[FOM] Fwd: Re: reply to S.S. Kutateladze (19 Mar)

Gabriel Stolzenberg gstolzen at math.bu.edu
Sun Apr 1 21:29:33 EDT 2007

   In his March 19 reply to my "Antonino Drago on Leibniz," S.S.
Kutateladze wrote,

> It is at least "impolite" or "progressivist's to speak of
> infinitesimals or monads of Leibniz or the nils or zeros of
> Euler or the hyperreals of Robinson as shorthand notes.

   I don't agree.  These are factual claims and should be treated
as such.  By the way, who said that the hyperreals of Robinson are
shorthand notes?  And on what evidence?

> A progressivist considers the current state of affairs as better
> then anything possible ever before since by the definition he or
> she favors progress, implying that newer things are better, and
> the newer guys are smarter. This is not so....

   Except for the bit about newer guys being smarter and the fact
that things AREN'T better BECAUSE they're new, the progressivist
has it pretty much right, at least for mathematics.  It's not that
new things are better, more progressive, but rather that, among
the new things, we value mainly those that ARE better.  Or rather,
it's not the new things alone that matter but how they contribute
to the picture as a whole.  That's what we want to be better.  E.g.,
when Robinson published his book, that was a new contribution that
enriched our picture of mathematics, making it better than the one
that preceded it.

   Gabriel Stolzenberg

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