The Consistency of predicative fragments of frege’s grundgesetze der arithmetik

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


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

Author's Profile

Richard Kimberly Heck
Brown University


Added to PP

575 (#13,880)

6 months
42 (#23,847)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?