Notre Dame Journal of Formal Logic 38 (3):437-474 (1997)

Authors
Richard Kimberly Heck
Brown University
Abstract
Frege's intention in section 31 of Grundgesetze is to show that every well-formed expression in his formal system denotes. But it has been obscure why he wants to do this and how he intends to do it. It is argued here that, in large part, Frege's purpose is to show that the smooth breathing, from which names of value-ranges are formed, denotes; that his proof that his other primitive expressions denote is sound and anticipates Tarski's theory of truth; and that the proof that the smooth breathing denotes, while flawed, rests upon an idea now familiar from the completeness proof for first-order logic. The main work of the paper consists in defending a new understanding of the semantics Frege offers for the quantifiers: one which is objectual, but which does not make use of the notion of an assignment to a free variable
Keywords Frege  Semantics
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DOI 10.1305/ndjfl/1039700749
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References found in this work BETA

Quantifiers and Relative Clauses I.Gareth Evans - 1977 - Canadian Journal of Philosophy 7 (3):467-536.
Frege and Semantics.Richard G. Heck - 2007 - Grazer Philosophische Studien 75 (1):27-63.
On the Consistency of the First-Order Portion of Frege's Logical System.Terence Parsons - 1987 - Notre Dame Journal of Formal Logic 28 (1):161-168.
Whence the Contradiction?George Boolos - 1993 - Aristotelian Society Supplementary Volume 67:211--233.

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Citations of this work BETA

Truth in Frege.Richard Heck & Robert May - forthcoming - In M. Glanzberg (ed.), Oxford Handbook of Truth. Oxford University Press.
Formal Arithmetic Before Grundgesetze.Richard Kimberly Heck - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 497-537.
Frege's Proof of Referentiality.Øystein Linnebo - 2004 - Notre Dame Journal of Formal Logic 45 (2):73-98.
On a Consistent Subsystem of Frege's Grundgesetze.John P. Burgess - 1998 - Notre Dame Journal of Formal Logic 39 (2):274-278.

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Similar books and articles

Grundgesetze der Arithmetic I §10.Richard Heck - 1999 - Philosophia Mathematica 7 (3):258-292.
Frege and Semantics.Richard G. Heck - 2007 - Grazer Philosophische Studien 75 (1):27-63.
Referentiality in Frege's Grundgesetze.Martin Edward - 1982 - History and Philosophy of Logic 3 (2):151-164.

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