David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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)|
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
No references found.
Citations of this work BETA
A. P. Hazen & J. M. Davoren (2000). Russell's 1925 Logic. Australasian Journal of Philosophy 78 (4):534 – 556.
Gregory Landini (2013). The Evolution of Principia Mathematica; Bertrand Russell's Manuscripts and Notes for the Second Edition. History and Philosophy of Logic 34 (1):79-97.
Similar books and articles
Brice Halimi (2011). The Versatility of Universality inPrincipia Mathematica. History and Philosophy of Logic 32 (3):241-264.
Peter Milne (2008). Russell's Completeness Proof. History and Philosophy of Logic 29 (1):31-62.
Gregory Landini (2010). Russell. Routledge.
Saul A. Kripke (2005). Russell's Notion of Scope. Mind 114 (456):1005-1037.
I. Grattan-Guinness (1984). Notes on the Fate of Logicism Fromprincipia Mathematicato Gödel's Incompletability Theorem. History and Philosophy of Logic 5 (1):67-78.
Gregory Landini (1987). Russell's Substitutional Theory of Classes and Relations. History and Philosophy of Logic 8 (2):171-200.
Gregory Landini (2000). Quantification Theory in *9 of Principia Mathematica. History and Philosophy of Logic 21 (1):57-77.
Bernard Linsky (2011). The Evolution of Principia Mathematica: Bertrand Russell's Manuscripts and Notes for the Second Edition. Cambridge University Press.
Gregory Landini (2005). Quantification Theory in *8 ofPrincipia Mathematicaand the Empty Domain. History and Philosophy of Logic 26 (1):47-59.
Added to index2009-01-28
Total downloads35 ( #93,308 of 1,726,249 )
Recent downloads (6 months)3 ( #231,316 of 1,726,249 )
How can I increase my downloads?