|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. |
Number variables/Prior: no names. E.g. if exactly 3 things φ and exactly 4 things ψ, then more things are φ than ψ. Then "3" no name but inseparable part of verb operator"Exactly 3 things __".
Variables/Quine: (bound) can only stand for names. So for things, not for sentences.
QuineVsFrege: names are not for sentences, only for things - E.g. "For a φ, φx" is the only way to read this, that there is at least one thing, so that x "does" this thing.
Quine himself does not do that but he has "E" for "is element of".
Bound variable/name/Prior: E.g. open sentence "x is red-haired": what is x? - It depends on how we stand for" understanding:
a) x is for a name, such as "Peter" (Substitute)
b) or object Peter
PriorVsQuine: bound variables can also stand for sentences: "J. believes that p" (anything), then stands for a sentence.
A propos I 93 (external):
Sentece Variable/Wittgenstein: Tractatus: The term presupposes forms of all sentences in which it can occur - Tractatus 3.312: It is therefore represented by the general form of the sentences which it characterizes - Witt.: namely in this form the expression will be constant and everything else can be variable - sentence variable: Aristotle's innovation "a" for a whole sentence.
Bound variables/Prior: represent logical proper names - "For an x: 1. x φ-s, 2. nothing else than x φ-s and 3. it is not the case that x ψ-s".
Bound variable/PriorVs American logicians: not any stands for a name._____________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.
Objects of thought Oxford 1971
Arthur N. Prior
Papers on Time and Tense 2nd Edition Oxford 2003