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)|
References found in this work BETA
No references found.
Citations of this work BETA
Russell's 1925 Logic.A. P. Hazen & J. M. Davoren - 2000 - Australasian Journal of Philosophy 78 (4):534 – 556.
The Evolution of Principia Mathematica; Bertrand Russell's Manuscripts and Notes for the Second Edition.Gregory Landini - 2013 - History and Philosophy of Logic 34 (1):79-97.
Similar books and articles
The Triumph of Types: Principia Mathematica's Impact on Computer Science.Robert L. Constable - unknown
The Versatility of Universality inPrincipia Mathematica.Brice Halimi - 2011 - History and Philosophy of Logic 32 (3):241-264.
Notes on the Fate of Logicism Fromprincipia Mathematicato Gödel's Incompletability Theorem.I. Grattan-Guinness - 1984 - History and Philosophy of Logic 5 (1):67-78.
Russell's Substitutional Theory of Classes and Relations.Gregory Landini - 1987 - History and Philosophy of Logic 8 (2):171-200.
Quantification Theory in *9 of Principia Mathematica.Gregory Landini - 2000 - History and Philosophy of Logic 21 (1):57-77.
The Evolution of Principia Mathematica: Bertrand Russell's Manuscripts and Notes for the Second Edition.Bernard Linsky - 2011 - Cambridge University Press.
Quantification Theory in *8 ofPrincipia Mathematicaand the Empty Domain.Gregory Landini - 2005 - History and Philosophy of Logic 26 (1):47-59.
Added to index2009-01-28
Total downloads44 ( #118,110 of 2,169,706 )
Recent downloads (6 months)1 ( #345,460 of 2,169,706 )
How can I increase my downloads?