[FOM] The lure of the infinite

Alasdair Urquhart urquhart at cs.toronto.edu
Sun Feb 19 10:07:16 EST 2006

Martin Davis wrote, in reply to Arnon Avron:

> This is bad history and dubious prophecy. Deaf ears are exactly what
> Berkeley's work fell on.

This doesn't seem quite accurate, in that the great Scottish
mathematician Colin Maclaurin wrote a two volume "Treatise
on Fluxions" (1742) specifically designed to reply to Berkeley's
criticism.  Maclaurin's basic idea is to take the notions of
motion and velocity as primitive.  Some excerpts are printed
in Ewald's excellent collection "From Kant to Hilbert."

That said, it is true that a fully satisfactory foundation
for the infinitesimal calculus did not appear until the
nineteenth century, and Martin Davis's remarks about
Euler's freewheeling methods are on the mark.

Alasdair Urquhart

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