From groups to gestalt - varieties of structuralism as responses to quantum physics

0:00 I think it concretes to itself varieties of structuralism as a response to confidence and indistinguishability. Well, first of all, I'd like to thank Jeremy and Harvey and Simon for giving me a second chance to present this because I couldn't make the January workshop. And this is more or less the same paper that I gave at the Leagues workshop on structuralism and physics last summer. things that I talk about there on anything I've since spun off into other works, and it's more because it's got more stuff in it. But I should emphasize this is primarily a historical piece. So what I'm doing here is reporting a piece of history of physics that I found interesting. So it perhaps sits a little awkwardly in today's proceedings, but I think there are general philosophical issues that one can draw out of this. And it arises really from the entwining of two historical concerns I've had. One is just looking at the early responses to quantum indistinguishability in the 1920s. So this is part of the stuff that we've been doing for donkey's years now. But Desiree Krauss and I are supposed to be writing a book on on identity and individuality, and how you can capture certain aspects of quantum indistinguishability in terms of quasi-set theory and so on. And we thought, at one point, foolishly, that we should look at the history, thinking we could just have a few historical paragraphs, that would be all right. And then we discovered more and more history, and so we've left all that out. But I became interested in how these guys responded to quantum indistinguishability, quantum statistics, I think about Bohr and Heisselberg, Australia, or Bohr himself. And typically, and not surprisingly, the way they responded was to say, well, gosh, you know, what quantum statistics seems to tell us is that quantum particles are not individuals. So that's very familiar, and we all know how the story goes now that that doesn't necessarily follow. Well, then, so I think, well, how then, given that, given that many of these guys had philosophical backgrounds and interests, how did they accommodate that non-individuality? and it's very easy to find one way of accommodating it in the works of Cassira and Eddington and I've called this group, slightly inappropriate but group theoretic structuralism

2:30 Cassira and Eddington were sort of working away on foundations of general relativity had a general group theoretic notion of general relativity, space-time in general and both of them, both Cassira and Eddington in slightly different ways this supposed non-individuality into this kind of group theoretic structuralism. And what that structuralism emphasises is first an understanding of objectivity in terms of invariance rather than substance. So one thing is that the philosophical notion or category of substance goes, according to these guys, gets squeezed out of physics. And so what we have or forms the ultimate stratomological activity, says Kassira. This one, 1957, it's actually 1935 edition, briefly. The invariance of relations between magnitudes. And that structure is defined, according to Eddington and Kassira, by group theory. So we have these famous statements by Eddington, you know, what sort of thing is it that I know? The answer is structure. It's quite precise. It's a structure I find in the mathematical theory of groups. And what particles become For Cassira, nothing but nodes in the world structure and so on. And I thought that was interesting. It seemed relatively unlined by historians of physics. And it gave me a new perspective on my second interest, which would be the history of structuralism. And this comes from running along behind James Ladyman, who, as some of you know, has suggested a form of structural realism that is different from the form espoused by Worrell, which essentially follows from Russell, and the Russell-Worrell form holds that, like Ennington appears to be saying here, all that we know is structure. We don't know the intrinsic character of things in the world, as Russell puts it. And James, as I do, has quite well known, well, actually, all that there is is structure. that James I've been trying to pursue in a recent issue of Synthese, I think Simon has a paper in that, and Chan Sao, is trying to spell out the sort of metaphysics of this ontic form of structuralism. And it made me start thinking,

5:00 well, what about the history, the history of structuralism? Have these ideas occurred before? And if you start looking into the history, leaving aside John Worrell's inappropriate reference to Poincaré in his first structural realism, paper, typically people refer to Russell. The kind of structuralism that they think Morrill is espousing is Russellian structuralism, goes back to the analysis of matter, which, and this is significant, was first published in 1927. And the way the story goes is that the kinds of objections that were raised against Russell by the likes of Newman are taken to apply to modern forms of structuralism, to Warrell's form of structuralism, to Leibniz's form of structuralism. And Geoff Kecklin was here not long ago, essentially putting forward that view, that you can resurrect a form of the Newman argument against modern forms of structuralism. Now, some may have doubts about that, but what struck me is that there's more to the history of structuralism than Russell, and that modern-day structuralists, Worrell, Demopolis and Friedman, even the likes of Michael Redhead ourselves, don't seem to be aware of these other kinds of what you might call structuralism, and somehow Russell's come to dominate the history, and there are other shows in town, other games in place. Now, one question that gets asked repeatedly by certain people is, well, what is structure? What do we mean by structure? And one of the things that I've tried to suggest is, you've got to be really careful here not to take a modern understanding of structure and simply project it back. And that actually, when we talk about structuralism, it's a multifaceted thing it's okay many different strands um and there may be some question as to you know whether a particular uh development or or epistemological view counts as structuralism or not you can think of the modern view as simply well you know a structure surely you know something you have a set of elements and you have some relations defined you know relations defined over that set As Solomon pointed out, that's not the definition that Russell himself had in mind, although the differences are not, some might think, are not terribly important.

7:30 Eddington, just to give an example, seems to have a second-order notion of structure. For him, the structure is not so much embodied in the relations, but it's a pattern of interweaving, a pattern of how the relations are interrelated. And significantly, and I've talked about this and written about this at length elsewhere, Eddington insists you can represent structure this way and you can read it mathematically left to right you begin with a set of elements then you have relations to find over that set but conceptually it's not necessary to read it from left to right you may think of this as kind of a package he thinks it's kind of a package that somehow the relata can't be detached conceptually from the relations and that's I think an interesting view it's within that view that he situates his view of quantum non-individuality. So it becomes quite difficult to define what structuralism is, particularly if we're talking about the 20s and 30s, which is my historical interest. Crudely, what seems common with Cassira, Eddington, and Russell, there's a rejection of focus at that time, there's a focus on invariance, understanding objects and things in terms of sets of invariance. And there's a shift away from relata, either epistemologically, so Russell says that all that we know is, you know, the sort of, the relations between things, we don't know the intrinsic characters of the things in themselves, or ontologically, Cassira says, you know, it can affect these get understood in terms of things. So that's, that's the background. Is that the claim that the relations and the relata can only be understood together? That makes sense as a complete package. Eddington's claim is, it's to do with the metaphysics. Russell has the view that really what you've got are objects out there, and there's sort of intrinsic characters we don't know anything about. But what we do know, what we can infer, are the relations that hold between these objects. But necessarily, there are still objects out there. And so conceptually, you can imagine the objects out there, independently of the relation. And Eddington says, time and again, no, that's mistaken. It's a mistaken way of looking. It comes together as a package. And you can look at it from one way and think of it in terms of objects that have relations. You can look at it another way and think of it as relations which, of necessity, have to have relata.

10:00 But the relata, in a sense, are methodically dependent on the relation. so that's just by way of background I've written on the Eddington stuff elsewhere what I became interested in that's fine, that's Cassira and Eddington those are two Eddington's okay physicist, but he's not a quantum physicist so those are two more philosophically minded folks what about the likes of Bourne in particular, what about people like Bourne and Schrodinger who are not enamoured with group theory for example Bourne famously responded to London when London sort of gleefully told him, you know, whoopee, look, I've reduced chemistry to physics, and Heighton says, you know, now we can eat chemistry with a spoon because we've got this group theoretic reduction. And Bourne says famously, you've made so many idealisations to get group theory in there that really you're not dealing with reality anymore. So Bourne was famously sceptical of the introduction of group theory. this is. But also, he's supposed to be, standardly, defending a particle ontology. So how does he accommodate this idea that particles are not individuals? And that's what I'm going to be talking about today. It's a bit wacky, but I think it's interesting historically to understand what Born was on about. And I'll do it by introducing Schrodinger first, but then I'll skip over this. Standardly, we understand Schrodinger and Born as having different ontologies, and this comes out in the 1950s in the BJPS articles that they He comes back, it seems, in the 50s to this wave ontology. Bourne says no, that doesn't make any sense, they don't have a path to ontology. There are certain common elements between the two. One is, of course, they both think that quantum statistics implies that particles are non-individuals. The other is they both think substance is now blown out the window, metaphysically. We have to get rid of substance. The other is, they talk of objectivity, permanence, and so on, in terms of invariance, or, as Schrödinger calls it, gestalt. Now, Schrödinger's notion of gestalt is fairly simplistic. I mention this, I think it's interesting, because we think of Schrödinger as, you know, well, the old fool, really. He's trying to maintain a wave ontology, doesn't he realise that once you go to more than one particle, it becomes really problematic?

12:30 Well, of course he'd realise that. And I think Michel Bitbold's edition of the Dublin Seminars are worth reading, because, as Michel points out, Schrodinger's idea is actually a little, well, considerably more sophisticated. it. And one of the things he's concerned about is moving from his sort of general wave ontology to things, macroscopic things. And what emerges in that is a consideration of what counts as permanent. And he comes back to decide that what counts as permanent in these ultimate particles or small aggregates is their shape or organisation. And he makes statements like are pure shape, nothing but shape. What turns up again and again is this shape. And what he's, the German word here, is the notion of gestalt. And he says, crudely, we may think of gestalt as like geometrical shape. And then when we move on to more sophisticated models, that gestalt is given by sets of invariant properties. So that the basic idea of a thing is the result of this fundamental process of forming invariance. I was surprised It's an interesting aspect of Schroding's work, and I think it could use further development, but I'm not going to do it here, because I became interested in Bourne's understanding of Gestalt. There, Schroding is just talking about Gestalt in this general sense of form or shape, and he spells it out in terms of invariance. But Born goes into much greater detail and ties this in with what we think of Gestalt. You know, you think of Gestalt, you think of, and if you teach fossil science, you think of, you know, the stuff in Kuhn, you know, the Gestalt switch, or, you know, pictures that look like the young woman, the old woman, like Gestalt switch. So I was surprised to find Born referring to Gestalt psychology here. And in his, this is his inaugural lecture in Edinburgh, and he's thinking about the problem, well, look, given quantum mechanics, how can we speak an objective world? Given all the usual stuff, you know, Heiserberg uncertainty, we've got non-individuals out there, where's objectivity now? And he says, look, the positivists, according to the positivists, this is just a pseudo-problem. and he's very dismissive of the positivist

15:00 and duly so he says the problem with positivism, it rests on unsound psychology it rests on this idea that what we perceive are, as he puts it, uncoordinated impressions, you know, I see green here now and that's false, it's been shown to be false and stark psychologists have shown us that that what we really observe, he says is a totality and this is quite a significant remark which is not the sum of the single impressions not more or less than this sum but something new and the example he gives it's a classic example from psychology is of the melody which is more than simply the the string of notes it's something else and he says he goes on to say modern psychology is fully aware of this fact i do this the gestalt psychology of erenfelds kohler and bertheimer and what Gestalt means is not just as Schrodinger said, shape but the totality which is really perceived and he goes on to say that Gestalt psychology has shown that the unsophisticated mind produces these Gestalt and he concludes, well because I'm sorry I cannot see any argument for abandoning that view that we can sort of shift that view to the scientific sphere that seems odd. In what sense is Gestalt psychology applicable to the kinds of unities or structures that we might come across in science? And that's what I became interested in. Born's framework for Born's discussion of this is, he thinks, the kind of analysis that we that we can develop of macroscopic objects should be has to be necessarily applied to microscopic if we're going to retain this notion of object and he talks you know he gives the analogy with number you know we have you know the the natural numbers and then we have i and we have square root of two and so on he says you know we can we can extend our notion We can send that notion of object from the macroscopic to the microscopic. And if we think of macroscopic objects like chairs, what that object is, he says, is a gestalt. It's an integration of impressions that's independent of changes in my position.

17:30 And what is invariant is what we mean by saying there really is a chair. And so it's that expression of invariant, he says, which links the psychology with exact signs. And he says it's a mathematical expression first used in geometry to handle these spatial gestalten, which are simple shapes. It's very, very missing, of what Schrödinger was saying. And then the methods of mathematical physics are just the same. We eliminate the accidental, and what remains are the invariants describing things. And so the invariance is the link between the macroscopic and the microscopical common sense and science. Well, the connection with Gustav's psychology is made explicit in, and this comes out in his paper in physical reality in 1953, and, you know, he gives the example of a dog, a dog chased after a rabbit, and you still know it's your dog, and he introduces here the Gestalt psychology of Kohler, Hornbussle, Wertheimer, to name only a few, whom I personally knew, and I will translate this word, Gestalt, not just as shape or form, but as invariant, okay, and I know something about it, I once had close relations with some of the founders And indeed, that's true, there's a sociological point here, that Born, Einstein, and Wurtheimer were close buddies. I'll come on to what Gestalt psychology was doing but Wertheimer was very interested in our perception of motion and our perception of sound localisation and in 1915 he was doing work on that and the data of course is significant if you're there in the trenches and you hear the coming over you want to know where it comes from and so these psychologists were actually more or less employed by the relevant German ministries out psychology to figure out where the shells were coming from. And he did this with Bourne. And Bourne and Einstein, in 1918, the students were revolting, as they always are, and so Bourne and Einstein, with Wurtheim, that intervened, and with the university. Kohler, who I'm going

20:00 to come on to shortly, studied with Planck and read quite widely in physics. And we'll see why in a second, and thought that many of the questions that Gestalt psychologists were asking themselves had already been asked by a physicist, by Maxwell, for example. And his classic book, Physical Gestaltant, was favourably recommended by Einstein. I don't know how much weight that carried at the time. So what is Gestalt psychology, and what is of the Gestalt. And what I'm about to present, I mean, people who know the history of Gestalt psychology are going to think this is extremely crude, but I don't have time to go into more details. There are essentially two criteria for the notion of Gestalt. One is this idea that a Gestalt is, as some people put it, more than the sum of its parts, so super-summativity is how it's expressed. Kohler wanted to say, no, a Gestalt is different from the sum of of more than there is problematic. And the other is what they call transposability, that a gestalt involves the retention of relations in the same order despite shifts in the parts. And so the example is, for example, the classic example that was given by Ehrenfels from 1890 is a melody. So you can whistle your favourite melody here. Whatever, smells like a teased spirit from the bar. white stripe, whatever. And it's not a mere sum of elements, but it's something novel in relation to this sum, something that goes hand-in-hand with, but is distinguishable from the sum of elements. And Bertheimer's work on motion perception, the claim was that there was experimental evidence for the existence of these dynamic mental realities that cannot be composed of or built up from the elements. You can do experiments on how we perceive motion and you can show these can't just be decomposed into the kind of you know a sequence of cinema films stills I'll come back to these two criteria shortly these are the two basic criteria there is some differences between different members of the Gestalt school over which

22:30 of these have precedent. Kohler, for example, thought that you could drop this one, transposibility, in certain cases, but only in certain cases. Now this is where it gets really, really creepy, because I'm going to ignore really geographical differences between the Gestalt psychologists. There are different schools. There were the German Gestalt, psychologists in Berlin, which is significant, because who else was in Berlin in the 20s? There were the Graz gestalt psychologists, there were Italian gestalt psychologists. And the notion of gestalt underwent a number of significant shifts. Ehrenfels were essentially thinking of the unconscious mind as creating gestalt. This is something that we do. and that under Wurtheimer came to be understood as no what's actually going on is that we are we are apprehending gestalt there was the shift from gestalt feature in perception to a kind of isomorphism hypothesis I think eventually came to be rejected that these gestalt or gestalt in perception correspond to brain processes destructive whole brain processes it was applied by Kafka and Curler to actions and behaviour, that ourselves, also animals, Curler during World War I was isolated on the Canary Islands with a bunch of chimpanzees and did a bunch of experiments on chimps and his claim was that chimps will suddenly just see a situation, they will suddenly see the solution to a particular problem just like we do, this is just a stout understanding standard of action and behavior. Towards the end of his life, Wirtleimer was arguing that thought in general operated on gestalt principles. It didn't operate, for example, on deductive principles. It operated in terms of seeing something a certain way. Digression here, of course, the impact on the philosophy of science is quite interesting. Geordie Capp has quite a nice paper on this, where he points out that who else was in Berlin during the 1920s, well, Reichenbach, for example, and Gustav's psychology at, certainly at this

25:00 level, had a big impact on Carnap, and the story that Carnap took part in some of the experiments. And, of course, when I mentioned Kuhn, at this level, Geordi doesn't actually sort of distinguish these developments. But at this level, the idea that, you know, when you get under, when science goes to paradigm change, it involves a notion of a pre-start switch, you come to see the world in a new way, and what Kuhn is drawing on is Wertheimer's work here. But what I became interested in is Kohler's work, where Kohler starts to, in his physical Gestalten book, claims that these Gestalten are out there, they're not mental products, they're not mental apprehensions, they're actually out there in the world, in inanimate nature. And this is what Bourne, I think, is in part drawing on, that physical systems should be understood as gestalt. And he has different examples. As I say, I'm not I'm not defending this, I'm just reporting what he says. So he makes a distinction between strong, this is Coa, between strong and weak gestaltum. So he thinks of strong gestaltum as where you have a mutual dependence among the parts. So it's so great that if you make any change to one part, it influences all the other parts. And so he thinks of, I guess, he's thinking of the usual, I should have had a picture of this, the insulate conductor, you introduce a charge and you get the charge spreads out in equilibrium all over it. and so the charge density is greatest curvature, smallest at the least that charge distribution has a definite pattern of organisation he says it has a natural structure that he thinks can be extended to the field itself and he thinks this is what we learned from Maxwell that fields should be understood in terms of these physical gestaltons and I've come back to this there's this interesting question in that case what are the parts and he draws on I mean these guys essentially are descended from

27:30 Brentano and so you've got they do tend to draw on the same vocabulary that the likes of Hassell draws on so they talk about rather than parts or elements, they want to talk about moments of structure that carry one another so this is it's not clear that this can be picked into this sort of picture for example, I'll come back to that and he actually goes on to say that a physical structure is not modically secondary relative to the moments, it's not like you have the parts and then you get this gestaltant that just appears, rather it's that the two come together as a package and then he has another notion of a sort of weaker style so that's, and he develops this in his book physical gestata and there was quite a bit of discussion in the 30s on how we should understand this notion of gestata, how it should be fitted into the new modern logic of Russell and Whitehead and Hilbert. There's a very nice collection by Barry Smith, where he reproduces some of the original papers by Ehrenfelds, and particularly Grelling and Oppenheim, who have a nice paper, The Concept of Estalt in the Light of Modern Logic, and Peter Simons has some commentary on this reversing the order transposability um grilling and oppenheim essentially say that all all you mean by transposition all the gestalt is really mean is a structure preserving isomorphism between complexes and a gestalt is simply the invariant under these transpositions and that's taken to be to be relatively unproblematic the idea of supersummativity is more problematic and this gets into a whole lot of philosophy of myriology in what sense is anything well, in what sense is it is anything not more than the sum of its parts depends what you mean by parts Popper famously thought this was trivial you think of a thing as composed of parts between which they hold relations, then everything is more than the sum of its parts, because you've got these relations there how you understand supersummitivity depends on how you understand the whole part relationship

30:00 and that depends on how you answer the question how do you distinguish this whole structure, this gestalt, from a mere sum? And Koehler tries to deal with that. He thinks of summation, or and summation, as a process where we conjoin parts, and that conjoining or removal produces no alteration. And so a summative grouping is where we have each piece occupying a definitely prescribed place, there's no change in the property of the parts themselves. And the example would be, we have three stones lined up with one in Leeds, one in Bristol, not on Bristol. Freudian Smith. And a gestalt is different from that, or would be different from that, because there would be reciprocal influences among these parts. And again, he gives the example of the structures of static charges upon conductors of a given shape are physical gestalt and in this sense we remove one of the charges jiggle around everything jiggles around now grelling and oppenheim are quite keen to deal with that local supersomativity how can we deal with it and i won't go into all the details because it's not at all clear that they can deal with it in an adequate way basically they say look think of it in in this way we have a whole that can be divided such that every part in this division stands in a relation R to every other. Every object which stands in the relation R to at least one part is itself a part of the whole. And when R equals, or is what Carnac called a determination relation, you could think of that as a relation between the properties of the parts as given by some law, then we get a system, and turns out, controversially, they identify that with the notion of a gestalt. And this whole idea of how we capture this notion of gestalt, you can see this is really part of the general question, how do we capture the notion of structure in terms of, well, in set theoretic terms, and can we do so? And if we do so, are we getting anything more out of this notion of gestalt than we would get simply by writing down something like that. We'll come on to that in a second. There's a number of issues that arise from this.

32:30 One is to do with the part-whole relationship. As I've already mentioned, Kroler, so let's accept some of the other gestaltists, insist that the parts are determined by the whole. So it's not the case that you have parts and then the whole, the gestalt, emerges from the parts of a structure are not logically prior to the total structure itself. So there are problems with fitting that into the kind of framework that Grelling and Oppenheim seem to have had in mind, and Peter Simons talks a little bit about that. He focuses more on issues to do with modality. One of the issues that modern structural realists like James Leidman have had to contend with is, how do you accommodate modal aspects of the world in terms of these notions of structure? And Peter Sinus says, well, look, Grelling and Oppenheim don't actually do that. They don't take account of the modal nature of functional dependence because they're elaborating their idea of this stuff within an extensional framework. And there's still a lot to be done on that. Schlick, let me just mention one of the positives, Schlick was quite taken with this notion of Gestalt, but he ends up by saying, if that's what you mean by Gestalt, if that's what you mean, if Gestalt is understood in terms of functional dependency between parts, then the distinction between the Gestalt and the aggregate, which Kohler took to be so important, to be so fundamental, is actually just a convention. And so this is, Schlick applies a sort of conventionalist approach. It says, you know, very positivistic, what do we mean by Gestalt? Grelling and Oppenheim have shown us, what we mean is this, we mean by, you know, a determinational system in Karnat's sense. If we understand functional dependency in terms of the operation of laws, then this distinction that the Gestalt is set so much store by is just conventional. The lawful behavior of the parts can be expressed through that of the whole. The converse is also invariably the case. A mere difference of notation is involved. The layman, like us, will see this most easily if he's alerted

35:00 to the fact that the whole is present only when all its parts are present, and hence that the assertion that some occurrence is determined by the whole is equivalent to saying that it's determined by all its parts and their relations to one another. And so Schlick Gestalt, nice idea, but in fact, we can just translate it in terms of, you know, sets of elements between which they hold relations as given by certain laws, and there's nothing more to do. Now, it's not clear to me that that's what Kohler and others were getting at. They seem to have something else in mind, and one thing that I haven't fully worked out, but they seem to have an idea that this gestalt does not, or the properties of the gestalt, the properties of what you might identify as the elements composing it, to use loaded language. And one worries, I worry, that really Schlick is assuming supervenience here, when he says, you know, the whole is present only when all his parts are present. Well, is that what the Gestaltists are saying? No, it's not quite true. Kohler certainly seems to think that there's a difference between having a set of elements, the whole bunch of properties, and having a gestalt with that set present. There's something extra that is brought in the case of the gestalt. Now, it's not clear that the appropriate way to understand fields, for example, is in terms of non-supervenience. If you take the classical electromagnetic field, why can't we understand that in the standard way? I think that we have the observant space under that. of quantum physics, of course, many people have suggested that entangled systems exhibit a form of non-supervenience. The only reference I've found within the works of a Gestalt psychologist to quantum theory is a paper in 1930, the New Psychology of Physics, a very enthusiastic Basically, Kohler says, aha, you all thought I was mad, didn't you? But in fact, I wasn't mad enough, because quantum theory has revealed everything I said was true. I didn't even go far enough, I should go further. Physics has found it necessary to follow this second way, where we have to acknowledge that there are qualities possessed by the system as a whole.

37:30 They can't be split up and located a little bit here, a little bit there. okay and on the base of that he said we say that the leading ideas of modern physics sort of gestalt psychology tend to coincide i think there's there's some work to be done on whether modern notions of supervenience non-supervenience can be applied to some of these physical gestaltoms that's the tradition that born is drawing on he's not simply saying Ah, yeah, the Gestalt, what I call you, duck, rabbit, rabbit, duck, the kind of coon stuff. He's drawing on this rich tradition that proceeds through the 20s and 30s. I'm going to finish in a few minutes, but I will mention that there's a very interesting paper by Cassira. So what we've got now, as well as the Rossellian traditional structure, we've got the Cassira-Eddington group theoretic tradition. And we've also got this Gestalt tradition, which was a live one, because Cyril has a very nice paper, which is hardly ever commented on, where he connects the two. The aim of the paper is to set forth an inner connection between the mathematical concept of group and certain fundamental problems of the psychology of perception. And the idea is to expose the same kind of concept behind both. In geometry, the real foundation of mathematical certainty is no longer with the elements, it lies with the rule by which the elements are related. In perception, we reject the bundled viewer sensations. What we now have is a gestalt of sensations connected again by a rule, by some structure, some interrelationship. And the notion of invariance, again, is important for both. And his fundamental point in this paper is that these concepts of group and invariance function as necessary conditions for both the constitution of the perceptual world and the construction of the universe of geometrical thought. and here he cites and in both cases we find the constitutive factor to which perception owns its objectivity manifests itself in the possibility

40:00 of formal invariance and this is again related to transformability transformability, sorry, transposability transformability in geometry corresponds to transposability, and it's a very interesting paper, the whole framework of course is Kantian, so it doesn't particularly serve or neo-Kantian, it doesn't necessarily serve the reals. Ultimately, this ability to apply group theory and to form Gestaltant comes down to Kantian categories in here. just to finish off how does this differ how does all this this sort of gestalt madness how does it differ from the kind of structuralism that Russell was defending we know how his theory goes the idea he's got causal theory of perception we have percepts our experiences are represented by percepts those percepts are related stimuli. And the fundamental assumption is that differences in our percepts, so red-green, imply differences in the stimuli. That, together with the assumption of spatial temporal continuity heatrains, suffices to give a great deal of knowledge as to the structure of the stimuli. The intrinsic characters, you know, things out there must remain unknown, and all that we know about the external world is its structure. So when we're dealing with the inferred entities, the entities of physics, and the whole analysis of matter is an attempt to come to grips with the physics of the day, of the year, of 1927. When we're dealing with these inferred entities, we know nothing beyond structure. We may be said to know the equations, but not what they mean. So knowledge of structure essentially consists of direct knowledge obtained by the analysis of percepts, red here now, green here now, plus the knowledge that is dependent upon the inferences involving these understeed particulars. Now that's what most people think of as structuralism. That's where a lot of the criticism following on from Newman has been directed. But it's a peculiar, and in some senses it itself is an odd kind of structuralism. First of all, with regard to the nature of percept, Russell explicitly rejects the gestalt analysis. He adopts this summative sensationalism. He advocates a kind

42:30 of non-holism here. It's pretty poor. Russell can be very poor sometimes, and this is really poor, because he says, ah, these gestaltists, they say, you know, look at motion. It can't be decomposed into sort of separate elements. But we know from the cinema, right, that it can. You know, we can string together a set of images and give the impression of motion. Vertheimer's already dealt with that. He's set up experiments to show that that's not what's going on in the experiments that he claims reveal, you know, that motion, our perception of motion, has to be understood in a gestalt way. Russell says, ah, it's all really, it's just vagueness, that's what's really going on. And Vertheimer has already said, no, it's not that. So Russell's quite sloppy there. But he takes this to be characteristic. of scientific analysis that it enables us to arrive at a structure such that the properties of the complex can be inferred from those of the parts. Without that, he says, you don't have science. Now, if you think of the kind of holism that crops up in discussions of foundation quantum physics, you're going to wonder at this sort of state. He's kicking off his whole, he's presenting his form of corrupturism in such a way that it seems to exclude the kinds of holism that one might want to accommodate, whether one's a gestalt psychologist or working in the foundations of quantum physics. The book is also interesting, if you read it, and it all normally seems to have done that, as a book that's published in 1927. The philosophers tend to quote the analysis of matter as if it's somehow timeless. Put it in a historical context, it's quite an interesting read because it's quite frustrating. He hasn't quite got it yet. It's 1927, so the results are coming in. Demopolis and Friedman are very dismissive of Russell on this. They say, well, you know, he talks about Lewis, not David Lewis, but G.M. Lewis. quite understood quantum theory. Well, give the guy a break. It is 1927. The results are only just coming in. If he had waited a few years, like Eddington did, it might have been very different. I mean, you get these odd references to quantum theory. So, you know,

45:00 he claims that Heisenberg's work shows that there's a problem of transtemporal identity. We've lost the notion of indestructibility of matter because of electron-proton annihilation. We, you know, we've lost the notion of, you know, mass, and what we perceive are not substances, but events. And his overall conclusion is, well, what we have to do is move away from, and this is what he shares with Cassira and Eddington and others, from the notion of substances, objects out there which have properties, to groups of events. But he retains the idea that these groups of events give us, or can be thought of as constituting in some way, our metaphysical notion of an individual object. That's retained. There's no suggestion, of course it's too early, that he's thinking about quantum individuality and non-individuality. So it's an odd book in two ways. It's odd because he's just dismissing all the Gestalt stuff. the quantum stuff. And yet, that's the structuralism that, according to many people, is the only game in town. That's the only structuralism worth considering. That's the only structuralism that we should be criticising, we should be resurrecting the Newman problem against. But it's clearly a deficient kind of structuralism. One would think, from the word go, that might not be the thing we should be looking at. Or at least we should try adjusting it, developing it to accommodate these results. So that's really just to finish off. The first, just a general lesson, it was a very general sort of almost trivial remark, the attempts to accommodate the perceived impact of quantum mechanics varying. Kassir and Eddington had all that group theory stuff to hand. Eddington worried for many years, oh, you know, the atomicity that quantum physics seems to be giving us, how am I going to accommodate that within my structuralist scheme. Quantum statistics, indistinguishability, boom, that's it, no problem. He accommodates all the results of quantum mechanics in increasingly bizarre ways as he went on to develop his work, as some of you, I'm sure, will know. Others, such as Born and, to an extent, Schrodinger, in Eschewi group theory, had to look elsewhere. In a sense, you can see Born as defending a path in ontology,

47:30 but he needs to accommodate this supposed non-individuality. And so he looks to a form of structuralism that he was familiar with, and that was Gestalt theory. And both these strands, both the Cassira-Ellington strand and the Born strand, emphasise the conception of particles in terms of invariance. That's how we must understand things, in terms of sets of invariance. The second point is, the Gestalt framework drawn on by Born was actually quite rich and quite complex. it kind of peters out what happens is well we know what happens right we know how hitler happened and so all these poor guys go to america and the americans just look at them like they're mad because all this gestalt psychology has developed within a philosophical framework in germany and austria you've got brentana you've got her soul and you know the germans are going yeah yeah we can understand you transpose it over to america and the american psychologists have no idea what these guys were on about or very few of them and they just get swamped by behaviorism after the war in a number of ways, and it starts to come back again. But in particular, when he's talking about Gestalt, he's not just talking about or referring to these psychological phenomena. He knows of Kohler's work with this physical Gestalter. And contemporary issues concerning the nature of structure, the relationship between structure and the elements, the things that Worrell, Ladiman, and others are concerned with, were also raised within that context. that stuff. And finally, Russell's epistemic structuralism is doubly conservative. It advocates this summative sensation at the level of percepts. It pushes out Gestalt's psychology. It only partially accommodated the impact of quantum mechanics at the level of the unobservable entities. Nevertheless, that's what most people think of as structuralism. But historically, it was not the only showing tact. And it can be situated at a particular point in time, and it's a product of its time and my historian colleagues hate it when I do this so that's why I do it counterfactual history if Russell had written the analysis of matter a year later in 1928 when Eddington first starts to think about quantum industry the history of structuralism could have been very different and James' task trying to elaborate an ontic form may have been a lot easier because we wouldn't have been lumbered with this epistemic

50:00 inadequate form of structure. OK, I'll finish that. We've only talked about structuralism in the context of stuff, you know, matter, things. What structures take on space-time, or space in themselves, so far as I need to talk about that? I'll refer you to, I guess, John Stachel. I mean, he has... Some of us have been looking at that, and John has a take on space-time in terms of structure. So in that paper of his... I think he presented it here. Was it the thing between relations, relations between things? What I take him to be heading for is a kind of... I don't think he actually... Maybe he doesn't know this, but he should know this, and I'll tell him each time I see him. understanding of space-time so that you shouldn't give if you think of the normal the usual way of approaching it again in mathematics we start with a manifold point and then we sort of add things to it and we somehow think that that mathematical way of doing it signifies conceptual metaphysical priority then we end up in all sorts of problems right if we get away from that and say well that's just a way of describing it then there may be ways of articulating a philosophy of space-time That is, that is structuralist. I mean, all of them knows probably more about this than... No, I'm not going to talk about that. So that's what he would, that's what you call structuralism. He would say, for example, you shouldn't talk about the space-time manifold in the aftersymmetrics. That's the mean of his concept. Is that... I mean, again, there could be different forms of space-time structuralism, but one form would be, you know, you might want to say, various structures that we define on the manifold. And the manifold, I think this is partly what John says, the manifold is there because it's sort of a mathematical device in terms of which we can describe space-time structures. But we shouldn't give it ontological, we shouldn't give it any ontological priority or any seriousness. What's really out there are these structures that we may describe this way. But you mustn't think that simply because I've introduced a set of elements here, that somehow there's really a manifold of points out there. So the notion of a space-time point would be very dodgy. The notion of a space-time point would be extremely dodgy.

52:30 There's two ways you can go. You can simply say, well, there is no space-time point. There's just the relations. And then it's not clear how structuralism differs from relationism. I think that's an interesting issue, how the two differ. And again, I think Oliver might have something to say. Or you might say something like, look, we've got these structures, And mathematically, we have to have the manifold to support, you know, mathematically support this stuff. But we might want to reverse this and say perhaps we should understand space-time points as emerging out of the structures. That would be another way to go. There seems to be a variety of possibilities in that context. Well, there are lots of questions. I mean, how long have we got until about six? Yes, I just wanted to say something, I didn't disagree with anything you said, but there's another aspect to the analysis of matter, which I have actually read, only right through when I've been, I think, 19. I think there's a Kantian aspect, because Russell's position was this, that we can't know what anything outside our own consciousness is like in itself. All we can know is that by perception that there's something out there which is structurally, in a kind of abstract sense related to what we've got going on in our own text. And that's why mathematics is the language of physics. And he says that this language, you never really know what you're talking about. It's just there's a something out there that has that abstract character. And it seems to me that that is crucial. It's a kind of Kantianism. I mean, Kant is like the sort of, you know, the dark Sauron-like figure behind many of these guys. It's in itself, but you can't ask. Yeah, I mean, you look at Kassir, of course, Kassir is explicit. He's a neo-Kantin. I mean, it's odd that, for example, John Worrell in his dialectic paper on structural realism as a response to the pessimistic meta-induction, he cites Poincaré. I mean, he's a bizarre, you know, ancestor for a realist. I mean, Poincaré says things like, look, he says similar things to Eddington,

55:00 the structure of the world is group theoretic, and the groups, they're in here, right? I mean, we have the sort of general notion, it may be a question about which one applies, but the notion of a group is something that we bring. He calls it, what a canton, I can't remember my canton. is it a form of intuition I think Poincaré said but this lies in the heart of it I don't think they have the psychological I'm sorry I'm speaking of time I don't think they have the psychological way of putting it that you suggest it was not in the head in the mind no no no that. No, I'm suggesting that, I mean, ultimately, the notion of a group, I think Kassira, like Poincaré, thought the notion of a group is something that we bring to the world. He understands that in a Kantian way. I may be wrong with that, but that's my understanding of it. It's certainly true of Poincaré. Poincaré says in the Science and Hypothesis right at the very beginning. I'm surprised that, you know, Warwick would cite Poincaré as the ancestor of scientific realism. It's not realist. You know, well, it is and it isn't, but it's not really in the scientific way of the sense. And there's a considerable amount of work to be done in pulling out, in exposing Kant, or where the Kant's influence lies. Also for the Gestalt psychology, when you think about it, coming much of it being tied up with stuff that Husserl is doing with Brentano and so on, reacting to aspects of Kant, but also absorbing aspects of Kant, that also comes out. there's a couple of points in the biggest exchange with Chris about space time were you referring to John Roman's position or was that John Stachew John Stachew I mean I suspect well maybe one but I suspect that if he has misgivings about the nature of space much more to do with general covariance than some kind of principle but I'm just Of course he has concerns about that, but I read that thing-between-relations paper as a kind of an attempt to form a kind of structuralist account

57:30 of space-time. And when I talk to him I mean, I can give you the horse's mouth when I talk to him in, what was it, Milwaukee? I mean, Jonathan is really doing anything that I think, but he says, yeah, yeah, yeah, that's what I'm getting, that's what I'm arguing for. And he wants to get away from this idea that you've got elements and you've got relations defined over them and the elements or the set of the elements is what's ontologically fundamental because it leads you into all sorts of problems. I'm not saying that what's motivating that is some kind of philosophical concern and structure because what may motivate it is the whole argument but the solution for a framework in which to elaborate a solution to the whole argument would be this general kind of structuralist position. Could I just raise a question about your start It just strikes me, and it must have struck many people, that when it comes to super-submitivity, and this idea that somehow, in some sense, they're all integrated into some of the parts, surely the Gestalt psychosis, if they were interested in quantum mechanics, they'd become much more excited by entanglement, and by things like indistinguishability. So it's really 1905 rather than 1927. Sure. Well, there's two separate issues there. One is the interesting variability thing. This is Gestalt's Bourne's way of making sense of the notion of non-individual objects. so you understand objects in terms of sets of invariants and if you think of as people took me here individuality is given in terms of substance what makes a thing individual is its underlying substance if that's gone, if you've just got sets of invariants and if you can understand that set of invariants in a way you can understand a chair then that's okay for board the entanglement issue and the supersubmitivity issue is a kind of separate issue did the gestalt psychologists look at quantum physics and understand entanglement in a non you don't need a holistic way incorporate within the gestalt they don't seem to have but part of the problem is i've missed out a lot of history um gestalt some of the gestalt ideas were adopted by disreputable forms of sort of holistic political philosophy so some of the more

1:00:00 right-wing guys around in the 30s started talking about holes, racial holes even. And a lot of damage, I think, to the Gestalt movement. And I think they had other things on their minds in the 30s than looking at issues of entanglement. But there is an interesting issue. There is an interesting question there about when that issue kind of emerges. And we have Schrodinger in the 30s saying, what's that famous quote This is really the crux, as you imagine, this kind of ghostly... Now, that's emerging in the... What was that? That was like... Well, that's around the time of the EPR stuff. It was 1935. Yeah, but 1935. So, by that stage... You know, if the notion of entanglement had emerged a little bit earlier, five years earlier, you may have seen Kohler incorporating... By 1935, he's already, you know, heading off towards America and the whole field then changes. himself doesn't seem to talk about entanglement in those terms. He's mainly concerned with how do we recover a sense of objectivity? What is their objective that's out there? And it's these gestalts, these sets of invariance, that's objective. Simon, have you had your question? Actually, I've got two questions. Can I ask one now? I hope I'll ask the next one later. I was realizing that I've done Sal a disservice in this business and painting. I was accusing him of, well, I was calling him Worrell anyway, as not being the old-fashioned handed-down ideanism that I was calling it, which is the only secrets in my head. Right. I mean, I've received an acquaintance within my head, or something. Now maybe it's wrong, Worrell now, to take Pancre as his model, but surely Russell is no more a realist here than Pancre. I mean, is Russell really a good model now for Worrell? I know Worrell's got all the geography for the human stuff, but is that really what you see when I was driving his form of structural realism? He told me it is. Well, it's not how I read his paper. in the appendix to Zaha's book I don't know if it's exactly in these terms

1:02:30 but it seems to be suggesting the kind of structuralism they're referring to is Rossellian, that's what we're talking about but with the motivations that Russell had that's what I find surprising I didn't read more like that I thought Warren's point was more something from history. Yeah, sure, sure. It's not really to do with what is immediately available to some perception or anything like that. No, no, no. Well, you're right on that point. You're right. But he does refer to Russell. Right. And in responding to the Demopolis Freedom paper and the claim that if you represent the structural content by the Ramsey Centre and that's what's screwed up Russell and then they say well not if you make a distinction between theory observation they claim to get around and that's that I mean they seem to be saying that to Russell This isn't my second question it's just an interjection a question of a theory I find these instinctual Did Russell really talk about the annihilation of electrons and protons? It's a bit ahead of the game, isn't it? Yeah, I know, it's odd but yeah, it's in the analysis of matter I'm looking at it last night but I'm not quite it's not quite clear what he's referring to it's all a bit but certainly to Mottles and Friedman In their paper, where they resurrect the Newman problem, and they say, in the analysis of the matter, you used to have rather pitiful attempts by Russell to talk about quantum physics here, because he's still talking about G.N. Lewis' stuff. That is unfair. I mean, he is making an attempt to come to grips with the physics of 26, early 27. Right, we've got Chris and Carl and Julian in that order over here. First, a very quick comment on Harvey's question. similar states of the, as many particle systems are going to be entangled anyway, a maximum entangled state, so it's the same organ. But the actual question I wanted to ask was, that would point me a little bit of counterfactual history at the end, and how life could be easy if the ontological structural realists. I can see how that could be the case, but I'm still,

1:05:00 with the epistemological structural realists, as Simon has just mentioned, they're trying to get, sort of, respond to the pessimistic meta-induction, see how the ontological structural realist is doing that, because however you can screw objects as nodes and relations, you've still got them, you're still talking about them. So is structural realism, the ontological type, trying to respond to the same epistemological worries as the epistemological structural realist? The claim, yeah, the claim is that, I mean, this is not what I'm sort of really talking about today, but the claim is yes, it is, it's responding to that, and it's accommodating James, I'm ashamed that he's not here that was his main motivation okay, structural, moral structuralism answers, or is a response to the pessimistic meta-induction fine, but it doesn't seem to be appropriate for accommodating quantum physics so can we find a way that can and that, so the thing is the answer is yes but, you know it is problematic because what does moral mean in the dialectical paper of biostructure, well he just talks about the equations right now that's that's not enough that's not quite what we mean leaving some of the problems about to what extent do you recover newtonian mechanics in relativity theory itself we don't just mean that instead of mathematical equations when he's talking about structure so what you want and worrell indicates is you want some robust notion of structure that will enable you to respond to the pessimistic meta-induction. I think that's what James and others are trying to elaborate. Michael Redhead, too, and Sam. As you're going through your talk, I noticed with alarm the huge set of transparencies that still seem to be waiting to be on hold. So I wanted to ask you a question that might push you a little into there, because you didn't really get around. You don't really want to go in there. because the title you put up on the first slide was different and it talks about indistinguishable particle quantum mechanics, you never really got there you got close in the end so I wanted to hear how you think a more sophisticated structuralism of the kind that maybe brings in the insights of the Gestalt people would help you talking about whereas the Russellian simple structuralism doesn't work very well No, okay, careful now, I don't want, again, I don't want to defend Gestalt theory, you know, I don't want people to go away, I know this will happen. People go away and say, ah, that's Steve French, he's really gone mad now. He thinks Gestalt theory is the right interpretation of quantum physics, and that would be it, you know, that has left my reputation.

1:07:30 I'm not suggesting that I'm not suggesting you should all go away and read up Gestalt psychology and apply it to the relations of quantum physics I think let me put this really I think there are common issues that come up in the discussions of Gestalt that one finds coming up in Cassira and in Eddington which is to do with the relationship between the structure and its elements to do with issues, as I said, to do with modality, and how we accommodate, how we can accommodate the things of the world. Now, if you read Kassira, he has this idea, he talks about the electrons are the nodes at the intersections of structure. You skip to this very metaphorical language. In Eddington, it's quite similar. what you have is this structure which can be described in terms of group theory and much of Eddington's work is devoted to showing how you get physics out of that out of that structure the structure that he calls the uranoid rather, you know, bizarrely and everything comes out of that, including the very notion of existence itself this sort of item-poking aspect of the structure blah blah blah blah and objects emerge out of the structure as nodes in the structure now here's the question that's an interesting frame it seems to be the kind of framework if you want to accommodate quantum physics that seems to be an interesting framework now these guys all thought that the implications of quantum theory were the particles were non-individuals Eddington thought that, Cassira thought that because we've all read the relevant papers written by the likes of me that that's not an implicate no it's not a necessary implication that you can in fact maintain that the partners are individuals right so the kind of thing that james ladyman and i want is to get away from the very notion of object entirely right so instead of talking about non-individual object as no

1:10:00 sort of intersections we want to get away from objects entirely and just talk about structures And Michael Redhead now leaps up and says, well, how can you have relations without a ladder? I have a response to that, but he's talked about that elsewhere. Can these forms of structuralism accommodate that, not just partial monogamous reality, but the loss of objects altogether? I think that's an interesting question. Can any of them do it in a way in which we can go beyond the metaphor? It's all right to talk about nodes, you know, oh, it's really cool, nodes of intersections, blah, blah, blah. but what certain people want is this stuff write me a structure as soon as I do this they go, aha, right you've got your objects back, haven't you Stephen and then I have to tell some complicated story along the lines of John Staker where I've introduced these but I'm not really serious about them ontologically or as Donald Mertz does and he's got quite a number of papers where he says, well look you can actually reverse the whole history of philosophy for the last two thousand years and instead of thinking of everything in terms of an object a monadic property a dyadic property relations right you think you start with relations and you look at instances of relations and you obtain a notion of monadic property from that so you start with an addict properties and you obtain monadic properties an object out of those so you reverse that now to do that you have to rewrite everything philosophy logic it's quite a job i mean he's doing it i'm glad i'm not um so that would be you know to get that to be on the metaphor you'd have to one suggestion is to do something like that the other suggestion is to say i'm going to avail myself of set theory and then simply say i'm not going to take these things seriously i don't think there are objects or if you're born you know what you might do is say what these should be understood in terms of say Dalqiaran's Kwasef, or Desi of Haram's Kwasef, rather than Proposet. So that's part of what's in there. First, a little story on ruffle of motion. Carol Kukash has a lovely story in a mountain pool in Utah with his three-year-old daughter, a frog jump. and Carol said to Kamala,

1:12:30 did you see the frog jump? I didn't see the frog, but I saw the jump. I would actually sort of like to make a comment about space and things, and it's a bit of a comment, but I'll ask you, do you agree with me? I would think, thinking about geometrical relations, I would rather think about distances between points in Euclidean space. Suppose I'm given 45 positive numbers. That's just a heap of stones in the way Leibniz could talk. There's no real unity in those 45 positive numbers. But I might look at them very carefully and suddenly see that they are consistent with being the Euclidean distances between 10 points in three-dimensional Euclidean space. Suddenly there's a principle of unity there. Now this takes me right to that wonderful passage, paragraph from Cassira you have. This protean quality of geometrical relationships is that once you've got the idea one configuration and you've cracked the secret of that one configuration, these relationships tell you that, then it will generate the whole thing. And this is why I think the configuration space is actually the most fundamental concept of all. Because the configuration space is this ultimate taking out of everything that is, it is the complete exploitation of everything you can get out of those geometrical relationships, so to speak. it's a possible world in which there are rules which would create all the possible worlds and on that then you can do a rational discourse of sort of rational thinking and that seems to me the way to think about structure and why I think that the configuration space is important and the individual configurations are actually the instance of time, the instance of time are the ultimate gestaltment right, that's very interesting, there's two comments on that one is, I mean, the extent to which you can do If you read Eddington, you find in the early 20s he's thinking in terms of beginning with events and defining certain relations and then getting everything from that. And the one thing that he can't get, he claims he can't incorporate the apparent atomicity of matter, the lumpiness of matter. And that's where he effectively, you know, he almost despairs of approaching this completely rationally. That, as it were, something empirical has to come in, and that quantum indistinguishability. Born, now, Eddington, in a sense, tries to accommodate that within a purely rational framework.

1:15:00 Obviously, Labat-Lambass here, Born thinks that non-individuality is supported by experiment. It's experimental fact. It's not something that can be deduced in the way that Eddington tries to deduce it from the structure of his urinoid or whatever. So on that point, I don't think that the whole exploration can be done purely rationally. The interesting question about understanding configuration spaces or doing something like Eddington saying that all that we know is structure and the structure is given by the structural configuration space. I think that's interesting. The philosopher is going to say, well, what is that? Just like saying, well, all the properties of the world are sort of group theoretic properties. What does that mean? You could be a platonist about it, or what's the alternative to that? You're saying this somehow represents the structure of the world. And there may be alternative representations of that structure. configuration space and other that's the kind of thing that I would be interested in, how we understand configuration space metaphysically who is it telling us I'll start I don't know if there are any final announcements but first can we thank Stephen Thank you. please do come I'd love to I'd love to come to the wheel I'm living to France tomorrow morning five and a half thousand clocks and I've still got to probably work through the night to get off the finish box and stuff up. I'm all about coming to 9 in the morning.

1:17:30 Yeah, yeehaw. Yeah, I might have a cup of drink. But I don't think I'm going to be able to stick it there. And I'm going to try and force myself to think very much. Unfortunately, I should have... I've got very enhanced...