Willams Lecture

Willams Lecture

[Peter Freyd]

If one goes to itunes or ipod and searches for "antiphilosophy" you
will find two free downloads (one with and one without video) for "An
Anti-philosophy of Mathematics." I attempt therein to give a definition
of math. (Before you get there you might first be taken to a page that
gives you a choice of "Lectures and Events..." or "The music of
Awannabepoet." Choose the first: it leads to a chronological list of
the Williams Lectures at Penn and antiphilosophy appears at the end.)

You might well skip the first 14 minutes and 50 seconds (it's mostly
about the 1960s history of the Penn philosophy department. Just in
case you do watch it, the Aravind I refer to after the first 6 minutes
is Aravind Joshi sitting in the audience, the distinguished computer
scientist best known for his "tree-adjoining grammars" in
linguistics).

If you get as far as 42:40 I start answering questions and, as usual,
on these things, you can't hear them being asked. So here's something
of a list:
     42:40  Zoltan Domotor asks if my definition sheds light on
       issues of objectivity and truth in mathematics.
     50:20  Someone asks if my definition depends on assumptions
       about the world
     53:00  I forgot this question most likely because -- as
       becomes evident -- I didn't answer it.
     55:15  Murray Gerstenhaber asks if math [just as every other
       subject, I might add] is defined by the questions that are
       asked  and don't those questions ask themselves anyway.
   1:02;15  "How can we be non-arbitrary in this arbitrary world?"
   1:04:00  A question about machine proofs.
   1:06:20  "Would your analysis lead to a 'fusion' of logicism
       and formalism?" Which --,wonderfully enough -- immediately
       took me into the coda I had planned.

If you listen and don't see the video, it's worth knowing that I only
twice used a projected image. The first use -- it appears at the very
beginning -- displays the following email I had received (from an
author who insists on not being identified}:

   How could you? An "Antiphilosophy" for mathematics? You -- who
   sat at the feet of Curt Ducasse, Wesley Salmon, Stephan Korner,
   Roderick Chisholm, Carl Hempel, Alonzo Church, Kurt Godel, John
   Myhill, Ernest Nagel, Marvin Farber, Nelson Goodman, Dana Scott,
   Stanley Tennenbaum, Paul Bernays, Alfred Tarski -- you're now
   an antiphilosopher?
   Please: tell me it's a hoax.

The other projected image (at 21:50) was a web page that can be
found at:

   http://www.math.harvard.edu/history/peirce_algebra/005.html

It shows the famous opening line of Benjamin Peirce's "Linear
Associative Algebra," to wit:

   Mathematics is the science which draws necessary conclusions.


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