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Syntax in Basic Laws \({\S}{\S}\)29-32. (English) Zbl 1205.03011

Summary: In order to accommodate his view that quantifiers are predicates of predicates within a type theory, Frege introduces a rule which allows a function name to be formed by removing a saturated name from another saturated name which contains it. This rule requires that each name has a rather rich syntactic structure, since one must be able to recognize the occurrences of a name in a larger name. However, I argue that Frege is unable to account for this syntactic structure. I argue that this problem undermines the inductive portion of Frege’s proof that all of the names of his system denote in \({\S}{\S}\)29–32 of The Basic Laws.

MSC:

03A05 Philosophical and critical aspects of logic and foundations
00A30 Philosophy of mathematics
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