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Single Idea 15595
[filed under theme 5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
]
Full Idea
In the 'algebraic' approach to variables, we move from a quantified sentence to the term specifying a property (the λ-term), and then reducing to the algebraic operations for atomic formulas.
Gist of Idea
The 'algebraic' account of variables reduces quantification to the algebra of its component parts
Source
Kit Fine (Semantic Relationism [2007], 1.C)
Book Ref
Fine,Kit: 'Semantic Relationism' [OUP 2007], p.13
A Reaction
[Bealer is a source for this view] Fine describes it as an 'algebra of operations'. I presume this is a thoroughly formalist approach to the matter, which doesn't seem to get to the heart of the semantic question.
The
19 ideas
with the same theme
[symbols which do not yet have a determined value]:
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5772
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The idea of a variable is fundamental
[Russell]
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14114
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Variables don't stand alone, but exist as parts of propositional functions
[Russell]
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17699
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Variables are auxiliary notions, and not part of the 'eternal' essence of logic
[Schönfinkel]
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7784
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'Object' is a pseudo-concept, properly indicated in logic by the variable x
[Wittgenstein]
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12221
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'Corner quotes' (quasi-quotation) designate 'whatever these terms designate'
[Quine]
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1618
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We study bound variables not to know reality, but to know what reality language asserts
[Quine]
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13839
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Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers
[Hacking]
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17558
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Variables are just like pronouns; syntactic explanations get muddled over dummy letters
[Inwagen]
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9148
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I think of variables as objects rather than as signs
[Fine,K]
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15590
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It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that
[Fine,K]
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15591
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In separate expressions variables seem identical in role, but in the same expression they aren't
[Fine,K]
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15592
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The usual Tarskian interpretation of variables is to specify their range of values
[Fine,K]
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15593
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Variables can be viewed as special terms - functions taking assignments into individuals
[Fine,K]
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15595
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The 'algebraic' account of variables reduces quantification to the algebra of its component parts
[Fine,K]
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15594
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'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification
[Fine,K]
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15409
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All occurrences of variables in atomic formulas are free
[Burgess]
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13696
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When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity
[Sider]
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9135
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We now see that generalizations use variables rather than abstract entities
[Sorensen]
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12797
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If plural variables have 'some values', then non-count variables have 'some value'
[Laycock]
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