constants it is specified. The logical constants are terms like ‘and’, ‘or’, ‘not’, ‘implies’.
They are a subclass of logical operators (which go beyond them by including things like quantifiers (see QUANTIFICATION)). In school algebra, x, y, etc., are numerical variables, ranging over numbers, a, b, etc., are numerical constants; and ‘+’, ‘×’, etc., correspond to logical constants.
A variable is bound or, occasionally, apparent, if it occurs within the scope of a quantifier containing the same variable (see QUANTIFICATION); a bound variable is rather like a pronoun. Otherwise it is free or, occasionally, real; though the variable within the quantifier itself is sometimes called bound, sometimes neither. In (x) (Fxy), the second x is bound while the y is free; the first x can be called bound or neither. In mathematics a ‘real variable’ is one ranging over ‘real’, as against imaginary or complex, numbers.
For intervening variables see LOGICAL CONSTRUCTIONS.
A hidden variable is something unobserved but postulated to explain, by its variations, variations in observed phenomena that we cannot otherwise account for.
I.Copi, Introduction to Logic, 6th edn, Macmillan, 1982. (Elementary introduction. See its index under ‘variable’. For fuller treatment see, with its index, his Symbolic Logic, 5th edn, Macmillan, 1979 (treatment differs somewhat in different editions).)
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