[FOM] induction and reducibility
Mongre at gmx.de
Wed Oct 24 02:48:51 EDT 2007
Poincare is right in that without reducibility you can't get
unrestricted induction. Russell thought you could, and in Appendix B
of the second edition tried to prove it, but as Goedel pointed out in
his article on Russell in the Schilpp volume the proof is fallacious.
For full details see John Myhill - 'The Undefinability of the Set of
Natural Numbers in the Ramified Principia' in George Nakhnikian (ed)
- Bertrand Russell's Philosophy.
(from gloomy but dry Berlin)
>In section 4 (dedicated to the axiom of reducibility) of his last
>paper "La logique de l'infini" ("The logic of infinity"), published
>in Scientia 12 (1912) 1-16 and reprinted in the book Dernieres
>Pensees (Flammarion, 1913, translated as Last Essays, Dover 1963)
>Henri Poincare says that he suspects that Russell's axiom of
>reducibility is just another form of the principle of mathematical
>Any thoughts on this question?
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