Against Pointillisme about Space & Time — Part 2

0:00 And a partial effect of earlier position. Partial because the forces regime in the intervening time period is also crucial to the causation of later position. But he wants the present velocity to be a partial cause of later position. The orthodox view makes present velocity a logical construction of recent and imminent history. It's a logical construction of what has recently happened and what will soon happen. being logically involved in later position orthodox velocity is logically entangled with later position and it cannot for a Humean be a distinct existence from later position and so for a Humean it cannot be a cause of later position that's Humeanism about causation you see so this is the motivation it means that velocity, being functionally defined, has nomological but not logically necessary relations to the functional role. And this does have a paradoxical consequence. By paradox I mean strange, but it's something that Thule would have to accept, though he doesn't explicitly say it, but it is in the spirit of his position. It means that it's logically possible for the particle to go to the right while its intrinsic Thulean velocity points to the left. That wouldn't happen nomologically possibly, but it would happen logically possibly. Well, I won't spend any more time on Thule. I've made it obvious enough what I think so let me go to Robinson and Lewis this brings us back to the topic of persistence Robinson in 1989 is discussing the rotating discs argument he makes a certain proposal he eventually denies it

2:30 Lewis in 99 revives it and endorses it. They don't use the word shadow velocity. That's my word for it. They're going to propose a notion which is meant to be, it's a property, it's vectorial, it's intrinsic to a point, it has the numerical value of instantaneous velocity, but it ain't velocity. which they consider to be extrinsic for the reasons we've discussed. So it's like shadow velocity. And I regard it as, again, metaphysical postulate, not necessary because we need not be pointillist. So on this slide, this is their doctrine. Then I will object to it. First of all, they say a vectorial property at a point can after all be intrinsic to the point actually number one is for Robinson in 1989 what we would call the stumbling block he makes the proposal but then he admits to the reader I can't really believe the first step directionality connotes relationality and therefore extrinsicness but let's go with the flow of the idea number one we put it down Then they say, and again I'm not going to try and defend this, but this is the doctrine, it is trying to solve the rotating disks argument, the propagation of continuous matter through space-time involves such a property at every point. The properties distinguish the straight world lines of the non-rotating disk and the helical world lines of the rotating one. they do this because the vector is always time-like that's a space-time jargon for it's like a velocity and in fact it always points in the very same direction as the instantaneous velocity never mind the phrase for velocity if you don't know it and then the point is Robinson and Lewis agree that persistence over time and this is common to both sides of endurance and perjurance persistence over time is a matter of appropriate causal relations

5:00 or relations of qualitative similarity over time maybe a chain of small causal changes make for a large change or a chain of small qualitative changes build up to be a big change but there is lines of causal and qualitative dependence And they claim that their postulated property is to determine or subvene these relations of similarity and these relations of causal dependence. And therefore it will determine the lines of persistence. So this is the proposal. And the challenge is, thank you Lewis and Robinson, but tell us more. schema of how it's going to solve all the problems but you must tell us more what this quantity you're saying there's something that isn't velocity but has the same value actually for solving the problem the numerical value the magnitude doesn't matter what matters is the direction in space time of this vector so in physics terms you would talk about a time like direction field on a patch of continuous matter and to solve the problem Lewis and Robinson really need a time-like direction field which is always parallel to the velocity direction field so tell us more and Lewis tries to tell us more and he admits it's hard but he says it might go something like this and he calls it a vector field actually not a direction field his idea is that you can specify the vector field by saying that if there's been matter along a certain integral curve of the field up until a certain point then there's matter at that end point as well or Ceteris Paribus there is why Ceteris Paribus? because he's doing conceptual analysis very close to the details of physics. He wants to allow that matter might self-destruct or in some other way not appear at the end of this trajectory,

7:30 having been there along it. So this is what he in fact says in the 99 paper. I won't read it out. I'll mention that Lewis being, of course, clear-headed, says this is not a law of causation, it is a law of succession, means I read it as in particular the final statement that there will be matter at the end of the curve that has to be regarded as a material conditional that then, that final then so the the trouble is say I, this is my objection that Lewis' proposal is far too weak it hardly constrains the vector field at all in continuous matter there are ever so many integral curves which will conform to the specification he gives this is written out in some detail here he makes a certain proposal that's paragraph one it's too weak because every smooth vector field on an open region has integral curves if you imagine that he can stipulate in a non-circular way that it has to be time-like and it has to be smooth enough then he's saying a certain thing but this hardly helps to distinguish his proposal from alternatives all those alternatives okay, now I have a final closing proposal which is floating another notion which is in a sense a peace pipe for Lewis and Robinson and this is my final thing, if I have three is it possible to have three minutes so I've so far made a criticism of Lewis and Robinson But I would like to throw in one more topic for further discussion, and it is something which is halfway to what Lewis and Robinson want. They want a cousin of velocity that does not presuppose persistence,

10:00 that does not have any extrinsicality. well there is a way of in a sense avoiding the presupposition of persistence I'm going to introduce a quantity which really will be well defined I will call it because it will be weak it will be without presuppositions of persistence I'm going to call it velocity with a W this is a mnemonic which works a lot better in English than in German for obvious reasons so I apologize but I will call it velocity for weak and without presuppositions and it is going to use Hilbert's epsilon operator as a way of disposing of the presuppositions another German hero that's the merit So, what do I aim for? The first paragraph tells you, I aim to have the value at a time t of the velocity of the object O must be defined in such a way that, unlike velocity, you cannot infer from the value that O exists, or that it has a differentiable world line in some neighborhood. Okay? so that's what I want if you now imagine that you have a term which stands for velocity for the normal notion velocity it can be empty it can lack a bearer it can lack a referent because either O does not exist for an open interval or it does exist for an open interval but this limit of the averages of velocity is badly behaved it exists but there's some kind of sharp corner in the world line now I have to admit that the slide is a little bit rough here because it is possible to be differentiable at a point but not differentiable nearby but I'm going to simplify and assume that velocity at a point

12:30 has the implication that you are differentiable in your space-time trajectory in some neighborhood maybe very short of that point. And in this sense, I would ask the mathematicians amongst you for some help because the books are full, so to speak. The books give many examples of something like continuous but nowhere differentiable. have not found a clean statement of what are the implications for the good local behavior of a curve of it being differentiable at a point so I would ask your help about that if I could know that from a maths book I could make a better statement of this presupposition not diff but at the moment I'm going to just be simple and strengthen the orthodox concept of velocity and think of it as implying differentiable world line well as we know Frege Frege proposed that empty terms should be given what my logic teacher called a dustbin referent that was to say something like the empty set so the greatest prime in Frege's system would be assigned in order to make the language logically well behaved that terms had reference it would be given a dustbin referent, the empty set if we do that when this presupposition of velocity fails if we say the velocity of an object O that only exists at T will be the empty set because stupid O it doesn't exist at other times so it cannot have a velocity If we say that, our dustbin referent will give the game away. Anybody will tell, of course, that it doesn't exist. And so, because the empty set is not a normal value of velocity. So, we'll tell that the presupposition has failed. And therefore, we will instead use the Hilbert epsilon operator to assign the referent arbitrarily. In that sense, you will be unable to tell. So, what's going on? Well, we take the velocity. The velocity of O at a time t in a given coordinate system is this triple of real numbers.

15:00 It's a triple of real numbers v, such that for some open interval, and therefore any smaller one, O exists throughout it and has a differentiable world line in it. v is the common limit of average velocities for times t-dash compared with t as you allow t-dash to approach from above or below. Now after calculus you will take this in your stride, but it's worth writing down and celebrating whatever else we do this morning, the achievement of two millennia of thought in acquiring this subtle concept of instantaneous velocity. uses a material conditional it will be vacuously true for all triples v if the antecedent is false for all the i around you can see now what I will do I mean it will be false if velocity's presuppositions of continued existence and differentiability fail and therefore I would like to write down this entire open sentence as f f of v The displayed open sentence. And I would like to form, this is my final move, the velocity as epsilon v of fv. So, final slide. By the Hilbert-Bernay's semantic rule, this velocity is equal to the instantaneous velocity if O is a very well-behaved object that does exist and therefore has a velocity. it's some arbitrary triple of real numbers if the presuppositions fail and in this sense I've got the desired features the values don't give the game away and this is in a certain sense halfway to a Lewis Robinson proposal but it certainly would not fulfill the role in their argument that they need it in no sense solves their problem but it is a sort compromise. But the main message is that pointillism is false, not that there's a compromise with it. Thank you.

17:30 Thank you very much for this beautiful bridge building between the philosophy of physics part and the metaphysics part. Before I take your question, I just announce That's already on the board at the entry. But today, the talk by Maurice Stanley in Section 1B, Room C, Wittgenstein and Time, has been canceled. And the talk of Iharat Tomoaki has been shifted on the place of this talk of Maurice Stanley. So the talk of Tomoaki won't be at 6.10, but at 5.25. So please take note of that. I was glad that you at the end said there has to be, I mean, a careful distinction between if people talk about tensors and vectors as extrinsic properties, this is not very good because these are first of all mathematical entities. But what is meant physically is the properties of a force field or a direction and so on. I think this has to be kept apart very sharply. This is my first one, but this is only a short remark. But the second point, which seems to me, I mean, for me, more important. Frege was concerned with empty terms. But the important thing, I think, are incomplete terms. So the question is whether the objects in a theory, say the classical mechanics objects or the points or material points or space-time points or whatever they may be, whether they fulfill these kinds of principles. Kant has already such a principle. for instance he formulate is that every object has to have one property of the pair of opposite, of the pair of possible opposite properties. But already Meinung, before quantum mechanics, Meinung said this is not a good requirement

20:00 because we in many cases we have incomplete objects objects do not obey this principle and then you have it then one has to talk really about very different things but and also that the distinction between extrinsic and intrinsic sometimes is not so clear anymore if you take in account that the objects at least in modern physics in also if you introduce only quantum mechanics. Because the freedom which is allowed by the statistical law for the individual case leaves also open a lot of properties. So certain properties are not determined. Objectively not determined. So what is at stake then is the incomplete object, which does not have all the possible properties at a certain time, at a certain state. Well, thank you. I think I can be more confident about your first point than about the second. The second involves many issues that I don't quite understand, but I do agree about the first point. I think it's, in getting clear about Thule and Bricker, it was important for me to distinguish vector and vectorial property. And it is, in everyday philosophy talk, almost always people say, can vectors be intrinsic, if they're discussing this topic. But it's fine, provided you mean, clearly in your head, by a vector but it can be confusing if you don't distinguish but concerning your second point well I am sympathetic but I think I don't have that much I can helpfully add unless we discussed for example objective chance which amongst the metaphysicians I am discussing would count as highly extrinsic

22:30 perfectly grammatically correct and philosophically alright to attribute it to the individual case but the implication there's a very widespread, subtle and in its details controversial implication about other cases. So that's just to but I guess they wouldn't see incompleteness there, they would just say extrinsicality is widespread even when people talk about objective single case chance, a neo-Humian would say that does not mean intrinsic but this would mean that one has the opinion that there are, so to speak, hidden parameters which determine everything and which we just do not know. In other words, this would be an epistemic interpretation of, for instance, a statistical law. But I think this is rather untenable. I think this is the question, I mean, this is an ontological question, of course, whether you admit that there are degrees of freedom in reality, and not just as degrees of ignorance. Thank you, that's helpful follow-up, because I should have made it clear, if a neo-Humian like Lewis says, and Lewis would certainly say this, I have the concept of objective single-case chance, I believe in it, but being a neo-Humian, I consider it extrinsic. I want to reassure you, they do not mean I hypothesize unknown degrees of freedom, I must be epistemic. The other material that is implied by the attribution of the single-case chance, the implications are about, roughly speaking, other similar cases across the whole history of the universe. So you should think of these neohumians as trying to do better than traditional frequentism. It's the global pattern of occurrences which subvene the truth of the individual's single-case chance attribution.

25:00 But the determination or the supervenience is meant to be much more subtle than the traditional frequentism. and they then admit that it's very hard to say exactly what. Yeah, but it's not meant to be epistemicism in disguise. If I understood you correctly, you hinted around that one of the broader targets in your antipontalism is human supervenience in general, and I mean including the supervenience of laws of nature facts of the world in a moment, that sort of thing. I was wondering if you could comment on that, if that really is one of your larger targets. I actually do not want to deny the tradition of the regularity analysis of laws of nature. In the metaphysics class on the metaphysics of laws of nature, I would like to be a Lewisite, a Mill-Ramsey-Lewis systematic regularity theorist. And so this part of Humean supervenience I'm attracted by. But of course it doesn't need the pointillism that was my target and was in that quote from 1994 Lewis. So, no, in fact, I'm very sympathetic to the idea of neo-humanism as at least a great deal of the story of the world, in particular perhaps laws of nature, is determined by the patch-by-patch of current facts in the world. So, in fact, in this, I regard myself as in the kind of Mill-Ramsay-Lewis-Ehrman tradition in this way, because John Ehrman has written also with co-authors on exactly this topic. Herr Tichtmeier, please pass on the microphone. Since you argue about the alternative pointillism

27:30 pointillism, it's of course undesirable. If you presuppose in the definition of other alternatives, you consider pointillism, but it seems to me that the alternative endurance versus peradurance does just that. and not only Lewis, of course, is a pointillist. You said the perjurientists has temporal parts and temporal parts are object at T. So what's T? It's a time point. And most, I will talk about this in my talk and I gave, I made this point before and the reaction is mostly, well we can translate it into relation, relation to some, a T means relation to some measuring event, simultaneous to that and that, but it doesn't work because the object has to be a subject of predication. So you cannot have some relational property and then combine it with an object and still have the object as a subject of predication. Well, I think concerning the second half of what you said, I would disagree. We have to talk privately. But the first topic you mentioned about perjurance and endurance and surely perjurance requires the rock at a time it is a time point I should have emphasized more clearly I try to be friends with perjurance by suggesting to them that they should not believe in instantaneous temporal parts they could have a metaphysics in which there are arbitrarily short-lived temporal parts

30:00 but none that are absolutely instantaneous and in these other papers I argue that almost all the jobs which a perjurantist wants to do can be done by a sufficiently rich family of non-instantaneous ones, and then there is a little bit of width with which you can, you have enough material to distinguish the two disks. So, well, it's not going to satisfy you, but that's my answer. My question is about the possible relation or distance between a non-quantilist interpretation of classical physics and quantum theory. I mean, it's true, of course, that there are dramatic differences, but I wonder in what way non-pointilist interpretation of classical physics might be closer to quantum theory or a sensible interpretation of quantum theory than a pointilist one. And the idea is are there so to say blurred properties of regions of space-time in classical physics already if you interpret them in a non-quantilist way? Thank you. I'm afraid the answer is a bit boring, in my opinion. I don't think that there is blurred properties of regions in classical physics. I think there are ways in which the subtleties and problems of classical physics give you glimpses of quantum theory of the necessity of quantum theory and in my opening or second slide I wanted to stress that classical mechanical structures underpin quantum theory in deep ways but I don't think it is anti-quantilism that is really going to give you a line of thought let alone an argument for indefiniteness or blurredness.

32:30 So these issues about the mystery of quantum mechanics, about superposition and so on, they, I think, are sui generis to the quantum in that way. Yes, of course, but for example, how about the position of a material object in space over a certain time? Might that not be a blurred property classically but non-pointilistically? Ah, yes, okay. Well, it's true that, and I suppose there's probably a literature on this in the philosophically oriented foundations of mechanics, but it's not anything I know references for. But you can imagine that just as in advanced probability theory people propose, let us have probability functions whose values are intervals of real numbers, because that is more realistic than point-valued, real-number-valued probabilities. You can imagine trying to model the macroscopic description of an object's position by assigning it an interval of real numbers if it's moving on a line or a region of space. and you can imagine trying to mathematize that in a useful way and in a sense you have blurred the position of the object and I can imagine that in machine vision there are formalisms for that but I would say that this is probably scientifically important, it's probably been done, but it's not going to be really leading into the quantum Okay, Julian Barber Do all these endeavors, like people like Lewis, really have any value for modern theoretical physics? It seems to me extraordinarily removed from the really central issues of theoretical physics today. I mean, quantum gravity and general relativity, the interpretation of it, goes right back to the Leibniz-Clarke correspondence, I think you would agree. It seems to me from the quotations you've been giving from people like Lewis that they have an unbelievably naive notion of space and time, if I may say so.

35:00 Is that a fair comment? you've put your finger on it that most of these modern English language analytic metaphysicians when they talk about space-time object causation whether they're endurantists or perjurantists whether they're Humean supervenience or not however they wish to analyze law of nature they will tend their examples to talk about matter classically. They will talk about particle. They will not normally say point particle, but it will not matter for the example whether it is extended or not. They will talk about particles and spatial points and space-time points. So it is absolutely standard, unthinkingly, to bring in as counterexamples to theses or examples in support of a thesis thought experiments about matter in motion in a space or space-time which is conceived, as the philosophers say, substantivalistically. And if you then are all, absolutely. And if you then, very often, it doesn't matter for the philosophy purpose that they have adopted substantivalist talk. But if they are actually doing space-time and objects, as their philosophy of nature topic, many of them will be substantivalists. In that sense, they are disconnected from the modern debate in general relativity and quantized general relativity. They're disconnected from the fact that relationism is a live issue. In that sense, they're disconnected. There is a more general disconnection, course. I mean, even if you are a substantivalist, it's hard to do stochastic geometry. Classical stochastic geometry is not really very well-defined, but there's a general discussion in a substantivalist way about an indeterministic universe. So there isn't formalism, but then again the physicists haven't given formalism in great

37:30 detail to discuss such a thing, but there isn't much connection between the two communities of how you would write down such a thing. So there's two little parts of the answer. well I'm afraid that we are already over time so I have four or five people on the list so I'm sorry that we have to conclude it at this point but I'm sure that there's Jeremy's here through Friday that there's enough time to settle many of the issues in private discussions so thanks the speaker and all discontents once again Have an unjoyful lunch. We reconvene at 2.15 in sessions.