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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic

[symbols which do not yet have a determined value]

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