FOM: the interface between philosophy and f.o.m.

[palma, adriano p]

I appreciate the concern and I see the seriousness of the question.
My own view is the following.
Philosophical positions (whether one is subjectivist, or
verificationist, or relevantist or what have you) have little direct
bearing on mathematics.
The reason is that the techniques of proof in mathematics are far more
established and secure than the arguments one can give for philosophical
positions.


I shall take one easy example. Much has been said abotu Fermat's last
theorem proof (a crowning achievement of recent mathematics.)
What bearing would a philosophical quibble have?
someone who says.... BUT the principle of the excluded middle is to be
banned an dthe proof is thereby to be ignored.
I thinkvery little and rightly so.
The question is thorny indeed when one looks not *at* mathematics but at
the foundational work.
Here philosophical positions have a lot to do in terms of inspiration.
I assume that whatever final judgment one has on the subjectivist line
taken by Brouwer (or at least one reading of his early work) spurred
much work.
At least to that extent it seems to me Neil Tennant is correct.
Largely philosophicla work is done with unpredictable consequences.

Intuitionistic mathematics can be judged independently from its
philosophical inspirations (in terms of results, techniques of proof,
new proofs altogether, for instance.)


What philosophers ought to worry about are (IMHO) metaphysical questions
(is mathematical work producing necessary truths? for instance) & try to
learn what they can from one of the few cases in which a body of
knowledge is established without any appeal to empirical facts.


adriano palma

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