Synthese 121 (3):309-328 (1999)

Authors
Kai Wehmeier
University of California, Irvine
Abstract
In this paper, I consider two curious subsystems ofFrege's Grundgesetze der Arithmetik: Richard Heck's predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T in monadic second-order logic, consisting of axiom V and 1 1-comprehension (in a language containing anabstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both Heck and T prove the existence of infinitely many non-logical objects (T deriving,moreover, the nonexistence of the value-range concept). Some implications concerning the interpretation of Frege's proof of referentiality and the possibility of classifying any of these subsystems as logicist are discussed. Finally, I explore the relation of T toCantor's theorem which is somewhat surprising.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
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DOI 10.1023/A:1005203526185
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References found in this work BETA

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.

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Citations of this work BETA

Impredicativity and Paradox.Gabriel Uzquiano - 2019 - Thought: A Journal of Philosophy 8 (3):209-221.
What is Neologicism?Bernard Linsky & Edward N. Zalta - 2006 - Bulletin of Symbolic Logic 12 (1):60-99.
The Logical Significance of Assertion: Frege on the Essence of Logic.Walter B. Pedriali - 2017 - Journal for the History of Analytical Philosophy 5 (8).

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