WHAT ARE THE "RULES OF THUMB" [as distinct from presumably
nonexistent exact criteria, and for which it would arguably
be absurd to ask] BY WHICH THE HISTORIAN OF MATHEMATICS
RECOGNIZES SOME BIT OF CULTURE AS BEING MATHEMATICAL OR OF
MATHEMATICS?
[[END OF SUMMARY]]
Dear Dr. Cabillon,
Thank you for your as always gracious and thoughtful response.
Perhaps in trying to provoke a complex response I did so in a
way that was inadvertently rude or insulting.
I think that "the history of mathematics" has become an
astonishingly profound and wealthy resource, and HM has brought this
home to me more than whatever I have been doing in the library has.
As a philosopher of mathematics, or as someone trying to be
such, I am interested in a number of problems, including the role of
logic in mathematics and the (I firmly believe to be false) claims of
the reducibility of mathematics to set theory [which reducibility is
dear to some on the sister list FOM]. These questions have taken me
down a number of paths, such as the role of intention in mathematical
thought, the role of "intuition" and intuitive understanding in
mathematical thought, fringe mathematics that is on the borderline
between the a priori and the a posteriori, etc.
Let me simplify my question to HM, making it less contentious,
and to avoid calling up the question I thought I had tried to suppress,
for I, too, agree it has no sense, as I thought I had indicated in my
post [viz., the question What is mathematics?; though I suspect that
some prominent contributors of the FOM list would say, "whatever is
formalizable in ZF"]:
WHAT ARE THE "RULES OF THUMB" BY WHICH THE HISTORIAN OF
MATHEMATICS RECOGNIZES SOME BIT OF CULTURE AS BEING MATHEMATICAL?
I don't believe that Dr.Cabillon's quotation from Courant
and Robbins would constitute an answer to this question Isn't that
quotation aimed more at saying what is praiseworthy in mathematics
than providing a rule of thumb by which to recognize mathematics?
I raised the issue of Marshack's bone [N.B., I see I had
inadvertently said "stone" not "bone"] notchings [viewed as something
like a lunar calendar] because it does seem to me to be a place where
knowledge of the historians' rules of thumb would be instructively
brought to bear.
in gratitude, robert tragesser