Evening discussions on Petitot's paper incl A Peruzzi, FW Lawvere & M Wright

5:00 Antinomies and tri-intuitive things, but there is a foundationalism of these different groups of variations. Then you are free to ask the question, can I just need a foundation as a merit course, a figure of speech? To bring this up, here in the School of Architecture, real foundations, like, is mathematics like a tall building that needs a foundation? Well, maybe in some way it is, but there are many things that don't need a foundation, like a bird, a whale in the ocean. The idea is that the idea of a building is a foundation is the best way to think about its role. Being a foundationist, or a skeptic about foundations, I came from foundations and I hope that by coming here I reviewed my reading on how many different kinds of foundations I have encountered by collaborators like Phil Davis. Very critical of Platonism. I was immediately approached by destructivists who were sure that I should join their group. I had difficulty convincing them that I didn't agree with them either.

7:30 So I've anchored in that. By your standards, you're actually playing very well.

10:00 No, I play an open attack. Well, I just want to say between tact and dishonesty, I mean, one and two. Yeah, I'm in it. So you were talking with... Well, mainly about Bill Mabry. Oh, I see. Well, I really can't talk to anyone else for the day, but I look quite sure somebody was just chasing people out of the room where we're having coffee. It doesn't look like we're about to start any. Yeah, yes, sure. Are you already spoken for for dinner? Are you able to join Albert and myself? Right, well, enjoy your dinner then. I hope you didn't think that Bill was being patronizing and saying that he wanted to rescue you, but I thought, you know, there was much more than I agreed with than I had expected. Can I ask one quick question? Have you ever come across a philosopher called Paul Churchill? Paul Churchill. There's a quite interesting book about 20 years ago now, I think he and his wife wrote about, nowadays they write mostly books about neuroscience, but about 20 years ago he wrote a good general book on philosophy of science called Scientific Realism and the Facility of Mind, and there's a very good chapter at the end of that which addresses the question, I think, that you were addressing in the book. That's his wife, that's his wife, his wife Patricia, yeah.

12:30 She wrote the book about neuroscience, about which I have no expertise at all, with mostly fairly hostile reviews, but Paul's book, which is quite an old one now, does have a chapter at the end. Addressing this issue of the epistemology of mathematical concepts and arguing, for a few I think, very much along your line, except that the emphasis is more on the kind of plasticity of concepts that comes from their emergence across the many levels of stability of structure in the natural environment in terms of the gravity of the problem. I mean it has an interest in me. Oh yeah, I want you to give me your website details too.