FOM: mathematical induction

Martin Davis davism at
Thu Feb 25 19:32:51 EST 1999

At 05:01 PM 2/25/99 -0500, simpson at wrote:

>Poincare and Detlefsen want to say that mathematical induction is
>illogical.  What are these people talking about?  What's going on

Poincare's position needs to be understood in historical context. There was
no first order logic. There was logicism: Frege's that had turned out to be
inconsistent, and Poincare was especially interesteed in Russell's. Russell
proposed to develop arithmetic from "logic", and Poincare was attacking this

There's a lot more than could be said about this, but Poincare's objections
had nothing to do with formalized arithmetic as we understand it today, and
certainly was not directly relevant to the more sophisticated remarks of
Colin McClarty.


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