FW Lawvere / Colin McLarty / Angus MacIntyre / Michael Wright / John L Bell Rencontres, Fougeres 2005
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Recorded at Rencontres, Fougeres (2005), featuring FW Lawvere, Colin McLarty, Angus MacIntyre, Michael Wright, John L Bell. From the Michael Wright Collection, held by the Archive Trust for Research in Mathematical Sciences & Philosophy.

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Michael Wright Collection
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0:00 What the tools are going to be for proving the proofs 20 years down the line for what these guys have done, without actually explaining what it was that they did. Yeah, that's part of the distinction. And I think that... And if they were painters, I'd say Bill is Jericho and Angus is Angra. Then I don't know any Jericho. The Medusa? Rock to the Medusa? Oh, you do know one. It's one that used to be on the French... Thank that, sir, Humphrey Frank, weren't they, for liberty leading with the... Oh, look, it's Delacroix! What am I saying? Oh, no, it's Delacroix. What am I saying? No, it's Delacroix. The speed limit here will be, uh, 50, but... Oh, 50. Oh, yeah, 50. Okay, I was thinking 35. No, no, no, and those people were clearly impatient. Oh, yeah, yeah, no, no, you've been much too slow there, no, no, no. And in fact, once you get on here, it'll be more than that. The size, I mean, just basically observe the speed, the other cars, and tell you... Yeah, yeah, yeah, yeah. I mean, Frenchman, it's about... We'll see you next time. So it's just we're going a different route from the way we came yesterday to get around that bloody deviation to get you off the Cote d'Orson. Actually that would be the, that would be a quicker way to go anyway I think. Yeah, yeah, yeah, yeah. Great time to go on the Autoroute du Sud.

2:30 Mm-hmm. 105 miles an hour. Yeah. Nothing over here. Uh, sir, could you work out which seat is the air conditioning? Ah, there you are. And that was the, yeah, I followed the traffic. Eventually I followed the best of the traffic. No problem. It's coming out your side. For some reason, it's not coming out of mine. I wonder why. No, it's coming out of your side, isn't it? Yeah. Oh, okay, right, that's it. That's great. I did not know at the time, but Mont-Galimar is the place to find it. Yes, and the reason I can tell you that is because I took the infantry division down there. Not once, but four times. Very interesting place. They had a huge battle down there in 1944. Totally unknown. Anybody doing the... ...Hollywood history because most people know nothing at all about the subsidiary to and then when you get on the autoroute you'll stay on it for two exits and come off at exit 32. That will get you around the... August the 15th 1944. That was a huge operation. By the time it went in the battle of France had been decided. I mean the German army was being broken to pieces in the... And what was left of them was just screaming back across the side until they got back almost to the German frontier. What they did do was to hit up the Rhône valley and stop Vlaskovits' Southwest Army Group from escaping back to the Vosges. They cut off most of them at Mont-Elemaire, where they had a tremendous battle all along the side of the Rhône wall.

5:00 Just two relatively weak, as they were only considered, elements of two American divisions, basically blocking an entire German Army Group of 15 divisions from escaping. They did succeed in stopping most of them. Actually, a lot of them broke through, but they had to leave behind. The course of those trips, I met this extraordinary character, who in some ways, not intellectually, but in some ways, Bill, slightly reminds me of him. In that a very powerful personality with extremely decided ideas was never going to be intimidated by anybody's opinion on anything except his own. Thank you very much for your time. I've coached people, some of them have become three-star generals, one guy who has acted as the deputy supreme commander of NATO, was there any question in anybody's mind as to who, if you had actually been in a fucking foxhole with people shooting at you, who you would have wanted to have over you to get you out of there in one piece, this guy Phillips, by the Germans, together with the Germans in the boat itself a little bit later in the cold, wounded, his leg was shattered, you know, it's an agonizing pain. He was actually captured by the SS. He was immediately given a massive pain-killing dose of morphine. By his account, a very good treatment in a SS.

7:30 An uneducated, non-political sexist. You can probably guess the rest of the story. He goes back to anything left. So you see the cynicism of probably the guys who were killing him. They were trying to find a loophole, an escape. And of course they were. Why are they treating this American prisoner so well? He's given pain-killing drugs when he knows they haven't got anything like enough for their own men. He's given their rations when he knows they're not hard enough. He's seen that they're absolutely superb soldiers. He's there in Germany in 1905 when the French army comes in that area around 5. It's an unwritten story. It turns out it didn't happen. But you take this one towards Cannes, and you come off on exit 30. 20 years later, of course, he's corresponding with these guys, of course, who, well, they left their addresses with him when he went back home, you know? And he's attending SS comrades' reunions. He even goes to Madrid. He meets de Grelle, the leader of the Belgian Nazi party. He was the guy who organized the Wallonian, the SS Wallonian, the two SS divisions from Belgium.

10:00 It was a fascinating study in psychology, I mean, how people like that could be sucked into fascism. He wasn't a racist at all, he wasn't the typical racist. I don't think he had any obvious ideological affinity or predisposition to become a Nazi sympathizer, but of course he ended as an out-and-out Nazi apologist. Part was, did I ever hold this? It was, you know, I'm glad I met him. It's an interesting study. It's fascinating, he only died about six years ago, lived to a great age. He had, he formed a thing called the Rexist party in Belgium before the war, which was a social, a Catholic social party, very Rex is as in Christus Rex, but then became, after the rise of Hitler, a primal pronoun that was, in fact, kind of kicked out of the... He is said to have been the original Tantan, including photographs taken when he was the leader of the... And especially early ones, taken in the late 20s, early 30s, when he was very young at the time. He had the moon face and the crypt. It's difficult to believe there isn't some truth in it. Also called Sergei. He was, himself, a pious The Eleventh Boy scout, as you can detect from reading the Tauntaun books. The political line of Tauntaun is really pretty, not hard to decode.

12:30 And later, he cartooned for Le Petit Van Diem, which was the main Rex's newspaper. It became the main mouthpiece of the Belgian collaboration, with the result that Hergé was actually sentenced to national degradation after the war. In fact, if you look carefully at some of the early... I don't know how much of a town-town fan you are, but you're probably a little bit... Well, if you call to the age of six or seven, obviously the draftsmanship is absolutely superb. ...frames, particularly from the free world. I think he redrew a lot of them after 1945. But there are some frames... There's one set in South America where the villains, the oil, you know, the oil magnates and the arms... There are actually quite a few images in town, heavily, and I think it's undeniable that there is an anti-Semitic populace, for instance, the Nerva Dillon, the Nerva Bresci. The Catholic Boy Scouter is the, he always denied that De Graal was, the time film was based on De Graal, but I think it's, if you look at photographs of De Graal, it's Chuck Case, as I say. This is the exit, number 7, we come up here and head towards Mont-Saint-Michel. I like Asterix a lot better than I grew up with Fountain Time because as a kid I discovered Fountain Time when I was about six or seven years old. Asterix only came along when I was too old to be reading kids cartoons. I've been a Frenchman of course. French people go on reading cartoons and books all their lives.

15:00 I started trying to learn French again in graduate school. I wanted to know spoken French. Well the only way you can read spoken French is... Absolutely. This is why I was saying to Bill last night, actually I think I may have made a mistake there, a boo-boo, I thought he would really appreciate, as a gift for little Adelino, his grandson when he grows up, this, I think, marvellous series of books about the commune. Obviously I read them quite carefully. But Bill will know more about his secret program than you do. That's the problem. And also it's got, you know, well, it's him sort of sensing what he obviously needs. I don't understand how, but we must have shot part 32, unless it's a very... I can't figure it. Definitely. Well, it's not the end of the world. We can retrieve it, because if we can't come up with 33, we've got dual carriageway. Oh, okay. No, you're right, it is. Yeah, it's okay. And as I say, take the time to... And even this is too... Yeah, just come off here and head to Pont d'Orson. We're already halfway to the airport. Yeah, it could be that. Anyway, he obviously leads the courage figure who's people against the attempt by the normal martyr, but she's actually a prostitute. And she has a guy who then... That's an old image and I think even goes back to the time, right? This image of virtuous prostitutes. Yeah. Exactly. It's there in...

17:30 He just said I may have been reading far too much into a casual remark. No, I think it was critical. It's a pity, but you'd appreciate them, because they're terrific. First of all, because they've got so much colloquial Parisian dialect. And not only do they speak it, but they speak, you know, the 19th century Parisian dialect. Yeah. And it's got... Well, obviously one has nothing but, you know, but I think when it comes to his sort of literary taste, it can be a little, you know, supleased, and I think the fact is that, well, the good guys lose, you know, but then, like a fair story, they come in. Well, he's stretching a little, though, as he started appreciating Goebbels and other right-wing propagandists, he's beginning to believe that there's at least that much to style. If you say things the right way, you persuade them. Ah, yeah, well, I hope that, that's a horrifically cynical view, I hope. He'll be the first man in history who read Goebbels for his prose. Here we are. But he wants to say, I mean, Goebbels spoke to people the right way in some sense. I mean, not the prose he published under any produce. He knew how to talk to people. Yeah, he knew how to speak to the Germans at a particular point when they were so young. Actually, have you seen this movie, Downfall? Huge critical acclaim over here. It's this German movie made by this German Swiss, it's the last, obviously a theme that's not been done before on film, but this is in a very long way the most impressive. The last ten days, the last week in the bunker. Seen very much through the eyes of Karl Jungl and Goethe Christian. The dictator is, of course, survived and who kept daring.

20:00 And the performance is superb. It's very well done. They get absolutely right. It's, you know, the mental great cities just fall into pieces in a, you know, kind of street fight, you know, kind of sense of cosmic judgment hangover. You don't see a single Russian soul for the last ten minutes of the film. It's as if this is all an addition from the gods. The god of Dhamma and the element is extremely well. The guy who plays Hitler got tremendous praise for his performance. I did have a few difficulties with it. He's a very fine actor. He's Swiss. Totally unknown. I've never heard of him. Nobody outside of Switzerland or Germany has ever heard of him. And he also, the German accent is exactly right. The way that, you know, the kind of string, and the more hysterical, the more he loses control. I can sort of hear a Swiss accent in German. The guy who plays Hitler, the guy who plays Goebbels, and the woman who plays Magda Goebbels, you know, in some ways are more, there's a culmination, the culmination of the film is not the suicide of Hitler and Eva Brown, it's the shooting themselves. That's really the kind of emotional climax of the break out of the bunch. All world in that, all world was gone. Absolutely, it was dying in front of their eyes and they obviously knew there was no way out for them personally. And they'd obviously convinced themselves that.

22:30 They really believe that what the Russians would do to our children to get their hands on them is better than by the, you know, the striking poses, the... The Great Kingdom days, I mean. Yeah, and also in Goebbels was sufficiently intellectual to see the Greek aspect of it. It's, it's, but it's a very powerful film. The, the atmosphere of it... It's, if you get a chance, I saw it in Paris, but it wasn't, it was dubbed in French, but it's, which is helpful. Well, I'm sure he's come from places that just shows things once, but he was depicted as being easier than Hitler at the end. Oh, I have seen the movie. I believe it was Goebbels who made that movie about... Not only did he make the movie, he made it in the autumn of 94, when the German army was obviously under sort of believable pressure on all fronts. They'd just lost a million men in the east and a million men in the west. ... virtually in the space of six weeks. They were vocalizing it. They lost their reserve in virtually 16, 15, and cripples in about 16, could hardly walk to throw them into the line, and yet he ordered the Wehrmacht to find four divisions of troops to play the part of the extras in that movie. Absolutely incredible. It's called, I've seen it too, at once it was shown on the, something like, it's a one-word title.

25:00 What he told me was that Goebbels, at that time, suspected the army of betraying Germany, that the people were going to have to rise to... Yeah, because remember, Goebbels was always the left nasty. He was always the one who really believed the Volksgemeinschaft then. The Volk would always be betrayed by the elite and the institutions. He believed that even more passionately than Hitler. That was why he was so... He was pleased by Hitler's reaction to the bomb plot. He was the one who was most delighted at the thought of all these aristocratic opposites being strung up with piano bars, except in fact they were, but they're not safe to say. The whole thing I'm saying is a Holocaust desire. ...by Yannick Lukács, the Hungarian conservative historian about Hitler's general... And the fabrications can be traced and documented to the original sources of the fabrication, and there are several well-known things that everybody knows about Hitler, which just turn out to have been successful, like all-time propaganda fabrications. What about his testicles? Was that true? No, that wasn't true, but that was always just a... No, that's really tough. That one wasn't true. At least we don't think it was. I don't think anybody got into trouble except for Dr. whatever his name was, the guy who... Dr. Morel. I can't really vouch for that one really, I don't have any expertise in that. But the business about, of course I know the song, every English schoolboy knows that song. The British Army marched on the bloody song all the way through, after all they were the ones who wrote the tune to it. I hope you don't want me to sing it now. It was as true as a, you know, two million British soldiers singing it could make it. And, you know, it's not even true. I don't think his mother, the dirty bugger, cut it up when he was small. Splendid song, but then Colonel Bogue used a splendid tune. No, the thing I'm thinking of, the thing which, as everybody thinks they know, that he ordered the 20th of July plotters to be hanged with piano wire so that they would die is simply not true. ...and certainly no evidence at all that he made in it. It was just a piece of straight earth, rather similar to the famous jig at Compiègne, you know, there's that movie clip of him dancing, stamping his feet and dancing when he arrives at Compiègne to receive the...

27:30 French Armistice Collegation. Oh, no, I don't know that. Well, it's quite a famous clip, but it's fabricated. The British just got some old movies of him doing a beret gun snap and fed them into the... and retouched it so that it would look as if he was dancing this odious little jig of triumph in the light of the humiliation, which he wasn't, of course, I'm sure. Revelling, it's given the action of the French, but he didn't actually make himself absurd by dancing a little gig on the clock with that sort of straightforwardness. The clutch, it's a very interesting book. He's dug up some very interesting sources, including the book that was handled by Nuremberg, but probably without real justification, as far as he's concerned. Now, what was his position? He was chief of the general staff. It is credited with suggesting the implementation of the final solution. Absolutely not. No, no, no, not at all. He did, it's true. He'd been privy to the Commissar Order, which was the pretext on which he was there. Now, we have to be very careful. We'll carry on towards Mont-Saint-Michel. Oh, it's another circle. That's nice. ...left here, and let me navigate you onto the road. I don't know if I've seen a stop sign in France before, and I'm glad that I've seen it, because, you know, somebody, about ten years ago, actually, an anglophone in Quebec, he was nice and said stop, and that was English. Oh, it would be rather good to have come and photographed that, you could have got it back.

30:00 And the result is they're being replaced all over by signs that say arrêt. No, they always say stop, whenever I've seen them. Not in Quebec. It's straight on, it's straight up this road, this takes you straight to... I don't go there, but in Montreal, there's a whole lot of signs that say ah, eh. I've never seen one in France. I've only seen one that says stop. Oh, no, in France. Yeah, in France, they all say stop. Yeah. But in Quebec, and the appeal was thrown out of court. They said stop is not English, it's French. Good, they knew that. But the PQ anyway replaced the signs all over Montreal, the ones that say ah, eh. You know, if they gave Nobel prizes in making yourself look ridiculous, the party kept a crowd with walking every year, I would say. Yeah, it's no use having such a... Well, there's a bloody Englishman, no wonder he's... I mean, the French did take some words from English. Yeah, yeah, it's obviously frankly... Actually, when I was trying to find the first use of the word gasp for Bill this morning on me, I googled and found this very useful... I've learned about six sites on etymologies and word origins, one of which gave me the lowdown on gas, and I should imagine I'll probably be able to find out the stock of the same sort. Because it doesn't sound like a Latin word at all today. No, it sounds. It could be Anglo-Saxon, but it could be Celtic. It's funny, going back to Taunton and Hergé, of course the Bordurians in Taunton, who were ruled by Marshal Kirby Tash, was obviously meant to be Stalin. Well, he's a dictator with a moustache, but from the kind of moustache he has and the kind of build and the kind of break he has, well, he's obviously a moustache, but the borderians and border guards and other, for those guys, the secret police, all out, of course, in the English translations, and again, straight towards triple Z, S, Z, O, P, P, S.

32:30 Splashing orange would mean proceed with caution. That guy treated it like a stop sign. Yeah. I think here it does actually mean the same, but oh yes, the back actually like stops saying for the reason he's English, he's got a G.V. sticker on the back and it's, uh, he doesn't know. No, it does mean the same here. He probably thought orange means, yeah. Well, it certainly means pay attention and the safe thing to do is stop. Yeah, that's what I was supposed to say, but yeah. And we should get, we'll get the dual carriageway in a moment, and then we'll... I've begun taking it for granted, but the first time I grew up in France, I was on pins and needles all the time thinking, I don't know the French Highway Code! They've given me this car, and they're letting me use my U.S. license, but I don't know the traffic laws here! Well, the only thing you really need to remember driving in France, he said, speaking of a non-driver running in France, is just priorité de la, and all the intersections and the roundabouts, you know, always remember that the guy coming to the right has priority. Oh, and they don't really honor that around those. They don't, you're right, but that's what they're, that's the official. I hadn't known that it was official. No, but that is the official, the official is always priorité de la. Apart from that, it's really no, nothing much different. Yeah, nothing much, but the signs are a little different. We don't know what you want, and they're quite orange, I don't know. Ah, hang on, sorry, I'm getting a bit, wait a minute. How long have you not had the same here? That's right, that's exactly what we want. Okay, we want to use the highway, we don't want to go on the coast road. Pretty though it is, we don't have time to do that. Yeah, that's actually extremely pretty rude, because you go, the route de la Baye takes you right past Mont-Saint-Michel. When we do have the excursion, I... I was going to push for Bayeux and the beaches because I think that would be more interesting. Leo Corrie definitely doesn't want to go to Mont-Saint-Michel. He doesn't? No, because he's been before and he knows what a tourist... what a bloody tourist trap it is. Yeah, it's absolutely beautiful from the distance, but when you get on the island itself, it's just cheesy, overpriced tourist trinket shops and very, very bad restaurants.

35:00 Why not the Tideway? Will they let you do that? Yeah, they let you walk on Tideway. They let you walk on Tideway, but it's just not worth going over the island yourself, because once you get there, it's a place where you can find a really bad meal along this coast, but anywhere else, you know. I didn't know it was in Paris. It's probably more difficult in Lyon, but it's very easy to find a really bad meal in Paris. I think that's pretty well. That place where we went last night, I think, was really excellent. Oh yeah, yeah, yeah, yeah. Yeah, she's really, that woman is really delightful. I find them extraordinarily friendly lumbar treasurers. I think it's the leek fondue, that's what they have in my mind. Leek fondue around these scallops. Did it taste good? Oh yeah, it was lovely. Well, my fork was absolutely superb. I am, I guess. Yeah. That looks good. Yeah, that looks very good as well. Yes, he had a rack of lab and Angus didn't have a book, but it was very good. The source was super. When we get John and Mimi back, the first thing we're going to have to do is to sort out an extra bed because Angus will have to sleep upstairs in the one room that's not up by now. And then I've got to work out what's going to happen on Friday when Claudia gets here because I think I'm going to have to give up my room. I'll just put a mattress in the library and sleep in there and throw them in the back. I'd certainly have to do that if he brings his wife because it's the only remaining double bed. Listen, the one thing which is worrying me is trying to be me-me, entertained and amused. I know it's selfish, but having gone to all these lengths, I'm not going to give up the chance of listening to you guys.

37:30 Not just in order to be a good host, but I'm going to have to work out something to keep her at. If she does, there won't be any problems because there's loads of people that look after her. Yeah, I know, that's the problem. Don't get me wrong, I like her very much. I'm very fond of her. She can. I saw it when I was in Florence with them a couple of years ago when we were speaking. I know John and I went 15 minutes or so. You could really see. I mean, OK, don't expect her to be. I've got to say, she's been married to him. That's what these people are going to talk about. Yeah, there were a couple of times when she was obviously getting really pissed off, and so I had to kind of drop out of the conversation with John and Alberto in order to... I have any problem at all with that, but I do have a problem with it on this occasion, because it's the object of the exercise. No, no. And Patricia and I have a contract. No, exactly, and Patricia has so many interests of her own, and so many other things to talk about with Phil anyway. If she wasn't, it wouldn't make any difference. She knows the Cartesian closed categories and stuff. A hell of a lot more than I am most... But she doesn't know what any of those words mean. I know. That's like saying, I know the works of Shakespeare, I have an English dictionary.

40:00 Professor, in my philosophy department, what I most want to do is to listen to that. Jamie gave a good talk as well, too, one on visualization and mathematics, a strange one, called purity of method. It's a big topic, and I have to say, Jeremy Gray said by far, this is a non-topic. What are these people on about? You know, you're a pure... Geometric proofs or something. Yeah, yeah, yeah. What in general makes the purity of method as such, which is what the geologists like to do, seems to be crazy. A man's purity is not what Jeremy pointed out, though, so... ... that has destroyed the purity of algebra. Or is it something which has unified and assumed them and made them... This is a radical purity... Quite a political point for Jeremy to make. ... talking in any other context than the history of mathematics.

42:30 At this point, the humbells would have started ringing. Yeah. That he was talking about. I've always liked Jeremy Gray's work, but I like it even better now that he's done it. Well, good for him, and good for you for being so honest, I suppose, so we went down and had a couple of, and he is actually backing this meeting in October, even to the extent of actually giving some funding from the British Society of Physics and Mathematics to all the, only a, you know, it's a gesture, it's $500, it's helpful, I mean, it'll probably cover about a tenth of our costs, but it's, it's fabulous to have it, and to put it this way, he actually puts his money where his mouth is, when, uh... Of course I've invited him to come, I don't know about category theory, but it's something that Bill's brought down. Bill had said he was going to come and speak but, well no, Bill was going to come because he was going to be in France anyway that week because of the Amiens meeting, the Erisman-Sapeniel meeting, which ends on the 9th and our meeting started on the 10th. He had also agreed to speak at guitar, any guitar seminar at Josue three or four days later. I had to move the meeting to Paris, make an open meeting, I asked him would he agree to speak, yes of course he said I did. I got Benabu Akati to accept. I thought this was looking a bit like a serious philosopher's story, but it's beginning to show he might be a really good leader. Then something just before he came to Belgium, I got this thing saying, really sorry, personal reasons, had to pull out of Amiens, won't be coming to France that week, won't be coming to France at all. I can rest him on what they are, but I think they might have something to do with that as well. If he wanted to tell me what they were, he would have done so, but it was a great pity. So it's not going to be anything like a loony, it's all in it, it's the whole thing.

45:00 Some of whom I've met a few times in these seminars, they've even liked this guy, Shishiniak, because he's okay, but a couple of other people, he's a flimflam merchant, he's a flimflam merchant, he thinks there's a category of apples, yes, had some functors between them that express relations of descent to morphology, you could make a category of apples, but you can't just say it's a category of apples, okay, obviously not with the detailed argumentation that you just presented, but With, you know, I think more or less the same perception, you know, in my senses in which apples form a category depending on which maps that you're going to see, he doesn't really know the map. He knows more category theory than almost anybody you're going to find in a French philosophy department that isn't a philosopher about mathematics. So that thinks that that's not saying at all. Yeah, he probably knows more than that. No, no, he knows a bit more than that. He knows the category of categories. He can give a kind of pure expository talk on elementary category theory. ...philosophers and, you know, quite confident, he has no idea of his own, but done by who, Decaux-Nomal, through the, well it's not his seminar, he hasn't even got an appointment yet to come in and give his thoughts, but he took these, he explained it really well. ...philosophers and Decaux-Nomal. He did, I'm not saying he's a... I saw, he gave me that paper and I told him I thought he was... I actually told him there is no point in submitting a paper like this, it's just been so...

47:30 You just make all these assertions about what Plato, that Plato had a theory of relative identity, because Plato believed in the fact that the mathematical objects were intermediates, and because only the forms could be truly so different from one another, so because the mathematicals are in between the world of appearances and the forms, they must enjoy, they must be subject to some kind of theory of relative identity. What on earth? I mean, he was almost as bad as that. You know, I think Stanley Rosen is right. Read Plato as if he was Aristotle. When he says they're intermediates, we're just figuring out, okay, exactly what kind of intermediates. When Plato says intermediates, he means they're not exactly anything. Yeah, yeah. Don't try to explain exactly. Yeah, I mean, I missed that point, but I could see that he just had no justification for saying that Plato and Nietzsche have the same theory about, you know, the identities of terms which flank, you know, the identity sign. No, they did not. Which flanked the identity sign, but they weren't the identity sign anyway. Well, there was a word of it. I mean, he saw us in Euclid functions like a Euclid sign. Got to turn off the air to, you know, 250. Yeah, okay, fair enough. Well, put it this way, he... But he will say some complete nonsense. But he has said that, in that paper, he said complete nonsense. His expository jokes on Capri are very believable. I think we're not, we're not bad. It's better that they should hear that than that they should... They went away knowing a fair bit. They knew, for instance, the contents of the category of calculus. They knew that that pursued much further. He even explained the Eisbell and adequacy, co-adequacy. He said a lot of quite sensible things about naturality and the way it's made work.

50:00 But he just, when it comes to doing philosophy, he just talks nonsense. I think part of the problem is the learning. He's attached himself to Aluni because he thinks Aluni is some kind of great French academic spring puller, which of course Aluni fancies himself, and that Aluni will, if he stays on the right side of him, and people come and appear at Aluni's seminars, then, you know, he might get him a job. I think he's completely deluding himself, completely deluding him. He's totally skipped, I mean, you know, this is personal, don't ever repeat it to anybody, but he's borrowed money off me and not returned it because the guy has skipped. And yet he's constantly boasting about how he knows people in the Soviet Union who if he really knew them, if they were in his face, he certainly wouldn't be having them to beg the price of a cup of tea if he really had all these connections. What pisses me off is that he and the Lunar now are trying to move me in and take over this meeting. Just because I have no official standing at all, of any kind, with any pressure, I'm not in a very strong position to stop them from there for the last few years. Other than just saying, sorry guys, you know, can't write the cheques any longer, so it's going to be a meeting. ...which I certainly don't want to do, but now, in fact, it makes sense. It makes me look like a petulant dilettante, which I'd like to think I'm neither of those things. I've been trying to benefit from R13 by becoming... And it's not as if it hasn't been explained to him why it's so bad. John Mayberry, who is, as you know, very forthright, and is...

52:30 It never leaves you in any doubt at all about its meaning. I mean, it's always crystal clear, as told Shapiro, and, you know, again, it's something that's very explicitly why his theory of structure is just a complete thing. Here, these guys have no serious theory of structure. Because they know nothing about it. Because they know no mathematics, and they particularly refuse to learn of mathematics, which is the source of the serious theory of structure. Yeah. It's completely crazy! Yeah. Well, it's widely taken for granted today that mathematicians use categories, which 20 years ago it was widely assumed that mathematicians didn't really use categories. It's become almost derogatory now that philosophy of math will have a footnote claiming that there's one guy, McCarty, who knows something about categories. There'll be a footnote. Stuart actually explains my view of categories, that the categories think of a category as a collection of structured sets and structure-preserving functions, and he put them as being. I wrote to him and I said to him, Stuart, nobody thinks this way, and the reason is they know it's not true. And his answer was, well, I won't argue about it. Even this one. No, you don't go into the other whole point. You stay on this and go across the rounds. That's exactly where we came, yes. The barrage. But just as really dismissive, I wouldn't argue with you about that. Oh, wait, wait, I need to be in the... Oh, you need to be doing exactly the right thing. That's exactly what we did yesterday. But this is where Bill nearly took the corner rather too fast. No, you're going absolutely exactly the right place.

55:00 And Maddie used to try to put it on me. I'm afraid she's angry at me now. I don't know. And the signs for the airport said get in the middle lane. They end over the barrage we're there in about three minutes now. I'm afraid that PEM believes the point of philosophy is to win the arguments, and if somebody else is trying to win the same argument, well, they're not your friend. Well, you probably know she got the Lakatos Award about three years ago, and she came over to give the Lakatos Memorial Lecture, which was more of, you know, it's the first time there's been a philosophy of math, but it was all this. It's the same stuff, you know. ...cumulative hierarchy-based reasons for believing or disbelieving, V equals L, and she would know. I'm curious, I think she's a bright girl. I think if she had heard it explained more clearly than Bill ever explains it for the first time, that she would get the whole point about cohesion. Because I've tried doing this. She thinks the point of philosophy is to win the arguments. And here I am trying to win, I'm trying to win the argument by telling her this stuff. Well, telling her, the point is it's a complete new argument about something totally different from what she imagines it to be. Yeah. Okay. Well, I'm sorry to learn that. But we even have told a lot of people that she does the best work currently being published in philosophy and mathematics, and I blame myself for that. Well, I think that's... I don't think that's right. I think I know who does, but we aren't to embarrass you further. But... Well, of course, I blame myself for that. I wasn't publishing enough... But not only... ...the last couple of years. Right. You... That's... That's... That's... That's... But I think even, I think that there probably are other. Well, yeah, I mean, now that David is publishing, I like this stuff. But Penn, she has done, her study of the UCLA set theory is really important philosophically. Yeah, it's really, the philosophy of set theory is a very important branch of the philosophy of mathematics.

57:30 But it's simply not to be identified with the philosophy of mathematics. So, she'll say this is just philosophy of set theory, not of all mathematics. But as we know, all of mathematics is set theory. Yeah, well that's the point where it's unforgivable, but that's really about it. Yeah. And Crote and Deacon, they'll have, yeah, essentially a scenario which has it subsuming, which has got to be taken. I really think... I still think philosophy of set theory is an interesting area. Oh, yeah. But I will push, and I mean to push, over the coming years, as explicitly as there's any use doing it in public, To put the 20th century, late 20th century philosophy of math in three words, it's McLean, Grote, Diplomio. I absolutely agree. I mean, if I were to say that to Maddie, I mean, she wouldn't do it. Well, if I tell you, this is an absolute issue, she must promise not to repeat it. Yes, exactly. Witten and Connes have heard of them, obviously. But even physicists who follow them, they didn't hear that name. Actually, one of the things I wanted to ask Cartier about is that stuff at the end of his network. Popular expository paper, the one in the bulletin, you know, the man at his work when he set about this business, read to me in, obviously this got back to, when I sent off the list of, you know, what people have written in, your suggestions, John's, I just, and he said, well, in brackets, he is aware that, you know, you don't have a very high opinion of this paper, would like to understand why.

1:00:00 No, I didn't, I didn't tell him anything, Bill. You know, you told a lot of people you didn't like his work. I didn't say that, I didn't remind him of that. Um, no, he, he, he was being a bit bearish. Bill does not want to be part of any controversy. He'll take controversial stance, but he does not want to fight about them with anybody. Difficult balancing act to maintain. Well, but you do it by not talking to people that don't agree with you. Yeah, yeah. Well, it's never stopped me marking with Peter Fryde and with plenty of other people. The idea of me telling Cartier is so ludicrous anyway. Cartier just about knows me to speak to it. A strange English guy who comes to his seminars and who has a place in Foucault, who wants to organise meetings between lots of people. I've noticed he's like Norman. This is a complete yes.

1:02:30 What's with the memory, Tom? He's here again. We're actually back. No, he wrote a long paper which he sent to me to revise. Much more recent, this is just in the last couple of months. ...religious cult. That's, I think, really upsetting. Well, she was always, she was always inclined to spirituality and, well, I thought she might, I'd guess that she might even sort of, you know, contemplate entering a religious order, but always assumed that she'd remained a Catholic and kind of, you know, in the main council. She's joined the Boonies. Almost as bad, no. She's joined the bloody Mormons. Yes. She's joined, she's with a bunch of Mormon missionaries in Rome. If you don't, if you speak to Alberto, don't raise it, leave him to raise it. Well, I don't, if we were... Of course, he's always been completely mad, but then he was a fellow at my college. He'd been given by the Georgian government in exile.

1:05:00 Very good meeting. Oh, yes. Oh, yes. I went there in 2002 for a meeting on history and philosophy. There was actually a very good meeting about Bell, about Hammond Bell. Yes, I'm going to one in December. Oh, I was trying to get down for that. Thank you for watching this video, please like, share and subscribe to our channel. I saw him in Cambridge and I sent him an email. He said reply to me and I haven't replied. He's still going to be stuck in Reunion for the next 10 years, a gloomy thought, because he was in Barcelona for about a year, just the last year, and in fact he was organising some philosophy and math meetings in Barcelona, which looked quite interesting. I don't think he ever quite understood what it was that MacLean was getting at when he did have the... But that's a beautiful paper, I think. What is the MacLean and Anthology?

1:07:30 I keep going around here, Colin, sorry. I said keep going around here, I'm sorry. No, I'm so sorry, I should have made myself clearer. Okay, this takes you straight to my house. Fine, sorry. Yeah, this is just an area, we're on the outskirts of Puget. And now, I couldn't say what an important difference it makes. The local, kind of, stores. That's why I got your bed, yesterday. Thank you for watching. Well, I don't think it's being... Well, I think being elected to the House Fellowship didn't help. Didn't help. Yes, I'm afraid so. You're not supposed to write books for reviewers for math reviews, but I did. And I did for... You saw that. I did for Bill's book. Yeah, I saw that. I saw that. But it was nice because it was a feature review. No. Oh, what should I do? I don't think I did see one of the Bill and Rose books. Yeah, yeah, that's a feature review. No, I thought the one that you did... Oh, no, you must dig that up. Is that on the web or is that amongst the stuff? Oh, I won't dig it up. Colin, we're just coming to the place where you turn off on the right of my house. You probably realized that. That is the Chateau of Bouger, just ahead, and you're going to see my house in about three seconds. Now, I have to do a wholesome one for the person lying in the schedule. They sent me a little letter, thank you. Yeah, they've changed the policy. Are we going to go straight outside, too? They're getting a little more flexible about it. That's a book I would not like to have had to do. God, I'm excited. It's an amazing work.

1:10:00 Yeah, it just looks like a story. Yeah, well, you didn't have to review the first two volumes together. Yeah, I was a little miffed, though. And then I finally broke down and bought it. And then they sent it to me. The numbers were connected. So apparently, is this true of this other culture? The Zapotecs? I mean, the Zapotecs. Did they have large numbers and use... Maya evidently developed. The positional system, you know, it's 18-20 based, it's got 360. They use the 300, you know, it's a mixed base system with 18 and 20. Oh, 18 and 20. And 18-20 is not 360, and it's clearly, you know, the number of days or, you know, in the year, or these are the astronomical cycles. Is that true? I don't know. I wonder, it would be... It's hard to see to what purpose, you know, I mean, in the Maya case, these numbers were so huge that clearly they had some kind of, either astronomical or, I mean, they don't seem to have been used in any kind of practical computation. Did they have a great year in the Mayan calendar? I think they did. They had some great cycle, you know, and of course it was calculated and they sorted. I would bet that these apothecates did something similar. They were certainly into astronomy. Yeah, well, that's where it probably came from. And then, so the puzzling is... Thanks, Carl. I appreciate it. Well, maybe we'll do that when we go out to dinner. Yeah, well, I don't want to stay here. We'll leave it running on the panel now. But it can do it on its own. Yeah, sure, of course it can. Has he detected anything yet? No, this isn't detected, this is just a regular. Oh, this is just a regular, okay, right, that's just a regular. Thanks, that's obviously needed doing. Dare I ask if you did get talking about tape? I don't believe you.

1:12:30 The Aztec did have a big impact on the Mayan church. Have you got that? Have you got that on the, okay. Yeah, I, oh good. I've actually got the book, the Tame Topology book. Oh, you've got it. I've got it in my library, but I don't know how long it would take me to put my hands on it. I need four days completely on it just to get all those bloody books out and read shelves. I'm going to try and do something tonight. I left it in Edinburgh maybe three years ago. They turned it to me the other day. I had simply assumed that most... I mean, I can't pretend that I... I'm not able to follow it more than the sort of introduction and the, yeah, qualitatively some of the... There's still a lot to be heard that has not been... I mean, he has this section in his... I mean, he explicitly talks about... He makes a number of predictions which are correct. I mean, there was no... He believed that... He called it Herodotus. He semi-analytically says... That's what everybody calls them now, that's right. I know, and so therefore they're the ones you see having to be cast as, well, not more the Aztecs than the Incas, of course, because the Aztecs did apparently, and I presume they did actually have these, these bloody, the Mayans. What was the right and the left? Was it cow? I guess I should have said the further left I joined it.

1:15:00 Is that what we're going to do? I'm easy, I'm new. What's the suggestion that you're putting? I don't know. I mean, you could do that, or we could, you know. We could order something collectively, or we could just order each our own. Yeah, and then share about it. That's what I normally do if I'm with friends. I go for the fairly mild stuff, being a weak, feeble Englishman, not like a Scotsman, and the porridge, and I'd probably stay with the puree, shan't I? I mean, if you survive porridge, you can survive in Duluth curry. Oh, don't, yes, for God's sake, that will be beyond, beyond the hot. Sorry, while you and Bill were chatting, there were no calls, were there? No, I didn't look... OK. I'm surprised that Cartier hasn't rung to let me know what time he's arriving. I hope he hasn't forgotten all about the thing. No, I don't think he corresponded with... said he'd known that he would have done it. Well, I'm just surprised he hasn't got in touch. He's actually arriving. But I'll... The problem is I have no phone number for him, only his number at the IHS, which is probably not there. I won't be there this time. It just slightly stymies us tomorrow. Oh, it's okay. That door is a problem. That always slams.

1:17:30 I'll check. I'll just check. I'll just check. Well, you might even send an email. I'll check my email. Exited the recovery ward after the window there. No, no, me? No, I've got ulcers, I have. I had a fibroscopy in March last year and my larynx and windpipe are absolutely riddled with ulcers. I've been taking drugs with them for the last, actually it's much better now, it's far, far less normal. I say that I was really impressed with French medical services, they, well, if I had had that exploratory procedure at a British hospital I would probably have had to wait six weeks for the results. I went in, they gave me this draft the previous night, I mean obviously we're about to eat, so. Also, you don't want the graphic details of what they do in a fibroscope, but after they'd withdrawn the tube and everything, this gave me a sort of soothing thing to ease the discomfort, and said, would you like to wait here for five minutes, and then they bought me a sort of cup of very milky tea, and, you know, Photographs, everything, and a dossier, you know, about 16 pages thick with a complete diagnosis and a set of all the photographs they'd taken of my galatins, excuse me, this is, these are ulcers, blah, blah, blah, you don't have, you definitely do not have any, they do not have, and that was five minutes after I'd had the tube. As I say, in England, you'd have to wait weeks for the bloody results to come, and I was really impressed with French hospital medicine, yeah, I was just given all the anti-ulcer drugs. So this is no curable diet? Yeah, it's just a diet, just your diet and anti-ulcer drugs, quite curable. To mercy? Yeah, sure. But I think they were in any case much less inclined now to... ...operate in the case of ulcers. There was a time when the peptic ulcers, it seems to have been a routine thing, and now they seem to regard it as something which is crucial. It's absolutely fine. It's just that, you know... I just had these symptoms. I was obviously bi-anxious. You know, after you're 50, you do worry about certain symptoms. I went to see them, and within 48 hours I had the appointment, the procedure, and they gave me the results on the spot.

1:20:00 I was very impressed. I suppose it varies. It evidently varies because George had a long travel in France when he was here. That was a long time ago. George Wilmers, you know, had Hodgkin's disease. He had Hodgkin's disease. I didn't know that. Not quite a long time ago. Oui, merci. In practice, in principle, you still get arguments on the same side of that barricade. But then with Big Bang, that changed, which was a derisory. That's right. You know, Catholicism, they weren't arguing about evolution at all, but they were very happy when Big Bang was... George Lemaître, after all, was a Catholic priest. A considerable physicist. I mean, Einstein could have invented the thing, but he put it off, you see. He said it would produce bottomless problems if we actually have an evolutionary universe. Well, because they'd have to pop the origin again. And that's apparently one of the reasons why he didn't like the, he introduced the cosmological common, he didn't like the idea, he only admitted initially static solutions to his equations. Bottomless speculations, that was his joke. To do otherwise, he said, would have introduced bottomless speculations. He's broadly right, young man, yeah. It is something like that, you see. Well, he was right, wasn't he, essentially. There was a 12th century people order about teaching science. They said, okay, we believe the Earth does not move, but you may not teach that the Earth could not be moving, because if God wanted it to, it would be. Modality upon modality. That's exactly the opposite here. At the millennium, in their people, it was an article by... This is somebody who is quite known. They often work. He works in Arizona mostly. He's an astronomer of the Vatican. His story, his deism, consists of some of those in all detail, since some of those laws are inherently statistical.

1:22:30 It's a very intelligent line by comparison what fundamentalism is preaching. It's perfectly, I know, no, no, it is, it is, but deism was a perfectly, this is the official, I know, yeah, I suspect he's going to have a little bit of trouble with the present pope on that. But the point is that this has no conflict whatsoever with evolution. Evolution is always as awful in comparison, right, in connection. That's always why it's never been a problem. The issue was always over the ultimate origins. That's what theology was really about. And that's why Hoyle made these big... To be fair, there's also the question of the origin of life. Oh yes, of course, of course, but when it got completely intellectualized, I know, but nevertheless, the period of the Catholic Church saw that there was a natural development of the matter in fact, I don't want to argue about fossil monkeys. No, no, no, but that was a complicated, you know, Thomas and Klein, they took sort of for granted somehow. Talk about Bernard's cells and clays and smoke and self-replicating. But now we're back to, now it's very interesting, I mean, you have, they say, well, it's simpler, perhaps, to explain the idea, it just, it's impossible. You know, you have to be some kind of ultimate monist in a kind of hermetic way in order to accept the idea of one unique universe and that's all there is, and the impulse to actually find an explanation for it then is... Well, like Wheeler at the time, he was... Well, Wheeler, Wheeler, Wheeler, we all know the old banker, you know, but he had this, this, this, this, he had... Well, he became a kind of mystic in a suit, you know, but you could see why he'd be forced, but the Catholic view of it was actually very interesting because they were waiting, not for evolution, the only reason I brought it up was because evolution was not a serious issue at the intellectual level in Catholicism.

1:25:00 We've got that, yeah, we agree. And now they've got Big Bang back, now they are new, oh God, all these things about, the design argument isn't a bad argument. You know, given, you know, this is why a lot of people go for it. No, no, what I mean is, I mean, I know, because it's one thing and what the creationists are trying to do. I agree, I agree. Of course it is. Of course it is. But the fact is that there is a difficulty at the level of origins anyway in cosmology, and there always has been, of course. I mean, Hoyle was very dismayed, of course, when he was vehemently against it, you know, the idea of big—the term big bang was— It was his own kind of— It was a thing he introduced to the BBC, is it derives a return for these people with O'Reil and so on with their big bang. And then, of course, it's true that the evidence shows that there's an evolution of some kind in the universe, at least that's the thing that seems to be consistent with the rest of it. And then where's the escape into infinity? Wow, we all still look for it. At least I do. This is the amazing position of the internet. They're saying the eye could not involve these things. And if I go back to the 13th century, even if God wanted to, God could not have brought the eye about in small steps. Some guy at Lehigh University has discovered that even if God wanted to, he could not have created mammals with all seven factors in one. I mean, of course, you know, they're not thinking of their own way. But you have to, you're neglecting one great factor, which the Protestants are saddled with this problem, which the Catholics are not. And the equation is in two. But at any rate, it is an issue, clearly, of whether you're on the way from or to first principles. The Protestants are saddled with this bloody holy book, which the craziest amongst them want to take as literally true, in the same way. Well, of course, which is the great knock-down argument the Catholics always had, saying, which is why you need authority and why you don't want to be scum so hung up on the scriptures, you know. Precisely. It's better to argue about a vacuum than it is something specific. Exactly, exactly. It wasn't, but the ultimate thing was there's some kind of mystery, you see. It didn't actually have to be presented in terms of a rather crude document. Catholic intellectuals rapidly got over that question, as we all know. I know that Western philosophy comes from the Catholic Church. And an awful lot of science too, let's face it.

1:27:30 No, no, it's very, I mean, you know, I'm not, I'm not, the movement was partly, went back to what they called roots, which meant, I don't know, some kind of historical, I think this is connected with this whole issue of the renaissance and the source, you know, renaissance, humanism, and textual. And this obsession with textual authority. But so also was this obsession with textual authority and the sacred text, the scripture. Well, physics, you know, did leak into... Rather than for natural theology? But no, the evidence, certainly in astronomy, one has to say in mathematics, is it interesting. The one thing that was really continuous, actually, you know, from ancient Greek, like completely different, presumably totally different philosophic views at some level, what was Constance's one-to-one? The old mathematics, right, the old mathematical notion. That's right, I think there aren't, and I think that's the, but that's a very powerful, that's a very powerful, yes, philosophy is at least partly art, and there have got to be revolutions in art. Is mathematics art? Well, yes, but it's a, it's a, well, we're going to, we should be, I hope we're going to have a discussion on this, on this question. The difference between mathematics and art is always, it's clearly, it's not, you know, it isn't simply the book of nature. It's something we create. Well, it's created in a party with play, but also with very considerable constraints. Constraints which then reflect in some way the objective reality, although it's very difficult to explain exactly how that's done. And also the pattern of accumulation of the biggest constraints. Yes, and also of course whether the thing would actually be, because we wouldn't expect art to be the same in another culture, or in an alien culture, for example, would we? It would be an enormous coincidence. Mathematics, we probably would. But would we?

1:30:00 Bruno didn't provide us with a clear prediction of what the alien culture is. No, no. I know. But if you see, there were... Numerous episodes of Star Trek. No, I know. But nevertheless, the continuity among cultures, at least terrestrial cultures, if there are any others, fine. It's largely through mathematics and largely through, of course you could say it's because of the use of symbols. There are many attempts at explanation, but it is really a reflection of the 17th century. European mathematics was different from Arabic, from Indian, from Chinese. They're all the same worldwide now because they're all European mathematics. Well, there's that, but none of these. The fact is, the connection is that it was used in the case of science. If you actually look at the calculation of areas of law and all the things that have that subjective character, it's exactly the same, you know, as it was in Greek times. Well, that's right. The Romans used the wrong formula. The Romans were not very, let's face it, were not very good mathematicians. They used computational methods that probably inherited from other cultures, too. But they certainly didn't, the thing that was transmitted was perhaps the engineering, but not the mathematics at all, because they didn't produce any. Is there a definition of a Roman theorem? No, not that I know of. Well, there is a Roman definition of the area of a triangle because surveyors use it for taxes. Okay, okay, oh, I know, I know. It is just not. But if you ask why it is that dark can meet all these principles, it's because it's a kind of a synthesis, if you like, of imagination, of something that is... You know, that requires a kind of subjective input. We all share a deep revulsion at the Roman so-called civilization. Yeah, but the classical civilization... Why is it the calculation of the area of a circle? In all the ways they did it led to the same result. At many levels, not only in terms of rough approximation. But we all know this, we're mathematicians. I mean, the answer has to lie there. It isn't an art, and it doesn't change, as Bill said. In the sense of art, there are no revolutions in mathematics. There are in art, and that's what makes art very interesting in that respect. In mathematics, a revolution would be some ridiculous claim that 2 plus 2, we finally discovered that 2 plus 2 equals 5. Well, I mean, those aren't the old-fashioned revolutions. I know, I know. But those are already compatible, you know. It's not like overthrowing the whole of the previous order, as in politics, or indeed in art.

1:32:30 In physics, it's the one that has remained very close, you know, to its origins, at least in physics. I was going to ask you about how, there have certainly been revolutions in music. There have, that is my point. And yet those revolutions are probably never known, not nearly as great as the revolutions in visual art. Well, more dimensions. It's a continuum, it's, well, it's continuous rather than discrete. Yes, changing the 12-tone scale, things like that. He's discovered, he's discreet in fundamental number theory. The object of attention has, I believe, is not. Which was to knock off, knock off Everest. Well, I'm a division of labor. His goal was to understand the question of the elliptic curve, which is not, it's a deeper thing. His goal was to prove it.