FOM: mathematical induction

[Martin Davis]

At 05:01 PM 2/25/99 -0500, simpson at math.psu.edu wrote:

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

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
program. 

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.

Martin