Post-session Discussions (contd.)

0:00 The point is, if I take the case, and then we find something profitable of that, that's the way to describe it. So existence and disjunction are things that are expressed in positive objects and classifiable. There is a classifying purpose to these models. I don't know what kind of purpose they are, but they are perceptive. You could add in a natural number too if you wanted. So this is the case where it splits the full product or more restrictive than different? Well, is that more restrictive? Is that just the Boolean case? You know, so that the variation over one part has always got a specific complementary variation over the... Other parts of the domain, you know, where... Oh, well, this is Boolean. This is the Boolean case, yeah. Yeah. Why Boolean it? Yeah, and therefore that it's... Yeah, yes, okay. But it doesn't imply there's two values. No, no, no. Yeah. Or I even say this is internal and external existence. Saying that the map is epic is... Yeah. Yes, yes, that's right. At least in the other layer. But then the disjunctive one, because if you have it, it's hand-generated by sub-objects.

2:30 Yeah, yeah. It's not an arbitrary thing. It's a two-second action. It's a disjunctive one. The rest of the actions of topology is essentially the extent of the model. I told this to Seth here. They think it's an arbitrarily complicated quantifier. Actually, there's only these model that are more serious. Well, they can't think without sub-objects, and, you know, they... No, we're okay, I think. Which, of course, really does come from their factory. Yeah, their distillery. Some of these models are all of those things. Yeah. Some of these models are all of those things. Yeah. Some of these models are all of those things. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah.

5:00 Yeah. Yeah. Yeah. Yeah. Because that's grounding logic in serious understanding of material reality, which it's not supposed to be. Well, they don't get the point about, you know, the relative determinations of cohesion and variation as being involved in the considerations about the continuum hypothesis at all, although maybe they would get it if they were forced to think more about it. The axiom of choice and the reasons for its holding or not holding in the real world. In fact, that was the thing you wrote in relation to Penny Maddy's thing about equals, wasn't it? That was a lovely paper. You made the point about that. But John Steele afterwards comes up and says, you know, you just said the same thing as John Steele. That's dis-pray? I was going to say, that's dismissal? That's dismissal? What Saunders talked about was that mathematicians don't really use large cardinals. You have that really nice point about in that paper I remember which I picked up on which well obviously I picked off it because I'd read a bill and your own expositions about the one aspect of the axiom of choice being of course from the point of view of Homology, the non-existence of obstructions to the inverse of the existence of inverses of maths.

7:30 One thinks in terms of the existence or non-existence of obstructions to inverses, and that is the whole content of the axiom of chance. But you try explaining that to a dyed-in-the-wool set of theorists. You might have more chance than they ever explaining it to somebody in the philosophy department who does so-called philosophy of maths. True, but that's not setting the bar very high. Keele actually excluded me when we went to dinner afterwards, of course, and Keele excluded me from the back of the table. Sheesh! Keele excluded me from the back of the table. At least they're still confident that they've been excluded from the back of the table. I hope he was really wrong. Well, I hope he planted a bomb, because I hope he managed to convince the grad students, but it just beats me that these people are so... It does seem to be a particular disease of Zermelo, Krenkel, well, of Epsilon-tics more than of any other position in mathematics that they are, you know, they're so fanatically attached to this particular... Yeah, yeah, yeah, true, and the whole business of that. But I've always thought, ideally, we should take the mind that these people have this fantastic technical ability, they can help us solve problems and solve this. I've never succeeded in doing that myself. Yeah, the problem is that I've tried that, probably because it's me and they wouldn't take me seriously, I'm not even a mathematician, but my impression is that that makes them even madder. Because, you know, you mean that what we're doing is not the one true foundation, you're just simply insinuating that all we've got is a piece of useful machinery. Yeah, that's exactly what I'm saying. I'm not insinuating, I'm telling it. I'm telling you that's what you've got. That's already enough to make them mad, in my experience. Oh, dear. I dare I say, I was watching with Pierre Cartier on the plane on the way over, watching The Third Man, you know, the wonderful old black and white Carol Reid movie set in Vienna with Orson Welles, you know, it's nice.

10:00 You shouldn't have done that, Holly Oatman. You shouldn't have gone and talked to the police. That was a bad idea, Holly. You shouldn't have talked to the police. Well, then, is that the reason for the conspiracy to deny them funding? Oh, dear. Tony Martin, he's a mustache. It's called hard copper, soft copper. It's the oldest trick in the book. They usually actually do it the same day. It's called hard copper, soft copper routine. Yeah. My colleague Scott Williams pointed out it. You will excuse me, I just need to use the loop. Accumulate the elements before you can collect them. Sorry, I just passed out. Yeah. Yeah. What was the, you mentioned this already to me the other day, but what was Emmy Noiter's point about, it was actually about, sorry, that's the point, yes, yes, yes, exactly, yes. No, that's right, Emmy Noiter just asked, you know, what is the definition of a set. Yeah, what's the, yeah, what's the controlling, yes, fundamental notion. And Cantor, and who's the third of the greats? Hilbert. Hilbert, who was quoted to me by Max Vaughan, who discovered the instant cell that was congenial from the point of view, that if you, it's not true that you simulate the elements

12:30 and then collect them into, like the real numbers, you don't do that to the real numbers, that's the third. Of course we have to do that. You define the real, or even the powers that are set, if you know a set, then you... This idea of the power chain has the following universal properties, or however you describe it, and you know several examples of elements of this power chain, and so that's what it is, you can then further investigate it, or not, but you don't have any original idea that you have to accept that it's element. Yeah, exactly. As in the cumulative hierarchy picture, which is absolutely incredible, and so much damage has been done by it. In some ways I have more respect for people like Charles Parsons who champion it but who really do take the question of trying to found it on some kind of serious epistemological account, which of course they have some variant of subjective idealism to do. If I pick some subjective idea as the account of temporality, then I do the people who just lazy-mindedly accept it without even thinking it through, and who just accept that, well, this is, of course, the only possible basis for, you know, the ultimate ingredients of definition of mathematical concepts. Yeah, but about, you see, about media tools now, I don't know, see, I'm not technically competent, you know, but I feel these people are needed, so you have to tell them some stuff. My feeling is, you know... Suddenly, V equals L is too strong. It's a generalized continuum hypothesis. It could be true, but it can't really be true. No cohesion, no variation. I think there's something stronger still. The mathematical nature of it. Where V equals L is not a mathematical nature. It's a super-glorified subjective concept. It's not even the extreme case of constancy. I basically feel all stories about iteration are way overblown. Even the so-called natural numbers are an exaggeration. A useful idealization. I call it a useful idealization. Well, of course, you're singing to the choir when it comes to John Mabry, although, of course, his motives are slightly more different.

15:00 You said you could see the natural numbers. Well, you see, that's the point at which I was probably coupled with. Yeah, yeah. Who can see them? Yes, what? No, exactly. Well, it's the point that John Mabry repeatedly makes. People just are so, you know, they just never think about the dots and ellipses, you know, what the hell they actually mean. Of course, he's got a different argument because of the dedicated construction of the natural numbers of the simply infinite system rests on already this very strong set of principles about power sector. There are now known ways to also qualify. You take a model that you assume satisfies that, and you omit some of the ordinals, omit the ordinals from the way, but that now all of a sudden you have things that have been omitted. You can do this in such a way that you still get a model that says that? Yeah, yeah, and it's not like it doesn't qualify. Oh, sorry, we haven't, yeah, you'd like to pay now. How are we going to do this? Okay, well, let me. They put it that way, but I don't mean to ignore it, but it's quite omitting some instances of this iteration. No, I had heard that there are much other than horsing, but I didn't understand it in a straightforward way. Yeah, that's most of us at the moment, who's the very urbane good company I've never actually had. Yeah, I've often thought that I was like a great student. He just missed me. Oh, a bit like Harvey Friedman has dismissed Grotendieck for God's sake. Well, no, that was part of it. No, but there was also that Steve Simpson bit when somebody tried to, it may even have been you, tried patiently to explain to him, you know, just what was so absolutely great and profound and astonishing about Grotendieck's work in the task of homology. Oh, did he do that before or after he was fighting with the Vietcong? Well, I hate to say it, it's a little bit like listening to... I'm sure the man is a member of Ayn Rand's society. I'm sure that reaction to him, when I goaded him about Ayn. Well, Ayn Rand, I goaded him at one point, because I said he came up with this incredible crap about, well, socialism has been tried and it's always failed. It always will fail. It will fail everywhere, necessarily, because socialists just do not understand that, you know, because socialists just don't understand it. And that's why every social society will always screw up.

17:30 Blah blah blah. I said to you at one point, I said, well gee, you know, did you get that from the Ayn Rand Society? And he said, what have you got against Ayn Rand? Thank you. But he didn't quite say what he got against Ayn Rand. He said, well, I think you haven't distorted the view of Ayn Rand. I mean, you know, I mean, she wasn't anything like a fanaticalist. So he didn't actually come out and say, you know, how dare you attack Ayn Rand, but I suspect that he might be a closet Ayn Rand. Well, I do know that Heissel and Ransdown are not even conservative. No, they're not. They're just because it's not rational. I got to watch this marvellous movie clip, which you can download on the web, and which I think I could probably get tonight. Which, in fact, I sent to John Stachel, which, believe it or not, is on the Ludwig von Mises Society website. Mies is obviously an arch-conservative right-wing economist, but nonetheless a friend of mine sent it to me. I wasn't flousing on his way. A friend of mine sent it to me. Okay, guys. Okay, but he's a friend of mine. You must have had your reasons. Yes, but he's had a friend of mine send it to me. However, once he sent it to me, I must confess, I did go to the website it came from and looked at some of the other videos for the moment. None of them were anything like as funny as the Ayn Rand one, believe me. But the Ayn Rand one is very funny. My family has $20 million. I'm part of the Wheeler class. But I made some comment about the Wheeler class in some paper you see. I'm actually part of the Wheeler class. My family has $20 million. People who have only $20 million, these are easily, easily likely to be captains of the Wheeler class. But they themselves are likely to be captains. Magnificent. What you should have said, well that was a very good indeed put-down. But I would like you to use John Mabry's model.

20:00 Well, you can't do it in terms of mean molecular kinetic energy, because there are no molecules, obviously, at that. And that's the state of time that's made very guilty. Yeah, exactly. This is like temperature, like 100,000 degrees. Yeah, exactly. Yeah, the guy is never going to know what his bank balance is, or let alone anything like it. He might know within a... You, well, depending on the stock market, you might note you're within a few hundred million, you know. But if we tried to sell off the stock, the prices would all plummet. Sure, of course, of course. It's a little bit like crazy, if the Queen decided to sell off the Crown Jewels, it would be a really bad move, because, you know, first of all, you'd ruin the market, too, you know, who would buy them, really. Yeah, yeah. Sorry for the guy. Harvey was there for a couple of years, and he always got along. Oh yeah, it was always on the iPhone. I always thought it was on the iPhone. Until the moment of death. And this came as a surprise. Probably. Yeah, yeah, I know. I had to say that they kind of gave... But still, the fact that he later... Sure, sure. So it's just a little bit tough, huh? And actually, John Mabry has made the point to me about, you know, Harvey's papers on the intuition of physics. But, you know, the nonsense of his end of the taxon... Nobody said this to me in a couple of years, but up until a few years ago, people were periodically watching, you know, the... without knowing anything about it. The first word that that artist gave them was, these souls represent an artist. And yet, they spoke knowledge that they hadn't read yet. Did you actually ask Harvey when you were talking, when you were up with him until half the night, if he confessed to having read the economics? No, I didn't. Ah, pitty. It would have been interesting to hear.

22:30 No, we just, that night, we talked about... This is an article by my hero, actually. Oh, sorry, I thought you were talking about... And Goodman. Okay. Sorry, I was the top servant. Yeah. That night, we talked about his plans to blow the lid off mathematics.