Vermeir Koen / Ori Belkind Concepts of Space & Time in C17th - Newton as Philosopher workshop, Brussels 2008
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Recorded at Concepts of Space & Time in C17th - Newton as Philosopher workshop, Brussels (2008), featuring Vermeir Koen, Ori Belkind. From the Michael Wright Collection, held by the Archive Trust for Research in Mathematical Sciences & Philosophy.

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0:00 So he uses concentric circumferences to describe the acceleration of motion instead of the plastic. So I think that here we are explicitly laying the geometrical problem in the form of... And here it seems to suggest why we have a new circumference in place of the triangle of speed. Because there it's more likely that we can have, that, often, the dark circles are at the center. You can establish a one-to-one correspondence between the points, but still they become visually different. And it happens in the days of acceleration. That, you know, the degrees of speed, more and more degrees of speed are acquired. So, you know, um... Galileo would say that all the problems of this time period, which has arrived here after the interval of time period B, has acquired an infinite number of degrees of speed, but when the body comes here, it's still infinite, but here it is infinite because of this infinity. Okay? So in both notions, there is a passage for infinite degrees of speed, but still, this is the degree of speed that we need. This is part of this one. I really liked your paper and in a way you got me so involved that I'm going to ask an egocentric question. So of course I was thinking about more when you were talking about things I'd been studying yesterday. And as I see it now, thinking maybe more in your terms, more seems to suggest that Well, matter is divisible, but not indivisible at the end. Mathematical space is infinitely divisible, but real space is indevisible. Which is even much weirder non-ism or bism than Newton. And so I was wondering how this might fit in your whole story. I don't know. What I know, I think that when a young human writes that this is minimum.

2:30 I don't know, but I'm not claiming that they all do. I think it can be that more of the age of this. I don't think that once these people start reading about these two phenomena, they end up, they want to explain both of them, end up with a certain amount of information. So I'm not sure, I don't know where we discuss this specific topic. But I always think that the only end up we touch more than once you start discussing this specific topic. My point is that the reason why in all this, the work of all these atomists, what is most important for them, their priority is clearly the theory of nature, and they sacrifice, in a sense, their theory of motion, which ends up being inconsistent, because they wanted to make it consistent with their theory of nature. For Garibayev, the theory of motion was clearly... At a certain point, he sacrifices his former atomism because he also wants to establish this internal coherence. So, in a sense, it is the main, the chief interest that determines the choice being made. Because all these atomists end up with theories of motion that are completely absurd, so it is not their main intent for them to build a theory of motion. Does he discuss the problem of space and not very much about space? Well, he's not so interested in motion, he's definitely interested in matter, and also prime matter, and that, of course, theory, and that probably accounts for his, but then again, Newton's view is kind of, but it's something about space and so forth, so we might see that different lineage going, and that's an argument. No, I know that Newton... The interesting thing about Mohr also is that motion is so intimately linked to spirit.

5:00 And even space is spirit, so motion isn't even possible without it. Yes, but at the same time you might guess that you said that mood treats spirit and mind in different ways. So it can be that in his case the reason is because the notion of space is more linked to the notion of spirit than it is to the notion of man. So that just this notion of spirit breaks this link. Okay, now this is interesting. If you have another entity besides matter, you should be defining compositions into matter, then the space will be more similar to the sphere, then you'll be splitting the sphere up and closing it. Well, he says spirit is like this matrix, it has motion unless you extend it. The question is, how do we get from... First you have intangible space that's spread out, which we can talk about, because it's an action. Intangible space, or taking central space, Spread out into various fields and get different kinds of things. So, he moves on from that kind of talk about cool space and empty space.

7:30 All, you know, I think this is really your idea of the concept of math. If you take the same kind of mathematical space and then let it reside in different volumes of space, you have the basis of the concept of math there. So, the thing is that what he's doing is taking the notion of intangible space and Thinking about their fashions and empty space in one reading, so that might fit into your story about this moment of remaining extra time and continuity of their fashions. It's a nice moment to end the discussion, and I'm very excited to see what we will be talking about, so it will be useful. So, first, I'm jet lagged. Second, I'm kind of lying to all my brothers in my stomach. So I'm just going to give an overview of what I'm going to talk about. I'm going to talk about the basic theory of mathematics in particular, where we argue for space. What I'm going to try to do in this talk is to suggest that there is an internal reading of the argument presented in the school of mathematical space. So let's first account what exactly is the reason for thinking, for Newton thinking, about absolute space. So the first thing we're going to do is we're going to survey traditional readings. One can actually differentiate between two traditional readings as follows. First is the real traditional one, which is taking Newton's argument to be an inference to the best explanation of numerical forces. So we can start out with saying we have this phenomena called inertial forces, we can actually observe it in rotating bodies, accelerating bodies, and the best way to explain this phenomena is to posit the existence of absolute space.

10:00 And many commentators think that this is basically what Newton is doing. He's inferring the existence of absolute space because absolute space is the best explanation of inertia. Some people say it's not that Newton says that absolute space is accurate, it's just that Newton is able to provide a definition of absolute motion, and given that definition of absolute motion, that's basically what Newton is doing. There's no physical account of the relationship. What I'm doing in this talk is to argue that the second line of interpretation is our way to choose between If I were to use this argument as the definition of absolute motion, thinking about an argument as an inference rather than an explanation, I would choose the latter interpretation, but I still think that there are points of the scolium that provide a misunderstanding, or at least a very conical picture. So, that would be the first part of the survey, the additional accounts. And the second part that I'm going to try to do is walk through some of the basic definitions in basic terms, and I've realized that this is not actually defined in today's day, but I'm going to just think about the basic terms that we discussed and go into these basic terms, and I'm going to try to suggest that the way that these terms were used in some of our understanding of these arguments. So I'm going to walk us through this place.

12:30 And then I'm going to go through quantity of motion, and then I'm going to talk about the distinction between true and apparent motions, and the distinction between absolute and absolute motions. And part of the argument is going to be that we have to keep those two things apart. So then, we're going to look at the first argument, which is that Descartes' problems are conceptual. The concept of the concept is going to be the definition of true motion, how do you define true motion, how do you define the other kinds of motion, the quantity of motion, and basically the conceptual argument is going to be, The first argument from Schilling to be the chief of an existing scientific paradigm, to take this argument more conceptually, to require a temptation to be set without space or without from him, we're not going to be able to define the content of account one.

15:00 I'm a little bit more hesitant about this argument. This argument is very implicit in the account though. There are additional meanings of what is an entrance to the best explanation? What is the nature of that entrance? Usually, the account goes as follows. We start out with a phenomenon. We come up with various kinds of explanations as to how is this phenomenon possible? What makes this phenomenon? What's responsible for it? We might come up with one explanation, an ideal gas. We have a theory, it's called the caloric theory, it's often called caloric, and there are two kinds of substances found in caloric, in free caloric, and we might look at the phenomenon by dealing with this theory.

17:30 And then we might think about different kinds of explanations, we might think about the existence of molecules that have mechanics that we might deal with. We have various kinds of explanations floating around, and this one, because it has several problems, And we end up with the explanation that we like best, and we say, we can't really think of any other better explanation, but it's actually, the explanation is available, we ask one, we replace the argument with the case of the developed emotion, from the properties of emotion, and then the second set of, given from the causes of emotion, and that's what we're facing, and the third type of argument is easy to provide, the bucket experiment, where we start off with a bucket, bucket and a little bit of water, What we try to do is run through a big push. So initially when the bucket is rotating, the water is at rest, so you know something happens to the bottom of the bucket.

20:00 The cavity there, that's the inertial flex forming. As I stop the bucket, the water will explain how it is at rest. In case number four, case number three, the water at rest on the same key cavity, this non-existent case, is the thing that this cavity is related to. The motion of the water relative to the object itself would be one possible explanation is that the motion of the star, you have to see what this explanation is about, it doesn't work. This zero and zero is also the same kind of motion, but there's a difference in the cavity, so you cannot correlate the motion of the water relative to the star.

22:30 The explanation is one can obviously see that motion cannot be completely fixed. In much detail here is an explanation. He is calling them carefully. He doesn't exclusively that nobody has offered the motions of water relative to the earth, it's impossible to look at it and explain that there are some other relative frames that will be found when he talks about this. We'll think that he would claim that the motions of water relative to the earth is also excluded by his argument, but not to never claim this. If we look at the center of the map of the whole universe and we use that as a universal reference frame, then meaning we can provide an intuitive explanation of the whole inertial set. But this is not something that's actually taken up in Newton. There's no way from what is the nature of the explanation given here.

25:00 We actually understand what comes out. We've ruled out all relative. There's a kind of tension here. On the one hand, we want to say that there's an inference that could have said, or what Keith had said, that space has causal powers. There's actually no causal relationship between some of these bodies, because bodies can move in a straight line aren't even a little bit that hot, because the only function these forces have is to cause bodies to move in a straight line, so it's not much of an explanation. Newton's laws and the law of gravitation can be used as an empirically valid set of laws that enable us to do the concept of absolute motion of space, just implicitly defining the concept relative to some of the basic differences.

27:30 Let's see what the argument is. I'm not obsessed with the correspondence between clocks and magnets in this position, but my point was that we should rate Newton's dichotomy on this one. Let's see how Dichotomy defines the notion of place. I'm going to argue that Newton's account of what place is in Soconium actually takes up using that as a polemic with Dichotomy about how to go about thinking about place. Is Soconium wicked yet? Yes, it is wicked. Sorry, I had to use it. We always take space to be an extension in length, breadth, and depth. There is an internal to the things it is sometimes as an external place is exactly the same as space,

30:00 but an external place we'd be thinking of as being the surface immediately surrounding what is in place. So if you think about bodies, Descartes, really what differentiates a body is the fact that it has boundaries and is spaced. So, for us to actually individuate the body, I have to look at the boundaries that are kind of relative to that. So, I think that what he's trying to say is that there are two concepts of the place. This is the body. One thing about the place of the body, I think, is that I have to sort of bifurcate the notion of the place into two concepts. One is the actual intention that this body takes out, and this is the internal place of the body. The boundary that this has relative to the external place would actually be this body relative to itself had a notion of it. And both of these are significant because if you wanted, for example, to describe the motion of the body, change of external place. One place where the body was relative to its surroundings, then you had another place relative to it. This is not the position of the body or its atomic surface in place the way that Descartes does, but what he's basically saying, it's not that take this internal place that the body has, but replace it simply as part of the larger space, whatever that part that this body takes up is depending on the space, either absolute or relative.

32:30 If I think about this whole space, the whole space is going to determine what the nature of the place is. Now we have a little argument. Without thinking about places, one of the arguments is not going to be the relative position of the body to other kinds of bodies, part of the place that the body takes up within a larger space. You shouldn't take it to be the position of the body, or why should we not take it to a place? You said this is the argument, that the places of equal size are always equal, while the surfaces are for the most part unequal, conditionally speaking. There are a number of ways to understand the concept of place. If you want to understand the concept of place, you need to recognize, according to Newton, that place carries with it a certain kind of quantity, the actual volume of the place. We cannot understand that the place has the volume that the place has.

35:00 The place is just a position of the body because the body, again, doesn't carry. It's really important to understand here that by place, Newton does not mean relative positions. Place doesn't mean there are relative positions of the body either face or to the body. The body takes a part of space that the body takes up. Now there's a part from their places, and that's the place of the whole is the same as the sum of the whole body. We may have a lot of arguments here, but it seems as if what he's trying to talk about is first there's kind of a particle relation between motions of the body.

37:30 The concept of quantity in motion is the general outline of the concept of motion. Motion is simply a mode of the matter which is moved and has a determinate quantity. In this, we easily understand that they are constant and in the universe as a whole while they are in any given part. Thus, if one part of the matter moves twice as fast as another which is twice as large, we must consider that they are the same quantity both in each part. If one part slows down, we must suppose that some... There's some other part of people who try to beat that by the same amount. So, what is the similarity in language between the sum of the motions, which is the part that you find out here, and the quantity that's determined by various parts having the same quantity. An important concept that applies to motion is that you have to underwrite this particular quantity for quantity of motion. He says, the way that he explains it is the motion of the whole is the sum of the motions of the body, there is twice the length of motion, and if it has twice the velocity, there is four times the motion.

40:00 Same language as the motion of the whole is used in parts. Here you can use the parts definition. Think about it. Emotion is the product of size and unit definition. So the question is, what is going on in the problem of the parts? We can tell a little bit of the story of the genealogy of the concept, the management and creation story. We may suppose that there are any design hypothesis that is manifest to reflect them, assuming all properties of the co-operative particles except that it would be regarded as a motion test.

42:30 We can suppose that the content of the building is not always maintained in the same part of the space, or even there, according to certain laws, yet so that the quality and shape of the intangible space will not change, there will be no property of body which it does not possess. So how does this creation story work? How do we think about this creation story? Well, there's this empty space in the beginning, and then God takes a certain portion of space, a certain part of space, and then makes it impenetrable. Then the third step is, if you suppose that we move around with certain things that the interior of the body, I mean, probably the core of the interior of the body, is that. The philosophy is that we have a distinction in Newton between tangible space and non-tangible space. There was a young author discussing density, inertia, and tension. When he discussed density, he first discussed it as intangible places that are spread out in volumes. Those would have different densities as a result of contention. But then we can imagine the supposed parts of the force that the whole composite body All of the components of the body, there is not the least particles of the planet, and there is a perfect mixture of infinite divided particles before any such reasoning ensues a complex environmental decision.

45:00 So take the various intentual spaces that we have, contract them or expand them to different sizes, then take a mixture, a perfect mixture, a uniform mixture of all plates and force it into space. And quantities of motion are quantities that indicate the various parts of the body. These are quantities that have been derived from the parts. Let's talk about the volume that takes up. And the part formulation that you have in describing the volume, then you have to make sure that that is consistent with the notion of quantity of motion. I mean, that's the volume that you're describing. One distinction I want to mention is that for Descartes, we have to distinguish between all the apparent motions of the body and the two motions of the body. The stand-by motion is not uncommon in physics, but it is important to the truth. Descartes aims to assign a determinate nature to it, to give a determinate property motion to a particular body.

47:30 Then Descartes thinks we need to develop the motion after the motion of the body from possible states to another relative motion. So if you think about the motion of this body, its relative motion is the motion of the body relative to its absolute motion, its relative to the body relative to the space that we're going to explain about and the distinction between that and science. And to manage that, there are three types of arguments to think about the motion. The first argument is, there's a complicated motion that the parts which keep you in a position to support participate in the motions which are told. And here we have the same kind of language that is trying to find the emotion. So if you think about the motion of this block, first we can think about the individual emotions of each part, and then we can think about the motion of the top of the thing. If we want to keep the concept of quantum emotion, we have to suppose that all the emotions of the parts contribute to the concept, otherwise we don't have the concept. This is what he said. It is a property of motion. This is an important property to keep in mind. This is something that I think all commentators are missing. When he's using the language of the property of motion, he actually, he wants to make sure that we have a consistent account of this property of motion. The property of motion cannot be determined by means of changing of these factors. The car's definition of proper motion cannot be sustained. Why is that?

50:00 The exterior bodies ought to be regarded not only as being addressed, but otherwise all contained bodies besides being subject to true motion of the contained bodies and are regarded as being addressed. Containing bodies are the devoted side of them that the outer part of the pole and the shell moves so does the terminal also, without being changed to the position of the shell moves as part of the pole. And this is a little computing, so I don't want to get distracted by what's going on. The clock definition of true motion, not only does it mean that the parts are moving, Even though the whole composite thing is moving, the inner parts are not, according to Descartes. This is the definition of true motion. The composite has to be a mass from all the motions of the parts. Because the inner parts are not moving according to Descartes. The composite cannot be moving, so the composite cannot amass its motion from the parts. The two concepts cannot work together. I have two ideas of motion. One is supporting the quantity of motion in parts that participate in the whole. On the other hand, motion is defined, you know, if both of these claims are true, we have to give up either the first argument, the first argument is the doctio ad absurdum of the Carver's theory of motion, and it's just a conceptual analysis, there's no empirical analysis, no analysis of phenomena, there are no intellectual reports, an internal critique of, if we want to give up this definition of true motion, we have to...

52:30 If this is given up, I have to come up with another definition of two-motion and do that, and obviously that, there's other opportunities in how concrete alternatives can be carved out. It's not a universal argument. It's in some places where somebody takes up relative surroundings. So if we start out with that definition of place, that's an argument as to why he's going to say, basically his argument is going to be, if we're going to define the quality of motion, the quality is going to be a determinant quantity. We move places in a way to quote a property akin to the preceding one. So again, he's talking about the part of a location that is implicit in quantity of motion, that's why he says a property akin to the preceding one, is that when a place moves, its place in it moves along with it, or the body moving away from a place, it moves in every whole motion, moving the body away from the initial place, going from this place away to the next place, and so on in the involvement of the example of Taylor.

55:00 I'm going to go into that a little bit closer. What is essentially going on here is, let's say this body moves relative to the space that's around it. So the body itself and the place. So if we want to analyze the motion, I need to take into account both the quantum motion of the body and the moveable places in it. So analysis of quantum motion is always going to be involved, if we just accept relative places, it's always going to involve the relative place in which the body moves. The quantum motion of this body, I mean, it contains it. I want to figure out how much quantum motion is the quantum motion of this group. It contains space, etc, etc, etc. So, an analysis of quantum motion is never going to end. In short, after quantum motion, we determine that only when we move to unmoving places, and therefore, in one type of speed that I have referred to, we know that the motion is moving.

57:30 Moreover, the only places that are unmoving are all those that keep in a position, one another, from infinity to infinity, and therefore always remain movable and constant. So this is really how we reach the conclusion that absolute space exists. The whole analysis began by saying that in the far space the body occupies relative to the surrounding space. It's not that the place is going to be defined by relative positions. It only makes sense once we define the motion relative to absolute space and the body. So the whole analysis begins by accepting the fact that we need to start a science of motion by articulating quantities of motion and the whole concept begins there and again it's conceptual analysis. It's not that we're starting with certain effects and then trying to explain them. One thing to notice is that this shifts the whole significance of the argument. It's not that there's one set of effects playing by absolute states. It's that general notion of quantity of motion requires absolute states. And that's a much wider claim. It means that if you want to have a causal relation using positive motion, then you need to have the whole science to actually point to this argument is actually required.

1:00:00 I really enjoyed this and I can tell that you might have been expecting crap. Let me just ask you a question about Descartes. I have lots of questions, but I don't want to talk about them. The view is that parts can be motionless, and of course this conflicts with his view of time now, and all these strange examples, these are things strange to me, so they turn on the shelves, and I'm like, well, who knew about that? Why would anyone think that the olive pit doesn't move when you throw the olive well? You read Descartes, you know why. But I guess I wasn't entirely sure why you think Descartes admitted to the idea of the parts. I thought, he definitely probably thought so. Is this to do with his view of volume, time, speed, meaning, and quantity? I wasn't quite sure how that was connected. It's really the relationship between God and the world is such that God is superior in quantum motion, but he's basically in control of the whole world by looking at the quantum motion that's around him. So you don't really have a concept like that. You need to have a concept of quantum motion. Yeah. But, you know, they correspond to this indeterminate number of parts during the course. It's going to be indefinite. Vision. Each part of the assumption.