Discussions, incl. M Wright, FW Lawvere & A Kock on objects & subobjects

0:00 Thank you for watching. Thank you for your attention. For the classical way of thinking of the variable in terms of the main base element, the classical body of one assumes that there is. I mean all of these, yeah, I say all of those effects are suppressed, I mean they seem to have... Yeah, it's all human, it's all identity, it's triplated, separated. I must go away and understand this really, but it's certainly a little bit... Thank you for your attention. Thank you for your attention.

2:30 Sub-objects of the top three of anything, of anything. And yet people did, there were people who seriously talked in terms of failure of transitivity of intel, weren't there? Yeah, well, I guess it followed us for only a few years, but... It certainly seemed as though they'd actually discovered something. Rather than that, rather than that they discovered that the formulation was wrong. Hmm, hmm. It's the Tarski standard of formalization. Yeah, sure. Can I have the dark gold? You can, of course. In fact, there's your crystal. Is it the same? No, it's smaller than yours. In fact, it might be a bit of a better one. Yes, because of course the people who pointed out the failure of the substitution group of the logic in the case of quantum logic, the beads, it's not the full symmetric group, but of course made that exactly that equation. Aha, we're learning something about the transitivity or relativity of entailment. It's all very confused and I...

5:00 You've explained it very, very clearly how one does kind of think about in terms of presentation that this is the general, the general spectrum. Is this what I assume? It does seem to me, you know, we really do need to write this up for the philosophers, the philosophers from the bad, falling into bad companies. I think it's actually due to, I think it's actually due to Schroeder. It's actually due to Schroeder and it's implicitly there in Des Moines. He's actually treated logical relations as an intended subject. But I think it's actually in Schroeder. But yes, it certainly comes up. No, it's not actually in Frege, because Frege is not really thinking of a perceptive retort. It's a calculus of extensions of the predicate. It has all the criteria for identity building, rather than building up the elements of debate and extensions of the predicate. Carrington's syntactic level was in addition of the inbuilt criteria of identity rather than from the semantic side. But yeah, it's certainly there in Ruffel. But I think Ruffel himself takes it from Schroeder and other people who were writing a little bit earlier. My life hung up on this. The reason I'm verbal about it now is because I'm afraid so, yeah.

7:30 You see, at the time when I was impressed by people, it was all connected with some kind of protagoreal relativism, a relativity of all levels. There was a time when I knew no real mathematics. I wasted years pursuing these, none of the rest of them, and if I'd had a good... Introductory text, in which the order of exposition is a basic concept, like somebody coming from the outside. It would have saved me an awful lot of weight. What do you recommend for quantum mechanics? I'm going to tell... Oh, this man is swift! What do you mean? Recommend us on the outside? The answer to that is I don't think there is any good, I'm absolutely convinced that there is no good introductory text that approaches things from the philosophical side at all, and I'd love to see it written. I'd love to see it written.

10:00 I think the right place to begin is actually Hacker's theory. Existing expositions of quantum theory from philosophic side are very, I guess, best misleading. No, the only one that's quite not been misleading on that, where it doesn't get quite deep enough into the first of us, is Feynman's undergraduate lectures. Yeah, I think they're good. He lays out the problems. Squarely, squarely and properly. I still think Dirac's 1930 book, the very few motivational, very few conceptual remarks in that, I think are still amongst the most carefully considered things ever written by physicists about the subject. And he certainly thought very hard and carefully about what he said. There's nothing to stop you. Thank you for your attention. Yeah, but if at the end you're going to say, learn to give up trying to understand. I think that's what most of them have done.

12:30 Exactly. I don't think they don't like it. I don't think they like it. It becomes positive immediately. If you're young, you go in there and you don't like it. Jump into the deep end and learn to swim. Yeah, but I think if the advice is to start by giving up the ethical understanding, it's a matter of, I would say, as good a short conceptual introduction as I've read is actually, is a historical essay, is an essay by Clifford Hooker in the book called Conceptual... I don't remember the title of the book. I think it's Conceptual Problems in Foundations of Physics, something close. I can't remember right now the title of the book. It's probably from the 70s. It's a essay called Metaphysics of Modern Physics. And I think there he actually gives us rigorous aim. The presentation, as I know, for a general audience, of what the fundamental mathematical and conceptual aspects of the difference between field theory and particle theory are, and relates them to the whole discussion of thought about the plenum of mathematics, and actually isolates the relevant logical algebraic structures and how they work. And, you know, he has this position that he analyzes everything that comes with the tension between, uh, Plymouth and, uh, between two theories, um, and he regards quantum theory as one that is flawed, um, and, uh... And if you don't share that particular philosophical position, then you may not judge that he's done a very good job of presenting the theory, but I think he did a very good job of presenting it. The other good introduction is what is coming out this year from Redhead and Teller, Paul Teller, called an interpretive introduction to quantum field theory, which I think is amongst the most...

15:00 See, I think Cambridge University Press, yeah. Michael Redd, who's a professor of philosophy and science at Cambridge, and Paul Teller, who's a philosopher of science at Chicago, the son of Edward Teller, the physicist, and called it an interpretative introduction to quantum field theory. That, I think, is as good as anything I've read. I mean, I've read it in my proof. I've read it. Quantum Mechanical Wave. So can I ask what is... I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry, I'm sorry... In particular, I'm interested in category and the correlation of quantum models, and there is a lot of interest in that, particularly context-based. Did you read Penrose's book about Oberammer? Yes, I did. Yes, I did read it. I like the book, but it's a lot of, you know, I suppose when you've reached that level of distinction in your subject, it's the kind of book you're allowed to write. It's certainly to be preferred to Hawking's book. Hawking's book, Hawking's book, Hawking's book, Hawking's book, Hawking's book, Hawking's book, Hawking's book, Hawking's book, Hawking's book, Hawking's book, Hawking's book, Hawking's book, Hawking's book, Hawking's book, Thank you for watching. No, Penrose is... I think there is a great need for more books pitched out precisely at that intermediate level in terms of what I call a high popularisation, a serious-minded popularisation that Penrose has pitched in that book.

17:30 I think it's excellent in terms of the level at which it's pitched. I think it's a pretty... I was actually after I finally finished it. I know many of you have been in there. Steve, you know, gave up on it. He got annoyed. Well, that poor Schrodinger's cat came home. I got to get in. There's an idea of the relevance of quantum gravity to metaneuro science. It's certainly very weird. But what about the mysterious view, or our insight, being reduced by aspect to a path that he wants to avoid? Well, he wants to avoid having to come clean and admit that he's been half-and-half pregnant in that year. No, no, no, I'm not talking about that. He's a pregnant, rather peculiar sort, a rather kind of spinozistic sort. He really doesn't believe in the pre-adapted, there's a kind of convergence between a pre-adapted structure and a pre-adapted mind. In terms of a kind of simple reflection of the reality of the right door or wherever else the equipment is located, he actually sees it as a kind of evolutionary dimension. Actually, I don't know of any research, I don't have a map, a single research mathematician would just have that same feeling of everything, that there's something out there. No, invention is certainly not the right metaphor, but discovery in the sense that we're really... The set theory conceives of it, I think, is also equally the wrong metaphor, because I think it's all objects, pictures of objects, existing out there, the same or different, absolutely, to be the values of the theory, but it actually goes with certain very classical ways of thinking about the domain that already build interest in the level of the way the... Extensionality gets expressed in topos theory one season. It's actually equivalent to a relative uniform central ability in the applied topology.

20:00 There's a great deal of geometrical and topological structure being assumed in the domain. I think they're trying to let us know. I think probably they've saw as soon as we can. Can I get your opinion? Well, let me give you one. Okay, that's good of you. Do we have beer? Do we have beer around? Yeah, beer right. That's pretty good to me. No, I agree. It has become an almost undefined term. Back in the 50s and 60s, it used to be said that it was jobless. You are bugging me now. Well, then sit down here. Thank you for watching. Well, I hope this provides a little bit of an overview for you. Two reiterations that we found in some of the public presentations as well. You see, there's a lot of media out there. You will find that there's a lot of media out there. There's a lot of media out there. I'm sorry, you've just chosen the wrong place to sit. Mental act. Of course, that is there in the very loose where Timothy was born. Not in here.

22:30 Not at the moment. No, it's real quick. We'll get there later. Sorry, I'm not going to drive outside. There's no point in letting it go to waste. But that is, of course, implicit in the Born Interpretation and, of course, in most of the, what was it, physicals with the Copenhagen view. The whole question of the split between the observant system and where to locate it, anywhere between the back of the retina and the mind of God, is a very arbitrary boundary. It's just a question as to how many points can we get there. I really didn't realize until about five or six years ago that there was no such thing as a tree in the park. No. The keys of a view of reality like we have here is not set in stone. And that was the focus of the whole lecture. Which is nothing more than just thinking about this myth all over again. It's not exactly what you would call a maximally important statement. It's literally showing us something clearly different. So we don't have any reason to keep on going. Here we go again. Thank you for your attention.

25:00 All because they are very lengthy and time consuming. What is this video? Sorry? Please hold down. What is his name, I don't know. Thank you for watching. I very much want to take up Bill's standing invitation to go visit him, probably in conjunction with Jerry here in Alberta, or perhaps two others, maybe not at the same time. Thank you for your attention. Not just in the bosonic project also, but you can actually do the symmetric algebra as well.

27:30 Quite well. Especially what Jerry's thesis is all about. Thank you very much for your time, and I hope to see you again soon. We want to stay firmly on both sides of the boat. Our relationship will stay firmly on it. It's amazing how much you don't get to explain though, isn't it? Thank you very much for your attention and I hope to see you again soon. So say that again. It's between the domain and co-domain you introduce another, another, so I break the mapping, yeah, into two mappings. To all the co-domains. To all the co-domains. So that's what I do. Domain is a co-domain. Although, although this, this will go there, because it's going like that, what I'll do is I'll take...

30:00 So maybe that way, with a pair of portable mappings, I may be able to express explicitly the fact that it winds that way. Yes, simple notion, but that of winding numbers. That was the theory of topology in the conference. He doesn't have anything. No, he doesn't have any. Because most, I don't know, if I was left in the room, I wouldn't. Most of them, without knowing who they were, just going by appearances, I'd be very wary. Most of them, you would get it on the street. There are one or two very cardinality of decisions, especially when they get to the point where they get to the point where they get to the point where they get to I was frustrated because all the conferences I've been to in the past 20 years, I never, never had to look up a book in the library. You just didn't let me have the book. Yeah. And now I would like a book. Yeah. No, but the first time... But you see, I'm quite sceptically...

35:00 What's so objectionable about the lecture, though? I mean, I thought it was... I don't know enough about... I did all this clock and stuff, being as careful as I could, and given that I don't have anything like the necessary background, looking at things, I mean, okay, basically it's looking at closure conditions, and all that stuff about the way that one thinks of the domain, when one goes outside the domain of a partial map, in terms of a kind of valuation map, the natural numbers actually have to be thought of as numbering in the computer science context. I...

37:30 I think, you know, I thought it was really rather... Listen, I will say what I think. Well, tell me, I'm... Whatever it deserves and so on, I assume it's competent enough to manage the eight categories and so on. Well, yes, I'd say more than that. I'm looking for something that relies on what I may be doing when I call it. And all I find is... Well, sure it is, but it doesn't make any claim to be anything else. Does it? No, he's making a claim about, you know, when he makes a claim by proxy, of course. I mean, he's just saying that the way that computer scientists think about that. Yeah, let's walk back on the table. Yeah, sure. Anyone who does name something a quantum is by implication making some sort of claim that this is something to do with quantum theory. Sure, sure. If he's on a bullshit, then you see, even Jerry has presented his paper in the introduction. It's having something to do with quantum mechanics. All this is a little bit of mild sense-making. The computer science department should take on... I'll tell you what it is. If I was a software... You brought me all the PhDs in this type of computer science. I wouldn't expect to do anything else. I wouldn't, would I? No, nor would I if I was a software analyst, because I'd assume that... They do not know how to program. Well, so would I, but then, I mean, the ability of knowing how to program is... So what is this label, computer? Yeah, but he isn't a computer scientist, he's a pure mathematician, he's a category theorist of a very pure sort, he's done very fundamental work in category theory and functorial semantics, because he's not talking about computer science, I mean, he's just taking that, I'm sorry, maybe I'm missing something, I don't think he even claims to be, he's saying that there's something which computer scientists, there's something in the way that computer scientists think about their programmable functions, that...

40:00 Contradicts the way one thinks about limits or appears to be and here I'm in all this business about the you know the fixed points over the map when you go outside the domain of a partial map and the way that you think about the natural numbers of it I thought what you had to say about the way you think about the natural numbers of it the way that you know the computer scientists think about their effective natural numbers of it was actually Oh, I have, but I, of course, I'm not able to do it. I don't have the equipment, but I thought it was very interesting. What can I say? But on the other hand, Bill, Bill obviously... To you, to you, it's interesting. To me, it's... Yeah, but on the other hand, Bill obviously did shit of a rather dangerous sort, so... In fact, to me, it might have been very interesting, but I... It almost doesn't occur. No, I don't, I just don't know. At least we've moved from black to blue. I want to go to all of these. I'm very interested in lambda-calc, aren't I? Yeah, well, we'll see how we get along. We've got three hours, for heaven's sake. Okay, I'll see you. Some sort of multiplication, yes, yes, yes, right.

42:30 That's kind of one thing. That's good to know. Very general result. And one way to do it. Aha, aha, aha, aha. You can remember that one. Can't we talk about what's basically, what's made interesting in context? You know, what one imposes. I'd like to know more about that. You have the kind of not just fuzzy membership, but actually fuzzy equivalence really. It's the way you go from the external to the... Well, I'd like to understand a little bit more about that. I suspect this stuff at Highlands is also very interesting, although I don't know anything about recursion theory, how it connects up with computing.

45:00 The amount of structure you have to impose to get the size of the letter. What is this that you're reading? What's it about? Knots, yes. It does look interesting. It's not, um, Raleigh-Browns, is it? No, he does a lot on those. Oh, put me down for one as well. Oh, let's read this. It's interesting. Oh, beautiful. By the kind of, uh, by the kind of action.

47:30 If you ask him a question, he has an answer. If not, he will just plainly say, no, I don't understand what exactly you mean. But if you hit the right question, he's prepared to answer. He will. But it's very much in the computer context, in the context of, you know, computer science. So where's the payoff for your... It's kind of interesting to hear the science from the top of the stage. Making models who master those types of things. It has to be quite rich. And it's very interesting because you've got lots of ways of, you know, you have to make lots of distinctions between some internal and some external. So I'm interested in that from the point of view of this, you know, interest in relative identity. Well, it seems to me that's a piece of very interesting mathematics and computer science may be a good excuse.

50:00 Why do people study that from a scientific point of view, knowing absolutely so much about science? What is it about, particularly about mathematical type theory? I don't know. I think it's a good thing. It would be useful. It's just like linear logic. It's much more interesting than linear logic. Yeah, I think linear logic is far more interesting. I'm not doing it. I'm not going to do it. Alberto Peruzzi, the guy who was here, unfortunately left yesterday. He's a friend of mine. He's very interested in mathematical mathematics. So, I left him for a while. I'm gone. We're still waiting for Bill to write up his deep thought. Well, he's promised that he will, yes. John Bell, who's sitting in Canada, he's asked the other people to send in their papers, and he's actually solicited contributions from a number of people who were there who didn't actually give papers, so I come. He's submitted a couple of interesting papers, one on versional expansionality across the speech, philosophical significance, and some strength of difference, separability. And I think in fact everybody's now sent their papers in except for Bill. And the whole point is it's meant to provide the papers are kind of, since a lot of them are kind of reactions to Bill, it doesn't really make sense unless we actually have his contribution. So hoping that we can persuade him to get on and write it, write them up. But the problem is he goes on having ideas at such a rate.

52:30 And, you know, they're so fertile and you never have the time to sit down and consolidate them and actually write them up as well. Well, we're not going to write a book. No, John was just asking when we were going to, if and when the book of the Cambridge Medium was going to come out. Oh, that's right. And I said, you know, it rather depends on Bill. He actually gets down to writing anything. John Bell has said to me today that he's got Master Gallagher on his vision, so I'm going to look at my own Gallagher's vision. One minute. What do you think about that? It's hard to judge. I thought he believed in it very much. I mean, it's shocking. We're talking all the gulf, mathematicians and ex-physicists, constructionists. Okay, I'd like to ask a question that we've heard, well, there is a question, and I think we ought to be honest with Berwick, while we don't know the manga-banger that went up there. It is a good question, I mean, unless it's a friggin' one. It could be actually adding one repeatedly in successive. If I think about it, I may perhaps determine that this is not a very deep question at all, but I'm not interested in it. So he seems very strong with that, because that's his personal idea. Certainly it is. I asked him about... I think that I didn't get the clear cut answer for all these things I don't understand. I'll put it down.

55:00 He also has to watch it. I'm really interested to see his confidence and see if he can tell me. Because this is a bit of the bonga bonga, you know? Yeah. Well, well, well. Well, well, well, well. I'm trying to decide whether that last lecture did in fact shed any light for me on the natural numbers or not. It was an undecidable question. He certainly leaves me very passionately. But he has something important to say. I don't know what it was. I'm not going to go for the next session. I'm going to come back for the last meeting. I just want to get my case out.