[FOM] The lure of the infinite

Arnon Avron aa at tau.ac.il
Sun Feb 19 15:54:46 EST 2006

On Sat, Feb 18, 2006 at 02:39:58PM -0800, Martin Davis wrote:
> This is bad history and dubious prophecy. Deaf ears are exactly what 
> Berkeley's work fell on. Certainly Euler paid no attention and did 
> beautiful work. It was only when the foundational issues 
> forced their way  into mathematical practice. that the 
> reforms were developed. 

The prophecy is indeed dubious, but not less dubious than other
prophecies we hear here so often on FOM (including yours). I tend 
to believe it, but I certainly cannot be certain, so I would not argue 
for it (or for any other prophecy).

  As for bad history: I was not talking about an immediate effect
on the mathematicians of the time, some of whon explicitly declared
that they have no time for rigor (a declaration that shows awareness
of the lack of rigor in their work!), and so were immune
to Bekeley's attack..  But in a long run I have 
no doubts that works like Berkeley's had their effect
(and just note how well his remarks on mathematics
are remembered in the history of mathematics!). You will never
convince me that mathematicians were not not aware of the problematic
foundations of analysis (especially when they have Euclide as the
golden standard of their time), and that the total elimination
of differentials in rigorous mathematical texts (but not in Physics!)
in favor of the complicated delta-epsilon approach was only because
this was forced by mathematical practice.

  Berkeley won at the end. If you think that what he had written had
contributed nothing to this victory, I would answer that this
is impossible. Anyway, I am not going to argue about this chapter
of the past anymore, and I am leaving you the right to have 
the final word in this debate. 

Arnon Avron

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