On the consistency of the Δ11-CA fragment of Frege's grundgesetze

Journal of Philosophical Logic 31 (4):301-311 (2002)
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)
DOI 10.1023/A:1019919403797
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 23,651
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

Add more references

Citations of this work BETA
Gabriel Uzquiano (2015). Modality and Paradox. Philosophy Compass 10 (4):284-300.
Bernard Linsky & Edward N. Zalta (2006). What is Neologicism? Bulletin of Symbolic Logic 12 (1):60-99.

View all 10 citations / Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

49 ( #98,171 of 1,902,713 )

Recent downloads (6 months)

9 ( #99,313 of 1,902,713 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.