Notre Dame Journal of Formal Logic 51 (2):253-277 (2010)

Bryan Pickel
University of Glasgow
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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DOI 10.1215/00294527-2010-016
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References found in this work BETA

Frege's Proof of Referentiality.Øystein Linnebo - 2004 - Notre Dame Journal of Formal Logic 45 (2):73-98.
Grundgesetze der Arithmetik I §§29‒32.Richard G. Heck - 1997 - Notre Dame Journal of Formal Logic 38 (3):437-474.
Semantic Descent.Joan Weiner - 2005 - Mind 114 (454):321-354.
Referentiality in Frege's Grundgesetze.Martin Edward - 1982 - History and Philosophy of Logic 3 (2):151-164.
Referentiality in Frege's "Grundgesetze". E. Martin - 1982 - History and Philosophy of Logic 3 (2):151.

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The Proper Treatment of Variables in Predicate Logic.Kai Wehmeier - 2018 - Linguistics and Philosophy 41 (2):209-249.

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