Journal of Philosophical Logic 31 (4):301-311 (2002)

Authors
Kai Wehmeier
University of California, Irvine
Abstract
It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing Δ₁¹-comprehension schema would already be inconsistent. In the present paper, we show that this is not the case
Keywords comprehension  consistency proofs  Frege  recursive saturation  Russell's paradox  second-order logic  value range
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DOI 10.1023/A:1019919403797
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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.
Models of Peano Arithmetic.Richard Kaye - 1991 - Clarendon Press.
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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Citations of this work BETA

Impredicativity and Paradox.Gabriel Uzquiano - 2019 - Thought: A Journal of Philosophy 8 (3):209-221.
Modality and Paradox.Gabriel Uzquiano - 2015 - Philosophy Compass 10 (4):284-300.
Notions of Invariance for Abstraction Principles.G. A. Antonelli - 2010 - Philosophia Mathematica 18 (3):276-292.

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