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

Kai Wehmeier
University of California, Irvine
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
Categories (categorize this paper)
Reprint years 2004
DOI 10.1023/A:1019919403797
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 69,043
Through your library

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.

View all 9 references / Add more references

Citations of this work BETA

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

View all 28 citations / Add more citations

Similar books and articles


Added to PP index

Total views
112 ( #103,149 of 2,498,734 )

Recent downloads (6 months)
1 ( #422,193 of 2,498,734 )

How can I increase my downloads?


My notes