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Single Idea 15590

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

Full Idea

Once Frege had provided a clear syntactic account of variables and once Tarski had supplemented this with a rigorous semantic account, it would appear that there was nothing more of significance to be said.

Gist of Idea

It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that

Source

Kit Fine (Semantic Relationism [2007], 1)

Book Ref

Fine,Kit: 'Semantic Relationism' [OUP 2007], p.6

A Reaction

He later remarks that there are now three semantic accounts: the Tarskian, the instantial, and the algebraic [see xref ideas]. He offers a fourth account in his Semantic Relationism. This grows from his puzzles about variables.

Related Ideas

Idea 15587 That two utterances say the same thing may not be intrinsic to them, but involve their relationships [Fine,K]

Idea 15592 The usual Tarskian interpretation of variables is to specify their range of values [Fine,K]

Idea 15594 'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification [Fine,K]

Idea 15595 The 'algebraic' account of variables reduces quantification to the algebra of its component parts [Fine,K]

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]