FOM: Aristotle, name-dropping, reverse math, juicy quotes

[Stephen G Simpson]

The postings of Detlefsen and Tragesser about Aristotle are very
interesting to me.  I am a big fan of Aristotle from way back (as
Stanley Rosen will attest, if we can induce him to join us here).  One
of the treasures in my library is H. G. Apostle's book "Aristotle's
philosophy of mathematics".  I got it from Craig Smorynski in trade
for a copy of Turing's mother's biography of Turing.

Tragesser writes:
 > In Aristotle one obtains closure, self-containedness, by deducing the
 > cuases or first pricnples of a theorem (backward) from the theorem.

Yes.  The following quotation appears in my book, at the beginning of
the section introducing reverse mathematics.

  Reciprocation of premisses and conclusion is more frequent in
  mathematics, because mathematics takes definitions, but never an
  accident, for its premisses---a second characteristic distinguishing
  mathematical reasoning from dialectical disputations.

  Aristotle, Posterior Analytics, 78a10.

This quotation is pretty juicy, but I'd like to find some even juicier
ones.  Can anybody help me?

-- Steve