FOM: attitudes of core mathematicians and applied model theoriststoward f.o.m.
marksa at vms.huji.ac.il
Thu Jan 27 11:04:58 EST 2000
Re: FOM: attitudes of core mathematicians and applied model
Thu, 27 Jan 2000 17:16:29 +0200
Mark Steiner <marksa at vms.huji.ac.il>
Steve Stevenson <steve at cs.clemson.edu>
simpson at math.psu.edu, fom at math.psu.edu
1 , 2 , 3 , 4 , 5
Steve Stevenson wrote:
> I think this is a great point and perhaps hints at another point:
> "foundationalists," regardless of discipline, probably have more in
> common that they know.
I'm sure this is true, though impossible to know, on pain of
logical paradox or other.
It wasn't until 1948 that philosophy of science
> first asked (Hempel) what the scientists themselves taught in the way
> of the basics of science and how they (scientists) actually go about
> doing theory.
This is not true; I believe there are scores of counter-examples
Britain, the European continent and the United States, well before
1948. And I actually think that Ernest Nagel would be a better example
than Hempel (I studied with both of them). Aside from his work on
philosophy of science, influenced by scientific practice, there is of
course his famous work (with Newman), Goedel's Proof. Though it has its
detractors on mathematical grounds, it did convey the immense interest
of the proof to the "general" population.
On the other hand, Steve could point to one of the greatest
philosophers of science ever, Nelson Goodman, who did believe that
philosophers should keep their distance from scientists (my mentor,
Prof. Sidney Morgenbesser, told me that Goodman used to warn him against
"whoring" after scientists). He felt that philosophy should be free to
criticize the scientists, if they strayed from the path of Empiricism
and Nominalism. This does not mean that he felt that scientists should
stop what they are doing--but, as he put it, that philosophers are
around to "keep the books."
And this reminds me that I should have mentioned precisely this
critical role for philosophy and maybe even f.o.m. concerning science
and mathematics. Goodman's Empiricist predecessor, George Berkeley,
leveled a devastating critique at tne Newton/Leibniz infinitesimal
calculus, calling the differential "the ghost of a departed quantity."
I believe the consensus in the mathematical and philosophical community
is that Berkeley was right, but that mathematicians were correct to
ignore his criticism during the pioneer days of analysis. I think that
f.o.m. can play this critical role today better than philosophers, given
the advanced technical training often needed for mastering the practices
to be criticized.
Much suprise.... It took another 30 years for philosophy
> to act on the 1948 insights.
I'm dying to know: what happened in philosophy in 1978 (aside from my
arrival in Jerusalem)?
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