Structuralism & dependence / Unknown speaker: response / discussion

0:00 ...for those speakers that look like Wasteland must come straight back. Very, very briefly comment on that. So thanks a lot for your interesting comments. So just briefly about this minimal characterization of structuralism. So can't we just say that according to the traditional plate-in-it mathematical objects occupy positions and structures, and according to the structural form of plate-in-it mathematical objects, there are positions and structures. I'm actually not terribly opposed to that in any way, and I guess I find it a little bit obscure, I know you are for the same reasons that you talked about in the way that this is instantiation business. So how can the position in a particular relation itself instantiate the relation? That is in general. It's a particular relation of a parent of. It's not the first argument, so to speak, instantiates. It's itself a parent, certainly not. But such things are being made by the structure. So that's to some degree of security remains perhaps. But maybe that can be dealt with, and if it can, I'm not actually terribly proposed to this way of code-based structuralism, but I think it's actually more specific than what I'm saying, and not less specific. Because this is one way to just look at if mathematical objects just are positioned in these universals, say, I think this is just more specific and not less. And one way of seeing that is that at least two of the three most prominent structuralists would disagree with this her position of structuralism. So Parsons and Resnick can say that they don't believe in the structures. They believe that there are mathematical objects that whose whole nature it is is exhausted by being positioned in structures, but they don't want you to accept some ontology of added in structures. So they can want you to go that way because it's key. So that's positions in structures or barastructures?

2:30 Something like that. I'm not saying it's a good idea, but it's a one-way model to see that. But this proportion is actually, instead of it more minimal, it may actually be more specific. First, just to remark, you're an example of the group of alpha and beta. Alpha and beta are obviously functioning as three variables there. So it's not, okay. But let me just put the following point to you. Well, the difficulties that arise in all these discussions is that you posit that there's, alongside each ordinary structure, let's leave it unspecified what that is, there's this ghostly entity called its abstract structure. Now, as a mathematician, I ask the question, what's the point of this doppelganger, right? And one obvious point would be that if you have two systems, and if you perform this operation of abstracting to get their forms, then the two systems are the same, essentially the same, if they give rise to exactly the same abstract form or structure. Okay, but in conventional mathematics, there's a perfectly straightforward definition of what being the same, being essentially the same structure or being identical quad group or whatever. And that is to say they're isomorphic. And if you look at the etymology of the word isomorphic, it says same form, right? the point is the definition of things like isomorphism were introduced precisely to avoid getting entangled in these metaphysical questions yes sure again I guess comment on the dialectical situation I'm in here so often when you try to have some sort of moderate view you think of yourself as a peace broker to settle this dispute between two Warren parties and instead of making twice as many enemies. And this is some of an example of that.

5:00 I don't have a lot to say about it. What I said in defense of there actually being such objects as alpha and beta was just to defer to other people who have different structures. I didn't actually propose to add anything to that rather than just to say that Whatever possibility that has, you shouldn't go all the way with that. That may work in whatever it would be introduced as algebraic structures, but it doesn't work in case of sex. I possibly want to have examples. But I didn't attempt to defend that idea that there should be such things that help them with different people and people. My question is about the role that individuation is playing in your analysis of evidence. I think it sort of touches on this dispute between the structuralists who want to talk about the abstract thing, the B-Jaws to play, the stick, the isomorphic collection of things to the individuation of things within that lower level connection. I mean, you say you're talking about metaphysical individuation as the ground of the object's identity. So what I'm not really understanding is this talk, in the plural, right, so... So there are various ways of individuating directions, we're going to have many different lines. I know what direction the north is, in that direction, and what's in that direction. So those would be two different individual issues of the direction of the north. So there are different ways of getting at the identity of all the objects. So what I'm not getting is why that's metaphysical problems. I mean, it seems that we, I mean, I have this sort of ghostly picture of just, you know, space with all the directions in. And then I think of these, you know, actual concrete lines or something, and then I think, you know, consider those and, you know, lots of different ones can get you to one particular element in that space.

7:30 But I think what we're concerned about is, you know, what grounds are distinct just sort of one element of that space from another. I guess I'm also not quite saying why you think it is semantic, so I point to give you in any way two particular lines and then I say that so then we're talking about the lines, we're not talking about semantic two lines specify or pick out determine the the same direction So no semantic claims made, I mean, surely it wouldn't lend itself to semantic theorizing very, very nicely, and to put my cards on the table, I am very attracted to spelling it out in that way as well, and hopefully trying to connect up the semantic and metaphysical notion of integration, but for present purposes, I intend to remain squarely on the metaphysical side of this. Well, what I thought about semantics was just to say, well, you don't want to say that these are different situations, you just want to say that different tokens are the same time, so in the same way that, I mean, if you've got lots of instances of red, you've got lots of situations of the universal, you've got lots of instantiations or simplifications of the universal, but, so, that's why it sounds semantically. direction is in the equivalence class of the lines or something, but it's not individuated over and over again in each line. It's exemplified and satiated and tokened over and over again. Yeah, I'm not aware that to do that with people, I guess, but let me explain why I'm not putting it in that way. So integration is a matter of giving criteria identity. And when you do work with these two-level criteria identity, then there are, just in which we are not, and many ways of getting at the same object. So what I call a specification,

10:00 if it's subject to a equivalent relation, if two specifications stand in that equivalent relation, then they determine the same object. So that comes with that whole idea of perceiving by means of to that whole part of it. But it might be none of them on their own determined the object because it's insufficient. If you say that that line determines the direction, you make it sound like the direction can be understood just in virtue of that line. It can't be understood in terms of the equivalence class of certain lines or something like that. So the direction is historically determined by the line or metaphysically. Well, metaphysically, what more could you lead other than that? it is something exemplified by this particular line and what kind of exemplification you have in mind is that which is preserved under the parallelism. So you needn't proceed via this particular line there would have been many ways of doing it but there's nothing more to be being of that direction than what is getting in sort of personally that line and secondly the equivalence relation of parallelism. That's it. That's what I'm doing. Oh, sorry, my sort of question, a question about your concerns about historiative places and associations. Now, is it that your concern is really directed to the places? Because you can see places have already, objects occupy places and structures. So then you have to think, well, here's the base of the structure, and then here comes the number two, and it's occupying that, and then, what is this? And then you ask Stuart, you know, what's the base of the structure? He says, well, there it is, so there's number two, and there's another one, number three, and there's another one, four. And so to worry about the obscurity of that is like worrying about the obscurity of what are the bases in the space-time structure versus the point. So there's that. And the second, to get clarity, if you're worried about if mathematical objects are positioned in structure, how do they instantiate relations?

12:30 I guess the counter-worry of the structures might have is that perhaps you might need to be careful that you're not begging the question. Because when you think of instantiating, you think of, well, right, objects instantiate, you know, properties and relations. And the structures can say, but look, that's precisely the image I'm trying to get away from. and so instantiation talk might involve you in certain question-begging moves against the struggles. You might well, give me another term that describes the relationship to the macro-object in the relations, and that's, I think, a valid request. By insisting on, well, tell me how will you instantiate the relations? you might be taking a question. Now I've got the first question. Sorry, I did the same one there. So I guess it probably depends on what kind of thing would they have a structure to be like. So whilst I was just going with something that structure was a big property or a big relational, you know, a thing of that kind of a little category, well, what the things in that category do, what the properties do, lots of things that instantiate them. Now maybe that's just, that's the kind of thing that's coming out of something like this in the songs. It sounds like so long. I mean, the structure of the thing that, well, I guess, I don't know, but the thought was that we understand the structure by thinking of it as something that's abstracted from all the things that have it. And without those things, those collections had been funded and they stood in those relations. And so that's how you get to stand in those relations, is by doing things that are fancy under the structure. And I'm kind of saying it's like what we'll have to do is come up with some other, counter the little abortion tie between a thing and a structure that's explained. And first I want to see you about the difference between the types of students, is that just a problem? No, just as I know, but again, it started with the idea that you understand what structure is in terms of property or relation or whatever. I'm having to say that, well that's, you know, it starts from the idea that you've got an object,

15:00 I mean it sounds like a property, and then when you take the object away from the property, you've got a hole or a gap or something. because I was thinking that there's a whole gap in the noise. You just talked about it. There's a hole there. What does that mean? It means that it's an all-space property. Once you put one thing in, then the whole thing is saturated. It's a thin notion of reference. We'll put it in another way. It was a gap. I mean, I'm really, I'm really about structures off this hangar, but non-limited structures when it says that the objects, the objects are all the positions of the structures. I mean, you think the next view would be, well, you eliminate the objects and you just have the structures, but no, the most of the structures, you get the structures as well. I'm just wondering whether there's a kind of intermediate position where you just have the structures. You do, and the objects are twice as in. Maybe it's just homological. It's, you're saying it's analogous to Frege's description of functions, right? As, as things with gaps in them. So there's something analogous in your... Oh, well, that sounds like a trap. It was. Boy, you were on the ball there. You guessed it exactly. You guessed it exactly. I mean, I don't think... John, no. Stuart's going to get a talk about it. And I don't want you to go through the effort of forcing yourself to be blood together. But this is a question to Oystein. And about the notion of dependency. So I found it very good what you said. But it seemed to me that you ran together two notions of dependency, both ontological. And you ran them together perhaps for a very good reason. I mean, that might be the outcome at the end. But it seems to me at the beginning it would be good to distinguish them, and then later it would almost be a result that they coincide, or perhaps they do not. So what I mean is there is ontological dependency in the sense of existential dependency. logically dependent on something else if the existence of the former somewhat depends on blah, blah, blah, blah. And the other thing would be dependency of individuation, if you want. Whether something is identical to something else depends on blah, blah, blah, blah, whatever it is. And the two, at least at first glance, not necessarily collapse into one notion. So the first one you referred to when you said standard analysis. It's impossible for

17:30 something like that. But then what you present is something along the second line, right? Individuation given by abstraction principles or criteria of identity and things like that. Now, here's a reason why they are not necessarily the same thing, but let me explain it semantically. Okay? Because then it's easier for me to explain. So you might think under which conditions does a term refer at all? That's close to existential dependency. But then you refer, and now let's check whether they refer to the same thing. And that would be individuation dependency. And as I said, it might be a final result that the two are the same, but not at first glance. What do you think? No, no, that's good. You're clearly right that these are different ideas. So they're intentionally different certainities to notions of ontological or existential dependency, let's call it that, and identity dependency. Absolutely. Do they nevertheless coincide extensively? I'm somewhat inclined to think so without being deeply committed to it for the following reason that I too want to have a very, very lightweight or minimal motion of an object. And so lightweight and minimal So, in fact, that once the criteria of identity have been specified, then I'm satisfied to say that there is an object here, and nothing more is required for there to be an object. So then, once the identity question is settled, then you get the existence question for free. That's the idea. So that would bring these two notions together on the extensional level, at least. whether one should separate between them, I don't know, and I don't really have an analysis of existence or existential dependency to offer over and above the one I have here. Maybe one should explore it, but given that additional premise of mine, that objects are easier to get by and identity suffices for there to be an object, Okay. Can I apologize for the temperature?

20:00 You mean indoors or outdoors? Right, so on the schedule, we're supposed to start at 20 past again, but that seems silly. so we've deliberately packed in extra space so I do suggest another short break but let's get back here at my five past four That's five minutes? What? That's a ten minutes Alright, that's a ten minutes How about fifteen? We'll get it started five minutes before we're supposed to Let's take a few minutes back in here. Thank you.