pillay at math.uiuc.edu
Fri Sep 26 11:44:32 EDT 1997
I found Harvey's comments interesting and reasonable and I will comment
briefly on some points later.
Concerning Steve's response:
1) If you are going to give your own definition of foundations and "what is
of interest to any educated human being" and eliminate from consideration
that which doesn't satisfy it, that's fine, but is not the basis for a
conversation. Also it does not take too much imagination to see that what
is of general interest to an educated human being is an historical
phenomenon, and what is at some stage in the realm of specialists can
filter its way through to general mathematical culture.
2) About the axiomatic paradigm. The point is that a certain view: that
mathematics can be defined by and reduced to the activity of deriving
theorems from axioms, which was widely in circulation when I was a student,
is no longer seen necessarily as the paradigm. This is a separate issue
from that of rigour and rationality. In any case, it is not from a bunch
of fashionable wierdos who are trying to undermine the traditions of
Western Christian civilsation which we all love and hold dear, that this
emanates. It is from the mathematical establishment; Atiyah and co. etc.
Whether or not you know the meaning of the words you used (postmodernism,
primitivism etc.), these are the last people who they are appropriate to
My only point was that these developments whether right or wrong have a
nontrivial effect on logic. Of course one can say that all these people are
idiots, but that is neither useful nor true.
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