Syntax in Basic Laws 29-32

Bryan Pickel

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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.

Original languageEnglish
Pages (from-to)253-277
Number of pages25
JournalNotre Dame Journal of Formal Logic
Volume51
Issue number2
DOIs
Publication statusPublished - 2010

Keywords

  • philosophy of logic
  • Frege's proof of referentiality

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