FOM: Aristotle; critique of Platonism in mathematics

[Stephen G Simpson]

Background: In my posting of 19 Jan 1998 19:37:33 I commented on
Aristotle and the unity of science.  Tragesser in his posting of 20
Jan 1998 02:55:52 expressed doubts because Aristotle's "being" is
equivocal.

Look here, it's not really that bad.  When we say "squares exist", and
"square floor-tiles exist", we are speaking of different but related
senses of existence.  Aristotle in his treatise on metaphysics makes a
valiant and largely successful attempt to classify all the various
types of existence ("being") and their interrelationships.  This kind
of groundwork is essential for the unity of science.  To impose a
false unity would be to disregard the needs of science.  Books M and N
of the metaphysics are a potent critique of Platonism in mathematics.

I am reminded of discussions I used to have with Stanley Rosen.  Rosen
is a Platonist and I am a sort of Aristotelean, so we had a
junior-grade "School of Athens".  (I'm referring to Rafael's painting
where Plato and Aristotle are walking together discussing philosophy.
Plato's finger points upward, toward Heaven.  Aristotle's hand is
stretched outward, palm down, blessing the earth.  This image is in
the picture gallery at http://www.math.psu.edu/simpson/PSOC.html.)

-- Steve