British Society for the Philosophy of Science Meeting — Quantum Gravity Session

0:00 The book of order for the infinities that Feynman talks about, and the book of order for the non-lifficult theories, or the book of order for the problems that you serve with non-lifficult theories, with non-lifficult theories. OK, so the question I want to consider is, why is it that simple is a canonical loophole complexity avoid the infinities when the I theory doesn't? It might be that there is no connection, it's just coincidence, but the answer I want to give is that they resolve the problem, avoid the problem, by introducing nonlocality into the material structure and the space-time structure theory, respectively. OK, so what I mean by low-locality? Well, it's not the usual quantum mechanics kind of low-locality. What I mean is that the interactions and the observables and states live at points in space-time. Right, so I'll begin by giving a little bit of quantum field theory, and some perturbation theory and final diagrams and how that and how you get the divergent problems from that and how you renormalise it away. Then I'll say a bit about why the original theory was more renormalisable and then I'll go on to string-faring loop-hunter gravity and show how, by introducing it to non-locality, it avoids problems. Right, so the basics of quantum field theory, you have vectors in Hilbert space, H, the Hilbert space carries a unitary representation of the particle agent. You have observables described by operators acting on H and they're defined at each space time point. And I should have added that you generally add conditions to that, saying that fields evaluated at space-time separated points, space-like separated points, and loot. So that's basically the core. But there's a problem with that way of looking at things, and that's that there's no physically reasonable, mathematically inconsistent theory of interacting with field theory. That's because you have to consider products of fields at the same point, and the equation The first solution is to smear out the values over the manifold to test functions.

2:30 What that means is you operate, you act on the observable through some real value function and then integrate the result over the whole manifold, highly non-local. And that basically just agrees with what I'm saying really, that you need to introduce non-locality to get over the divergence problems. I'm not going to be looking at that one first, but that's good for me, that solution. The second solution is to consider interactions as perturbations about the well-defined free fields. That's a local theory. This is a theory that has divergent problems. I'm going to say that it directly is the result of the locality that has got the divergent problem. So, perturbation theory. Well, we use Feynman diagrams to visualise perturbation theory. Feynman diagrams are graphs representing space-time history. So, say you've got a parallel point there, the free propagation of this particle will just be a line where this is space and going over there to time. So that's just the propagator of a particle, the free pattern will go from a point X to a point Y. We use them to compute scattering amplitudes. So for example in quantum electrodynamics, if this is an electron, it will have an amplitude to emit a photon, and the amplitude is determined by the charge of the electron. To compute the amplitudes for processes to occur, for say this electron to go from X to Y, we have to sum or integrate over all the possible ways that it can happen. So not just the kind of one we get from the classical action, but all the ones we get from the classical action. So kind of these trajectories as well. And each would have a weight derived from the classical action. This also goes to where we've got pairs of particles propagating as well, so 2 to 3 particles would have a quantum diagram which is just like that basically. We create interactions that would be given by internal lines. So over all the ways that we can do that. So over all 500 acres. The three systems just have lines or propagators, interacting systems containing lines and vertices, and it's the vertices, namely interactions happening at points, which is where we get all the problems from.

5:00 You calculate the amplitude just by assigning the numbers to the vertices and the lines, and then you add them all together and so on. And then to get the probability you square the absolute value of the value of the result. So, all the divergences there. So, as I said, the Fermin diagrams contain singularities. These are the points where you have a vertex where you've got three lines intersecting. It's a singularity because it's not a one-dimensional manifold any more. It doesn't look locally like R1, but in the vertex it doesn't look like R1. In the case of interacting systems where we have the vertexes, we're summing over all possible Feynman diagrams. So say we've got this kind of diagram where we've got a photon being emitted there, a photon being emitted there, a photon there and a photon there. Well, there's also, so we're concerned with how this initial state gets to this final state, nB gets to cd. Well, that's one possible way of doing it. There's a possible three way where it's just the two lines propagating freely. There's also this way, where they go through the T channel, there's also one where maybe emits a pair there, decays into a pair. So you have to sum up all of these, and there are certain diagonals where these vertex points become infinitely infinitesimally close. And at this point the equations blow up, and that's where you get the short distance divergence from. So renormalisation is a procedure where the coupling constants, the bits that live out the vertex points, and determine the strength of interactions. A Tweet, so that you cancel out the divergences. So a quick example from electrolytes. Say you've got an elastic integral which has its large

7:30 short distance behaviour. So where you've got some really high momentum and you've got They go from log to infinity. So, renalisation, you see, we'll use the observed mass to compute the bare mass. Basically, you take the bare mass, the ones you're using in your theory, to be kind of dressed by the quantum corrections that you get in these kind of missions of photons in the Feynman diagrams. And then, what we have to do first is put a cutoff there, L, and make the integral finite. So we're saying that we're just going to ignore regions of integration where we get the divergences. I have a pack of the integral and then you make the integral finite. We know the observed mass of the electron from experiments. We then make the bare mass such that when we subtract from it this integral which we now know the value of, it equals the observed mass of the electron. So the two sides become equal. But we've got a problem because we've cut this integral and really we shouldn't have because The theory predicts these kind of, that we can prove these short distance structures. So all we do is we take this cutoff back to infinity, and as we're doing so, we keep tweaking the value of this biomass so that it always equals the observed mass, right? And we can take that all the way to the infinity, and we get the right results, the right scattering results. It's completely weird how it works. and Feynman's body was called the hocus-pocus. Most physicists think it's completely mathematically weird, but it works. You can't always do that with all theories, though. There's a dimensional reason why it works. OK, so why is the theory that Feynman was talking about, covariant derivative quantum

10:00 gravity, not reorganisable. Right, well, in that approach, we take the metric tensor to be... we split the metric tensor into two parts. We have a flat fixed background metric, the across the diagonals, minus 1, 1, 1, 1, and then we have a part H that represents a deviation of the flat metric from its flat state. We then plug the whole metric into the Einstein Hilbert action which is just... So we plug that metric into these bits. We put the empirical input to all we know about gravity, that it's long range and universally attractive. We get out the quantum field theory which describes a massless spin 2 of gravity, massless because it's long range, spin 2 because it's got a couple to the energy momentum tensor. We get out a massless spin 2 of gravity it propagates on a flattening Coffey background. So it's just an ordinary quantum field theory. And then we come to the scattering amplitude. I wouldn't know any other quantum field theory. You have six minutes left. Okay, so the exchange, so we've got two and three particles, that's the first on the first tone of the perturbation theory, no problem. But we have to have quantum corrections, so the first correction would be the emission of a graviton by the particle, which is proportional to Newton's constant, and it gives an amplitude which is E over M, well, M is a plane-lastic and bi-lastic, all squared. Which below energy is obviously going to be, you're going to be able to ignore the interaction, but that high energy is going to diverge. Okay, so it's diverging already at that point. In the second direction you get an even more divergent sound, so,

12:30 two grammatons correction gives you that. I'm not wrong with the equation, but it's an even more divergent integral. And at each time the divergences keep getting worse, so eventually you can't take it as an irrelevant, it should have observable consequences. There's a dimension, there's a dimensional reason already. Anything which is negative in a coupling constant is automatically non-renormalisable. Positive, super renormalisable, zero, just renormalisable. You could guess immediately that it is non-renormalisable. But the reason from this point of view is that at each step that you try and re-normalise the theories away by re-adjusting the coupling constants, you're not getting rid of the divergence, you're introducing new divergence at the next step, and then you have to introduce a new coupling constant to get rid of the other divergence. So eventually, as you go through the infinite sequence, you're going to introduce an infinite number of undetermined parameters into the theory, and that's called a re-normalisable theory, I think. So that theory is not really normalisable. But the crucial thing I want you to get is that it's coming from the part of the Feynman diagram, expansion, where these vertexes become infinitely close. So you're considering things happening at points. String theory. String theory next. So string theory simply replaces the idea of a point particle theory by one in which fundamental objects are one-dimensional objects, just strings. The history of a point particle is just going to be a single line, which is going to be a two-dimensional surface for a closed string. Two-dimensional surface, that's propagated for a closed string, a free string. So we have an extra coordinate, which is sigma, and it's also got a tan. When we quantise the vibration modes of this string, we get certain mass spin states, one of which is a spin to a graviton. That's the way to concentrate that. Okay, so a string's train is going to have histories, even though it's two-dimensional, so you can point straight out. The crucial point is, when we turn on the interactions on this theory, when we consider that the Copland constant isn't zero, the Copland constant in this case is tension of the string, then, well, say we want to compute the amplitude, but these two strings do evolve into these two strings, in a similar way we did to the other one.

15:00 Well, we've got no vertexes in this diagram, so we've got no interaction, so an observer will be in this way, I'll compute the interactions happen, but an observer will remain at different So there's no events and varied inversion of when the interaction occurs. Any part of the string looks like any other part of the string. So there's no integration region. I mean, this is a perturbative method as well, so some are all possible ways the diagram happens. But there's no region in the integration region where the points are going to zero, because there are no vortexes to go to zero. So it just simply sidesteps the problem of re-normalisability by smearing out the interaction over space-time. So it's a re-normalisable thing by introducing this non-local smearing by being extended over space-time. Two minutes. Right, Luke quantum gravity is in a slightly different way. Luke quantum gravity is a direct quantum theory. quantized it directly. It's background independent theories, it's on a differentiable manifold rather than a metric manifold. It's norm interpretive, and it's a canonical approach. So what we do first is we split the space-time, which is normally R4, into a free manifold sigma and parameters R. Choose a pair of canonical variables, so either kind of analogous to the position of momentum variables in ordinary quantum mechanics, but in this case it's an conjugate them into the Astracar variables. States in this theory in my spin networks, which are just trivalian graphs... Some good news, you've just got another five minutes that have been donated to you by the next few years. I've never finished actually, I've got a reference on time. Okay, so trivalian graphs, please give us an awful normal basis in the Hilbert space. We assign representations of SU2 to the links is intertwining tensors to the nodes. Tensors because we want to keep janet the variance. The observables are given by loop operators, which are just like Milton loops from Gagnon's theory, given by the trace of the homonymy moving something around the space,

17:30 of a connection, this is a connection, around a closed car on the signal, on the freemoth. So the physical picture of these thin areas is that they describe the one dimensional excitations of the gravitational field. So the nodes, these vertices, represent the contour of volume and the links represent and then the contour of area, there are surfaces, and from this we get a picture of quantum space, and we turn things like area and volume into operators because they're functions of the metric, and the metric becomes one size, quantite and very quantum gravity, and they have discrete eigenvalues, so we can compute the spectrum of the area operator, by 8 pi in Newton's constant, Planck's constant in that, so I've got two parts and got ingredient theories. And we can compute the spectrum of the area, and it turns out to have a discrete spectrum. So, sizes of area come discrete and discrete amounts. Rebellion is an alt-grote, basically what I've just said. Ensuring simple human view the nodes, the quantum chunks of space, the links representing the surfaces separating the quantum. The quantum of space. And the half-integers, which I understand that, represent the quantumised area of the surfaces. Okay, now, the next bit's important. Spin-out works for the relation of quantum states that are not located in space. The reason for this is that we're doing it on a background independent, we're doing it on a differential manifold, not a metric manifold. So we can't say where something happened, when something happened, and the distances between things happening. So localisation of value things must be relational. Alright, so we get two solutions for getting out of problems of ultraviolet divergencies here. Both as a result of introducing non-level structure. So the first one is that the discrete structure of space given by these kind of spectra, discrete spectrum, provides a real physical curve.

20:00 So if you remember when I showed you that integral before and put a curve in there, this time we've got a real physical region believing the curve where it is. We don't have to take it to infinity. So we don't ever probe the high energy regions. And we don't ever probe the small space time regions. And we don't have to remove it. So we don't consider these coincident points where we get the blow-ups from. The second way of resolving it is that loop-pongarity is based on a differentiable manifold, so there's no grained notion of where and where interactions take place. That's Rebelli's point. That's just like spin theory. So the idea of where interaction happens is ill-defined. Okay, so both solutions have introduced non-locality, both these solutions have introduced non-locality into the theory, and by doing that they avoid the problem of renormalisation, of non-renormalisation. Okay, so there are two test theories of quantum gravity, and both have avoided the problems which faced the earlier theories and other quantum theories by introducing non-locality So, conclusions. Well, I think the conclusion for this is that we need to avoid local theories. We need to avoid localization of points and interaction of points. There might be other ways of avoiding infinities, but given that general relativity has its We shouldn't want points to take any kind of significant amount of value anyway. Okay, so that's just repeating the main point of the argument. Okay, the two best things to get rid of the final result by introducing non-locality, which is the same thing to get rid of fundamental states with point, I think, or interactions at points. and what I want to show later I haven't approved this yet I suppose I haven't approved I think the same works for every mathematically consistent finite constant theory of gravity so I'll finish with a conjecture that's that there are no renormalisable space-time micro-local theories of gravity constant theories of gravity so any bets

22:30 that that's wrong I'll be taking bets Thank you very much for teaching us everything about quantum field theory, interpretation theory, string theory, and string ethics. I know it will be a test at the end of this session. But would you have time for up to ten minutes of questions, if there are any remaining answers? Could I ask a couple of things? So I'm a physicist, I'm your sort of resident visiting physicist. Did you migrate into philosophy from physics? No, I started in philosophy, I used to always be in physics. All right, well, so obviously the rest of you can't judge, but I agree with almost everything you said. I mean, your physics seems very solid to me. One thing I just want to correct an impression you made, maybe, that you said most physicists think of renormalization as being a bit wacky. Okay, some people do, it's true, and famous people like Dirac and Feynman didn't like it, but it doesn't bother me, and it doesn't bother a lot of people from sort of a younger generation, namely sort of the 70s onwards, when some understanding of it, it was understood from a different perspective as being in terms of sensitivity to short distance, and you know, some theories are very sensitive to short distance, and we call them non-anomalizable. so anyway, so some of us are not so bothered that's just a sort of, I don't want you to get the idea that we're all sort of trying to get rid of this renormalisation Well that's because you're a physicist Well there's actually a theory of renormalisation from the renormalisation group that's what I need to look at next actually OK, so let me get to my more substantial question which is so you're saying that you think getting rid of these infinities, it's crucial of local states, and that may be true. I just wonder why you restrict yourself to gravity. I mean, you could frame this question, your final conjecture said something about theories of gravity, and it could be, I thought it could be theories of answer. I agree. When I put two problems with quantum field theory, sorry, the two solutions, and there was a smearing, where you smear out the field operators, and that's not there. I think it goes for all quantum field theory, It's just that I've set myself the task of the quantum layers of gravity.

25:00 I mean, they're so much harder. I don't even study them because they're so hard. I mean, I'm frightened of them. I think you're right. I think it would apply to all theory on theory. You'll always need some kind of smearing out, so never considering interactions at points. right if you wanted to make them all really fun yeah but i mean i think i mean the algebraic does that i mean it's only in perturbation theory which isn't an exact theory anyway where you do where you don't have any kind of local smearing didn't understand what you said most popular theories don't think of things happening at points anyway even when you're So you're never really saying we're going to get to the actual limit point where we really are at points. You mean you never take the cutoff to infinity, is that what you mean? I'm not sure what you mean exactly. Well you're never considering certain loop diagrams. You don't take it too far, the expansion. so you're not going to say arbitrarily high energy when you're doing computations I think most people would agree that when you do that this is when you do get these divergences well it's true that what you said the divergences come from when you consider very high momentum or very short distances and the problem is if you find this theory its predictions keep changing I look at stuff happening at shorter and shorter distances and the predictions keep changing as I allow more and more short distance stuff to contribute. And that can happen even at the lowest order in perturbation theory. It doesn't matter how accurately you're treating the theory. You can find you come up with a very rough approximate treatment of it and there's this horrible infinity right there. What looks like an infinity, I don't like to call it an infinity. It's sensitivity to short distance. It's not really an infinity. But if I agree with you, I could say and I will say that it applies to any one thing. Right. Just to check if there are any other people eager to make a point. Otherwise we can't continue with this. Are there anybody who wants to...

27:30 No, no, I don't want to hear it. Your conference is not mine. Okay, well. Last one, for any more questions? We're going to say something about I mean, Teller, for example, translates the, perhaps, some of us might think the rather sanguine attitude of the physicists into philosophical justification for renormalisation, which he has in his papers, in various ways in which one can justify, which many people find unconvincing. does that have any impact on on what you are I mean suppose someone would say you know you're kind of worried by renormalisation and you shouldn't be the physicists are but they're physicists but physicists were worried many physicists were worried I think that was part of it not being framed in an appropriate way But there's an interesting historical question, why does this stop worrying about renormalisation? But even a philosopher like Teller isn't worried about it. I think it comes from the renormalisation group. We can see it there, these kind of things, changes, critical points. I mean, it gives it a nice, rigorous... instead of talking about infinities you talk about cut off dependence and once you talk about it that way it becomes manageable, it becomes a thing infinity is not a sort of a hole if you like it's a sort of oh my god that's what worries all the philosophers it's all to do with machinery for managing it the fact that infinity in the first place was from, actually this goes back to what was being discussed yesterday, taking a limit in a rather naive way, of sending cutoffs to infinity, allowing arbitrarily short distance processes to contribute. So you took that limit without worrying about it too much, because it had never mattered before in physics. And this time you found the behaviour in that limit was a bit non-trivial. So you need to treat the limit in a slightly more careful way. But if you just treat it in a reasonably careful way, you find that

30:00 doing it in a reasonable way is both mathematically and philosophically justifiable but the sorts of worries that one might have well in the context of field theories other than gravity it seems not to be a worry well gravity is notorious for being non-renormalisable but there are non-renormalisable theories that aren't gravitational theories and we even use those sometimes notorious for raising these conceptual issues about which you touched on in passing at the end when you mark about the diffeomorphism group that being the whole point that won't happen because one it actually calls into question the background structure of the manifold and just what its status is I mean the problems with the not just with the divergences but the problems it seems conceptually at the level of the plank state of quantum gravity or you know coming from the fact that you do have a diffeomorphism group in classical theory which is precisely shuffles points around so therefore is tied to this local understanding of the manifold is ultimately a set of points and I was wondering if you had any views, you just mentioned in passing that loop quantum gravity and string theory were in your view the two main ball games in town but there is as I understand also this program of Sorkin causal set theory which precisely tries to introduce a kind of finitary algebraic, finitary incidence algebra at the level, and therefore, of course, a diffeomorphism group which is not the C-infinity diffeomorphism group of relativity. And it just seems that conceptual motivation for that does raise, you know, much, issues of the kind which we are much more interested in as to philosophers. Yes, it does seem to raise issues, you know, in philosophy of even in philosophy of mathematics about the status of the continuum and the way one should conceptualise it. If we can move on to the next speaker, thank you very much. The title of the next paper is Towards the Transcendental Foundation of Quantum Physics. And in the program it says it should be presented by a crown man, Quindy, who isn't able to come,

32:30 so instead Christian Neronde will read it, who is also the co-author of the paper, and the donor of five minutes to the previous speaker, Which, considering you have only 20 minutes, it's like giving a kidney, almost a panther. First of all, I would like to apologize because I'm the second physicist in the room. I'm not a philosopher. And Hernán Brinti was the philosopher who was going to attend all the questions. so I'm not sure I will be at the level of the audience of trying to give some good answers in these matters. Well, the title is Towards the Transcendental Foundation of Quantum Physics. Introduction. With the development of Neo-Kantian at the end of the 19th century and the beginning of the 20th, the idea that Kantian doctrine was the philosophical systematization of Newtonian natural science became almost unquestionable. However, it was simultaneously clear that the fate of transcendental philosophy was not necessarily bound to the destiny of classical physics. Rather, just as Kecerer sustained in order to offer a philosophical foundation of the theory of relativity and of quantum physics, we should not only not abandon the road traced follow it beyond the stadium that the philosopher of konexper reached in this sense diverse authors adopted a transcendental perspective when offering a philosophical interpretation of the questions raised by the development of modern physics in this work we intend in the first place to expose the relevance and the utility of such a perspective in the case of quantum physics and in second place to point out the essential task that the transcendental foundation of this theory should perform. We addressed the first point of comparing the present state of the philosophical interpretations of quantum physics with a view that Kant had of the state of the metaphysics of his time. We showed that there is a remarkable resemblance between the way in which the philosophy of quantum physics tries to solve its problems and the way in which pre-critical metaphysics dealt with its questions.

35:00 Our thesis is thus that the critical reductions of quantum optimists to mere appearances in a Kantian sense may be very helpful for a satisfactory foundation of quantum physics, since it is precisely in this way that Kant overcame the problems of pre-critical metaphysics. However, we will sustain that the character of appearance of a quantum object is stronger than the one that Kant maintained for a classical object. The philosophical debate about quantum physics Among the philosophical interpretations of quantum physics, it is possible to distinguish two paradigmatic options, realism and empiricism or instrumentalism. Most of the physicists accept the elements of both tendencies in diverse proportions. According to instrumentalism, a physical theory should link by predictions measurable phenomena without being concerned with the what happens to the nature when she is not observed. The theory does not seek to describe what nature is, but rather it is a mere instrument of prediction, and only in that sense it is an instrument of knowledge. emphasis in prediction of the treatment to description is however questioned. The main objection against instrumentalism is that, from this point of view, the success of a theory cannot be explained. That is to say, we do not know how and why quantum physics is in general able to carry out predictions, and in particular with such a fantastic accuracy. Undoubtedly, a hard instrumentalist may simply refuse to look for such an explanation, since it is in fact the mere effectiveness of a theory that that which justifies it, so that he may not be interested in advancing towards a justification of that justification. However, an argumentative lagoon remains, and this lagoon has been almost naturally filled with realistic arguments that suppose an underlying reality which is somehow described by the theory. So there are diverse realistic interpretations of quantum physics, the most developed of which is perhaps that of Bohm, that insists that quantum physics refers to a reality in itself which subsists even when it is not observed, that is to say, in an independent way of any relation with a subjectivity.

37:30 From this perspective, some authors sustains that between classical and quantum physics, there is only a difference of logical algebraic order. Both classical and quantum systems possess properties that belong to them in themselves. The difference is that the properties of a classical system from a Boolean algebra, while those of quantum systems have a weaker non-Boolean algebra than of autocomplemented lattices. realistic interpretations have nevertheless their own problems in the first place at the moment there is no empirical way to decide in favor or against them the theory of bone for example reproduces the results of canonical physics without being able to experimentally differ with it in the second place in accordance with the theorems of bell and of cohen speaker the very mathematical structure of the quantum mechanics imposes severe restrictions to any deal with the variables, that is to say, with physical magnitudes that possess a definite defined value even when they are not observed. But the main objection against realism is that there is no valid justification of the pretension to referring to a reality in itself, properties that can only be revealed empirically. In other words, if the empirical data depend essentially on the interaction between an How can we sustain that those data give knowledge of an object which is supposed to be completely independent of that interaction? Shortly, neither instrumentalism nor realism provides us with a satisfactory philosophical interpretation of quantum physics. None of them answers properly the question about the limits and the justification of the theory. In the first case the answer is too poor, in the second is too pretentious. It is enough to sustain that the theory is appropriate in mere instrumental way. It does not suffice to affirm that quantum physics just works, since why it works would remain mysterious. We may then be tempted to accept that the theory deals with a transcendent reality that subsists even though it is not perceived, so that the predictive effectiveness of the theory

40:00 has its justification in the supposition that the theory somehow describes states of things in themselves. But in this point we realize that it is the very supposition that the theory refers to a transcendent reality which cannot be sustained. The ascription of properties which are essentially dependent of a subjectivity, as empirical data are, to a reality completely independent of this subjectivity is, if not unjustifiable, at least always in depth of very heavy metaphysical commitments. Kant and the metaphysics of his times. Up to here we have discussed different philosophical interpretations of quantum physics. We will now consider the transcendental doctrine in the same terms that Kant uses to present it the critic of pure reason, in order to expose the structural resemblance that the problem which the transcendental philosophy seeks to solve, bears the discussion just outlined about the foundations of quantum physics. Kant describes the situation of the metaphysics of his time as that of an endless war in which none of the opponent is able to definitely beat the other. The Emmys are, on one hand, the dogmatic rationalist faction and, on the other hand, the empirist or sceptical party. Dogmatics seek to reach, by means of mere concepts, the knowledge of reality in itself, that is to say, of that which is independent of any relation with the subject. Meanwhile, anchorists reject that position by maintaining that, as long as all our knowledge finds its foundation in experience, it is impossible to know a reality that cannot be reduced to a material given by the senses. This position, in its extreme version, affirms the impossibility of having access to something more than to the mere course of perceptions, which can neither be referred to an object nor can be described to a subject since those perceptions have no necessary connection among them. The Kantian view tries to overcome this dispute from a perspective that contains elements of both factions.

42:30 Kant accepts with the empiricists that our knowledge begins with experience and does not follow that it all arises out of experience. It sustains that there is knowledge independent of the experience or a priori. In a priori, knowledge are contained as elements of those same concepts, substance, causes and effects, etc. That rationalists treat in a dogmatic way. They are now restricted in its use to the spatiotemporal data, so that they only refer to that which is given in a possible experience. This critical use of such concepts guarantees that the empirical data are referred to objects so as to reach real knowledge. However, those objects to which empirical data are in this way referred will essentially depend on their relation with the subject so that they will always be mere appearances and never things in themselves. It is our opinion that essential elements for the solution of the disputes between realism and instrumentalism in the scope of the foundation of quantum physics can be found in Kantian ideas since, as we have seen, Kant understands that it is in fact his own doctrine that which overcomes a similar battle in the field of metaphysics. We thus propose to accept the character of appearance of the quantum object as the most appropriate way of overcoming the dichotomy realism-instrumentalism. Since given this acceptance, it is possible to provide quantum physics with a much stronger justification than the mere functional effectiveness without maintaining any statement about isomorphisms between the theory and elusive things in themselves. From this perspective, the theory refers with truth to objects of experience. It has empirical reality, but it says nothing about things completely independent of the subject. That is to say, it is transcendentally ideal. Conclusions Kant understood that physics proceed along the sure path of science because he had adopted a particular perspective on the way in which knowledge is related

45:00 with its object physicists approach nature in order to be taught by it however they do not do so in the character of a pupil who listens to everything that the teacher chooses to say but they act as a judge who compels witness to answer questions Physicists had accepted that it is not knowledge that which is governed by its object, but rather, on the contrary, it is the object that which it is governed by its knowledge. So, it might seem redundant to affirm the necessity of the critical reduction of the object of physics because this reduction would have already been verified in classical physics. Why, then, is it necessary to go beyond Kant, if the character or appearance of the physical object has already established by the critic of pure reason? In order to answer this question, you should note that the production purpose for the quantum object is stronger than when one Kant settled down for the object of Newtonian physics. Although it is certain that classical physics inverts the relation between knowledge and its object The Newtonian physicist does not need to be aware of this invention, inversion. As a matter of fact, he can and should consider physical objects as things in themselves in an empirical sense. That is to say, physics is developed as if it were dealing with a transcendental reality. On the contrary, Bohr's principle of complementarity shows that the dependence of quantum objects on subjectivity is stronger than the dependence of classical objects. The fact that an electron behaves either as a wave or as a particle depending on the characteristics of the experimental device that it is used to detect, it implies that not only the objectivity As long as object of a possible experience depends on a transcendental subject, but rather that later determinations of the same object as empirically given finds its foundation in the apparatus used for its measurement. In other words, although the philosopher discovers the critical reduction that the Newtonian physics carries out,

47:30 the consciousness of this reduction is not necessary for the scientist's activity. It can and should ignore it totally. On the contrary, since there is no place in quantum physics for a thing in itself in empirical sense, this discipline claims for a philosophical foundation that accentuates the transcendental perspective. Quantum physicists that empirically objects as appearances show a metaphysics of experience that makes natural objects mere appearances, but that allows the aforementioned object to be considered by physicists as a transcendental reality, is definitely insufficient. On the contrary, quantum physics still demands a more radical foundation which should make its object appearance not only to the philosopher's eye, but essentially to those of the physicist. This is the essential task that the transcendental foundation of quantum physics should perform. In this way, we will follow the road traced by Kant, but we will advance beyond him. and we have eight minutes it's more of a comment really than a question I mean I think this is sort of a nice beginning in a way but what you indicate at the part of the beginning of what you say sounds like this is a sort of a general approach to the realism anti-realism debate If you abstract away from quantum mechanics, you can just take your realism, instrumentalism. One way of resolving all that is to say, head to hell, I'm going back to Kant. What one would want, in order to show how that Kantian move resolves problems in the foundations of physics, is a specific input into that move from quantum mechanics itself. that. In Cassira's book on determinism and indeterminism, he does it very nicely because he says, for example, this is the thing I'm interested in, he says things like well, if you look at quantum statistics, what does quantum statistics tell you about the notion of an object? It's not

50:00 the standard metaphysical notion anymore. You've lost the individuality of the object, and the only way to accommodate that is through Kant. So he presents the Kantian manoeuvre as a specific way of philosophically accommodating what quantum physics seems to be telling. And physicists themselves, Born, Schrodinger, pulled not so much on Kant, but on other broadly philosophical views in order to accommodate what they saw as the results of the physics. Now at the end you sort of indicate that with the talk of complementarity. And famously, Bohr included Kantian elements in his own discussion of complementarity. But I wonder if you could say more about how specifically problematic, metaphysically problematic, elements of the foundations of quantum mechanics can be accommodated within the Kantian view. the main part is I would say to take account of the subjectivity of the system and start from the system itself to develop the from the subsystems from the from the composition of the to develop the system which you are going to study, and this takes into account, of course, the observer. There are several approaches in this. I'm just worried now about that, because what if the physicist, our friend here, were to say, subjectivity, Bohr was worried about it, Wigner was worried about it, but we've moved beyond that. When it comes to the measurement problem, for example, we don't need any notion of subjectivity or consciousness anymore, because we can appeal to decoherence theory, perhaps allied with the Everett interpretation, and so on and so on and so on. Well, there is a certain subjectivity. I wouldn't be so sure that Bohr, well, everybody that talks about Bohr, Bohr is completely right with the one who's speaking, actually.

52:30 so he's completely according with everyone so it's very difficult to point out where he is but still there is a subjectivity before you are going to measure because you have to choose the apparatus and the system which you are going to interact with and in that sense Pauli especially There is this objectivity, and afterwards, of course, when you have settled your system, then everything is objective, and you can still measure whatever you like, and you will have your observables with definite values. In some cases, it depends on the interpretation. Well, I'm not sure if... Other questions? If so, then we can move on to the third talk. Sorry, I wasn't there. You've got the signal. Okay, so here the title is, is it possible to normalize quantum effects? and the author of this is Otavio Buena, so instead he sent his virtual producer avatar. Otavio apologises profusely. There's a bureaucratic problem regarding his visa, such that if he were to come here, he might not be let back into the United States and decided not to take the risk. So they feel so threatened about being as a possible person. They don't deny it for a new space, especially as a state in America. We couldn't imagine anyone further than a possible person. So anyway, for the next 20 minutes, you're going to have to imagine, if you can,

55:00 that not only am I resilient and considerably better looking and more intelligent than I am, but I'm also an empiricist. And this is a case of an empiricist beating up on a particular way of nominalizing quantities. Okay, here's the deal, here's the deal. Many of you might be familiar with this. Is mathematics indispensable to our physical theories? If you think it is, then you've got a problem. If your physical theory is confirmed, So you say, yeah, I think that theory is true, or it's the closest to the truth, I think electrons exist. If the mathematics is indispensable, if the mathematical objects are indispensable, then it appears that you can slide over to the claim that you must be committed not only to electrons, but to mathematical objects, numbers, hilvers, spaces, and so on. The non-lust doesn't want this. Why? Because the non-lust doesn't want such objects in her ontology. She wants to get rid of them. How can she do that, given the obvious, perhaps inexplicable, as Deedman thought, but the obvious applicability of mathematics to physics? So how is it possible that there are no abstract objects, or we can get rid of abstract objects, if they're indispensable? Well, Hartley Field, many years ago, I think it was almost 30 years ago, provided an answer. Mathematics is not, in fact, indispensable. but we can reformulate our theories to get rid of mathematical objects. Strange but true. We can do this, we can adopt a particular strategy such that we don't need the mathematical objects. And he did it for Newtonian mechanics. Effectively, getting rid of numbers in favour of space-time points. Ballaguer tries to do it for quantum mechanics. Effectively, getting rid of Hilbert's space is for propensities. And what Tango's going to say is, that's a dodgy move, and he's got concerns. Now, it's quite important. He claims that here are the sort of general desiderata for a nominalisation strategy. And these seem fairly plausible. One is, nominalisation should be neutral. Let's be clear about what the name of the game is here. This is just pure philosophy. We're not going to do anything that's going to resolve any foundational issues. It's not going to lead to any new predictions, any empirical results.

57:30 This should be a neutral strategy. It shouldn't settle issues. There may be an issue as to what we mean by issues. Otavia says it shouldn't settle any empirical issues, and it shouldn't settle any interpretational issues. It should be neutral. In other words, you could be a nominalist by quantum mechanics and adopt the Bohm interpretation, or the Ebert interpretation, and obviously the second one the normalisation strategy should be ontologically parsimonious it shouldn't give you stuff that's unacceptable otherwise it's not really a normalisation strategy okay, Fields' nominalism and many of you well some of you I hope are familiar with this, proceeds in well, two steps the first is to say that mathematical theory doesn't need to be true to be good, okay, so it needs to be conservative. It's conservative if it's consistent with every good, you know, internally consistent theory about the physical world. So if you, I guess the idea is that if you have your mathematical theory and you append a bunch of non-normalisation claims and you draw consequences, then you should be able to draw them from the nominalisation statements of the people themselves. And the second step is to actually provide nominalistic premises for particular theories, i.e. you have to show that you can reformulate particular physical theories so as to get rid of these abstract objects. And Field draws on Hilbert. Hilbert sure and aware, which you can get rid of metric concepts in geometry, so you don't have complication over real numbers, by introducing automatisation based on concept point-between as congruence, right, so you just simply say point-wide, between, blah, blah, blah, this line segment is congruent to that one, blah, blah, blah, and that's a well-known, and that's a very famous programme, crucially, of course, what you need for it to work, although it's so cool, you know, neat axiomotisation, but you need a representation theory, right, so that you can effectively go from you know, the geometry with numbers to the geometry that just has concepts

1:00:00 of point congruence and so on. And that's the trick, you know, the neat trick of parties is to come up with appropriate representation theory in the non-organization program. Field extends this to physics, right? And in science about numbers, Field indicates how you can accomplish that program in the case of Newtonian gravitation theory. So you set up your axiomatization in terms of space-time points or space-time regions, and you have to have a representation theorem that shows that all the statements in Newtonian Involve numbers, mathematical objects, can be translated into space, and if you're a realist about space-time points, then what you're going to say is, those are the things that exist, not numbers. I don't need numbers. Numbers are actually dispensable, says Field. Malamont raised a well-known objection and said, okay, let's grant that you've done this to Newtonian theory. There's an enormous discussion about that. He says, I don't see how you can get started when it comes to quantum mechanics. Okay? Because suppose we think of the theory of determining a set of models, each model in a Hilbert space. What form would the representation theorem take? Well, there are attempts to do this. You can see this in the work of Jauch and Piron and so on. And they start, in their axiomatisation, they start with propositions, certain lattice-theoretic relations as primitive, and then seek to show that the lattice of propositions is going to be isomorphic to the lattice of subspaces, of sub-Hilbert space. But of course, Malamon says, that sort of program would be disastrous for Fields. What could be worse for the monoliths? worse than propositions. What could be more abstract than propositions? You've got rid of one abstract object, Hilbert's space, but you've introduced another, so that's no good. And that's the challenge that Balaguer in his book, Platonism and Anti-Platonism in Mathematics, that's the challenge that he says here's his main here's his main thesis

1:02:30 the closed subspaces of Hilbert's space can be taken as representing physically real properties of quantum systems, what he calls propensities, propensity properties the point five the English is clumsy the point five strength propensity of a z plus electron to be measured in the x direction The probability is 50%. And so that's represented by this propensity. And in general, closed sub-spaces represent the R-strength propensity of a state system to yield a value in this set for a measurement. So, in other words, what you want to try and establish is a representation theorem between Hilbert spaces and these propensities. Now, Balaguer only sketches such a representation theorem, but Ottavio says, let's grant him that he's done it. Let's give the guy some credit, give him his due, grant that he's got that. The question is, what are the ontological commitments of this nominalisation strategy? Is it nominalistically acceptable? And Fabi's going to say no. And the obvious sort of worry that you might have is propensities. I mean, we've been there before, right? Remember Popper? Popper was the big propensity guy. Popper on quantum cameras, it's all propensities. And I remember when I were a lad, my old professor of fossil science, Heinz Post, in his Austrian accent saying, propensities, these are just wood spirits, right? You introduce them because you really don't understand the irreducibly probabilistic nature of quantum mechanics. You introduce propensities, they're everywhere, like these wood spirits popping up. Now, Balaguer has an answer. He's not a noodle head. He knows that people are worried about propensity. So he says, does it mean that I'm committed to a propensity to a propation of quantum mechanics? going back to Papier index. We know that's dead. The most I'm committed to here is a broad claim. He calls it BC, a broad claim. Quantum probability statements are about physically real propensity to quantum systems. But he says you can understand this broad claim in a very weak way. All it's saying is that quantum systems are irreducibly probabilistic. It's all it's saying. Who could possibly

1:05:00 disagree. And then he says, so it seems to me that on that weak understanding it's compatible with all interpretations except for the hidden variable ones, except for Bohmian interpretations and they have their own problems. They have their own problems. why then are these propensities as a target was to say it nominalistically kosher. Why are they acceptable? Well, he identifies in Balaguer two arguments, sufficient condition argument. These propensities are physical properties. They are not abstract. They exist in space-time. They're causally efficacious, says Balaguer, in the way that mathematical objects are not. Mathematical objects don't exist in space-time. They're not causally efficacious, and that's one of the reasons the nominalists Furthermore, physical properties are all we need to normalize quantum mechanics. There's no need to appeal to abstract properties. In particular, of course, we don't want events or propositions. We don't want to have to normalize in terms of events or propositions because if we're working with events, basically you need to get a complete infinite set of events associated with the relevant observables And this will force us to speak of events that haven't occurred yet, and those events will have to be treated as abstract policies. And Ballardier himself says that's why we shouldn't appeal to events. Events aren't nominalistically acceptable. Now, Artavio would like you to remember this. Pay attention at the back, OK? Because he's going to say we can apply the same criticism that Balaguer applies to events to his invocation of propensities, that they're going to make reference to non-actual happenings. Balaguer goes on. The advantage of switching to propensities is that effectively that infinite set of events, we're talking about events we don't have to think of the events as out there these possible events are out there and the nominists pull their hair out and say no that's what we've got what happens to the propensity is

1:07:30 all those possibilities kind of get folded up into the propensity, they all get nicely packaged up into the propensity so it's not as if the events are sort of out there in any sort of Lewisian way or some sort of noministly problematic way But there's sort of, you know, each system, any system has an infinite collection of propensities that gives rise to the appropriate structure. So all the propensities that you need are contained in the system and all sort of is wrapped up in there. So it's not as if all these nominously unacceptable events are out there. The propensity is in effect going to generate them as needed. but the propensity is a real physical kosher property the second argument as to why they're normally supposed to be kosher is that we can then get rid of them okay, because you might say alright, yeah, yeah, yeah, propensity, propensity but, you've got numbers in there you said 0.5, right? 0.5 straight, that's a number well, Baragher says we can get rid of the numbers, just as field reference to number in favor space-time points, what we can do is introduce propensity relations that hold between systems. So instead of building up quantum structures from things like this, we're measuring in the x-direction, z plus electron, and the propensity is 0.5, we simply replace sentences like state 5-electrons over our strength propensity of leather, with sentences like these electrons are a delta propensity between state by one and state by two. And that, I think, you know, perhaps that's relatively uncontentious. We can sort of get rid of the numbers in the same sort of way that Hilbert did for geometry. But, says Ottavio. Now, you know, Ottavio's an empiricist, and he's kind of anonymous with regard to mathematics. for this program to succeed, okay, but he says it doesn't, and I'll leave you to sort of judge whether you think the problems he raises are good ones a lot. One of the problems is that sufficient condition doesn't mesh well with the rejection of events as nominalistically unacceptable. Some propensities aren't actual properties. They haven't been actualized yet,

1:10:00 So they're not at the nominal's disposal to quantify over. And so propensities can be abstract or may be abstract in the same sense that events are abstract. And if you're interested, we can talk about this in the discussion. Part of the issue here is exactly what kind of a property is a propensity. if you think of it sort of in dispositional terms what's when you think of this, what's the status that that glass has a dispositional property of fragility what's the status of that property if it's never actualised if I never chuck a chair through it through the glass is it a non-actual property well if it's a non-actual property then it's abstract in precisely himself identified for events, then it's non-lystically unacceptable in Baladier's own terms. So part of the issue here is that he really needs to say a bit more about what he means by propensity. Can he say that while recovering everything he wants to say about Hong Kong? Second problem that Baladier identifies, he thinks, well, Baladier says, we, you know, he thinks that Baladier requires a strong reading of his broad claim, not a weak one. Remember the broad claims that quantum probability statements are about physically real propensities of quantum systems. Any weaker reading, simply saying that quantum mechanics is irreducibly probabilistic, doesn't give you enough objects for Balaguer's account to quantify over. For example, Van Frassen's interpretation of the claim that quantum mechanics is irreducibly probabilistic. Van Frassen's mode interpretation, Van Frassen agrees that quantum mechanics is irreducibly probabilistic. He's not a Bohmian, doesn't have any trouble with that. He accommodates that irreducibly probabilistic nature by introducing the distinction between the value state and the dynamic state. The dynamic state, as the name suggests, develops dynamically in accordance with the equation. And the value state, the value according to the usual rules.

1:12:30 So Van Varsen may accept that quantum mechanics are irreducibly probabilistic, but this is not a claim about the existence of real propensities in nature. In other words, Van Varsen's interpretation can do, can capture this aspect that's irreducibly probabilistic without giving you propensities. If you adopt that weaker reading have the propensities that Balaguer needs to quantify over, that the nominalist needs to quantify over. Furthermore, we seem to have violated one of the requirements of our nominalisation strategy, first requirement, we seem to have violated the claim that it shouldn't resolve any issues. Balaguer's account, says Octavia, is incompatible with Van Frassen's version of the modal interpretation, because Van Frassen doesn't have propensities, Balaguer doesn't. Van Frassen can do what Balaguer wants to do without propensity, and as Atogu said, what we've done is effectively ruled out Van Frassen's interpretation on the basis of our non-linear basis, ensuring that we shouldn't be decided between interpretations of physical theory, much less decided, which obviously shouldn't be decided between physical on the basis of our metaphysics but we shouldn't be deciding between these interpretations should we of course you know you might say yeah but look field was committed to a realist view of space time point but field had independent reasons for that he wasn't committed to a realist view of space time point because of his normalization strategy so you may have independent reasons for knocking out both parts you may think the mobile interpretation is crap right but those reasons shouldn't come from your normalisation. Secondly, the second condition, illimitability, doesn't go through either. Why? You still, he says, propose a value for the propensities, and this is slightly trickier. You've got to order your propensities, okay, so you've got these statements about, you know, a, delta, propensity between, how are you going to order the propensities without appealing to particular values?

1:15:00 How are you going to establish that ordering relationship? How is that you haven't eliminated? two minutes sorry? two minutes I'm done how does Balogate's account fair with regard to our desiderata? Otago says two is it not is the normalisation neutral? it seems to imply the inadequacy of the modal interpretation and you might also be uncomfortable with the way it doesn't mesh with hidden variables what if? I mean well I guess that's problematic if the German Bonians sort of leap up and say you might want to say, well, your theory is not an interpretation of quantum mechanics, it's actually a new theory. Is that idea's account ontologically parsimonious? No, because propensities are dodgy. And so the account is 10 frames. So you still need to provide some way of recovering quantum theory, which, no doubt, in the form of time, Montaglio will provide. The first requirement of being neutral. The justification I could think of would be that if you do rule out things, you don't want to be accused of being ad hoc, because the only reason you've ruled out the interpretation is because of your normalisation stretch. But you can get out of that by saying, well, hang on a second, I've got reasons for being a normalist. I mean, I haven't just, I mean, unless you just are scared of abstract objects, I mean, if you've got rational or some arguments for being a normalist, then surely it doesn't matter. because that's independently justified speaking of Otavio you might say the reasons I have to be anonymous have to do with concerns over mathematical objects causal efficacy for example and those are different reasons and the reasons I might have to be an anti-realist with regard to physical objects for the existence of Germany, since some people may be anomalous with regard to mathematical objects,

1:17:30 well, maybe anti-Platonist with regard to mathematical objects, but be realist with regard to physical objects. So, we might want to keep, you know, some people might say it's a virtue to have an all-over metaphysics in which all our reasons mesh, and the reasons for being anomalous with regard to mathematical objects but others might say actually that virtue is a bit of a vice it doesn't give you a fine grained enough account and I want to keep those reasons quite separate and at least allow for that possibility, even though I suspect he himself is pretty much a recurring empiricist of the board because people can buy to at least part of your account absolutely I think either I misunderstood the fourth problem I didn't think it was a problem. Well, I didn't think it was a problem. I might have misunderstood what it was. No, I may have presented it back to the past. Now, the worry seems to be, okay, if these things don't have values, how can we do an ordering on them? Yeah. And that looks very analogous to what I take to be a bad complaint you might make about Hilbert. Yeah. These points need to have locations, because otherwise how could there be a betweenness relation defined on them? how could I order the points if they didn't have values if they didn't have real number locations it's a bad objection to Hilbert because the betweenness relation is the primitive and that's what's doing the ordering it's an anti-symmetric relation presumably Borreger can say something similar here yeah they are ordered all of these propensities They're ordered by the A-delta propensity between relation. It's not that they've got some intrinsic feature which is kind of mathematised or quasi-mathematised in virtue of which that relation holds. That's a primitive. I'm following Hilbert here. So I guess I think if that objection to Hilbert's a bad objection, this problem for Balaguer is a bad problem. I'm frantically flipping through the table to find if he discusses that. I mean, I entirely agree, one could, well, that would be the obvious response to that, would be to pack the ordering into your axiomatisation, and then what's the problem?

1:20:00 I thought maybe this was just in conversation with him, I thought he had a bit more to say about that, but maybe he doesn't, and in which case I'm just stumped because, I mean unless it's just a sort of, we'll go away and do it then, Balladay hasn't done it. But it looks kind of trivial to go from a real ordering to a ordering via a between-house relation. How can such a relation, this ordering relation, be characterised without presupposing an ordering from the probability assignments themselves? Of course, one could use the ordering from the Borel set, delta of real numbers, but that presupposed commitment to numbers. Note the difference between the ordering suggested by Ballaguer and the corresponding ordering put forward by Hilbert. Okay, Hilbert says a point Y between points X and Z, if Y is a point in the line segment whose endpoints are X and Z. The only commitment here is to the existence of an intermediate point between X and Z. There is no need to move beyond points to obtain the between relation. In contrast, the A-delta propensity between relation is tied to the Borel set of real numbers delta, and its proper characterisation cannot be provided without reference to such a set. After all, the propensity under consideration is the propensity that state phi electrons have an observable A with values in delta. See Balaguer, page 120. He considers a statement that Balaguer has put forward in this passage. But again, hasn't done what Hilbert did. In referring to the propensity between relation, he's still got reference to the Borel set of real numbers. He hasn't actually got rid of that in the way that Hilbert did. Yeah, that delta is essential because of its connection with... Yeah. Yeah. Thanks for the last question. No questions? I wanted to ask a little bit about the earlier objection about, you know, where we used the example of fragility. And I guess I, in some vague way, I feel, yeah, this sounds like something illegitimate, but I'm not really sure why, because, I mean, I don't want to think about fragility and say, is that a non-actual property? No, no, no, no, it's an actual property. The thing is fragile.

1:22:30 Of course, the way we verify that property or the way it can manifest is by, as you put, chucking a brick at it, but I don't see per se that that convinces me that the property is non-actual, and so what's the objection? I think the objection is that I need to say something more about the nature of these propensity properties. If you think about it in dispositional terms, I can think of it in terms of the classic dispositional versus categorical natures debate. Now, if you think that all dispositional properties are reducible to categorical properties, so that seems an obvious way of spelling out the way in which that dispositional property fragility is actual. It's actual because it's actually reducible to properties of the constituent atoms and particles of the glass. I guess that's ruled out here you don't want that so what's the alternative well then you have to adopt a sort of a dispositional the dispositional view that somehow dispositions are primitive but isn't the suggestion that that's actually already motivated by the probabilistic interpretation in quantum mechanics itself? Well, yeah, I'm sort of going around the houses here. I guess the answer would be yes. You're going to rule out the categorical. But Balaguer hasn't said anything about whether he adopts the dispositions as primitive account. if he does in what sense are those are those actual you said the fragility is an actual property but in talking about it we make reference to possible events right so it's got this here's what I think is really going on here I haven't talked about it it's the modal aspect that's bothering him and how are you going to address how are you going to nominally address the modal aspect of densities. You know, even if you go Lewisian, you know, the Lewisian worlds, those are still non-actual worlds. So the idea is that somehow, in addressing the modality, abstract are going

1:25:00 to kick in, and that's why the charge is being made. I don't see this as a, I don't see this as faithful, I do see it as a problem for Balaguer, because Fields, one would think, doesn't have that problem, right? He's got space-time points, and they are actual, and you don't You don't need reference to possibility in there. By appealing to propensities, Balaguer's got to handle this model. He's got to have, I think what Ottavio should say, in a way, he's got to have a noministically acceptable account of modality. Or a combinatorial thing. Well, maybe combinatorial, but we all know, and those of us who live with John Divers, who's at the moment Britain's greatest global expert, a sort of an empiricist broadly empiricist or non-listic account of modality it's just extremely difficult and I guess what you're saying that's really where Balaguer has got to focus some attention we have time for maybe one very brief question if not then we thank the speaker applause applause applause applause Thank you.