Philosophy Dictionary of ArgumentsHome
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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. | |||
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A. Prior on Variables - Dictionary of Arguments
I 30 Number variables/Prior: variables are no names. E.g. if exactly 3 things φ and exactly 4 things ψ, then more things are φ than ψ. Then "3" is no name but an inseparable part of the verb operator "Exactly 3 things __". >Names, >Operators, >Predication, >Is, >Equality, >Equations, >Sets, >Set theory. I 33 Bound variables/Quine: bound variables can only stand for names. So for things, not for sentences. >Bound variables, cf. >Names of sentences, >Quantification, >Objects. 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. >Sentences, >"Stand for", >Names/Frege, >Sentences/Frege. Quine himself does not do that but he has "ε" for "is element of". >Element relation, >Is, >Predication. I 35 Bound variable/name/Prior: E.g. open sentence "x is red-haired": what is x? >Open sentences/propositional functions. 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. ad I 93 (external): Sentence 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 - Wittgenstein: 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. I 148 Bound variables/Prior: bound variables 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". I 164f Bound variable/PriorVs some American logicians: not any bound variable 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. 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. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
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Ed. Martin Schulz, access date 2024-04-16