Morning discussions (contd.)

0:00 You don't even hear anything from him. What's going on? Are you ready to come out and switch us on? Is this back? In this case, it was your poster, yes. I mean, in this case, it's our APD and our operations. Uh-huh. Springer and... I have a friend, an economist in Tel Aviv, he has a book with humor and in his website he says, don't buy this book. It's quite clear the kind of strategy they're using. They know that they don't get overwhelmed by people publishing their academic books and they just want to make as much and that they can rely on institutional budgets. They don't give a damn about people out there who might actually want to read these books and learn this stuff. This is the fifth of June 2005, and this is the end of the session of our discussion.

2:30 We've just been having a very freewheeling exchange over breakfast over quite a variety of topics, but all of what a foundation of mathematics and what a foundation or perhaps better foundations of mathematics should issue was to wonder. We are closer to a unified conceptual framework for mathematics and for the description of the structure of mathematics in general today than we were approximately a century ago in the time of Hillman, and I think it would perhaps be useful in particular if some marks were commonly made about the role of algebraic geometry and mathematical algebra in providing the tools for general theory structure. ... situation by comparison with the one a hundred years ago when philosophically-minded mathematicians and philosophers were providing a foundation for mathematics or a framework. Its significance to philosophers seemed to be in terms of providing ontology for mathematics. Today, the connection between the conceptual organization of mathematics and the concern of the philosophers is perhaps much less clear. Perhaps we'll close it towards that, towards the end of the discussion, and particularly perhaps Mork and Bill on the theme of variation, of cohesion, of structure, for instance, in real-world structures, and the way that he moved from an early awareness of the centrality of variation structures to a later increased awareness of the cohesion.

5:00 I've talked about a lot of things. I've talked about a lot of things already. I'd like to kick off, comment on that, taking up where you left off yesterday. When I talked about that theme, I was thinking one of the things, maybe it's useful to approach this, but one of the things that you understated in your description of your book, just the structural ideas, I forget your exact terminology, and images of structure between what's going on and theories of what's going on. Could you say more about that? Looking at something that happens in mathematical theory and provide a formal theory of that, that's more or less what happens with category theory. It's a theory about mathematical theory, also model theory in some senses. I think that we were talking about it yesterday, about the foundations.