The definability of the set of natural numbers in the 1925 principia mathematica

Journal of Philosophical Logic 25 (6):597 - 615 (1996)
  Copy   BIBTEX


In his new introduction to the 1925 second edition of Principia Mathematica, Russell maintained that by adopting Wittgenstein's idea that a logically perfect language should be extensional mathematical induction could be rectified for finite cardinals without the axiom of reducibility. In an Appendix B, Russell set forth a proof. Godel caught a defect in the proof at *89.16, so that the matter of rectification remained open. Myhill later arrived at a negative result: Principia with extensionality principles and without reducibility cannot recover mathematical induction. The finite cardinals are indefinable in it. This paper shows that while Gödel and Myhill are correct, Russell was not wrong. The 1925 system employs a different grammar than the original Principia. A new proof for *89.16 is given and induction is recovered



    Upload a copy of this work     Papers currently archived: 94,517

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles


Added to PP

98 (#175,734)

6 months
14 (#257,475)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Gregory Landini
University of Iowa

References found in this work

Russell's Mathematical Logic.Kurt Gödel - 1944 - In The Philosophy of Bertrand Russell. Northwestern University Press. pp. 123-154.

Add more references