[FOM] Sazonov's vocabulary

[A.P. Hazen]

    Vladimir Sazonov comments on how surprising he at first found the 
philosophical use of the word "realism" as a synonym (in the 
philosophy of mathematics) for "platonism."  I suspect most students 
of philosophy have a similar surprise when they first encounter the 
jargon of their subject!  The word was introduced in the Middle Ages 
as a piece of philosophical jargon: a REALIST was someone who 
believed that some (controversial) kind of (purported) entities were 
REAL.  When  IDEALIST was coined some centuries later, it was jargon 
for adherents of the opposite view: the idealist holds that the 
disputed entities aren't real, but that we just have IDEAS of them. 
Alas!  The terms have evolved to have almost diametrically opposite 
meanings in ordinary, everyday, usage.  Outside the academic 
discourse of philosophers, "idealists" are the people who take 
abstract ideas seriously, thinking they have real meaning, and the 
"realists" are the hard-headed ones who  don't waste time worrying 
about what they don't think is real!  The only comparable inversion 
I can think of is with OBJECTIVE: the philosophical technical term 
"objective reality" (as used, for example, in Descarte's Third 
Meditation) means almost the opposite of what "objective reality" 
means in modern, non-technical, usage!

	May I lodge a complaint?  Sazonov himself uses a word loosely 
enough that it is in danger of losing its meaning.  He consistently 
accuses Platonists of MYSTICISM.  This is a word whose primary use is 
in discussing religion.  In that use, mysticism is NOT the same thing 
as (theological) BELIEF.  To be a mystic is a matter, not of 
believing that various propositions about the existence and nature of 
a divine being are true, but of one's  behavior with regard to that 
(supposed) being.  Mystics CONTEMPLATE and MEDITATE, and feel  an 
emotional UNION with the divine, and feel that the divine  being is 
in some special way PRESENT to them.  Mystics have typically 
dismissed rational thought-- even reasoning about theological 
questions-- as less important than a kind of non-propositional 
experience of divinity.  Someone  who  believes that there IS a God 
(perhaps on the basis of Biblical revelation,  perhaps by being 
convinced by some piece of "natural theology" (another technical 
term!)), and even that this God has made moral commands, but whose 
response to this belief is to try to lead a practically moral life 
and exhort  others to do so is NOT a mystic.

	There may be some Platonists whose attitude toward the 
abstract entities they believe in is analogous to the mystics' 
attitude toward the divine being: perhaps some Platonist, somewhere, 
believes that staring fixedly at a geometrical diagram will lead to 
some  non-rational insight, a kind of revelation about mathematical 
"reality".  Typical defenders of Platonism in the philosophy of 
mathematics are not like this.  They believe in the reality of 
mathematical abstractions, but they see this as a belief that is 
properly supported by reasoned argument-- or, at the very least, an 
assumption which can be defended by reasoned argument against 
reasoned criticisms.  They are thus more analogous to the 
NON-mystical theist than to the mystic.  I think calling Platonists 
"mystics" is simply misleading.  Sazonov has said that mysticism has 
no place in science or mathematics.  Perhaps this is so: maybe 
science and mathematics should be pursued entirely by reasoning and 
examining evidence, with no admixture of contemplation, and no role 
for an emotional response to the subject matter, and so nothing 
analogous to what is called mystical practice or thinking in a 
religious context.  But this is irrelevant to the question of 
whether Platonism is a  reasonable viewpoint in the philosophy of 
mathematics, because Platonism  is NOT (or at least not always) a 
kind of mysticism.

---

Allen Hazen
Philosophy Department
University of Melbourne