Syntax in Basic Laws §§29–32

Notre Dame Journal of Formal Logic 51 (2):253-277 (2010)
Abstract
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 §§29–32 of The Basic Laws
Keywords philosophy of logic   Frege's proof of referentiality
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