[FOM] induction and reducibility

[Robert Black]

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.

Robert
(from gloomy but dry Berlin)

>Dear FOMs
>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 
>induction.
>Any thoughts on this question?