Discussions, incl. M Wright & A Peruzzi on Lawvere's paper (contd.)

0:00 I just don't want you to tie yourself to mathematical abilities. I'm just about to ask you about this, because one's assuming a great deal about separability already at the level of this.

2:30 It's said that B is an open ending, but it isn't yet quite that. I mean, I can't answer that. It's a condition which it might seem very natural to relax with.

5:00 The only point is that, in this way, it is the emergence of out of matter. But look. You don't need that just to be like this, of course, but when I read, Bill, I found the general framework of biology, you have, what to say, in the case, in other words, of can we talk about the model of physics, the model of the model of physics, these are what we call, here, codicil language.

7:30 The logical options which manage and what is this. This one is a zero. This is one. Three is yes. Well, certainly three is yes. Until then, until then... I like that. The range of parts of the thing gives my idea of reductions and patterns.

10:00 Yes, it's beautiful and very, very elegant, the application of the role of adjoining, the role of adjuncts in understanding the emergent, constrained emergent complexity. The only thing that I find I'm still a little unclear about is how the ultimate effect of the ontological status of the structure of the cohesive active set as against that of the The components in the case of the level 0, but it's very difficult to go on, but it seemed to me that he did actually have, because this works perfectly for the case, as you say, of the emergence of properties codified at the biological level. Particularly at the level of organic, in terms of the emergence of that kind of constraint at a more fundamental level, the fact that you have in the downward, you do already have in the case of the second law of thermodynamics, very strong strength built in, in this downward direction, on why the level of, one has undrained strength.

12:30 In the context of non-separable systems, how would these ideas fit in with the suggestion that one might need to some kind of contextual factorizability condition in order to understand the kind of ontological holism built into non-separability, apparent non-separable behavioural quantities? I mean, there does seem to be a kind of activism built in in a downward direction. I've always thought that Lorbier really did think of the structure of the topos as a very special case. The cohesive abstract set has always to be constrained. There is something missing.

15:00 There is something missing. What is missing is that... Sir, that's okay. It is that we are involved. It is that we are global. The concept of global characteristics is not necessarily a matter of the fact that there are infinite levels to the cohomological hypothesis of minimal molecular complexity, and that is the minimum level given the boundaries of this.

17:30 The concepts of good descriptions are, I apply, and I must say this, the problem is not the size. I know exactly what you're talking about, when he remarks in the beginning of the lecture, which indeed is also borne out precisely by what he was saying about Eitan-Luke, about the way one has to understand there being domains of variation which are too large to be set. I would love to understand what exactly is intended by this remark about their two topological characters.

20:00 Presumably, it means that one does not recover the... In case one wants to have the global equivalence to the local equivalence. One will have no recoverability of the global equivalence to the local character. are naturally the ambiance, the setting in which logical variations. Back to your point about the ultimate topological roots of topological genesis of formal notion. But one wants to say this is also the ultimate topological genesis of the formal notion of being a possible element. Whatever happens to be the lowest level of structure in your particular construction. Now how would you understand the abstract case of constant sets? ...as emerging vis-a-vis the structure of the cohesive active states, the main ones, in this way. Particularly, I find this deep remark that he makes, which occurred in both papers, both in this paper, the Catalogic State and Quantity paper, and in the survey paper, the Catalyst paper, about distinguishability and indistinguishability. Level zero, as I can show in termologics, are the double nature of its inclusion in the lab of maths.

22:30 The double nature is its inclusion as both character of the orbit, the chaotic, the pure becoming, that notion of the physical notion of things which are there, the double nature of the thing, may help to resolve problems of distinguishability versus indistinguishability, and hence obscure distinguishability. In terms of general remarks, although it's still very insightful and illuminating and guiding, the discoveries that still propel our subject include the idea that a category of objects of sorts is not specified and still unexpected, and by means of which it can be distinguished. The core of it is that one does not have any absolute notion of distinguishability of objects initially. It is only through understanding the maps and the relevant categories.

25:00 ...that one has actually the means by which the objects are themselves distinguished. But at the same time, obviously, there have to be definite remains and coded remains, so there's a mapping and identity of that. As you get to the point, you see, there have to be definite remains and definite codings, and that there must be identities, and then you, of course, have to go. To this day, there are many who think one could usefully generalize by omitting these requirements, sometimes on grounds of dislike of the status they think they imply. This is how, in modern Greek, status means a bus stop. I used to connect a network of speeding buses with me without bus stops. How disembodied would the process be without a state? That's a fascinating remark. But of course it does, indeed, how disembodied would the process be without a state, but that does not necessarily, but again, when it comes back to Rosen's point, about there being an absolute notion of state for the system, complete separatism or separate. They're given in advance. The notion of state of the system is given in advance of the dynamics of the system as itself a very special limiting case.

27:30 ...an object that is not stable, with a certain intensity, with a certain quality, that it works, that we're here and that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, that we'd like to be here, With that dimension of mathematics like Bill, I think I have fully confronted what it is about that I have in mind. I have a presentation of some of your concerns in what Dulles says about the understanding of the domain, just the difference between the sense of articulation as having no intrinsic structure, no structure in itself,

30:00 prior to the articulation imposed on it by a particular... But, in the case of the debate over relative identity, which requires the choice of a thoughtful and material identity, it seems to cut against what he says here, when he says that, quite rightly, given their understanding about the category of maths which transform the object, by means of which they are being distinguished, the understanding of extension, whilst, I mean, that does seem to me to be in tension with what he... He says about the absolute incompensability of the framework for rational thought of, and this seems also to be, and yes, obviously, an action to do. In other words, whether he's an active set of the starting process, are they generalizations?

32:30 Sorry, I'm burbling. We're getting nowhere. I'm just burbling. Sorry, can I just have a very, very quick look indeed at what he says here? It is interesting, he does relate this Quotient to Decidable Objects paper of Johnston to his own paper in Boulder. If he groped to clarify in this paper, I just groped. But it is interesting that, obviously we're on for very important, so we'll leave that for now, but again I keep coming back to this suggestion that by thinking about identity, really the, not... As one does, very quickly, in the semantics of classical quantification theory, you can think of the domain as having an absolute identity object, therefore any equivalence with it as naturally of lesser strength, hence the very notion of partitioning and of the partitioning of the domain under the thing that gives you the structure of the domain as And this way of thinking of equivalence relations as, in the first place, equivalence relations in topology and the relationship between the local and the global, the local and global topological structures of the domain, determining whether you can get from the local to the global. And the case where you can, I mean, that, it seems to me, goes to the core of the difference in the way that the sex theorists and...

35:00 That seems to me to go to the core of what it was about sex theory that so naturally gave rise to the metaphysics of it, and what is it were the naturalistic core of thinking about equivalent relations and structures in terms of the quotients of equivalent relations that ultimately arise from some structure in the real world, which one has in this approach. Anyway, I don't know how you'd agree with that. I'm sorry it wasn't very clear, but it needs a great deal of careful thinking to make precise, more precise, carefully to be made precise, but I do think that for, I'll put it this way, I think that for... For analytical philosophers, it is probably one of the best points of entry into introducing the conceptual importance for philosophy of mathematics of Laugier's ideas, and particularly of the opposition between the way of thinking of structure arising from, constrained by...

37:30 Properties of structure and its concrete guises, its concrete instances, rather than as simply lodged, embedded as one instance of an already given abstract. Sorry. Sorry, I have a very bad catarrh. Very bad catarrh, which makes me occasionally want to... Eve. That's like a croup, sorry. No, of structure in its more concrete guise, structure instances, as actually giving rise to, forcing the development of concepts of abstract structure, such as those dependent on the extensional Platonist notion of object, rather than of... Just being instances, as the Platonist thinks of them, as physical structures, just a type of structure that is delimited within antecedently existing abstract structures. Also historically, I think that the point about the debate in the semantics of quantification theory... I think that the debate is obviously the ideas of Voltaire and yourself about the understanding of the three variables, what is already the metaphysical component of the notion of three variables and how that connects with the... In-built drive towards either a faceless or naturalistic ontology of mathematics is such a deep and ramifying point that it's very difficult to find the right point of entry into the discussion of the presentation, but I just think that one A quite useful point of entry into the discussion for analytical philosophy is perhaps in the discussion of the relationship between equivalence and identity.

40:00 The idea that identity might actually be a limiting case of equivalence rather than equivalence as presupposing identity. And that, historically, at least in the English school of analytical philosophy. Because they already know, is by definition has to be defined on a domain, which already has an identity related to the mind on it. Exactly, but that's the point. You can't explain this perceptive. But you can tell a philosopher that it is a very striking and important fact that you can't explain this perceptive, because that's the way that the fly bottle took its shape. To use a metaphor here, I'm predicting what's used in a very good... There is a good historical talk about epistemology of mathematics called Leibniz. They can't prove the eternal truth. Which I remember he gave as the lecture at the British Academy in 1973 when I was his student at Cambridge. He just wrote a lot about, I think the fly bottle, the fly is trapped in the fly bottle and only history can reveal the fly bottle's shape. And the fly-bottle that he was talking about was precisely the endless circuit of debates by, in analytic philosophy and mathematics, between Platonism, Constructivism, and Institutionalism, which he was saying, you know, rightly, at that point, the early 1970s, had really rendered the philosophy of mathematics a very moribund and unimpressive field of philosophy. Which at that point it still was. I think in fact that was perhaps already ceasing to be that, or of course that was the very year that, anyway it doesn't matter, I would say that was the year of the NASA paper which was probably the thing which marked the beginning of the renaissance of good work in philosophy of mathematics in the analytic tradition. But it's just that point about you can't... You couldn't possibly, what I have just said, the slogan of this lecture, which is that identity presuppositions, would just seem drivel, drivel, to defend the subject.

42:30 But you understand the point, obviously, though. Mr. Price, you've got to understand the point. So many deeply interconnected, ramifying intuitions. But I think that your article on categories and logic is easily the best attempt by any body, philosopher or mathematician, to present the philosophical and mathematical design in a very long way. Much as I like Colin's work as a clear expositor of category theory and toposphere itself, I don't think that any analytic philosopher reading his work is going to feel that there is anything... More here than one further sharpening of really the existing debate, you know, between structuralists and mathematics and, well, I mean, really the way that, I'm not, I'm not a chronicler, he's a lovely man, a very good friend with a good right and a good thinker, but I think the problem with his position is that the way that he presents the issues really just makes a lot of... Oh, you just want a piece? Yes, of course. It's a very quick antifasto without taking up too much time. Si, mis pistofrottini e bere. Si? Si, si, si, mille gratis. And then take two? Like we had at the... Si, bene, mille gratis. Yes, that would be fine. Then two pieces and then we're convict. Shall we have a litre of wine, one by one, and then we'll...

45:00 It'll help you sleep after you... Would you prefer a white wine, the top of the world? Okay. No, no, not at all. Whatever you're having, I don't mind. I just like wine. But when you've had a very sore throat, I think white wine is more of an anti-terrorist. Red wine always makes you feel you're rougher. White wine, I think, is more soothing. Thanks. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. But no, you see, although Colin's work is very important, I think that reading his papers, a lot of even good analytical philosophers, philosophers of mathematics, people like Michael Reznor, are really just going to see categories, theoretical foundations as just the latest mathematical state-of-the-art version of calculus, as it were, just as... And syntactically, as it were, as a way of internalizing the structuralist thesis at the level of syntax. And it's so much more, so much more than that. Thank you for your attention. Yes, I like this space very much. What do you mean by that? That is, you are at the core of a new kind of grand, new construction, new disguise. Which a lot are. What? Not in your book.

47:30 But... Yes, exactly that point. Not in your book. But of course... But as far as the business is about, it's standing. But there is a metaphysical point about state and process to be addressed, which Bill is, I think, not addressing in those preliminary remarks, but rather, you know, he is perhaps rightly setting it aside for now.