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2010 Syntax in Basic Laws §§29–32
Bryan Pickel
Notre Dame J. Formal Logic 51(2): 253-277 (2010). DOI: 10.1215/00294527-2010-016


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.


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Bryan Pickel. "Syntax in Basic Laws §§29–32." Notre Dame J. Formal Logic 51 (2) 253 - 277, 2010.


Published: 2010
First available in Project Euclid: 11 June 2010

zbMATH: 1205.03011
MathSciNet: MR2667936
Digital Object Identifier: 10.1215/00294527-2010-016

Primary: 00A30, 03A05

Rights: Copyright © 2010 University of Notre Dame


Vol.51 • No. 2 • 2010
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