Last part of morning session & papers / brief exchanges with P Freyd / lunchtime conversations

47:30 There will be no motion anyway. Exactly. Or as the reality is... So, of course, if all we know is the abstract sets, then we have no other guests. And then you've got some galaxy points, which is a nice thing to have when you're talking about the adult, but it doesn't seem to be a problem. One of the things that I've learned in life is that we can only matter with the guesswork of what's at hand. The notion of figure, how much of it is already an intrinsic, dynamical aspect of the human population, the notion of generating figures, the notion of generating figures, the notion of generating figures, the notion of generating figures. There was another thing I wanted to ask about, not directly connected to this at all, but something that happened ten years ago when you were talking here in Cologne. The exercise was about many, many topics. The one that I remember you led off with, which was about the question of the signable problem. Well, I wish I'd been 20 years old. It's usually quite appropriate. I tried. There was always a problem. But about the question beside the block, yes, the question beside the block, yes, oh yeah, yeah, yeah, yeah, and particularly about the asylum, the different proposals, yeah, the one that Johnston was writing about, his paper, yeah, and the one that you were writing about, so I still come up about the asylum. All toposes are 2D toposes in the sense that you get the same hiding out.

50:00 It's a purely logical point of view. You could hardly... Distinguished, so even though he knows that they are different, it's an unimportant epilogue in the spirit of his. I, of course, turned this around and said, this is a huge diffusion. This is the crack through which the entirety of geometry is going to come. This was my polemical response to it. His idea wasn't as good. And Freud, too. Freud even had a paper which is called, All Topoi are Locale, which is an absurd statement. But by it he meant, well, somehow the only thing that really matters is logic, and we can capture every aspect of pure logic faithfully and especially in quantum mechanics. I think it was Johnstone who later isolated that QD was a sufficient, fairly natural class to do that. But I still need to understand how... I still need to understand what it is about the distinction between the different hypotheses. In fact, is it the distinction between... Thank you for your time, and I hope to see you again soon. These would be locally separate, but nothing separate. It seems to cover most of the things on campus, includes groups as well as post-sets, but these are somehow based on groups, whereas they are parts of it. Well, that's what I was putting forth there. I don't know how that's refuted, but there were various conjectures in which we could have worked those things out, and how the community fits in all of that.

52:30 Yes, and how we both have a lot of responsibility for generating figures as well. But it's actually not only logic, because... More recently, we have Joel and Kierkegaard, and Bergdahl, and Woods, and Kohl, and Kierkegaard, and Kohl, and Kierkegaard, and Kohl, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Kierkegaard, and Where it's a category of spaces, so always pursuing in a way really this idea that it is like a space, so that they all seem to be a key. Well, the homotopic theory, like the logic, they explicitly construct, given an arbitrary total. Not only has the same logic, it even has the same homogeny. Hence, in particular, the same cohomology theory, but this is, you know, based on fairly natural but still topos-equal-space oriented fields, namely that it's very simple that you regard two geometric morphisms as homotopically equivalent even if there exists any natural transience between them. And this is always, by the way, a small set, even though the toku is itself very large. So there's a lot of content to this idea. In fact, it's very effective that one could... This was done by Joyal and, I think, Reitz. Joyal and Reitz. About ten or fifteen. You can exploit this very much by calculating the cohomology of spaces and more general topos by using actual non-locality topos, which are homotopically equivalent to ones that are locality, but which... Have some other nice feature like obviously they can classify tokos for a beauty group or complexes of beauty groups or something like this so that these two...

55:00 But they all ignore, you see, the aspect of, well, what about those topos that more than have to do with the objects in space? We have a different point of view. The other point about the capitals. Yeah, the topos are the capitals. They generalize space. Yes, and of course that is what gives you the, the decidability aspect of the case study. It's a good citability aspect, as in the case of the generalised space point of view, the question of the question. It becomes natural to think of that as a particular examination of this more generally. I think it's actually hard to explain, but I mean, there's a lot of content there that we've lost. And I don't think we understand it all, at all, in the form of these things. There's a passage on the road co-post to the two co-posts associated to an object. There's a fundamental rule in the classical application of sheet theory, even though it's not described in that way. In other words, put it in something like this, that the space as such is mainly coherent. This contains a potentiality for variation. So let's pluck it out and look at this potential variation. So it's contrasting the two aspects. The two dimensions. Not the same, but dialectically related in some way.

57:30 To believe him or not, to believe him or not, the mind of you will be minimally stable in between the maximally stable, maximally stable... And that would be expressed in terms of some kind of conditional hypothesis. See, here's another, I think, what we were thinking about, what is mind? If it's only, everything that could possibly be known about mind is contained in becoming. If we understand that fully, then we understand all there is to it, but if you fix any portion of it, then it takes on an aspect of being. So in other words, the border between being and becoming is not fixed either. I don't just mean mass and energy, I just mean on the very basics. So in particular, you see, variation describes becoming, which I think you can actually get from here to there by your first analysis is solely in terms of variation, and if you look at all these ways of varying, oh, well, you say, well, this, this. And that's one of the ways of modeling topological space sort of thing is the whole possible continuous path in the space. That is the space. It just tells you everything. So, one gives rise to the other. Ultimately, equally strong, equally fundamental, whereas in the kind of the platonic fiction, you always, you model, not to say, no, no, but insofar as we can form ideas about it, we take snapshots of the world, lots of snapshots.

1:00:00 But the world, of course, is not the metaphysically complete second snapshot that it is, of course, from the Platonist point of view, which is why they have no real analysis of motion, it's always been a matter of choosing a parameter. Yeah, yeah, that's right, yes, yes, posing, yes, and saying that, well, motion just is nothing, but the assumption that there is some kind of metaphysically fixed and eternal... The way these theorems look at the homotopy theory in that sense, and about the logic are precisely the same, and it's all going to be analyzed in terms of... You know, these people, some of them actually go so far as to talk about the space and the topos, because there's a theorem that any topo is covered by. In many unnatural ways, it's always an unnatural thing, you have to choose all kinds of good coordinate systems to obtain this, it's not in any way a natural property, but it's funny that they speak of these spaces as though it were somehow determined. They pretend to be doing mathematics, but actually they're always skating at the office of mathematics. They're always skating at the office of mathematics. Why would everything be set like that? It's a problem. In other words, they've learned thoroughly that they need to accept variable sets, but they haven't grasped that you have to accept also cohesive sets as a moment or an aspect. I've understood much more deeply now what you were saying there. And it's a very significant moment that I hold.

1:02:30 The great process of the re-description of stuff is to draw on topology. There are a number of things which are key. The proposal is a kind of hybrid. It's kind of a hybrid, you see, based on seeing all of the specific examples that seem to come up. Johnston's paper, especially. They show that this class QD is closely involved in the thing and on the other hand you can imagine all sorts of, actually I must admit, secondary philosophical arguments, oh yeah, that's sort of how it should be, but it's still being put together and it hasn't been taken up by anybody in spite of my predictions. The dialectical philosophy would play a big role in topos here. Well, a decade. It did for me. It did for you! Does that count? Does that count? Does that count? Does that count? Does that count? Does that count? Does that count? Does that count? Does that count? Given the layers of stability that there are in the world, it's natural that metallics should be a very powerful determination. It's a very good determination. Or at least it is for us, given the environment we find ourselves in. And I do feel that there are some good mathematicians around who can contribute something to this, but I don't want to make them understand that there are mathematical specialists. And they're not to be put off by the fact that the interesting mathematical questions are so clearly also bound up with each of the common questions. Well, I think they are, unfortunately. Lots of them. The trouble is that 90% of mathematicians really are perfect notions. Yeah, and even worse for that. Yeah, that's even worse for that.

1:05:00 You had a chance to talk to Bill O'Toole about that idea. Thank you very much for your time. I was thinking that I signed up for the excursion. Yes, you have to. You have to. Okay, right. Don't do that. Yeah. Right. For sure. For sure. Now that they know, they need to know how. Okay, I'll do that now. But, uh, the curious thing is, oh, yeah. That's the one on the right. So, the curious thing I find in Kant's approach to geometry is that he understands geometry as a discipline which presupposes portions, essentially, So, at the same time, well, but he left this at the stage. He had good ideas. For instance, he said that any motion in space is continuous function. For instance, he said that no motion is possible on the perimeter of a triangle.

1:07:30 So no discontinuous functions. And what is the theory of time? The theory of time, what kind of means does it make? What kind of means does it make? And how could you describe exactly the time through our effects? So I realized that in the latitudes of his living time of life, he distinguished between two kinds of arithmetic systems. One is the theory of positive integrals and rotation with no particular understanding for the arithmetic system. It's all combinatorial, isn't it? Yes. It is a constructive theory, but the curious thing is that this is also a very interesting idea that in the latter time, as he grasped at the latter time, since any eventual contraction, it involves... In both the constructions, as in any mathematical operation, both the constructions, this provides, for instance, Grau's idea that we have to take this from an idealistic idea that any mathematical language has to be constructed. But the curious thing is that any of these constructions presupposes the whole within. Constructions, but I was for governance. Like Hegel said, we start with being. We must start with being. And so we can even have a triangle inside space.

1:10:00 Yeah, inside space. Kant is one of the philosophers that Hamilton was talking about. Oh yes, Hamilton was great. He was very strong. He had also this slogan that algebra is time. One of the reasons he took so long to get to Eternity... It's because for 20 years he was caught up on the idea that the most fundamental algebra must be an algebra of triplets, because there had to be a position of time and space, and he said himself that one of the reasons he was taking so long to isolate them was because of that. It was because he had been sitting in the hall for so long on this triadic idea that the fundamental algebra must be, must as well, proven to be relevant. And this was something which he'd offered. I can't quite see why he was hung up on that, because it would seem to be very natural that you would have the space and time in your quaternary, and when you did finally arrive, it was purely formal recognition of your talent. I'd like to know more about that. There are a lot of them. And so I'd like to list them all. Of course, it says we have an intuition of the continuum. But later on he says that we have an intuitional theory of space, and this is coded by Newtonian geometry. So there is conflation of the intuitional of space with the specific intuition of a human geometry. And they are mixed up. It has worked. In such a way that he needed to say, he thought, and I need to say that, since this is the base of the quantum mechanics.

1:12:30 When non-Euclidean Germans were discovered and said, well, we can't do things even without non-Euclidean Germans, then Robert said, we only need to stick to time. So the lessons of history, yes, they're very curious. People's dress, the religious, yes. I haven't used the people I like now. I guess we have, that's it. But you're absolutely right, that was a great lesson. I think this is a great insight and a great start to our meeting. But that's not just from one of the primaries for us in the Women's Camp. Of course, the members of the Women's Camp were both great, great philosophers. No one ever lacked that insight in their time.