FOM: mathematical induction

Stephen G Simpson simpson at
Thu Feb 25 20:43:45 EST 1999

Martin Davis writes:
 > 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.

OK, so much for Poincare.  But what about modern-day heirs of
Poincare, such as Thom and other modern-day mathematicians, inspired
by Poincare, who are opposed to mathematical logic?  And what about
Detlefsen and others?  It's reasonable to ask whether their anti-logic
remarks make sense in the *present* historical context, i.e., in the
light of what we know now.

-- Steve

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