FOM: naive or brainwashed?

[Lincoln Wallen]

Charles Silver writes

   Date: Sun, 15 Mar 1998 08:36:32 -0500 (EST)
   From: Charles Silver <csilver at sophia.smith.edu>

   [...]

	   It's roughly the same point.  What the above misses, though, is
   how mathematical truth is established.  For example, contrast the
   verification of FLT with the verification of the statement "Food is now
   being sent to the astronauts on MIR".  Or, to make this sharper and to
   bring it back to my example, contrast the verification of FLT with the
   statement "Hersh wrote his book because he's a Leo".

   Charlie Silver
   Smith College

OK.  I now see your point in this sharper form, and agree completely.
Turning then to contrasts of this kind.  What is the nature of the
verification of FLT?  Or, for example, if I added: "or any
mathematical statement" would I be sweeping important distinctions
under the carpet?

To what extent is the in principle formalisability of mathematical
argumentation sufficient/insufficient to characterise mathematical
verification?  In this respect, I find the question: "what are the
practices which allow/support the communication of this in principle
formalisability?" of considerable importance.  That is, while logic,
and even set theory may help us to recognise *when* something is
properly mathematical, this recognition is itself a *practical*
achievement.  The basis and techiques for practical achievements of
this kind forms for me the foundations of mathematical practice.  It
is now very similar to questions sociologists of science have asked
about measurement and observation in actual practice (as opposed to in
ideal conceptions of that practice).  Once again, I do not subscribe
in large part to their conclusions or even how they seek to answer
this question, but it also seems to me that f.o.m. as characterised by
the major results of this century has little to say on these matters.
Or am I mistaken?

Some additional questions (for good measure):

Is the structure of mathematical definition/demonstration independent
of whether the defined notions are to be used in proof, or are to be
used in modelling?  How do we account for mathematical writing in
which the two are intertwined?  What can f.o.m. say about applied
mathematics?


Lincoln Wallen
Reader in Computing Science  \ information added by
Oxford University            / the moderator

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