Bringing structure out of the shadows

0:00 ...delimiting, delineating that position. And obviously that requires some philosophical and metaphysical work, just working on the internal nature of the position. But also, typically in the history of philosophy, one defines or presents one's position in contrast to certain alternatives. And I think one of the issues that have bedeviled these discussions about structural realism is really getting clear on what it's being contrasted with. So, first of all, yeah, sure. There is an invariable law of the universe which states that whenever Stephen French tries to use PowerPoint. Something inevitably goes wrong. Confirmation of that. This is the first time ever, and this is terrible, because I used to be very much into IT and math, but this is the first time I've ever done a presentation solely using PowerPoint. No overheads, no nodes, just put everything into PowerPoint. So, the contrast. Well, one of the difficulties in outlining the structure of realism is contrasting it with realism itself. Because many people will say, yeah, of course I'm a realist about structures. The theories in physics tell us what the structure of the world is like. So yeah, of course on realist abstract structures. So many people, when James Lehmann was beginning his PhD work on this, many people would dismiss it. How is this going to be an interesting realist position? So I'm trying to secure a kind of contrast with a particular form of realism. And James and I felt that many realists had this in the background and that they needed to be encouraged really to make it explicit.

2:30 by Statist Syllos, who, of course, is a defender of what you might call standard realism, and has initiated a whole series of critiques of structural realism. And I won't go into detail into his position, but it's all nicely set out in his book and subsequent papers. And he begins by saying, well, the standard view, that if you're a realist, you're going to take certain theoretical terms to refer, to refer to mind-independent objects out there. Which terms? Those that play the appropriate role in explaining the theory's success. So you look at caloric, you look at whatever, kinetic theory of heat, special effects, you look at the terms that play the crucial role in explaining the success of that theory, those who want to refer. Theory of reference, that's where it gets very softball, of course, and Sylvath prefers this causal descriptive account. Personally, I think that's problematic, and many others do as well, but we don't need to go into that. But crucially, Sylvath has sort of laid his cards on the table and said, what this secures is reference to individual objects and their properties. And so he insists, in a paper that was presented at the Posseo Science Association, the world we live in and that science cares about is made of individuals' properties and their relations. That's one realist view that structural realism is being contrasted with. Now, on the other side, we know that realism as a whole is contrasted with Van Frassen's constructive empiricism. And again, I won't go into detail on this, but Van Frassen and Octavio Bueno and others have developed constructive empiricism in certain structuralist ways. And Baz himself has produced some very interesting work on this. So, the empiricist view is the knowledge that we accumulate through the history of science is knowledge of the structure of the empirical phenomena. The phenomena are partially and selectively represented by our models conceived of as abstract mathematical structures. The models are known and described only up to isomorphism, and in that sense we can say we are dealing only with structure. So all of this is on the handouts, of course. So science represents the empirical phenomena as, and solely as, embeddable in these abstract structures.

5:00 These are described only as structural isomorphism. And this is the empiricist view, that all we are warranted in asserting is that there's this accumulation of empirical knowledge through theory change, and we can do that precisely, we can demonstrate phenomena counted among the empirical success of earlier science, that if they are embeddable in the new models, then they're approximately embeddable in the old models, and I've put C. Bueno, because Ottavio has, within the partial structures approach, a version of the semantic theory has tried to articulate a notion of approximately embeddable there. And Bayes has a very nice paper structure, its shadow and substance outlining his position. Now, in a certain sense, that's the silo-charybdis that ontic or structural realism is trying to negotiate a perhaps slightly stormy path between. On the one hand, you've got what I've always characterized as standard realism, what I now call object-oriented realism, the kind of, I think, perhaps rather partially, the thing that many fossils of science hold. It's a very crude, I think, kind of object-oriented metaphysics. And on the other hand, you've got constructive empiricism, which in a sense gives up the realist project and says, look, all that we can take to be true are the empirical substructures. Everything else we can accept, and we can accept them as structurally given, but we can't say that these abstract structures are in any sense true. They may be, they are a truth act, but we just never know. And that's the Van Vrasen famous Van Vrasen skepticism. Now, structural realism has two broad motivations. Okay? One is to respond to the pessimistic meta-induction. The Laudanian claim that through the history of science, we see a history of ontological change, and that's sufficient to undermine the realist claim that we can believe our best current theory could be approximately true. It's a kind of a meta-induction, meta in the sense that it looks over the history of the subject.

7:30 It's pessimistic in that it draws a negative conclusion. We can inductively, we have inductive warrant for concluding that we should not regard best kind of theory as being approximately true. and still also with his object-oriented realism tries to respond to that with his causal descriptive account of reference. Structural realism responds by saying well, although there is a degree of ontological change, there is this preservation of structure. And the second motivation comes from quantum physics and famously in the history of structuralism, this is one of the prime motivations We won't go into detail, but we can in the discussion that's been massively discussed. The claim is something like this, that you look at, not just quantum theory in general, but in quantum statistics in particular, to understand what's going on with quantum statistics, with Bose-Einstein and Fermi-Dirac statistics, you have to give up the notion, the claim is, you have to give up the notion that you're dealing with individual objects. This was a point that was perceived almost immediately by the great physicists themselves. Heisenberg, born in 1926, stated, that's it, you have to give up the idea that these things are individuals. And, famously, the great structuralists of the time, Cassira, Eddington, took that as motivation for their formal structuralism. They basically said, if these things, if these objects really are not individuals, they're not really objects, and so we can get rid of this object-oriented focus. Focus, quantum mechanics, pushes us to do that, and both Eddington and Kassir have aimlessly articulated structuralist conceptions. But of course we know that it's not the case that quantum mechanics drives us to this position. we can, if we wish, adopt this view and articulate the notion of non-individuality in terms of Desio Kraus' quasi-set theory or D'Alciaro's class-set theory. But we also know that or can we argue that quantum mechanics does support a view of

10:00 individuality that the crucial underlying feature here, that concerns the invariance under permutations that you find in quantum mechanics, and you can understand that in such a way that you can retain the view that the particles are individuals, subject to certain constraints. And this is a claim that Van Prassen made, and that I made with Michael Redhead back in the 1980s. And the difference, then, between our current motivation and the historical motivation is that So metaphysical, is it okay if I use it? Yeah. We have a kind of metaphysical under-determination here in the following sense. So here's the quantum physics, the theory is standardly understood, and we have two metaphysical packages consistent with it. Package one is that these things are non-individuals, and then there's these interesting formal questions, how on earth do you understand non-individuality, and so, since SEO is a friend of mine, I'll say the best way is class-i-set theory, but there's also Della Chiara's class-set theory. And then there's package two, which says that these are individuals subject to certain constraints on which states they can occupy, so make sure you get the right statistics out by imposing what's known as state accessibility constraints, so that in a way you can think of the following picture. You know, imagine, you know, God or whoever, you know, viewing the universe in terms of, you know, the Hilbert space of states, and he has in his hand, or her hand, a clutch of particles understood as individuals, and he throws them out across the space of states, and those that land in the bosonic states are what become bosons, those in the fermionic states become fermions. There's also a whole bunch of paraparticle states in between, but it seems that this world doesn't manifest those. And these things are individual. And then the interesting philosophical question is, well, what's the basis of their individual, their individuality? What's the kind of ground of their individuality?

12:30 And if you like, let me put it this way. There are two ways one can approach that question. Maybe this is not such a good way of doing it, but it helps me anyway. You can think about scholastically. This is an old question in the scholastic philosophers. but what's the ground in the visuality of something? Excuse me. Sorry. There will rain. There will rain. That's high. So much. There are two very broad ways of doing that. One is to think of it in terms of substance or exeity or primitive thisness. This is what makes the thing the individual that it is. The other is to try and cash out that individuality entirely in terms of the properties of the object. So over here you have lock substance. What is it? we know not what, but it has to be there. It's where the property is in here, and it grounds individuality of the thing. Over here we have Leibniz and the identity of indiscernibles. The identity of indiscernibles acts as a kind of guarantor of individuality. You can never have two things exactly alike in all their properties. And hence, simply by listing all properties of a thing, we kind of guarantee, we get a fix on its individuality. And again, skimming over lots of discussions, some of which, in my fair, was captured very nicely in the PhD thesis, the claim is certain, obviously depending on how you understand identity discernible, and depending on how you understand quantum mechanics, If you take the standard of the standards of both, identity of discernible is ruled out, that pushes you over here. So if you want to maintain the quantum particles that are individuals, you kind of push towards the view that they have this primitive thisness or exeity.

15:00 And that's not a claim that many people are happy with. Over here, Simon Saunders has adopted a slightly different approach, a Quinean approach, to the whole issue. And he's articulated in terms of that approach what he called the principle of indiscriminables that he now presents as a version of the identity of indiscriminables. So you can see he was trying to resuscitate the identity of indiscriminables. And he points out that you can articulate a form of weak discernibility in relational terms. So think of two electrons in a singlet state with spin. You know that one has spin up, one has spin down. You don't know which, but that's enough to discriminate between them. And it's a discrimination entirely in relational terms. And the claim is that this can be used to underpin the individuality of the terminal. And we've talked about this in the discussion. Two immediate concerns arise. First of all, what about bosons? You can't say that for bosons, of course. And Simon basically said, well, bosons you can't consider to be objects at all. And he said, that's alright, because that matches the physics. The fermions are, you know, the particles of stuff, and the bosons are the particles, you know, the force carriers. And so we should expect the stuffed particles to be individuals and the force carriers to be not, so it's okay. And some people have a sort of worry about why the metaphysics and the physics should match up in precisely that way. And the other problem is an old problem, and long before Thorne was on for indiscriminate quantum physics, the lies of Armstrong before him. Russell said, well, anyway, you can't appeal to relations to underpin the individuality of something, or its identity, or anything like that, because to present a relation, you have to, conceptually, you have to present the relata, right?

17:30 So the relata have conceptual priority over the relations, and you can't therefore use the relations to underpin the identity of the relata. And that takes us into one of the issues that I'll be talking about, because Saunders' view, in a sense, is a structuralist view of identity. And one responds to those kinds of concerns to say, well, that just begs the question against this kind of structuralist view In certain structures views, we precisely want to use relations to underpin the identity of it. That's jumping ahead a little bit, but I'll come back to that. And in addition, some of this discussion has been revitalized by consideration of this view. And the thought that instead of appealing to properties as universals instantiated in certain objects, we might appeal to tropes understood as particulars, so putting it very crudely, rather than thinking of this blue as a universal blue that happens to be instantiated in this object, we think of it as the particular blue that is here in this object. And I won't go into further details, but again, this is a view that MacLeod has defended in his PhD thesis and paper. And I think this offers an interesting new view on this particular metaphysical package. Now, the point, the point of all this, is that all of these developments could be seen as supporting this particular view. Okay? And this is what supports the claim that there's an underdetermination here. Now, you know, others like Teller and Redhead have claimed that Compton Field Theory leads us to pick this view. There are various well-known ways of trying to break an underdetermination like this. not happy with any of them in the discussion. But as far as certain kinds of structural realism is concerned, this presents a problem for the realist. This presents a problem for the object-oriented realist. It doesn't present a problem for the structural, constructive empiricist. In the very last chapter of Van Prysen's book on quantum mechanics, the very

20:00 section is entitled Goodbye to Metaphysics, and I take this to be a goodbye to realism. What he does in that book is set out these two forms, and I take him as issuing a challenge to the realism. If your realism is going to be metaphysically informed, as it should, and as Stathis has made clear, it has to be, then which of these, if you think that there really are objects out there, which of these packages are you going to adhere to? The physics cannot help you, and hence your object-oriented realism is undermined. The structural realist response is to say, right, the crucial factor here is the notion of object, and what we need to do is to get rid of that. And that's one of the main motivations for the form of that James Leidman and myself have developed. So here are these two kinds of structural realism. There's Warhol's, now known as epistemic structural realism, which says that, very modest claim, all that we know is structure. There may be more, but we don't know about that. And there may be objects out there, but we can't... Sorry, I just have a question to clarify, making the distinction sharper. On Sanders' view, right, these things are, in my understanding, are not kind of full individuals. If you say something like difference between up and down is sufficient to call them individuals, even you can't say which is which. So it looks like kind of weakened individuality, right? And on the left, on the other hand, you say something like non-individuals, quasi-sets. and would it be why would you still certainly qualify Simon's view on the right hand and wouldn't it be something in between or no no no I don't think so it's not how I understand him anyway I mean he takes this weak discernibility to underpin the notion of fermions as individual objects or as objects I don't see I don't quite understand the notion of partial individuality something's either individual I mean, if you say, you can distinguish them without saying which is which, something like this, right? It sounds like it's a weaker notion of individuality than whatever classical is.

22:30 Of course, it's weaker than appealing to substance abuse. It's still, like the claim is, they are individuals. On the left you have something like, you just give up this idea of individuality whatsoever. So here on the left, the claim is that none of these work, that you should conceive of the particles as non-individuals. And the problem with that has always been, how do you get a kind of formal and metaphysical grid on this notion of non-individuality? Well, the easiest thing for you to do is to buy my book. I agree. There, Desi and I try to articulate how you can get a grip on that by denying that particles have self-identity. That actually is a kind of bizarre metaphysical view, but you say they're still objects, they don't have self-identity. It needs further work, I think, on the nature and role of self-identity. But formally, you can then capture that in terms of a Schrodinger logic, the semantics of which is given by quantiseptivity. So the claim is, both of these packages can be appropriate. In Simon's case, it's perfectly clear the motivation is quine and these things are the reference of bound variables. And that keeps all the culture up. Yes, exactly. So, Worrell's view, then, is that all that we know is structured. As I said, it's kind of a modest view, but I think it's false modesty. I think we, you know, I've become quite frustrated with these kind folks. This has been quite crude and perhaps unpleasant to John Worrell, but this idea that, oh, yes, well, all that physics gives us is structured, but there could be more out there. Now, if you're going to be naturalists, as I am, with regard to metaphysics, that claim that there could be more beyond the physics needs to be treated with scepticism, I think. What more? What more could there possibly be beyond the physics? The Leibman view is that all there is, is structure. There is nothing but the structure. And let me see if I've got time. I'm running out of time. Let me just very, very quickly...

25:00 I'm going to put this on the handout, but I do want to mention it, that this is the view that's characterized as ontic structural realism. And in the last couple of years, I guess, it's become clear that there are two versions of ontic structural realism. The original, and best, is what some people have called eliminativist. And that, in a sense, eliminates the object. And so this is the view that James and I originally articulated. There are no objects. Now, people are going to meet and say, what are you saying? Are you mad? Are you saying there are no protons, there are no electrons? No, of course not. Of course we're saying there are objects in the physical sense, right? And so, when physicists talk about electrons as being objects, or, you know, philosophers always say, oh yes, you mean objects, putting little, you know, scare quotes around them. Of course there are those kinds of objects. Metaphysically, however, what are they? Are they objects in the traditional philosophical sense? They're either, you know, well let's just say, you know, as we understood as perhaps as individuals underpinned by exeities or some form of weak discernibility or whatever. No, the ontic structure really says no, they are nodes in the structure. now the problem with this view is that the claim is that it gives priority to the relations and more than that that there is nothing but these relations there is nothing but the structure out there a number of commentators have found that hard to get a conceptual grip on it. How can there be structure with no objects? People say things like, wait a minute, to have a structure is to have something that is structured. To have relations, you have to have relata. And I think this is, in fairness, this is quite a radical view, claiming that in some sense we have to conceive of relations as not just prior to the objects

27:30 that I'll talk about in a second, but actually as being all there is, and the objects are nothing but sort of emergent nodes out of this network of relations. And it's not clear that our standard philosophical and formal notion of relation is up to the job. Now that's a danger, because already people are saying, look, friends, you're a bit crazy, you know, structural realism, all there is is structure. Now you're telling us that our notion of relation that we've had since at least Russell and Whitehead is defective, we have to have something I mean, the history of the notion of relations, I think, in itself is an interesting history. There are episodes in that history where you get glimpses of people like C.S. Peirce thinking of relations as more than simply, or describable as entouples, as having some other quality to them that makes them the relations that are not, on the same ontological footing as, say, a monadic property. We can talk about that in the discussion. The non-elimitive view states that there are, in a sense, objects, in a sense, But the identity of these objects is given by the structure. So, the claim is, and this is a claim that Simon Saunders makes with regard to the Fermil's, John Stachell makes with regard to space-time points. The idea is that we still have a very thin notion of object, And the identity of this object is given by its relations to other putative objects. And those are the two views of OSR that have been developed in the last couple of years. Legeman has sort of crossed over from this view law to this view. He now talks of objects as having a kind of contextual identity, drawing on analogies of graph theory and so on. And this is sufficient to retain the notion of objects. There's a nice paper coming out by Anjan Chakrabarty. It was presented at a workshop that Elaine Landry organized in Canada last year. It's coming out. It won't be for a while, but you can always ask him for a copy.

30:00 It's coming out in a book. Where he basically says that, look, this view, this non-unlimited view, he thinks it's not sustainable. On any way of cashing out a notion of object in this sense, he says it just doesn't work. He tries various ways of doing it in terms of dispositional essentialism and so forth, and he thinks that basically he just collapses back into this view. Which would be great for me, because if I could say, aha, this is the only contender. work for reasons I'm going to talk about shortly. Primarily, he thinks it doesn't work because, and this is what I'm going to talk about in a second, he says, the notion of structure here as physical structure as opposed to mathematical structure, as concrete structure, it just isn't clear to him. You just don't see how it works. So we can come back to this in the discussion, but those are, in a sense, the two forms of ontic structural realism. There's a further form, Sorry, that's being a little bit unfair, moderate OSR, and this has been developed or articulated by Michael Esfeld and his student Vincent Lamb, And Vincent wrote a really beautiful PhD thesis on general relativity, space-time physics, and this form of moderate structural realism. And this is the claim, I think this goes back to Eddington, the claim that neither objects nor relations have ontological priorities. They come as a package. I think it's an interesting claim. Again, Chakravarti, and I tend to agree with him, worries that this just collapses back into this form again. And again, we can talk about that. Those are the views of structural realism now in play. I see that, I will get back onto the talk in a second, but I see that as a sign of the maturity of the position, that it's reached a point where it's able to respond to various criticisms, and now the various advocates, James Daniel and myself, Simon Saunders, Michael, Espel, Vincent Lang, and others, are beginning to articulate different versions of it. Now, historically, I'll just very quickly, typically in some of the early

32:30 discussions, both the defenders and the critics, and again, this comes back to how we delineate back to Russell's analysis of matter, this is the, it's in that book that Russell presents his former structural imperialism, famously criticised by Newman, and that criticism has been resuscitated in recent years against the form that James Lederman and I defend, and I think it can be very easy to respond to, and it has been in a very nice paper by Sartre and Mimi that I'll refer to in the second. The crucial point I want to notice point is, of course, Russell's book, written in 1926, published in 1927, what it doesn't have in that book is a full appreciation of the implications of quantum mechanics. If you read Russell's book as a historical document, it's very interesting. You get these glimpses of the emerging quantum mechanics, Heisenberg and Lewis, but it's very muddy. And it's overshadowed the work of Bourne, Kassira, and Eddington. Eddington, before he really got lost in the structure itself in the late 40s. Kassira's book, as Michelle knows, Determinism and Indeterminism, in Constance, is a beautiful presentation of a sort of neo-Kantian form of structuralism. And Michelle's editing the collection of papers on Kassira. That should be out. shortly. And there's now a lot of interest in those kind of neo-Kantian forms, not only from non-realists and people like, well, like Michelle, became a senior at UCL in London, who are very interested in these forms of structuralism, but also structural realists are interested because there are ways I can appropriate what Kaseo has done without having to be committed to the neo-Kantian underpinnings. then that saves me a lot of time and effort. So moving on fairly quickly, the picture, the intuition that the structuralist wants to defend is that we have this multi-layered or multi-aspected structure that involves a web of relations that can be replicated by the relevant laws. And these are tied together in some way by higher order symmetry principles that represent the structural invariance

35:00 of which the nodes in the structure can be described. I think this actually answers one of them, and I'll come back to this perhaps, one of the issues that Anjan Chakrabarty and others propose is, well look, you need objects. Why do you need objects? You need objects to answer the problem of what he calls sociability. What does that mean? He says, look, certain properties naturally come together. we get a certain charge, a certain mass, a certain spin, it's the electron. Or put more broadly, we get a certain symmetry, and we get bosons, we get another symmetry, antisymmetry, we get fermions. And we have to understand that in terms of the objects in which these properties in here. The structure of the spot is, no, of course we don't. In fact, it's much better to understand this group theoretically, and we can understand that in terms of higher order symmetry principles, and that they, in effect, give us the nodes. And the web of relations of this structure are inherently modal, and I would say they are inherently causal. And I'll come back to that in a second, but this is a point that James Ladyman has always emphasized, that this structure should not be conceived of as kind of a modally passive structure. It's an inherently modal structure. That's the kind of picture, and the issue now is to make good on that picture, and to try and articulate it in metaphysical terms, whatever version of structural realism it was to adhere to. Structural realism is taken to distinguish the structure of a theory, say, from its content, its ontological content. two questions then arise, how are we to characterize that ontological content that extra thing that the theory is supposed to give us over and above the structure and then how are we to appropriately characterize the structure itself and again this is one of the ways in which one defines one's structuralism in contrast to these positions Poincaré in that famous in Paris, I thought I should at least mention, in that famous quote that Worrell draws upon, about how nature hides the real objects from our eyes. He talks about these real objects, what does he mean by that, the real objects? Worrell talks about them as the natures of

37:30 things, somehow hidden from us, so that all that we can know is the structure, but there is this extra stuff. How are we to understand those, in terms of pre-revolutionary methods, physics, by pre-revolution, I mean pre-scientific revolution, are we to adopt this scholastic view that there's some kind of substance out there, over and above the structure. And of course, this is what Kassir and Eddington saw themselves as getting rid of from physics. In a sense, they defined their structuralism as, in terms of the elimination of substance. If you read their works, it's constantly saying, and hence, we don't need substance anymore. you're automatically a structuralist. Well, there are of course other views of objects which don't depend on the substance. Are these real objects going to sort of Kantian things in themselves? And of course Poincaré has this Kantian sort of element to his work, particularly when it comes to the group theory. Are they considered as substance, or just, Worrell says, unknowable objects? Yeah, and as I said, I find that view, I guess this is not an argument, this is just a statement of And this is, I think, what motivates, of course, forms of empiricism, of kinds of positivism. The claim that there's something out there unknowable, not just unknown, but unknowable beyond our physics, is something that I just find repugnant. If I can come up with a philosophy, a metaphysics, that doesn't have that, it seems to me that's a good thing. I don't think you need to be a hardcore naturalist to be sympathetic to that kind of approach. How the structure is understood, how you understand structure, the structuralism, is dependent, I think, on how you've understood the content. So, one of the interesting historical issues, trying to relate what Kistera and Eddington were doing with what we're doing today, I think is problematic in a sense, because what they saw themselves as doing, at least in part, is pushing out the notion of substance. and nowadays people are happy to push out substance but claim that it doesn't push out objects entirely. What the structural realist wants to say is that we need to take any content and in effect structure it, reconceptualise it so that objects become reconceptualised in structural terms. Well then how do we appropriately characterise that structure?

40:00 And there are then at least three different kinds of questions. How are we to represent it? And by we, I mean, and I'll come on to this to start, I mean, we as philosophers of science and philosophers of physics, how are we to represent the structure? What's the most efficacious way for us? How are we to metaphysically characterize it? And this is, I think, the central problem. People who say, I don't know what you mean by structure. and some of us say it's fairly straightforward, this is what we mean and actually what it comes down to is, and I'll get to this in a second, when they say that what they're having difficulty with is understanding this notion of structure in its causal manifestation, I think that's the real problem for many people, and then relatedly, how can we distinguish physical structure from mathematical structure the other contrast that features in current debates. It's not only the contrast between structure and context. Once we've dealt with that, the contrast between forms of structuralism that one finds in the philosophy of science and the philosophy of physics and mathematical structuralism, the form of structuralism that you find in the philosophy of mathematics. And although there are analogies between the two, there are disanalogies as well. I'll talk about that. structure. And I'll come back to this. I've called this the beasts of the field. These are the things we're trying to capture. Flossal science running around in the field with their butterfly nets, trying to get hold of these things. What are we trying to do with Flossal science? One of the things we're trying to do is to represent the structure of theories. And some of us think that semantic approach gives us the best way of doing that, in contrast to the syntactic approach. Trying to capture however one characterizes these, the relationship between theory, data, and phenomena. If you want to go with Bogan and Woodward and characterize phenomena in a certain way, how do you capture that relationship? How do you capture the relationship between theories? And this is what is crucial in the testing of meta-induction. How do you capture the relationship between one theory and another? How do you capture relationships in the math and theory. This is absolutely crucial, and I'll come back to this again this afternoon, because one of the things that co-motivates structuralism in physics, I think, is really the role of group theory in physics. This great work that was undertaken by the likes of

42:30 Bial and Wignam in the 1920s, and it's a nice case study of the applicability of mathematics, this sort of classic problem. How are we going to capture that, and how are we going to capture of physics. What we want is a way of representing structure that does all of that. It may not be possible. It may not be possible to have one form of representation of structure. So you think of the so-called syntactic approach, viewing theories in terms of axiomized sets of propositions. Or if you think of the semantic approach, representing theories in terms of set theoretic models, or if you think of what Landry, Lane Landry has advocated and others, going category theoretic. It may not be that each of those is best placed to do all of this. And so perhaps we have to be pluralist, and I'll come on to that this afternoon, and accept that we may need different representational resources at the meta-level, depending on what we're trying to capture. So the standard modes of representation for structural realism, the view advocated by Worrell, and goes back to, this claim goes back to Russell, is to use the Ramsey sentence, where you effectively pull out the theoretical terms, you have excessively quantified variables, and the claim is, first of all, that that represents a structural commitment, and John is, you know, Worrell is hard on this. That's it. That's all you need. Nothing more. You know, just straightforward little bit of logic, roundy sentence, that's your lot. Has to face the Newman argument, and the idea is that if your, or the theory that your roundy sentence is representing is empirically adequate, and you've got enough objects in the domain, so you've got, you know, the cardinality is right, then the roundy sentence will always come out true. and so your realism is trivial, and that's the problem that Newman presented to Russell. Russell, there's a famous letter from Russell to Newman where he basically says, yeah, fair game, that's it, and as far as I can tell, doesn't talk about structuralism anymore. And it's resurrected. It was resurrected by Friedman and Demopolis in a famous paper

45:00 20, 25 years ago, and it's constantly thrown up to structural realism. Structural realism cannot work, the claim is because of Newman's argument. There's various replies. It's been nicely presented by Jeff Ketlin, Pierre Cruz, and I think most nicely, best, and I would say that because Johan Satsi was a student of mine, and Joe Melio is a former colleague, have been most, I think, who have been best presented in their paper, Ransification of Content, where they basically say, look, there are lots of other assumptions that go in here. There are assumptions about how you treat mixed predicates. There are assumptions about how you treat symmetrical situations, none of which the realist has to buy into. And so they give a very nice response to that. I don't want to go into it in detail because it's been done. very nice paper. Alternative modes of representation, well, Van Braassen, Geary, others fall back on the semantic approach, the third semantic approach of Suppes, Suppe, Beth, and others, and a version of that that I have played a part in developing uses this notion of partial structures to articulate the semantic approach. This is slightly egotistical. It's now been labelled the French name of Bueno da Costa approach. It's been labelled that by Nancy Cartwright and Maurizio Suarez in a critical paper, quite critical of this approach. You still get a kind of pneumonian problem. You can always carve out a structure in extension in the domain of the right cardinality, and again, you have problems about triviality. And the way to respond to that is to insist that, look, there are, of course, constraints on the structure. The structure is, in some sense, theoretically informed. there's a nice, I think, discussion to be had on whether that represents a shift away structuralism, whether pure structuralism in the sense of somehow you've just got this absolutely pure structure, whether that ever made any sense in the physical context. I

47:30 think that's partly what motivates the accusation that structure has become Platonist, that pure structure is nothing but mathematical structure. There's a paper on the website of the British Society for the Philosophy of Science that I gave last year where I've trying to talk about pure and impure forms of structuralism. It's not paper, it's an MP3 file, so you can actually listen to me droning on, and then the discussion afterwards where everyone basically wading and trying to knock me out. But I'm going to talk about some of this this afternoon, so I'll get through this very quickly. Brady and Landry offer what they call a methodological minimal structural realism. they think that what we're trying to do by using set theory to represent structure, we're taking set theory as being constitutive of the notion of structure. And since set theory is committed to the objects, they claim that undermines the very rationale for ontic structural realism and they propose a minimal notion of shared structure. And I'll talk about this this afternoon, but the basic idea is you don't try and represent the structure look at what the scientists did, look at what Weill did with group theory, that's the shared structure between the mathematics and the physics, which is group theory, and that's all you need, that's all you need to say. The obvious worry is that amounts to a kind of meta-level positivism, that all you're saying is Weill did this, and Heisenberg did that, and you're giving up on what I took philosophy of science to be doing, representation of how science works. But I'll talk about that something. Third's really about the issue of how do we represent the structure at the meta-level as philosophers. How do we metaphysically characterize it historically? This was understood in terms of the question, how do we replace substance as the locus of property instantiation? If you don't have substance anymore, how are you to understand the properties of the physical world? And Cassira and Eddington both say, well look, you should understand this group theoretically. That's what's really crucial to you. There's a very nice quote here from Eddington, where he says, Russell, in his pioneering developmental structuralism, didn't get so far as the concept of group structure.

50:00 This is partly because of the time at which Russell was writing, 1926, when was Vile doing this magnificent work, when was it really coming to the full fruition, when was Dignes starting to think about 1925, 1926, too late for Russell to really understand what was going on. And hence, says Edison, that's why Russell fell prey to Newman's objection. Russell's vague conception of structure was a pattern of entities, or most of the pattern of relations. But the elements of group theory make it clear that pure structure is only reconciling a pattern of interweaving, a pattern of interrelatedness of relations. So this is Edison's claim, that structure is not just a web of relations, it's a web of interrelated relations. And he gives here the analogy with spin. So the idea, he says, look, the way you introduce it, you introduce it in terms of planes, and you think of rotations in the plane, and then you come up with an algebra, well, you can obtain an algebra of operators that represent rotations acting on rotations. And the pattern of interrelatedness is manifested in the associated table, multiplication table. And that's what represents the structure. and the planes that you use to start the program you just dispense with kind of a bit you climb up the ladder and then you throw it away and as John Lucas once said that's a very silly thing to do if you're repairing a roof but metaphysically it makes sense in this context because all you're doing is introducing this non-structural element in order to be able to use the resources of your mathematics in order to describe the structure. And once you've got to that level, you can dispense with the non-structural component. This is a manoeuvre that a structure is typically appealed to. And I can talk about the extent to which it's a viable manoeuvre or not. Again, since we're in Paris, I have to note, it goes back at least to Poincaré in his lovely paper in 1898 in Marnie, where he talks about the new approach to geometry of Klein and others. Essentially, he's talking about the group theoretic approach. And he says, what about the geometric objects that we've always thought about? What about the triangle, the square?

52:30 He says, well, these are nothing but a crutch for our intuitions. That once we reach the group theoretic level, you can dispense with the crutch. You can just throw those intuitions away. There's a very nice paper by Morrison, Margie Morrison, on spin, and how our concept of spin, our understanding of spin, is shaped not just by theoretical considerations, but by empirical considerations. She's very dismissive of the structuralist approach at the end, but I think she completely misunderstands it. Nevertheless, the rest of the paper, all but the last part of the conclusion, is fine. So the issue here is how, historically, the issue was always how do we replace substance? What's going to stand into substance? And Gassir and Eddington tried to understand it in terms of proof theory. There's some very nice work. I won't go into this. Bohr, the physicist, draws on Gestalt's psychology. And that might sound weird. That might sound, whoa, what's going on? But actually, of course, there's a nice history of Gestalt psychology. It's very much tied up with the history of physics, not just in the sense that the Gestalt psychologists were mates of Einstein, mates of Born, but also that they drew on results from quantum physics to defend their view of perception in these holistic out-turns. And Born, in his public lectures in Edinburgh, where he tries to sort of articulate a structuralist conception of quantum particles. And he's trying to, you know, people are saying, well, what do you mean? He says, well, look, draw on this analogy with gestalt psychology. I won't go into details here, but I think it's actually quite an interesting episode in the history of structuralism. And of course, there's a famous paper by Kassira in, I think, the very first issue of PPR, Philosophy and Phenomenological Research in 1944, something like that, where he basically says, you can give a group analysis of Christoph's psychology. Currently, the issue is how do we invest structure with the appropriate features? How do we make structure metaphysically viable and more than that, robust? And there's a series of criticisms arising from a comparison with mathematical structuralism from Jacob Bush, Statlis Silos, and I tried to respond to them myself in a recent paper in the Aristotelian

55:00 Society. The BBB papers are BSPS, Brazil, and Banff in Canada. These are three papers I gave BSPS a couple of years ago, and Brazil and Banff. Trying to just articulate the metaphysical do in just five minutes is go through that. This is the other comparison that I think is slightly invidious when we try to articulate structural realism. Because mathematical structuralism has been very well developed, and in a sense what you get are people looking to this, drawing to certain conclusions, and then taking them over to the Ladyman French version of structuralism, and that's inappropriate in many cases. Mathematical structuralism comes down to Resnick and Shapiro, and the basic idea is, as they said at the bottom, there's no more to the numbers, say, the number two, than the relations it bears to the other numbers. Numbers have no identity or distinguishing features outside the structure. And Oestein-Linebo at Bristol talked about this. It's a scarce properties intuition. There are no other properties other than, you know, of the number other than what's given structurally. And then this is carried over or the kinds of concerns that one might have with that view are carried over to the physical structuralism. I'll just mention these two. This is from Silas. He says, look, mathematical structuralism comes in two forms, anti-REM or in-Ray. Anti-REM structuralism is the idea that the structure is an abstract universal, right? In-Ray structuralism is the idea that what you've got is a system of objects and properties that is structured, right? He says, those are the only two forms. But on either form, physical structuralism doesn't work. Why? Well, if physical structuralism is a form of anti-REM structuralism, then you're claiming that the structure of the world is abstract, is universal. But the world is causal. The world is not, unless you're a Platonist, mathematics.

57:30 So that can't be right. If you go for in-ray, then you accept that there are objects and properties that are structured. So, eliminativist structuralism doesn't work. So, on either account, structuralism doesn't work, says Ceylon. My response is very blunt. This is inappropriate. This is an inappropriate analogy. It works in the mathematical case, because there's already issues of, well, we already pausally interact with them. There are issues of what Fraser McBride calls the accessibility problem, even for structuralism. But those are not issues for us. And so what I'm trying, what James and I are trying to articulate is a form of structuralism that is neither anti-REM nor in-REM. Of course, it's not abstract in the sense we think of the world itself as being structured. But precisely, and we shouldn't beg the question here, we're world shouldn't be understood in terms of objects and properties. Well, that raises the issue, then, if this is the view we're trying to articulate. What about causal powers? And this is a sort of classic distinction between the mathematics and the physics, mathematical structures and physical structures. The latter has, in some sense, causal power. And this is the very broad claim that is made by Silas and Chakravarti. requires objects, they say. I don't think it does, and let's very, very quickly in the last couple of minutes articulate why. Before I do, of course, many people will say, why are we even talking about causality here? If we can have a structuralism that's fit for quantum mechanics, we know that in the, you know, whether you go, you're talking about quantum mechanics, quantum field theory, causality is the very least problematic. And I'm, you know, I'm swayed by that. I'm also swayed by the claims that even in Newtonian physics, causality is problematic. There's a very nice paper by John Norton in a collection of papers on causality when he thinks of causality as a kind of folk notion. It's kind of a notion that we've arrived at by considering this stuff, and we kind of import it into the micro

1:00:00 it can't be sustained there. Nevertheless, it's very useful at certain levels. I'm very sympathetic to that view. But my response to those kinds of questions, why am I even worried about causality, why don't I just dismiss Silos and Chakramati, goes like this. First of all, I think I think I think structuralism can offer a metaphysics of causality, or can accommodate a metaphysics of causality. So if they are worried by this, I want to say, look, it's really not a worry. And secondly, I think what they're actually worried about is not causality so much, it's concreteness. What they're really worried about is, what makes this structure non-matical? What makes it physical? And that's all wrapped up in this notion of causal efficacy. And I think we can talk about it in the discussion, but what I'm really bothered with here is this notion of concreteness. And the intuition here is a similar intuition that motivates people's thoughts about causality. There's a famous episode of a talk by David.