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Single Idea 13839

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

Full Idea

For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier.

Gist of Idea

Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers

Source

Ian Hacking (What is Logic? [1979], §11)

Book Ref

'A Philosophical Companion to First-Order Logic', ed/tr. Hughes,R.I.G. [Hackett 1993], p.242

A Reaction

I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea...

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]