The consistency of predicative fragments of Frege's Grundgesetze der Arithmetik

History and Philosophy of Logic 17 (1):209-220 (1996)

Authors
Richard Kimberly Heck
Brown University
Abstract
As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell?s Paradox being derivable in it.This system is, except for minor differences, full second-order logic, augmented by a single non-logical axiom, Frege?s Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, Q, is relatively interpretable in the simple predicative fragment. The philosophical significance of the result is discussed
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1080/01445349608837265
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 38,878
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

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.
Fregean Extensions of First‐Order Theories.John L. Bell - 1994 - Mathematical Logic Quarterly 40 (1):27-30.

View all 6 references / Add more references

Citations of this work BETA

Modality and Paradox.Gabriel Uzquiano - 2015 - Philosophy Compass 10 (4):284-300.
Predicative Fragments of Frege Arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
Comparing Peano Arithmetic, Basic Law V, and Hume’s Principle.Sean Walsh - 2012 - Annals of Pure and Applied Logic 163 (11):1679-1709.

View all 29 citations / Add more citations

Similar books and articles

Analytics

Added to PP index
2010-08-17

Total views
334 ( #13,901 of 2,319,040 )

Recent downloads (6 months)
5 ( #261,128 of 2,319,040 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature