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Single Idea 5772

[filed under theme 5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic ]

Full Idea

I take the notion of the variable as fundamental.

Clarification

A variable is something like x in algebra, which has a value which isn't fixed

Gist of Idea

The idea of a variable is fundamental

Source

Bertrand Russell (On Denoting [1905], p.42)

Book Ref

Russell,Bertrand: 'Logic and Knowledge', ed/tr. Marsh,Robert Charles [Routledge 1956], p.42

A Reaction

A key idea of twentieth century philosophy, derived from Frege and handed on to Quine. A universal term, such as 'horse', is a variable, for which any particular horse can be its value. You can calculate using x, and generalise about horses.

The 19 ideas with the same theme [symbols which do not yet have a determined value]:

5772 The idea of a variable is fundamental [Russell]
14114 Variables don't stand alone, but exist as parts of propositional functions [Russell]
17699 Variables are auxiliary notions, and not part of the 'eternal' essence of logic [Schönfinkel]
7784 'Object' is a pseudo-concept, properly indicated in logic by the variable x [Wittgenstein]
12221 'Corner quotes' (quasi-quotation) designate 'whatever these terms designate' [Quine]
1618 We study bound variables not to know reality, but to know what reality language asserts [Quine]
13839 Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
17558 Variables are just like pronouns; syntactic explanations get muddled over dummy letters [Inwagen]
9148 I think of variables as objects rather than as signs [Fine,K]
15590 It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that [Fine,K]
15591 In separate expressions variables seem identical in role, but in the same expression they aren't [Fine,K]
15592 The usual Tarskian interpretation of variables is to specify their range of values [Fine,K]
15593 Variables can be viewed as special terms - functions taking assignments into individuals [Fine,K]
15595 The 'algebraic' account of variables reduces quantification to the algebra of its component parts [Fine,K]
15594 'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification [Fine,K]
15409 All occurrences of variables in atomic formulas are free [Burgess]
13696 When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider]
9135 We now see that generalizations use variables rather than abstract entities [Sorensen]
12797 If plural variables have 'some values', then non-count variables have 'some value' [Laycock]