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Topic: [HM] Language of Discovery
Replies: 23   Last Post: Mar 15, 2001 1:04 PM

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Gordon Fisher

Posts: 367
Registered: 12/3/04
Re: [HM] Language of Discovery
Posted: Feb 25, 2001 4:05 PM
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"Samuel S. Kutler" wrote:

<< Don't most of us have mixed feelings about what the
subject matter of mathematics is? >>

Yes, most of us do. But a few hardy souls (no pun intended, but
there it is) have speculated about the nature of mathematics. Some
of them were even mathematicians, like Brouwer (intuitionism) and
Hilbert (formalism) and R L Wilder (not sure how to classify him).
I take it that Hardy didn't go as extensively into such foreign
fields as these two, which may be why he called his little book "A
Mathematician's Apology". I suppose Bertrand Russell, and Schroeder
before him would usually be classified as more logicians than
mathematicians, or simply as philosophers (no slight intended).
Same for Plato, Aristotle, Nicholas of Cusa, and so on. And there
are people like Isaac Newton, who occasionally philosophized a
little, for example, in his Principia mathematica _philosophiae_
naturalis (general scholium to Book III), or Albert Einstein, or
Erwin Schroedinger (e.g., What is Life?) or Werner Heisenberg (I
forget the title of his philosophical work), or a whole host of
physicists, especially when they get old.

I guess most mathematicians, in our current usages of the term,
don't give much of a hoot about the ontological status of numbers or
the nature of the existence of mathematical objects and processes,
nor where proofs come from (storks, maybe?), except as the sort of
thing one might talk about over coffee, beer, wine, brandy, or on
a long airplane flight. Now in the times when the term
"mathematician" ("mathematicus") was still compounded with the term
"astrologer" ("astrologus"), there was apt to have been more concern
about foundations of mathematics, especially as related to theological
matters. This last reflection has no doubt been brought on by the
fact that I am currently scouring the Mysterium Cosmographicum
(Secret of the Universe), written by the young Johannes Kepler, who
loved to philosophize about the foundations not only of mathematics,
but of mathematical foundations of the whole universe.

Gordon Fisher gfisher@shentel.net






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