Bringing Structure Out of the Shadows (contd.)

0:00 And the chairman said, how? And David Armstrong punched him on the arm and said, there! Did you feel that? That was causality! Now, of course everyone's going, no, no, that's not it. But it's that sense of the punch that I think is actually what people are worrying about here. If I fire a number two at you, I'm firing lots of number two at Mateo right now, nothing happens. If I fire a beam of electrons at you, ooh, I can do some damage, giving enough energy. Or a beam of photons, slice them in two. So the physical world has some punch that numbers don't, and this is what they're worried about. So the claim is, look, we're going to talk about causal relations, we need causal relata. And Silos says, he has a whole, I'm really skipping over a lot of his examples here, but he doesn't think they work. But he says, look, typically in metaphysics, the relata of causal relations are events or facts, things that are described as being imminent, they are in the world, in space and time. And these have to be understood as objects and properties. them as particulars. They're still in-ray particulars. And so Silas says, the truth makers of causal claims require objects and properties. You can't do a choice. If you're going to be a structuralist, you're going to have to give up on causal claims. I don't see that at all. Right? Of course, the imminent basis for the causal claims are objects, right? But objects in the unreconstructed sense. The kind of examples that philosophers use punching you in the arm, pushing a table, they just go through for the structuralists as before, right? But the claim is once you focus on the notion of object, focus on the table, and here I'm afraid of a bit of a reductionist, what is the table? It's a collection of particles. One of those particles, they are nothing but nodes in the structure. I don't see anything there that should trouble the structuralists. Chakravarty said, well, wait a minute, wait a minute, wait a minute. Something has to be the seat of causal power, right? That has to be object. Ontic structuralism, he claimed, loses the active principle that transforms one set of relations into another. If you think of the structure of the world, it's dynamic, it's changing. At this moment

2:30 we have this structure, at the next moment we have this other structure. What is it that transforms them. And he says that power resides with the objects. You have to have objects in order to be the seat of causal power. Well then you can just do a kind of reductio on this in a way. You can say, look, what is an object? Where does this power reside? If you have a substantivalist view of objects, you can say, well, it resides in the substance. The substance somehow has this causal power. Well, if bare substance is causally efficacious in this way, why can't bare structure be? What is it about substance that makes it causally powerful, that prevents anything else from being that? You say that it's the properties that have the causal power. Then there's these interesting metaphysical debates. Is the causal power particular to each property? Or does each property partake of some generic causal activity? So if you think of charge, the idea is that the property of charge has this causal power of attracting or repelling. Is that attraction or repulsion a second-order property of that property? or is it some sort of generic causal activity that's partaking in? The former leads to a possible regress, the latter offers an interesting approach, but I won't go into details here. I think some of this, my own view, and this is harsh, I think some of these discussions actually get quite hopeless. And this is from Swoyer, who has asked on a page on the Stamford Encyclopedia about this, And he says, well, look, the relationship between properties and powers is very problematic. Why? Different properties can have the same power. Different properties, charge, gravitational mass, have the same power of attracting things. The same property can have different powers. So negative charge can attract some things and repel others. So it's hopelessly complex, he says. And the obvious response is, dude, come on, let's get a bit more fine-grained about this. works if power is understood too loosely. One can argue that, of course, the electromagnetic... I don't know how to argue. One can simply state that the electromagnetic and gravitational forces are very different.

5:00 And to regard them as somehow partaking in the same power is far too crude. Here, it seems we're understanding power too precisely. This attractive and repulsive force. I mean, it's just the same force. It's just the electromagnetic force. The way the structuralists sees this is to say, look, it's through the laws, through Coulomb's law, through Newton's law, through Einstein's equations that we get our understanding of the power. From that we articulate it in terms of, well, these things must have properties. The object-oriented really says, right, it's objects that have properties. The structure says, no, no, these properties are just features of the structure. Final point. Zylos says, wait a minute, if you go that way, if you say that all there is to a property is its causal powers, then you're denying that properties have this kind of this-ness, quiddity. Objects, scholastically, were taken to have as this, and it's called the exeity. Now consider your characterisation of properties. If you think that a property is something over and above its cause and powers, then you're thinking of that property as having what scholastics called liquidity. If you deny that, if you say that all there is to a property is its cause and powers, Silos says, that's hyper-structuralism. And that, he says, that's the way you go. that leads to nothing but a formal structure again. And you're back into a kind of Platonism. Here's my response. First of all, I don't see why you can't be a structuralist about objects and maintain that properties or relations have a thisness. It may be an impure form of structuralism, but it seems to be a perfectly viable form of structuralism when it comes to understanding modern physics. I think it's just metaphysics really at this point. I don't see how if you decide, no, no, no, I want to be as pure as I can, you deny that properties have quinnities, you say that a property is nothing but its causal powers. I don't see why that leads to the claim that we have nothing but formal structure anymore. To say that a property is nothing but its causal powers is still to say they're a causal powers.

7:30 That's not formal anymore. You're still able to account for the punch. for the laser beam slicing someone in two, right? All one is saying is that the causal empowerment is inherent to the structure, and I don't see that as necessarily leading to a non-structural element being included. At this point, I find it hard to breathe. We're in such rarefied metaphysical air Hard to breathe, hard to know which way we should go. We've got a number of choices, but I think that's good for structuralism. I think it's compatible with a number of further metaphysical claims, and you can have different forms of metaphysically informed structuralism, just as once you've defended and articulated object-oriented realism, you can have different forms of metaphysics of objects in terms of bundles of truth, bundles of properties. hexages, whatever. I think that's all to the good. I don't think there is anything in the metaphysics of causal properties that rules out structuralism. And that's really, sorry I've gone on too long, that's really my conclusion, that we have to strike this balance between this inflationary metaphysics of object-oriented realism and the more minimalist constructive empiricism. And in striking that balance, I think we do have to do some metaphysical work. But so far, I haven't seen anything in that work, or what's required, that actually rules out ontic structural realism. I think different metaphysics may give us a different notion of structure, and therefore different forms of ontic structural realism but that of course is to be entirely expected. I'll stop there. Thank you. Some questions? Some questions and remarks. A few points you mentioned group theory as some are related and important for structuralism and for me myself key remark. And then,

10:00 once you mention category theory, in relation of Leonard-Landry works, and is, for you, it's more or less wouldn't it change a lot just the switching from kind of group categorical approach to category theoretic approach? Oh, well, okay, I'm gonna talk about that I'll tell you now, and then you don't need to come to this afternoon if you don't want to. I think there's a difference here, and I think it's one that Catherine and Elaine don't draw as clearly as they should. And the difference is between what they call presenting the objects in the structure and representing the structure. I see group theories fulfilling an important function with regard to the former. So that's the reason for the Eddington quote. I think, and I'm not saying that I'm a sort of group theoretical reader. I think there are other forms of mathematics that may be more appropriate in the context of quantum gravity, for example. But certainly, you look at, say, the time at which Eddington wrote. How do you conceptualize these properties and objects? and the response is you do so in terms of group theory and the claim is that that's not just a piece of mathematics that gives you a metaphysical way of characterizing the object so instead of thinking of an object as substance plus properties, you think of it entirely in terms of group theory, and what does that mean? I think it's quite important what it means is it's an answer to the question look, what is the structure What is it beyond just properties and relations? And what Ennington says, it's the interrelatedness of the relations. And that interrelatedness is represented mathematically by group theory. So that gives you a very nice way of presenting what we used to call objects. In a sense, what it comes down to, if you ask Ennington and maybe myself, what is the structure that you're talking about? I'm just going to give you a whole bunch of group theory. Now that's different from the question, how do we represent that structure at the meta level in philosophy of science

12:30 so that we can understand the applicability of mathematics, the theory data relationship, and so on. Landry has argued for category theory to do that. from the first issue of presenting objects I don't think she gets that distinction as well as she should. The second issue is an issue not just for structural realists, it's for philosophy of science. What's the best way of capturing the beasts of the field? What's the best way of formally representing how science works? Some people say there is no way. Give up on the formal representation. Just describe in everyday language. I still adhere to, I guess some might say it's a sort of remnant of positivism that motivated suffrage. No, we want a formal approach in terms of which we can capture all these things. Elaine thinks category theory is the best way of doing that because you don't have the commitment to objects that set theory apparently does. Well, I'm going to say, I'm not convinced, right? I'm not convinced that category theory is the best way of doing it. But that's okay, because when it comes to the way in which we represent theories, I'm a pluralist. And I think some piece was a kind of course I'm gonna talk about that this afternoon okay I think the possibility to do that yeah I would like to come back to your three forms yeah especially on the third one. You were on the point to forget it in your presentation. It seems to me promising. Could you tell more about it and if I understand where it's a kind of of mutual equilibrium or mutual definition of the structure and why do you think that structure should be primary and why? I think if I understood well, you said that this form

15:00 will collapse in the first one. Okay, here's how I see it as going on. I should say I'm not so firmly opposed to this. I do have some sympathy with this view. It goes back, if I say, to Eddington, and Eddington himself, you can find bits of Eddington which appear to support this view, and bits that appear to support this view. And the central intuition is, if you think about it this way, on object-oriented realism, you have the object given in some way as a bare hexaity or substance. It has properties, then you have relations, and you represent that by laws and so on. The limits of this OSR says no, no, no. In a way, this is something you can draw from the Neo-Kantian analysis. Let's look at the laws, right? Let's see what we need to, you know, metaphysically understand the laws, what we need are properties and structure. We don't need any objects. Any notion of object that we have is a scare-quote notion. It's a notion of object that emerges as nothing more than a node in the structure, or as Kassira put it, sort of intersections of relations, just like points are intersections of Euclidean lines. So in that sense, the object is a limine, of course. This view presents itself as kind of a middle, a third wave between those two, and says, look, the object and the relations come together as a package. Eddington says, you know, we have this tendency to take the world and slice it one way or another, in terms of objects, in terms of relations, what we should do is just take it as it is, as a set of objects and relations. And there's a mutual dependence between them. And the way he articulated it, I want to give it as much positive support as I can. Again, he said, because this is a guy who's working with group theory, he said, you think of group theoretic operations. So this is very crude, so I'll be fairly quick with it. gives you gamma, where dot can be some operation and alpha and beta are elements, right, of the group. He says there's a tendency to split this up into alpha, a dot, a beta, so we have an object,

17:30 some kind of relationship between them. And he says, no, that's just the wrong way of putting it. You can't do that, he says. You just can't separate them up. You've got to think of this as kind of alpha dot and dot beta. They come together, and to slice them up, it's completely artificial. I think that's an interesting way. The worry is, in the way that it's been articulated by Espel and Lamb, you might say, wait a minute. And this is, I think, this is the way I tried to do it in a paper I gave at a Bristol conference on structures, and I think Anchan Chakrabarty has expressed it much better, think about it in terms of the relations of dependence. In some sense, the objects and the relations are supposed to be mutually dependent. Well, what is there to the object that allows you to describe it in such a way that it can stand in a relation of dependence with the relations. What can there be to the object that allows you to describe it in that way? If you say it's a primitive this-ness, etc., you're back to the old forms of object-oriented. If you say there's nothing to the object but the relations, then you just collapse into this. So this view, it's hard to see how this view is actually stable. of an intuition, you can think of the world, metaphysically, given to us in a package with these things somehow interrelated already. And I'm sympathetic to that intuition, but once you try to cash it out metaphysically, the worry is that in order to describe the dependence between the elements and the set of relations, you already need to presuppose some independent characterization of the elements, in which case you're back to, you know, ordinary object-oriented metaphysics, or you cash out the elements entirely in terms of the relations and you've collapsed into this. This is the same analysis that takes this into this, right? I mean, think about Saunders' view. If there's nothing to the identity of an object, but

20:00 with other objects, then there's nothing to the object but its relations with other objects. And hence, there's nothing but the relations, and so you've got this view. But having said that, I think, look, I don't want to be too dismissive, because although Eddington expressed this view in 1927, he never really developed it. I think Michael Espel and Vincent Lamb have only been developing it in the last few years, and there's some interesting work that could be done, I think, still. That's the worry that you've had to address. I just want to go back briefly, Steve, to what you were saying about the symmetric and group theoretical approach to the constitution of object work. There's a couple of observations. The first is, there's a historical context here, which I want to come back to. But the first thing is, it clearly is a very attractive program. plausible candidate for objects which are precisely, as you say, the kinds of nodes in a structure which are the intersections of just, you know, one level of structure up from that node, like points and elementary particles. It seems to work well for those. But intuitively, I find myself very resistant to the idea that it's going to work for the kind of objects whose integrity is supposed to be more complex kinds of organic adhesion. And I, such as human beings, take an extreme example. But, okay, that's just, as I said, it's an observation. I mean, his response was in. But I think this is related to another problem, which you touched on when you were citing the historical sources for the group-theoretic asymmetry, particularly on Vial and Eddington, naturally, and in the context of quantum particles, they're obviously the people to look at, and cancer as well. But of course, in the case of points, one can look further back. One can look particularly, I think, at the whole legacy of Klein, the philosophy of geometry. And I think that there is actually a problem there, which, if I put my finger on it, may actually be a problem for the structuralist program as a whole. And that is that Klein's whole philosophy of geometry

22:30 essentially centres on the idea that the notion of mapping between spaces in general is something which one can characterise at the level of symmetries in terms of objective correspondence. Now, there are people who thought that is inadequate, basically as a basis for the philosophy of geometry. There's something more going on with the philosophy of geometry which Klein tend to characterise. I think the same restrictedness of vision may give us some orientation, some bearing, objection I'm trying to formulate. It's very, very vague. But it is that this works very well for parts of ontology, but arguably may break down when you are dealing with systems which have kinds of cohesion and complexity that are more top-down than bottom-up. Sorry, that was a very long-winded observation. That's a fair point. I mean, there's a point that's come up again and again, so it comes up put more crudely than you put it when philosophy of biology said, well, I can see how this works in the philosophy of physics. How does it work in biology? One response there is just to be reductionist, right? And, you know, I still find, despite all the... A very big promissory note. It's a very big promissory note, but I still find reductionism attractive. I am not convinced by the claims of either the philosophy of chemistry or biology that there's... Well, Let me put it this way. One way of viewing the claims that reductionism doesn't work is that they're really claims about the representational resources that have been employed to try and capture the reduction theory. Sure. So I'm not entirely convinced. The second thing I have to say is even more promissory is that extending the structuralist picture to biological entities is actually the aim of a research project for which we've applied for a big government grant at the University of Leeds, together with Tim Lewins at Cambridge, who's a foster biologist, and Chris Timpson at Oxford, to try and see if structuralism can be extended to the notion of biological entity. There's some historical evidence that structuralists are not particularly famed by that. So again, Cacera famously commented I mean, his structuralism wasn't just pure physicalism. He was considering biology. Of course, he did have the advantage of being a Kantian, I think, in that respect. I don't know if the Neo-Kantian

25:00 gives you a particular advantage. The issue is about realism. But the core issue that we're talking about is whether the structuralist metaphysics and the way in which that metaphysics is represented can be adapted to the biological level. Because I think I've skewed the question and skewed your response to it by focusing too much actually on the biological example. I shouldn't have said human beings in response to your question. I actually had much more concern with the problems in the philosophy of geometry and the characterization of space in general. And that's actually where my... Just to that point, you mentioned that saying by Poincare, if you're not mistaken, that we could kind of forget about what we are intuition, notion, triangle, whatever, thinking about group. And at that time, it was kind of wishful thinking, which we now know is wrong, was wrong. Because what that program gave basically was homology and cohomology theory, which didn't at all reduce, say, geometry to anything like root theory. Absolutely. The man has put my voice in words. And what's really kind of promising thing to do is doing things, category theoretically, which at least gives some grasp, which we could call geometry rather than. But in my view, probably, I have no time to explain it now, it would really, how to say, it would in a sense refute structuralism. by something different in my opinion. I just don't see how it refutes structures. OK, that I just... I'm leery of drawing the analogy from... I'm leery of drawing... I mean, Poincare's point was not a point about phosphogeometry. It was a point about this maneuver that I've called elsewhere Poincare's maneuver. It's just a general maneuver in which the structures introduces something non-structural in order to get the structures you want, and then you dismiss... There may be, look, I'm not trying to defend a form of group-theoretic realism. As I said, there are other forms of structure that may be more appropriate. Particularly getting what he quote the interrelationship to interrelations, when they're not just simply matter-intersections. That's true in 1926 or 1927. I don't see how that's, never mind the reputation structure, I don't see how those developments are even an obstacle at the moment.

27:30 It may well be, I mean look, it may well be that developments in quantum gravity are such that we can't avoid a robust notion of object. I'm slightly skeptical, but that's going to be shown to be so. But it may well be, in which case, look, you know, I think one's realism, one's philosophy of science and of physics, if we're going to be naturalists, has to be associated in something related to the current physics. That's what Cassira, Eddington, and Russell and others saw themselves as doing. So if, you know, I don't know, Rebelli is right, or certain developments take place, then it may well be that we have to give up onto structural realism for something else. At the moment, I don't see anything that compels me to do so. And I think there are ways in which, with a broad enough notion of structure, And again, I want to make this distinction that I'm going to refer to this afternoon. There's one issue of how we present the putative objects of our theories. And that's an issue that, in a sense, is context-dependent. In a sense, it's the physical context that gives us that. 1926, it's group theory. 2026, it may be something else. That's okay. We're talking about the structural presentation of the object. The other issue is how we represent to ourselves, as philosophers, the structure. And there we have a choice between syntactic views, so-called semantic views, category-theoretic views. And one option is to be a pluralist and say, as a philosopher, I'll just use whatever I need is more appropriate. And it's not clear that there's anything with regard to the realist aspect that hangs on that. I wish now to ask you a question which is about the relations between your structural realism and, so to speak, the sense of the ideal version of structuralism. You said that somehow you can buy some parts of Kathera's views on structuralism and translate them into your structural realism idea. I think I can do the same thing, but the other way, and this is very useful because your analyses are very precise and so on and can help also this program. The reason why I think it's useful to do that, or at least we can have motivations to do

30:00 this translation from the structural realist to the transcendental idealist idiom, is that in the transcendental idealist idiom, you saw many of the problems you have in structural realism. First of all, you saw very easily, I think, the conundrum of relations with that releta. And Kant did that already long ago with his analysis of the problem of incomprehensible counterparts. He said, okay, we have a case here the case of the two hands, the case of incongruent counterparts, where the relations between them, the relations of left to right, are such that they are not grounded on properties of these hands, because the internal properties are exactly similar, the internal relations of the past are absolutely similar. Well, how can we explain these relations which are not grounded on properties of the reletta? It's very simple, says Kant. We have to relate them, first of all, he said, we have to relate them to absolute space. Okay, this was in 1768. But then, later on, he said, no, we don't have to relate them to absolute space, to an a priori form of our sensibility. And it's exactly the same, gives exactly the same results we can have here, what we call ungrounded relations. So they exist, but they are possible to think. So first of all. Secondly, we can solve the, well, we can understand why group theory is so important in structuralism, at least as you say in the present state of science, it's because it's a theory which gives rise to invariance. And invariance is exactly what Kant or K-Zero would call an object. And it's an invariance of K-Zero. Oh yeah, I could list a lot of other things, but you see that many problems I think of structural realism are solved, or at least I feel they are solved maybe in the idea of the idea of the framework.

32:30 Okay, first of all, I think I find the Neo-Kantian approach very attractive. And the more you read the series, the more you find it, the more you find it. Nevertheless, I want to resist it. I think the two examples you've given are very useful. I think some aspects we can simply appropriate so I think the notion of an object as really understood in terms of sets of invariance that I think you can just take over to the realist view and as I said before I mean Chakravarti has this worry how do we explain why we get certain properties cohering together and he's looking for a metaphysical explanation he says it can only be explained in terms of they're coming together in an object. But of course, that's no real explanation at all, because what is it about the object that somehow brings those together? The structuralist can say, well, look, what you're talking about here has to be understood in terms of sets of invariants. And again, that's where you stop. You simply say, that's all there is to an object. And it's a kind of structuralist conception. them. Now again, at this point, it's both sides are saying, well, you're just begging the question, because the likes of Chakravarti and Silos will say, well, that's no explanation. You get to a point of fundamental metaphysical analysis where, you know, what further explanation can you give? Nevertheless, I think the structuralists can precisely draw on this kind of analysis, a very beautiful analysis of Cassira and also Eddington that were driven, you know, really by their concerns, their consideration of general relativity, and then they took it over to the quantum physics. All there is, to an object, is cast out, physically and metaphysically, in terms of these sets of invariance. So that's one thing where I think it very nicely goes over. The first point, though, doesn't, because I think, I mean, you're right, So, on the Kantian view, you know, the relation is somehow to be understood as ungrounded because you've got this A prior or I form. But the problem is to, you know, in a sense to go that way, the cost is quite large, right? You're giving up on your realism. So how is the structural realism going to solve that?

35:00 Well, and this does need further work, I agree, but for example, in the case of entanglement, you know, we have the Teller view, the view of Paul Teller, that one way of understanding entangled relations is in terms of this notion of non-supervenience. So, there's a sort of a standard way of understanding relations in metaphysics, particularly in metaphysics of mind as supervening on properties, as being dependent on and determined by the non-relational properties of the object. So the claim is that all the normal kinds of relations that we have, the relations between two charges, two masses, which are classical relations, supervene on monadic properties of the object. And that's what Kudon's law and Newton's law tell us, right? Because, you know, when we describe the relation between things, we express it in terms of a law, right? And these are just monadic properties. And what Teller said, Well, in the case of entangled relations, we have to give up on that supervenience. They are, in some sense, non-supervenient, and therefore non-grounded in that sense. Now, I think that's interesting. Now, there's two points to that. One is, someone might say, okay, that's fine for entangled relations, but it doesn't work for non-entangled relations, the normal kind of relations. Well, again, Matteo has suggested that you could extend, or you might extend that kind of view to non-entangled types of relations and properties. Some might say that's too radical, we can't possibly consider that, but I think it's an interesting way forward. The second point is actually a more moderate point, is to say that that notion of non-supervenious, that Teller articulated as what he called an alternative to the particularist ontology, which I take to be very close to what I call object-oriented realism,

37:30 You can take that as a kind of metaphysical template for understanding the ungroundedness of certain relations in a non-idealist way. Now, what that might mean, there's still a cost. I think there's a cost to idealism. We all know the cost of transcendental idealism to the neo-cantitude. I think there's a cost to this kind of realism. I think the object-oriented realist avoids these kinds of costs by just not thinking about it too hard. I think the structural realist does have to pay this kind of cost. And it is really a cost in terms of a new metaphysics of relations. A metaphysics in which relations can be, in some sense, non-grounded. Now, even non-supervenient relations, you've still got relata. so the claim is you need to go further and think of relations as somehow not grounded in the relata as I said, Peirce C.S. Peirce the great American pragmatist philosopher who also did a lot to bring in the era of modern logic in the 19th century thinking very hard about relations and thinking about the quality that they have and thinking about he talks about these qualities in terms of firstness, secondness and thirdness it's a sort of quality that relations have over and above whatever grounding they have in the market. I think looking at that and articulating that is one way that the structural realists can go forward. So, you know, every position I think has its costs, and what's important is to really articulate them and lay them out, but I do find the neo-cantin position quite attractive, isn't it? Thank you very much. I think Matteo should talk directly because we don't have so much time.