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Ideas for 'Parmenides', 'Structures and Structuralism in Phil of Maths' and 'Quine on Quantifying In'

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2 ideas

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
12222 Substitutional quantification is referential quantification over expressions [Fine,K]
     Full Idea: Substitutional quantification may be regarded as referential quantification over expressions.
     From: Kit Fine (Quine on Quantifying In [1990], p.124)
     A reaction: This is an illuminating gloss. Does such quantification involve some ontological commitment to expressions? I feel an infinite regress looming.
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10175 Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
     Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types.