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

Journal of Philosophical Logic 25 (6):597 - 615 (1996)
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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
 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: 9,360
External links
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA
    Similar books and articles

    Monthly downloads

    Added to index


    Total downloads

    22 ( #65,949 of 1,088,854 )

    Recent downloads (6 months)

    1 ( #69,666 of 1,088,854 )

    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.