Peter Freyd has given that title to his 2011 Thomas and Yvonne Williams Lecture for the Advancement of Logic and Philosophy to be delivered on Monday, April 11, 4:30 - 6:00 p.m. at the Wu & Chen Auditorium, Levine Hall, 3330 Walnut Street, Philadelphia, PA. If anyone can report on the lecture, we’d love to hear about it.
Posted at March 25, 2011 2:44 PM UTCTrackBack URL for this Entry: https://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2376
Freyd says around 45 minutes in the video
“What happened to geometry in the uh 19th century happened to foundations in the 20th century. You took a much more expansive view. It wasn’t a single foundations. There were many foundations. You would pick the one that you wanted for to to make interesting theorems right.”
I wonder, if you took a poll of mathematicians around the world, how many are aware that the foundations of mathematics exist, and if they are aware, how many are aware that there is more to foundations than just ZFC or the framework of material set theory? I feel that in the 21st century the latter group of mathematicians still form a very small minority compared to mathematicians as a whole.
Re: An Anti-Philosophy of Mathematics
If this is still of interest, click here for the video.
You should probably just watch it rather than listen to me report on it. But this is a very Freydian address: delivered extemporaneously, with a lot of verve, very personal, gossipy, provoking, and thought-provoking.
I’m not quite sure why “anti-philosophy”. A major theme is, not quite “what is mathematics?”, but what are some defining characteristics that make certain subject matter mathematical. He settles especially on (1) lack of arbitrariness, (2) presence of theorems [sharpening Benjamin Peirce’s own definition “mathematics is the science of drawing necessary conclusions”]. He remarks on Eugene Wigner’s Unreasonable Effectiveness paper. There’s some lively interchange during the question period.