The metaphysics of sets; critique of Lewis "parts of classes"

0:00 So when you think about some of these boundaries and determine if we can remove the foundations of mathematics as well as the foundations of physics, I think that you turn out to be a little less powerful than that in any case. So frankly, it's not to do with how vivid it is actually, but we've had several seminars in connection with mathematics, for example, when we were here, we were able to do one of the lectures, but they were happening to be at a very different time. But today we're pleased to welcome Alexander Oliver Pondy of the Flotsam faculty, a compliment, compliment, compliment, compliment, compliment, compliment. Who recently had pointed out that the lecture in the faculty is a gratification of that. I reckon today we can use the paper to present this to Seps. Thank you very much. No philosopher can ignore Seps. Seps is a subject matter of important mathematical theory and moreover, many mathematicians have employed Seps theoretical machinery to construct their own logical adventures. Thus, the metaphysics of sex is not merely a crucial element of mathematics, but of metaphysics in general. It would be natural to think that a little investigation would reveal the metaphysics of sex to be a well-worked discipline. Natural, but what most philosophers believe about sex, along the hallmarks of folk metaphysics, are naive, unfounded, and inconsistent, and they are adopted as hand-me-downs in a quite unethical manner. Do sets exist? And what are sets? That sets exists without knowing what other sets exist.

2:30 I think the answer to it... So these are two theses of folk mathematics, the abstract thesis and the composition thesis.

5:00 Now, unlike the folk versions of other disciplines, such as physics and psychology, folk metaphysics is not a collection of beliefs held by ordinary people. That is, those who are susceptible. The thesis I have... I am a very common component. I intend to... ...properties, propositions, events... There's a sound fix that we haven't a clue whether they are or whether they aren't. So Aristotelian trickery is going to harmonize those things. A subset. So P and Q ought to be a part of P, not the other way around, according to von Neumann's plan, one with the...

32:30 Now I want to see, which is Lewis's evidence from Germany, it's true that tile mould is literally part-set, literally, but it means, means, subset.

35:00 Indeed, the emphasis on subset, but the parts are not, and so the ensemble des partis is not the original set, but the power set. Well, clearly Lewis must pick and choose his linguistic evidence, ignoring all these examples, because they contradict his small bit of linguistics.

37:30 Together with their product and various partials, can we define x as a... I would not want to say that one number is... It's quite straightforward. The analogy, as such, is not an ad hoc solution to the set theory.

55:00 You said something at the beginning which I didn't quite catch about the stuff about Lewis being based on the mathematics of the set theory being some elo-tranquil, is that right?

1:17:30 I don't, but then you came back to it later with the stuff on iterative. I wonder whether you really consider ZF to be a good type of set theory and whether you're considering the others at all. The sorts of arguments I'm interested in are that ZF, well for a start there are others which in some ways are philosophically more interesting and possibly useful. And also the obvious model of ZF doesn't have the sets that have anything in them except sets. They certainly don't have cats or anything real like that. True, but because mathematicians don't. You're saying you can extend ZF or you can make models of ZF that do have cats in them. Well, the standard model of ZF wouldn't. No, there's no axiom that puts them in, and they're not in language. I mean, yeah, you could... You could fix that up and just... Yeah, sure, sure, right, yeah, I'm just wondering... But I think that's just to curiosity of mathematicians. No, no, it's also because of the way that ZF is constructed, whereas something like Quine's theory is to do with predicates which don't have that, which... Are they constructive in the same way and don't have a natural range just of mathematical objects or do you have anything to say about that?

1:20:00 Not really. She asks that as a physicist the notion of existing existence has a clear experimental meaning. And also as a physicist we learn that it's a matter of things being composed of other things. This is a very non-tribal thing. It's not a statically believed. Now, in a study, I was told by my physician that logic and test theory are very much related. And the problem is that one would show up in some way in the other. Now, there is. There are different varieties of quantum logic and modifications of logic to take into account what happens experimentally in the real world. Now, is there anything that quantum theory can take into account that things are not as easily composed as other things that we practically use? I'm just wondering whether this is really classical description here. Well, the nearest I could get to it would be fuzzy set theory, I think, which might be thought to be altering set theory. This is where it's not determined whether something is memorable or not. And you could think of that as being invented to deal with a problem, namely to give semantics some vague predicates. We all want to associate with a precise predicate a set of things which fall under it, but if the predicate is valid then something like the case of quantum logic which is change, you change your, something which you'd like to hold dear but decide to change it more with the code, with some sort of more, with the calculus experience, so that's an example.

1:22:30 Doctor, I have a chip in one more question. I thought you were making the questions up. I'm not really interested in what you said about A and B, A and B. But this is the deep point that Dr. Miller made and I think that demonstration is the possibility that we have to follow this. And where all of us, including Dr. Hawking, have the same head and head and feet, then you can't say that B is the path. There are a lot of very good people out there who want to use the term quantum construction because they're the opposite of it. I think I took up that point. I'm not sure if anybody would be conscious of it. No, no, no, but there is this... I'm not sure about that debate. I think the methods would probably be very complicated. I hope you were getting the questions you were asking. There is a general difficulty here, which is this inverse relation between intention and extension, and that's exactly what we want to get at. People get, sometimes they want to get one way with the intention, sometimes they want to get the other way with the extension, or whatever it might be. To follow up Michael's first five questions on the materialism of agreement, you've got a quite contentious grid of all these five classes, but I don't want to wrap you in silence. I want to try and make a modest defence of composition of classes in terms as fusions of their in connection with what seem to be underlying logic.

1:25:00 We've got our own, and especially your final remarks, our only really strong grip on the notion. Nevertheless, isn't it true that you can understand something better by seeing analogies without the thing? These formal analogies, on the one hand, are subsexual, that the mirror, the cushion, does involve some pretty fancy, along the lines of... You shouldn't agree with me because I'm not saying that there's anything existing beyond what you already agreed with me. Together with the claim that I am making an ontological problem, and it's worth saying something to you, it's a rather, it's a tightrope, and it's a difficult, fancy football position to be in, but the idea that it's innocent because of the non-existence emergency process now is fixed by its part in their relation. It seems to me to be a reasonable, that you'd hope for a bit of supervenience there on that, or I think it would be informed to be told about molecules, I do know that molecules, and admittedly this combo of spatio-chemicals is less than expected of all technical molecules to be fit by the character of their atomic constituents.

1:27:30 And that seems to me to be enlightening, it's not. In the nature of full analysis of molecules such that with nearly innocent composition and thoroughly understood concepts, I've analysed molecules in terms of this innocent stuff, well, some problematic atom concepts, but I've certainly got enlightenment about the nature of molecules and stuff like that. Well, what you're told is about their nature. All we wish to say about them seems to follow logically from, so to speak, Proposition 1 in the handout. If you have the normal context of singletons and the normal notion of paths obey their normal properties, then you will get these holds, these sets, if you know what singletons are like, and we don't, according to Lewis. So, what we do know is that if we know what singletons are like, we know what paths are like. We understand. It seems to me that there's a big jump there because there's two parts to the understanding. It's not too much. It's probably too blemish-like. It's not a major effect. I think what's more significant.

1:30:00 Yeah, and this is why I wanted to find my reward. I get by that. I think Michael is first. Early in the talk, you claimed that the compositionality of physics is inconsistent with the view of the sector outside. I think you convinced me of something slightly different. You convinced me that you couldn't believe what sets are concrete without believing something out of the conventionalities. But I didn't really see why one couldn't believe both in what sets are concrete and in their conventionalities. Something like victim-science conception of a false proposition which imposes a meaning doesn't seem to force on me the notion that a false proposition couldn't be abstracted. No, I'm rather attached to the view that holes in at least some of their properties, parts of a composition, but I think at least with location, can't make much sense with the idea of a hole being I'm very happy with the reciprocal limitation.

1:32:30 Really, I thought this was an example that was really, in a sense, a very good example, because it really demonstrated very much that the whole is very different from the past, from being just a composition of the past, because even if you knew everything about the past, about the past state, you wouldn't know anything about the whole of it without supposing additionally that you know the loss and the gain, and the complete error of what you're saying.

1:35:00 And spatial location. And that location in time, there are two things. One is quantum mechanics. There is no such thing as full spatial location. And relativity is the second factor which says that, as you all know, that things being simultaneously relative things. And so I think it's just saying that the whole thing of things being composed, the very concept of things, everything in the world is composed of elementary parts, which are major.