Morning Discussions, incl. A MacIntyre — agenda / FW Lawvere & A MacIntyre — SUD objects & QD topos (& others)

0:00 There's also a division of labour, a treaty, which we've all heard of, which we spoke at the end of the night around 1960, I believe overall, when the SGA was in power. Look at the SGA, it's not the one set in space that we've talked about, but the SGA, and also I think I can take us pretty deep into the last development question. And then, sorry very quickly, I can't see it. Get tried and died all the way along the scene of how the whole machinery that was developed in the SPA actually got homology. It was being not merely homology required to demolish the very important problems in algebraic geometry, which are problems that tackle our perception, but they're getting to see much more broadly the unitizing framework for the whole. Well, basically algebra, algebra, geometry came to be seen as a potentially utilitarian framework for the redistribution of structure around the problem of mathematics, and logic and self-theory kept themselves falling into place within that, i.e. the point at which Bill first heard the word toposconverdias on the beach of the Pyre in 1965, and then, as it were, let the thought pass from Carnegie to Bill, and let him say a bit about the general and very broad theme, the way in which John Stanglitz... Key terms may include mathematical physics, geometry, algebra, algebra, mathematical physics, algebra, mathematical physics, mathematical physics, mathematical physics, mathematical physics, mathematical physics, mathematical physics, mathematical physics, mathematical physics, mathematical physics, mathematical physics, mathematical physics, mathematical physics, mathematical physics, mathematical physics, mathematical physics,

2:30 A good way of making the transition from, you know, Cartier's marvellous exposed head, obviously the last few days, to the discussion of Lauderdale and Schoenen, which we'll be covering in the next days. Tomorrow, we'll be trying to get through all of that today, so what I'm going to do is to make lunch on the table. I'll get some bread and stuff now, and have a relatively short lunch, maybe just soft drinks. Well, that's the other thing I was thinking, okay, well, you've said it for me, thanks. Thanks for saying it. So, and then, tomorrow, when Katya leaves, we actually have to go to lunchtime, unfortunately, or whatever, at four o'clock, have a final discussion on Grotendieck's, uh, points in Grotendieck, i.e. his conception of the foundations of geometry, carrying Kahn into the school. ... about which Bill, I know, has very fundamental background, is wrong, and I'd like to understand in detail why, and if possible get Carson's response to that while he's still here. It'll be an awful lot to get through in one and a half days. As you're right, the key to it is basically trying to draw up a bit about quite so... Oh no! He starts very interesting here, but he's taking us away from what I think, generally think, was a very good framework for getting the maximum abstract of real scientific value out of these discussions. Well, I think it was a very important issue to raise. We probably spoke too long on it.

5:00 All of these were developed in the course of, you know, the logic scene as flying within, you know, the constructors of the scene as flying within, and that's a great doctrine today, but there's a very important point here, which was brought out, which was that, you know, Samy, very early, was stressing the gravity of generality, you know, the frame of the very, very, very gravity of generality, you know, and the last of the four various reasons were, were not really picking up on that, but they did remain. Convinced that it was the Donatian Isomorphism which was the sufficiently general one for the very first foundation of interesting and important theory, Atiyah, Witten, Connes, Hawking. And I would say that next also, this is your current season, this is what I consider to be a charity in which you make a claim. If you have a chance to speak to Colin, Paul Johnston, if you can run some of that class here, and the Queen could serve you, and we'll just try and keep discussion broadly on those lines. But I would be disappointed if we... Yeah, actually yesterday, we were still stuck at 1600 from the start of the algebraic problem, because I took it a little bit further than we did yesterday. I know, I know. It's possible. It's possible. Yeah. I know the answer. I know the answer. Well, I agree, those are interesting, but I would say those are much more concrete to be discussed in these kind of foundational stances that we'd say we give ourselves after Leopoldi gets here. Well, I've got my card with me, so if you've not got one, you can look it up. I'm not saying I don't know anything about that, but we didn't get as much out of it as we had the day before, and especially, it seemed to me, that supersound might be algebraic geometry in the 60s.

7:30 I promise John that we can have the very general philosophical discussion on oppositions and bounds, consequences, etc. We don't want to be taken up into really rather general philosophical points, but getting something as valid as we are getting out into discussion, but be fair, and for discussion. So that's the one you want, isn't it? Yeah. Well, if that doesn't take your car, try my bag, which is that. That's mine over there. Okay. Well, that's credit agriculture, I say. If you have a problem, give me a shout, and then I'm just going to head back and get some bread. Actually, now I'm not going to get you to the supermarket, though. I'll go to the dairy. Okay. Thank you.