Steven French (contd.)

0:00 That shared structure, shared between the mathematics and the physics, is how the objects come to be presented to us. And what they call, and this is their term, what they call presentation, the structural realists would want to call reconceptualization. that, in effect, by presenting your putative objects in this way, you'll reconceptualize them in struggle with them, and, in effect, eliminate them. Representation is just a standard sort of claim that the object, the phenomena, the world is represented by a theory. and then there are and of course representation this is a discussion of much this is a much current discussion in the proper time with everyone from to a very minor extent myself talking about broadly structuralist accounts of representation The kind of accounts that exist as an isomorphic relationship between the theory in the world, or part-likeomorphic, or homomorphic, or whatever. Two questions then arise. How is this structure, the shared structure, represented, and what is the structural representation? As I say, I'm actually not going to say very much about the second question. I've started to think about it, and it just didn't take up too much time, but I'm happy to talk about it in discussion. What I'm going to do is focus on this first question in the context of what Catherine Bradenley-Lanthambridge talked about. and some of the issues I touch on are discussed by James in his in fact Okay, so in answering or looking at

2:30 question one let's remind ourselves again of the beats of the field, what we need, what we as structuralist philosophers, what we need to capture. Again Again, we're trying to capture the structure of theories, and in particular, if we have realist information, we want to represent the structure of theories in a way that most appropriately displays our ontological commitments. Okay? We want to represent the relationship between data, theory, and phenomena, however that is perceived. we want to consider interfering relationships and again if we're a realist we want to capture that in a way that enables us to address a pessimistic method we want to consider the relation, capture the relation between mathematics and physics in a way perhaps that will help us answer the vignarian problem or the capability of mathematics, how is it that this because these mathematical results are so useful, so applicable. I think they're actually fairly easy answers to that question, and in part they are a thing to be easy once you adopt a particular stand with regard to how you represent this relationship. And we want to capture the implications of modern physics, whether talking about quantum mechanics or space-time theory or quantum field theory, gravity and so on. So those are really what we're trying to capture. And as I said this morning, it may well be that no one mode of representation is capable of capturing all of that. These are the animals running around in the field and we've got this big net trying to catch them for the softening. It may well be that there's no one mode of representation do now. I'll explain what I mean in a second. Now, Braden and Landry advance what they call methodological minimal scientific structuralism. And this is their attempt to avoid what they view, I think, incorrectly as kind of ontologically superfluous features of, say,

5:00 set theoretic modes of representation. So what they call minimal structuralism, it's basically a commitment to their claims that the kinds of objects that the theory talks about, netrons, fermions, bosons, whatever, are presented through the shared structuralist threshold models. and the theory applies to the phenomena just in case the theoretical models and the data models share the same kind of structure. No ontological commitment, nothing about the nature, individuality or modality of a particular object is entailed. So there's a certain sense in which we could all sign up to that, right, and say, well, look, yes, of course, in adopting a structuralist stuff, we're going to begin by considering the relevant structures as presented to us by the direct model. But then, if we're going to be, say, staff is still also an object-oriented We're going to want to go beyond that and say, right, and what lies beyond that structure are these individual objects. If we're going to be a structural, an ontic structure, we're going to say, no, there is only that structure, and that's what there is in the world. So this refusal to adopt any ontological commitment might be seen as some, as simply a refusal to engage in the very debate that's raging in the fossil science. Can I just, to make sense of the notion of shared structure, one thing which comes to mind is you have these objects or whatever, constructions, and you have and it's exactly in them, something like Islard is tied to say that, is that, is that, how do you have to do that? Well, no, because, I mean, already there, okay, I'll come to it, I haven't got there yet, I mean, they're talking about, I would say, yes, it's a shared, you know, shared structure are represented in terms of partial structures related to partial isomorphism. They would say, no, no, no, no. They're talking about, they're talking about, you know, take

7:30 physics, take physical theory, and for example, take the case of I'm jumping ahead. Take the case of group theory. The shared structure is the group structure. And what you have there is just morphisms. That's it. Isomorphism. I'm not defending this view, this is their view, so I'm going to go on to say, well I don't think it's appropriate, but it's what they call a minimalist approach. Notice that they, and part of their paper is concerned with precisely this issue. This is a slightly odd, one might think of a slightly odd claim. a theory of why some phenomena just take the data models and the data models share the same kind of structure. You might think of it, you think of phenomena as being out there in the world. You think of the sub-esbian construction of data models, and those are related to, perhaps, some would say embedded or partially embedded into theoretical models and so on. What is it that, in a way, you know, bridges the gap between the data models and the phenomena? So this is a fundamental problem, it's almost, you know, particularly by Wittgenstein in terms of, you know, what is the gap between the word and the world. And they see this as just, you know, a gap that cannot be bridged in a sense. Everyone, they claim, um, a realist and anti-realist attacks in a different way, and they find that all of these ways is just problematic. Instead, they say, we're just going to refuse to say anything more than that. Theory applies to some phenomena just in case those models share the same structure. Already, you will have many people with strong objections to that kind of view. That kind of minimalism. But where we agree is in the claim that neither the framework of the semantically of the theories nor the appeal to shared structure alone offers the structures a quick route to representation. This is surely true, and this bears on issues to do with how we frame representation in the philosophy of science. It's not enough, as I indicated this morning, just to insist that there's an isomorphic relationship between the representation of theory, however destructive it is, and the

10:00 world. What else is required? Well, some would say some kind of intentional start is required due to the standard objections arising from Goodman. Because if you say, well, look, this painting represents the world because it's similar to the world. Well, that's a symmetric relationship. The world is also similar to the painting, but we don't talk about the world representing the painting, but typically a notion of intention is involved. There are ways of getting that directionality into representation that may not be committed to a problematic notion of intention, and that's That's the kind of stuff that Roman Briggs and Mauricio Suarez and others are concerned with. And on that, I agree that, of course, we need something over and above simply a view of theories which represents them in terms of structures to give us what we would call representation, and this is part of what you and I tried to articulate. But that's not my main concern today. what I'm mostly concerned with is this minimal approach of braiding and landry and this distinction between presentation and representation that they try and articulate. So in a recent paper Elaine tries to answer the question, well, what is the shared structure? What is the nature of the shared structure that they're appealing to? And what she's very keen to emphasize, and of course she is because she writes capital in theory, is that shared structure need not be shared set structure. So, she insists that mathematically speaking, there is no reason for our continuing to assume that the structures and or morphisms that we're concerned with are in some sense made up of or constituted by sets. To account for the fact that two models share structure, we do not have to specify what the models as factor-set structures are. It's enough to say that in the context,

12:30 this will be important, in the context under consideration, there is a morphism between the two systems, for our mathematical model, that makes precise to claim that they share the appropriate kind of structure. Now, let me just again indicate where I'm coming from. I don't think it's an implication of the view that the appropriate mode of representation is sector ethics. I don't think that implies that the structure that we are concerned with is really is in some sense constituted by a standard. Of course not. And I'll come to that in a second. But this is her basic view. How do we make precise this concept, then, of shared structure? This gives you a contrast. Now, you might say, well, it is one way to begin. And this is, again, sorry, it's like egotistical, the French lady from Bueno-La Costa view. And I only use that because Nancy Cartwright and Mauricio Suarez in their continuing criticism of me for reasons that I failed to understand, insist on calling us the FLPD. So you might say, look, here's one way in which you can capture, represent the shared structure between theories, between theories, physical theories and mathematics. You have these partial separatist structures, you know, partial in the way that Costner and I have tried to articulate, and partial isomorphism, homomorphism, holding between them. A lot of what we have to say is set out in the 2003 book. that's the view that Landry wants to represent a great deal of her paper is taken up with arguing against that because she insists that by representing shared structure this way we're committed to viewing this structure as constituted by sex so it what does Partial in the sense that the family of, in the family of relations, you have relations that you know hold, you have relations that you know do not hold, and you have relations about which you don't, you're unsure whether they hold or not.

15:00 And you can define the notion of partial structure in those terms that is related to the notion of a total structure. And it's pretty much laid out in... The origins are laid out in a paper by Meichenberg, Schwachy and Acosta from 1987, I think. But it's all set out in the book, so you can find it there. One of the problems that I'd like to talk about is that with that particular set theoretic view, it goes like this. So the claim is that on the Serpesian set theoretic approach, the so-called semantic approach or model approach, you're representing theories as families of models interrelated in a certain way, such that they have this shared structure. And typically, and, well, in every case, these models are Tarski-type models. And there's a problem with this, and Jerry Chakrabarti articulating it, which is, wait a minute, how are you going to regard your theories as true if you're using the very kind of mechanism in terms of which we articulate a Tarski notion of truth to represent the theories? And so, to say that the proposition is true is to say it's true in some task-type model. But if you're using those models to represent the theory, how are you going to be a realist in the standard sense? You could, of course, drop task-type form of truth and go to some pragmatic accounts, some other accounts, but then you've given up when you're really. And there's a response that Acosta and I articulate in the book, we haven't developed it very far, but it adopts a response from Patrick Subbis. And he makes a very nice distinction in one of his 1950s papers between what he called the extrinsic and the intrinsic characterisation of theories. on the extremity characterisation is as if you're standing looking at the theory from outside and you're concerned with the structure of the theory so this is one of the beasts of the field trying to capture the structure of the theory and the best way of doing that is to use mathematics itself not metamathematics, not logic

17:30 in the way that the hypothesis is, but use mathematics itself, use set theory and the theory in terms of families and models. If you want to talk about epistemic attitude, if you want to talk about belief, for example, then you have to adopt this intrinsic, internal perspective. And belief is typically belief in a proposition. So then you need to go to this intrinsic perspective and say that I believe that such and such proposition is true. That enables you then to articulate that notion of truth in terms of tasking models. You know, you can avoid track of artist concern because from that perspective you're using the models to articulate the notion of truth, you know, in terms of which the proposition is true. You're not using them to represent the theory. So you've got this extrinsic, intrinsic distinction. I think that's a, I I think it's a useful way of capturing both truth and the structural representation of theories. It raises the question, however, what is a theory? What is a theory ontologically? What kind of abstract structure? Quite often the semantic view is represented as saying These are families of models. Carlson himself, in some of his, in the side of the image, kind of made certain suggestions that perhaps led people to think that was his view. And then he later said, no, no, no, I'm not trying to reify theories in this sense. I'm trying to adopt the Serpezian approach that set theory is the best way of representing theory. And if you do that, and you've got this distinction, you can raise a quite legitimate concern. Okay, French, what is a theory? Is it a set of propositions, axiomotized in a certain way? Is it a family of models? And there's a nice collection coming out in Payser, edited by Gabrielle and Esser, on precisely this issue, the ontology of theories and models. not their ontological commitments, but what are theories and models in themselves?

20:00 Are they abstract objects or not? My view is that this distinction supports what I call a quietest view of theories and models, which is, I refuse to answer the question. Why? Because I actually don't think it's important in order to do the philosophy of science. This is, I mean, quite a controversy a sort of response that Rorty makes to many philosophical questions. He sort of berates philosophers for failing to answer the great problems of society. And Rorty says, on everything else, all these metaphysical issues, I think we should stop the quietest approach. Just refuse to answer it. Why? Because it doesn't help us. I think this kind of debate about what is a theory, a set of abstract models, a set of propositions, doesn't help us in the process of science. So I'm going to adopt a quieter view. Some have claimed that this is to sort of abandon what they saw as my commitment to pure structuralism. But I don't think it does. I think a structuralist approach is the best way of representing theory. It's way of presenting objects, but then to ask whether theories are structures, seems to be just a misguided kind of question, right? Because, I mean, again, I'll stop talking about it because we can follow up in discussion, but if you think about it, you know, you ask a physicist, okay, show me your theory. What is she going to do? She'll give you the paper which will scribble something on the board. Well, obviously, those are tokens. You might think of those as tokens of the theory. But what is the theory? Does it exist in some kind of superior third world? Is it like artistic objects where apostles of art say that these are, you know, some people claim that these objects are universal or types, which can be manifested in certain terms? I think it just gets completely messy. like you know this process out there called science this and it's got a whole heterogeneous complexion to it we've got theory we've got models we've got data multiple phenomena and we kind of arbitrarily point to various bits and say right that's the theory right i mean there is a real problem in the process of theory individuation how do you individuate one theory

22:30 how do you distinguish i don't know how do you individuate theory of quantum mechanics in a way that makes sense or, say, distinctions between the Copenhagen view and the Bohmian view. Are these different interpretations, different theories? The Copenhagen view splits and divides, and it's not clear that there's actually one going on to do, and so on. All of that leads me to say, look, let's just not even worry about that. What I'm concerned with is what's the best way of representing this heterogeneous set of processes and claims Now, Landry rejects that because she feels that the so-called semantic account, the so-called semantic account commits to, as I say, sect being institutive of a notion of structure. She says this notion that she has of shared structure is made precise by a morphism, and the standards of the Caffey theoretic point of view, and the context determines the kind of morphism, and I'll explain what she means by that in a second. But she says here, I want to distinguish between semantic accounts that consider what the concept of shared structure is, what the appropriate type of structure is, for formally framing the concept of shared structure. And those that consider what the presence of shared structure tells us, what the appropriate kind of structure is, and characterizing the use of shared structure in terms of some kind of morphism. And I want to place my focus on the latter. So she is claiming that those of us who adhere to the semantic approach are telling her, telling everyone, what the concept of shared structure is. is set theoretical, she said, is what we're claiming, and what she's interested in is how this shared structure is used. Now I deny that's what we're doing. So the essence of her claim is that two models share structure if there exists amorphism between them that preserves the appropriate kind of structure regardless of having to specify that kind of precise type of morphism. So it's, you know, what

25:00 structure is determined contextually. So she takes the kind of stuff that I did some years ago, group theory, how group theory was introduced into constant mechanics as a case study, and as we all recall, there's at least two very well-known strands to this history. There's Biles' more foundational approach, in which he tries to ground quantum mechanics in group theory, as the foundation of theory, and as far as Land is concerned, is one that preserves the shared group structure. They've been, of course, with this other strand, more pragmatic. Basically, it's very crude that the two strands are out there and the one. But the big area of the strand is simply saying, look, there's certain problems in quantum mechanics. If you can't crack them by solving, throwing information or whatever, you have to adopt a group threat approach to to get them the normal case for crack-ability issues. Again, says Landry, right, what is doing the real work there are the morphisms that preserve the lead-group structure. And this is the central part of their claim. What does the real work is not set theory, it's the group-threative morphisms. What she's saying is what does the real work in this historical episode is the group theory. those warpisms alone serve to tell us what the appropriate kind of structure is. And again, my concern, I'll see tell you this in the second, is work for who? What are we talking about when we talk about doing the real work? And appropriate for what? For physics or philosophy of science? So for her, it's the use of the concept of shared structure that determines the kind of structure and characterizes the meaning. And the work is all done by the context-defined morphism flowings. The context of what Violent Ligner did is the group-creatic morphism. In another context, it would be a different set of morphism.

27:30 And how she defines this in a more standard and more accurate way, right? Sorry? How she thinks about what is... It's in a category theoretic way. I don't care in a way. I don't care. I think the project fails anyway. It doesn't matter. It doesn't matter. I don't know where we can talk about from the discussion. Now, she sees this as opposed to the view, which she accuses me of, of taking the formalism as both defining the meaning as a type of set theoretic structure, and thereby justifying its use in all contexts. So she accuses me of claiming that in all contexts it's going to be a set theoretic structure that is doing all the work. Now this, I think, raises a perfectly general issue for structuralist accounts, but it raises particular issues for structural realism. I'll get to that in a second so this is really the heart of her view she's rejecting sect theories constitutive of notion she's proposing this minimal notion of shared structure the worry that I have now is that this minimal notion amounts to nothing more than saying in 1926 27 group theory of the dependent structure that we were concerned with. In 1956, it was another kind of structure. In 1986, it was another. So all you're doing as a cluster of science is simply citing the relevant physics and mathematics. And this just seems to be what you might call the meta-level posthumism about that. It's a bit like, if you look at the history of science, I think it's changed, but certainly five or ten years ago. Historians of science, if you ask them, what is your view of the history of science? What is your overall conception of how science developed in the 19th century? They would immediately rush up to do something rude to them. No, no, no, no, no. All I'm interested in doing is telling me what happened in the Leeds Botanical Society from 1873 to 1883.

30:00 All I'm interested in thinking is what happened in this laboratory. I'm not putting it in the general picture. I think this amounts to a similar approach in the philosophy of science. But it's important because it raises the issue. What structures are we going to go? Which structures are we to be realist about? Now, me, Eddington and others are going to say, look, we should be realist about the group theoretic structure. If we're talking about, say, quantum statistics, ultimately what I want to say is, look, the kind structure of the world, kind structure in terms of kinds of particles both on thermals, paraphermas, paraphermas, anyons, whatever. Those are going to be given in terms of the group theory structure, permutation group, ray group, whatever. That is the structure of the world at that ultimate level of time. Landry says, all right, fine. Where is set structure doing any work in that? You've presented the object of physics in terms of group theory. Why do you need set theory? you need set theories. And she said, if one wants to use this kind of structure as a tool to carve the world into natural kinds, then one cannot, in addition to claiming that group theory is the appropriate language, claim that all such group theoretic kinds are set theoretic types, unless one is ready to hold fast to, and to provide justification for the barbaric sub-easing assumption, that all scientifically useful kinds of mathematical structures are set-terrestrial, nor can one use this assumption to make it more reverse ontologically read structure really explain about the structure of the world, unless one wants to impose or presume that set theory cuts not only mathematics but indeed nature. And so in the sense she's saying you adopt the kind of line that I adopt, you're led to a form of places. Okay, now I just think that's completely mistaken. I think, if we consider the presentation of objects or properties via the shared structure, first we have to consider certain issues to do with the metaphysics,

32:30 how we understand these properties, how we understand them as possessing cause and powers, and that's the kind of thing that I'm trying to talk about this morning. Normally, the sort of normal metaphysical approach that the object-oriented realism is to begin with objects, give them property, have relations holding between those properties, and have those relations represented in law. I think what the structural realists and the transcendental idealists share is that, no, no, you think of it the other way around. It's the laws that give us the relations, that give us the property, and then people objectify this and say, right, we want objectivity, we have to have objects there. And what the structuralists want to do is say these things are derivative, right, and in my, the terms that I indicated this morning, are in that sense eliminating, the objects are eliminating. I've indicated this morning, symmetry is going to play a critical role in the physical representation of the properties by the shared structure. And I agree that that's context-dependent, in the sense, not in the anti-realist sense, not in some kind of sociological sense, but in the sense that the physical context, the world, tells us which structure is appropriate. It reveals that aspect of the world's structure. Okay, so think of the slide I put up this morning of spin. What, according to this year, what's the most appropriate way of understanding spin? It's in terms of, as Eddington put it, in terms of the group multiplication table of rotations acting on rotations. And that's it. If you ask me what spin is, I'm going to tell you that. If you say, well, what more is it? What kind of a property is it? That's it, dude. That's it. And in more than that, it's the right way of understanding spin. If you try and understand it classically, of course, as a little, you know, vector, you know, pointing at the top, we know that doesn't work. We know that spin can't be graphed in that classical sense. Of course, in that sense, I agree with Landry that there's a certain context dependence. It's just a trivial kind of context-dependent thing, the way that every reader will hope. The world will show us what's the appropriate metaphysical, ontological structure.

35:00 Further developments in physics will continue to do that. Now, she asked, well, wait a minute. In your case study, where does set theory do any work? Well, I think there's extinction to be made between what's doing the work at each level and who's using what. Okay? Physicists and mathematicians, of course, Weill, Wigner, von Neumann, use group theory and not set structures, except maybe in the physics sector, you want to be a reductionist and say, all mathematical structures are reduced to set structures. I mean, that's a different, that's a whole different issue. It's nonsensical to say that they were using particle sets, set their structures in the way that I know. No, of course, they used group theory. And of course, in the context of the quantum mechanical revolution, it was group theory, not set structures, doing the physical, mathematical, object-level representational work, presenting the objects to us. It was group theory that did that. But it's philosophers of science at the meta-level that use partial set theoretic structures to do the meta-level representational work. So I'm trying to get at this distinction that Brainy and Langley themselves articulate to undermine their accusation that somehow by adopting a set theoretic structuralist line, I'm saying that the structure of the world is somehow set theoretical. That just seems to be nonsensical, or, well, if you've misplaced it. What I'm trying to say is, at the object level structure, at the level in which we are concerned with structural ontology, there is a contextual determination of that structure. Okay, physics will tell us what the appropriate structure of the world is, and a naturalistic and inclined structural ridge will take that seriously, and will do as I said, will say

37:30 all that spin is, is given in terms of group-related structure, or whatever relevant structure physics comes up with, you know, the spin structure gets embedded in the broader structure. The context here is not problematic at all for the reality. Where I disagree is when we come to represent what's going on at the meta-level. If we abandon some kind of unitary framework, whether it's the syntactic approach, Samantha's approach or some kind of Catholic theoretical approach then we lose the ability as philosophy of science to talk about how science works to frame our case study in an appropriate way and it collapses, philosophy of science will degenerate into what history of science now is, simply a series of case studies Landry insists that if we adopt the approach to advocate, we will lose our explanation of what I call the beast's field of theory into theory structures, theory data phenomena structure, because she insists all the real work is done by the B groups, for example, in the case study of but that's completely wrong all the real work is done at the object level by the physicist using but we don't lose anything at all if we then represent that in terms of whatever framework actually we feel is most appropriate there's a general issue in the fossil science here about the about the usefulness and significant of these kinds of frameworks. And as I say, the worry is if you adopt this kind of minimalist line, the philosophy of science is losing a grip on the answer to the question of how science works is to generate into a series of case studies. And just to sort of quickly go through what I went through this morning. If we adopt this approach then, and then the question is, okay, the objects are presented as group theoretic structures,

40:00 and then the issue is how do we represent the theories themselves at the meta level? There are a range of options for the structures. Again, go through this, do a Dr. Ramsey sentence approach that is a syntactic view, so you represent your feelings like this, as containing theoretical terms, approbation terms, and you catch out theoretical terms in terms of exercise by variables. So, whether or not the Newman argument runs or not, there are claims, famous claims by Suckey and Van Praassen, Greg Suckey and others, that this sort of approach just can't capture the kinds of things that were interested in, inter-theory relations and so on. That relates to the whole discussion between Warhol, Friedman and Van Praassen about the relative merits of this impact versus the semantic use. I'm not really that bothered, but we can get into if we want. Landry herself feels that category theory is the best way to go. She feels it better captures the implications of quantum mechanics. Why? Because if those implications are taken to be problematic for the notion of object, her view is, well, set theory is still committed to a notion of object. Category theory isn't, so that's better. So she's always been, she's been saying for many years now, Stephen, Jane, quite a good doctor, category theory to which our response is, but it's hard, I don't really understand it. If someone would explain it to me, maybe I would, but I'm still not convinced because part of what, and this refers to Mateo's point this morning, if you want structural realism to do both jobs, capturing implications of modern physics and offer a response to pessimistic meta-induction, we want it to capture in theory relations as well, and it's not clear to me that category theories does such a good job on that. Set theory, on the other hand, captures the inter-theory relations quite well, I would frame, because you have partial isomorphisms holding between partial structures, not a problem. Does it capture the implications of quantum mechanics? Because, and this is the problem, this is the language problem, look, how do you write down a partial structure, or any kind of structure, set to everything? You begin, Well, I have a domain of objects. Over that domain, I define a family or relations, and then you can introduce functions, and blah, blah, blah, blah. And she said, look what you've done. You're supposed to be the ontic structural realist. You're supposed to live in this bad habit, and you've just introduced them again.

42:30 You fool. Don't have to be theoretic. You won't have that problem. Well, there are ways of getting around that. And one is this kind of, I called it this morning, Poincaré's manoeuvre, and the idea is you can say, look, look, look, I want to avail myself of the resources of set theory, because I think they're a useful set of resources, but I don't want to be ontologically committed to objects. So I'm going to write it this way from left to right, because it's easy. I'm going to introduce objects to find value of relations over them, but I'm going to read it, submit it, from right to left. Ontologically, this, these things are dependent on these. Okay? Now you might say, how can that be? You've just introduced these. I say, well, I haven't really introduced them. It's not like I'm God, I've introduced particles. The world is out there, and what we're talking about is the best way of representing it. And for the purposes of allowing ourselves, well, allowing the possibility of availing ourselves of modern mathematics, we represent the structure of the world as a set of objects over which we define a family of relations. But ontologically, we read it the other way. These objects are actually conceptually dependent on these things. Now, again, many people, and this is a common structuralist maneuver. I think it's interesting that you find this running throughout the history. Bancarré makes it, Eddington makes it, other people have made it. And it's a kind of a trick. Some people think it's a cheap trick. But in some ways, it does, you know, it's a useful way of giving us all the resources from modern mathematics without simply refusing to be committed to the apparent ontological implications. The alternative is to find a completely different way of representing structure. We might try to happen in theory. Professor Krauss has suggested a form of quasi-septive, where the elements in here, in quasi-septive, are regarded as mere place-holding.

45:00 So if you're going to do this, you really don't want to try and reduce the kind of object nature of these elements as much as possible. And quite as I said, theory, these elements don't even have self-identity. They're still objects, but they're non-individual objects. So maybe that makes further sense in the context of the Poincare manoeuvre. Another alternative that I've been looking at, partly just for fun, but partly also to capture the kind of claim that Simon Saunders makes, namely the structures all the way down, so there is no kind of ultimate foundation, it's just structure, structure, structure all the way down. You see non-well-founded sects, and there's someone at these, Laura Crossilla, from, again, another Italian athlete who's been working on non-well-founded sects, and this is a way in which these elements themselves are understood in terms of sects. It's not quite clear whether this is the appropriate technical device. It works very well in the case of circularity, but it may not work very well in a decorative context. I think what we have is a plurality of representational devices at the meta level, and these can be used to capture a structuralist ontology at the object level. Some of them may capture some of the beats more fully than others. So the presentation of objects is via the relevant physical context, or rather relevant physical context given structure. So again, If you ask me what a fermion is, I'll point you to the permutation system. If you ask me what a spin is, I'll point you to the relevant multiplication system. That's what it is, I will say, metaphysically.

47:30 This is what underpins the approach of metaphysics that I was talking about this morning. So in that sense, I agree with Landry. That's the kind of structures that we as structuralists need to focus on in this method in order to take structures to form. I don't agree that that commits our ontological notion of structure to being articulated in terms of set theory. That's simply to mistake the level at which we're operating. We need or we can use set theories at the meta-level. we represent theories via the meta-level structures that are appropriate to capture the beats of the field and here we have the possibility of pluralism in the way that I've indicated we may find as I suggested that more than one kind of structure offers better it works better as a representation device depending on what we're trying to capture that cap-view theory is the best framework for capturing the relationship between mathematics and physical theory. It may well be that set theory is best to capture into theory relations. It's not clear to me that once we adopt this representational stunt, anything hangs on that but a structural real. Because you're saying, I'm using these to represent. This provides a context for object level representation value between the theory and the world. Okay, I'll stop there in just about an hour and we'll follow up in discussion. Well, one reality that actually seems to me confusing is actually the consequence of morphism. Actually, I know it's quite a usual way to say that not just isomorphism, just any morphism kind of preserve structure. It might be, it's very confusing if you're just looking at some examples, like you know, you have a, I don't know, big group and you map it in just trivial group

50:00 consisting just of ideas, but it's kind of, everything is killed, but just you're, you're thinking kind of fundamental factors, right, and because the word is already, there is no difference between marketing and So, I don't know, from category of groups to sets, again, you would say, you forget your structure, but the very notion of, you know, factors are permissive to preservation of the structure, you usually get in terms of trouble, I guess. My own view is that actually the whole talk of structure makes sense in the photographer's isomorphism, right? So you have, like, isomorphism, then you say, okay, you just kind of identify up the isomorphism, you say, and they're both kind of instances or whatever, something which is structure C over and over there. If you just have morphism from A to B, there is no possible reduction of that kind. And actually, an example of group is particularly interesting because purely the so-called categories of A, you can think about group differences. Because what I still think is shared in my kind of traditional definition of what the homework is on group, And just saying, okay, then we can of course think of category groups and then say, okay, that's kind of morphism which somehow specific for groups and defines what group are for them. But here it was directly different, just you think about group as, you know, object with category with all the objects and markers in itself, which are all reversibles, all isomorphism. And that would be a homotis. And I think, you know, that way J. Janz's argument doesn't go soon that you can, I don't know, describe the structure for preserve, but for peace and whatever. And actually, in my own view, probably I'll talk to you later on in a general discussion later, but this is the reason why, in my view, this category of theoretical fortune actually is not structural, it's something beyond structural. It does go back to this kind of what you call object-to-end view, but not this, but certainly it's not structuralism in that usual sense in which we think over-structure artifies an object. The other point is that structuralism, probably to your subject, but in my understanding, structuralism is a way of making isomorphism, in a sense, more basic than whatever morphism, general morphism.

52:30 Category serenity views exactly when you're just trying to take on equal footing, Marxism and other Marxism. That's why, for me, it's a rather different story. Well, I mean, in a sense, what I'm trying to do is give her the benefit of the doubt. So let's take her view, let's accept what she says that, as far as she's concerned, these morphisms that are doing all the work, right, even on that view, there's nothing that, even, you know, giving her the benefit of the doubt, there's nothing that I think is problematic for the structure of this kind of view that I'm adopting. So even if I were to agree with her that it's morphism rather than isomorphism that we really need to be focusing on, she's missed the point in that I'm not at all claiming that at this level, this stuff is set theoretically in any ontological sense. I mean, she insists that, she says in one of the paper, she said if group structures really are partial structures and set theoretic, then group theoretical symmetries really are set theoretic relations. and then what should be doing and in the Wigner and Weill case should have done all the work in set theory, but clearly that is not the case. So she's saying if you adopt this structuralist view that we represent theories, we represent structures set theoretically then her accusation is that I must be committed to the group structure really is not just in the mathematical sense that all mathematics claims can be used to set things, but I'm actually saying group theory as a structure as metaphysics in a way is really set-directed. But I'm not suggesting that group structures really are set-directed. I'm interested to repeat what I'm saying. The set theory plays this representational role, right? And even if we, you know, I agree with them, let's suppose I do agree with them, I don't, let's suppose I agree with them.

55:00 And the reason I don't is because I might, you know, agree with you. But even if I agree that all the, you know, what's doing all the work, in a sense, is group theory. And that's the interesting question. How is it that group theory was so useful in 1926? it. What was it about, I think the way to answer that is, and the way to dispel Vigna's worries, or not Vigna's concern, Vigna's surprise, you know, he has this, it's so surprising that mathematics comes to be so useful. How is it? Does high-level mathematics develop, you know, in a certain way, apparently independently from physics, suddenly in 1925, 206, 207, comes to be so tremendously useful, and bile comes crashing into the sea. Well, one answer eliminate surprise by saying if you look at the relevant structures you can see how they're going to match and geniuses like vile can see look I can relate this math group theoretical stuff to what's going on in concept physics and that's really that the subject of this beautiful book is articulating that inside right even if you accept all that you write about it all that that is about, as I said, is the ontology, the metaphysical nature of the structure of the world. You can still represent it, sex theoretically, or categorically, or syntactic, however you want, because this is at the representation level, the meta level, in which we're trying to capture these case studies. So you've got to draw this kind of distinction if you're not going to get into these really silly conclusions that somehow James Ladyman and myself and Simon are saying that the world is really exact theoretic. I must say, I rather agree with you, and I even, probably a little bit strongly, I think that this, how I say, exact theoretic approaches are very intrinsically related to structural, for example, I would say. But on the other hand, you might probably get rid of that, as long as supposes, but in my view, you would go out of structuralism. I'm going to stand in this position and talk about this. I'll just continue to play on that. Other questions?

57:30 I have one. I have one. I would like to start by your criteria. When you say, oh, there is no point at getting whether there is a lot of structure, because there is nothing that you can show everybody saying, oh, this is the theory. In fact, and as you add, you said also that in some way, you could say that what you thought of was the use of structure rather than the fact of structure which can be exhibited here and now as constituting the theory. Now, it reminds me of several perceptions of pragmatic flavor of theory and of experiment also. Of course, the idea of Kuhn, who said that somehow a theory is a discipline which might, of course, be guided in a very efficient way by a certain structure, framework of any practice, practice of formulating, maybe, models to be compared with other models, which are the models of data, but even in that case, you can also say, oh, but I'm comparing my model, a classroom world model, with a theory, to something which is a byproduct of another practice, a practice of manipulation, of experimentation, and so on. So you have two series of practices which have to fit together. And so you have to completely, so to speak, pragmatically of the overall scientific perception. So would you buy this? I'm very, I think I'm very sympathetic to that. Bear in mind, it's not a pragmatic view about the ontological commitment to theory. It's a pragmatic view about what a theory itself is. So, I think you're absolutely right. I mean, I think, you know, if, you know, there is, as I mentioned, there is this problem of theory individuation that Fred Stocking, for example, has mentioned in a number of occasions.

1:00:00 How do you distinguish between theory and its successor, or its predecessor, or another? And if you adopt the kind of structuralist position, even looking at Stegmuller and Sneed and these guys, you can start to see how theories just become so interrelated. You have horizontal interrelationship between one supposed theory and other theories. You have vertical relationships. It becomes quite problematic to then somehow individuate this as the theory. And I think this kind of pragmatic approach where we can say, look, we've got this, you know, it's almost like you stand back from science. You can say, well, look, we can carve science up in terms of CUNY and disciplinary matrices. We can carve it up in terms of models. We can carve it up in terms of propositions. Those are just different ways of representing. And like you said, the pragmatic element is, you know, which is the most appropriate way for capturing that aspect of science that you're most interested in. And the Kuhnian way, although I'm not that keen on Kuhn, might be, if you're interested in this broader picture of how, or, you know, this thing, I don't like to use it, I'll just say Lakitop in the media, that, if you're interested in a very broader picture, research programs might be the appropriate way of talking about it. If you're interested in very specific relationships with a particular theory that you somehow identified and the data, the phenomena, then the sub-easian approach might be the best for that. And that's really the kind of pluralism that I'm thinking of these days. It is pragmatic in that sense, but it's metapragmatic, yeah. you are pragmatic, you feel as if you're a sign, rather than a sign. Absolutely, I like that. Metapragmatic, exactly that's the way it is. And I think it's, it seems to me, the more I think about it, the more I think it sort of, it makes sense. What it does mean is that you have to back away from this claim that a theory is an axiomitized set of propositions, or a theory is a family of sex theoretic models. But those kinds of things just strike me as slightly bizarre, and they strike me as slightly bizarre conceptually, and I'm not sure they do the job that we want pragmatically, which is to capture how science works in these various respects.

1:02:30 Well, just to add to your point that they also, of course, typically absolutely fail to do justice to the enormous heuristic plasticity of the formalisms of theories, which is precisely what Absolutely I mean, that's something that, I mean, Simon coined this phrase, this heuristic plasticity. It's a very good phrase too, so I In Paul, it must be almost 15 years ago. More, I think. Especially for Heinz. That's right. And he's thinking about how, and this is from a very early form of structuralism that he adopted. He's thinking about the classic examples, how elements of classical mechanics come to be used but in slightly different form in quantum mechanics, plus or brackets, and so forth. And he calls this the heuristic plasticity. And I think that's always, I mean, it's really good point, Mike, but you think about how then there's classical mechanics and quantum mechanics, how do they relate to each other? There are these elements of commonality between the two, but there's obviously clear differences. So this idea of stepping back and having a slightly more fluid, perhaps, perception of the identity of a different theory can help us. Similarly, I think there's a nice problem that we think about recently. Roger Jones had a very nice paper against realism, again, 15 or 16 years ago. I think it's called Realism About What, where he says, look at all the different formulations you have, even in classical physics. the Lagrangian, the Hamiltonian, you've got all these, you know, and they posit different things. You've got forces acting in a distance, you've got fields, you've got pensions. What are you going to be realist about? I think there's a... These days, you know, symplectomorphisms and metathetic, when you get people doing geometric quantization, which of course involves the reconceptualization of a lot of the mathematical machinery in the classical theory. And there's a very nice picture by Jill North, I mean, what she does is argue actually for the Hamiltonian form, He says it's basically sort of similar to the goal of the, basically, in case it's manifold death. That, I know. But I think in that kind of, you know,

1:05:00 if you're trying to say, well, which is the real theory? Which is the real theory of classical mechanics? Because it has formulated through LeBron's and it's formulated through Hamilton. My inclination, again, is to step back and say, I'm not sure you can say which is the real theory. I think both of these approaches have certain advantages and if you want to be a realist, as she does she argues for a Hamiltonian view and she argues for a kind of structural realism the world is this kind of structure to underline your own point this clearly goes to reinforce your point that when typically dealing with a plurality of representational devices plurality the sort of plurality of structural devices at the representational level, which in turn is trying to capture a multi-aspective and potentially sensitive notion of structure at the object level. So one would expect precisely this kind of extremely fluid notion of theory, of theoretical identity, which of course I would argue is one reason why you should go back and re-examine the issue of our category theory, but that's for a separate discussion. And why this point about morphisms is an important one. If I just get clear, I think, though, the point that may have got missed in your exchange with Andre, I mean, there does seem to be a fundamental difference between you, because if I've understood his point correctly, it is that he's saying that the category of theory should not be seen just as simply as a further device for the representation of an urgent structure, but that he does actually provide a context in which one can see the limitations or defects of the isomorphism-based notion of structure with which the structuralist is operating. I don't know if that's a fair gloss on his point. I'm not saying I agree with that, but I think there is an issue there, a fundamental issue between you. I don't know if I see, I have to think more about it. When Alexis said he's going to talk about this, I'll shut up. I don't know if I'm prepared to be. Can we have a five minutes break? Yes, we have a ten minutes break.