[FOM] John Baez on David Corfield's book

[Stephen G Simpson]

David Corfield, Fri, 3 Oct 2003 13:29:30 +0100, quoting Collingwood:

 > There are two questions to be asked whenever anyone inquires into
 > the nature of any science: 'what is it like?' and 'what is it
 > about?'.of these two questions the one I have put first must
 > necessarily be asked before the one I have put second, [...]

This approach seems completely lopsided.  It puts the activities of
the scientist ahead of the subject matter.

For example, this approach would define physics as "whatever
physicists do", rather than as the study of matter, energy, etc.
Ultimately, such an approach is not reality-based.  If followed
consistently, it would lead to a subjectivistic physics.

The same goes for philosophy of mathematics.  It is crucially
important to start with, not the activities of the mathematician, but
rather mathematical objects, be they quantities or shapes or whatever.

 > One of the ways in which mathematicians think is to ask themselves
 > whether what they are doing is of any value. With the freedom
 > gained by entering Cantor's paradise comes the responsibility of
 > selecting important topics to think about.

Yes, that's absolutely correct.  This is part of normal mathematical
activity.  This is how mathematicians and other scientists think.
They focus on the subject matter, and select its most significant
aspects.

Now, why shouldn't philosophers of mathematics do the same?

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Stephen G. Simpson
Professor of Mathematics
Penn State University
http://www.math.psu.edu/simpson/