Spacetime (Newtonian)

Transcription

1 McTaggartʼs Denial of the Reality of Time Letʼs begin with a picture: Spacetime (Newtonian)

2 The contents of a position in time [and I take T0, T1, etc. to be positions in time ] are called events. (458) Each of the planes in the picture above consists of, or is a set of, events. The events in each plane all happen at the same time; they are simultaneous. Note that each plane is infinite in extent and is really three-dimensional. Itʼs difficult to indicate this three dimensionality in a picture, but one should not forget about it. These planes are often called hyperplanes, since they are 3-dimensional planes in a 4-dimensional space. A position in time is called a moment. (458) Each of the hyperplanes depicted above is a moment. One can also call them times. Each of T0, T1, T2 and so on is a time. Times are exhaustive. That is, every event appears in at least one plane. Events have temporal as well as spatial positions. Times are mutually exclusive. That is, since the events that we are considering are instantaneous events or point events, no event appears in more than one plane. The times slice or foliate the four-dimensional space that is (partially) depicted above. 2

3 Moreover, they do so uniquely (in the pre-relativistic way of looking at the world). Each event occurs at one and only one moment or time. In our picture T2 is later than T1, and T1 is later than T0. Of course we can say the same thing if we note that T0 is earlier than T1, and T1 is earlier than T2, since ʻearlier thanʼ is the converse relation of ʻlater thanʼ (and vice versa). Since the times are ordered by (say) the relation ʻearlier thanʼ, the times above form what McTaggart calls a B- series. McTaggart says that the sort of relations one finds in a B- series are permanent. (458) If M [a time or moment, or perhaps just an event] is ever earlier than N, it is always earlier. (458) This observation raises two questions. First, the picture above is supposed to be a picture of time, but time is much more closely associated with change than with permanence. As McTaggart says: It would, I suppose, be universally admitted that time involves change. (459) Now ʻinvolvesʼ is a vague word, so it is not quite clear what McTaggart is claiming, but it does seem to be plausible that time indeed ʻinvolvesʼ change and perhaps also that change ʻinvolvesʼ time. Where do we find change in the picture of the B series above? 3

4 Our events are point events. Imagine a very brief, localized red flash or a very quick finger-snapping. The former may be red, the latter loud. The events can not change these properties. It is true at all times to say that the flash at t0 (say) is red and that the finger-snapping at t1 is loud. These propositions cannot change their truth values and, accordingly, the events that are their subjects canʼt change their properties. And how in the world could they, if they exist for only an instant? Can events change their time order? Again, McTaggart (plausibly) says that they cannot. If N is ever earlier than O and later than M, it will always be, and has always been, earlier than O and later than M, since the relations of earlier and later are permanent. (459) No change here. Or shall we say that one event M merges itself into another event N, while preserving a certain identity by means of an unchanged element, so that we can say, not merely that M has ceased and N begun, but that it is M which has become N? (459-60) McTaggartʼs remark is a bit cryptic, but here is what I make of it. He poses a dilemma. If M and N are really the same event, then nothing has changed. An event just continues to exist. If they are distinct, then he thinks he has already shown (in a previous argument that I have not yet presented) that the case is impossible. But we have seen that no event can cease to be, or begin to be, itself, 4

5 since it never ceases to have a place in the B series. (460) And indeed, on page 459, McTaggart argues exactly that. Could we say that, in a time which formed a B series but not an A series, the change consisted in the fact that an event ceased to be an event, while another event began to be an event? If this were the case, we should certainly have got a change. But this is impossible. An event can never cease to be an event. It can never get out of any time series in which it once is. And as, by our present hypothesis, time is constituted by a B series alone [as in the picture above], N will always have a position in a time series, and always had one. [The B series is exhaustive.] That is, it will always be, and has always been, an event, and cannot begin or cease to be an event. If this point is granted (and we will eventually return to reconsider it), then it looks very much as if there is no way to find change in the B series. It is static, as some say, non-dynamic, a block universe (to misuse William Jamesʼs phrase). This claim immediately leads to the second question about the B series, the Peggy Lee question: Is that all there is? 5

6 McTaggart says no. The answer, many philosophers think, must be no. Something, the dynamic element of time, seems to be missing in the picture. Letʼs call that ostensibly missing element the transitory aspect of time or temporal becoming or temporal passage (or just passage) or the passing of time or the changing of time. Here is a famous characterization of the transitory aspect of time, from C. D. Broadʼs Examination of McTaggartʼs Philosophy. The third, and much the most puzzling, set of temporal characteristics are those which are involved in facts of the following kind. An experience is at one time wholly in the future, as when one says "I am going to have a painful experience at the dentist's tomorrow." It keeps on becoming less and less remotely future. Eventually the earliest phase of it becomes present; as when the dentist begins drilling one's tooth, and one thinks or says "The painful experience I have been anticipating has now begun." Each phase ceases to be present, slips into the immediate past, and then keeps on becoming more and more remotely past. But it is followed by phases which were future and have become present. Eventually the latest phase of this particular experience becomes present and then slips into the immediate past. There is the fact which one records by saying "Thank God (on the theistic hypothesis) that's over now!" After that the 6

7 experience as a whole retreats continually into the more and more remote past.# [266-67] This dynamic or transitory aspect of time seems to be essential to the the idea of time and also to be missing from the picture of the B-series above. So to fill the gap Mctaggart adds a second series, naturally called the A- series. McTaggart puts it bluntly: Without the A series then, there would be no change, and consequently the B series by itself is not sufficient for time, since time involves change. (461) What is the A series, then, and how does it bring life to B series? As I would put it, how does one fit the A series into spacetime? Positions in the A-series are distinguished as past, present, and future (rather than earlier or later). But these positions are not permanent or static, as the B series positions are. McTaggart says that an event, which is now present, was future and will be past. (458) Moreover, McTaggart says that the A series is essential to the nature of time, adding that any difficulty in the way of regarding the A series as real is equally a difficulty in the 7

8 way of regarding time as real. (459) He says that the A series is essential to time because without it, the remaining B series seems to lack exactly what is characteristic of time, passage. (He doesnʼt think the A series is real, but that part of his argument we wonʼt cover in these notes.) It is worth noting at this point that the A series is supposed to add something to the B series that the B series lacks, passage. If it is to do so, it must be something distinct from the B series, so that it can be added to the B series. In order to do this job, the A series cannot itself be understood in terms of the B series, else it would not be an additional element, something extra, new, and different. If the A series could be (or somehow had to be) understood in terms of the B series, then the B series itself would have the resources to explain or model or exhibit temporal dynamism, the passing of time, even though it appears inert. While keeping this point in mind, letʼs see what the A series might be and how it might add passage to the B series, to Newtonian spacetime. Many serious philosophers believe that it is essential to add an A series to the B series, and there are two ways to do it that are often suggested. The first is to add, somehow, motion to time in the B series. Let us then say, as everyone does, that time flows, and it is this flow that the A series adds. When a river 8

9 flows, for examples, a small body of water in it is at one place at a given time t0 and then at another place (downstream) at a later time t1. If we paraphrase this sentence to describe the flow of time, we would have to say that a given time (say t0) would at some time (t0??) be at a given time (t0??) but then later (t1, say) at another time (t1). But is it nonsense both (1) to talk of a time being at a given time and (2) to talk of itʼs changing from one time to another time. It is very hard to see a way around talking nonsense when it comes to flow. This is a crucial point. One once sees that there is a problem here at all, one will sooner or later see that there is a difficult problem here. One graphic way to add motion while trying to circumvent the problem noted above with flow is to think of the present, or The Now, as a kind of moving light, illuminating one hyperplane after another. This is called the moving spotlight view (after C. D. Broadʼs description of it in Scientific Thought [1923] of the present as like the light of a policemanʼs flashlight moving along the stakes of wooden fence). We can imagine the hyperplanes of the B series lined up in order (as in our picture) and The Now gliding along it from past to future. All the other A determinations (like ʻ5 minutes agoʼ or ʻ1 year in the futureʼ) are arranged in a 9

10 series and similarly glide along the stationary B series. At each instant each hyperplane of the B series is aligned with one of these A determinations, though which one changes from instant to instant. Thatʼs the dynamic part of this picture. Of course, one could equally well imagine the A series as fixed, with The Now shining a very sharp light down onto the B series, which glides steadily underneath it in the direction of future to past. In this picture, events come steadily from the future, are illuminated by the present for an instant, then disappear into the past--a bit further past at each successive instant. Since the motion here is purely relative, one is free to take either series as fixed and the other as moving. But what is motion? The motion of an object is the change of its spatial position with respect to time. An object O is at place1 at time1 and then at place2 at time2 (and perhaps at the intervening places at intervening times if the motion is continuous). If we then try to describe, in parallel, the motion of The Now we are forced to say that it is at t1 at t1 and at t2 at t2. But this statement seems empty. Of course at t1 it is now at t1, and of course at t2 it is now at t2, just as at place1 it is here at place1... At this point, philosophers are tempted to say that the motion of The Now with respect to times itself takes place 10

11 in a second time dimension (sometimes called hypertime). The inevitable response to this line is that, if hypertime is to be a genuine temporal dimension, it too must have a moving Now, the motion of which is in respect to yet a third temporal dimension. We are clearly off on a course of reasoning that requires an endless infinite hierarchy of temporal dimensions, a surprisingly baroque and ontologically profligate answer to what seems a simple problem. Infinite hierarchies created out of thin air are methodologically suspect. Finally, letʼs look again at what motion is. The motion of an object is the change of its spatial position with respect to time. An object O is at place1 at time1 and then at place2 at time2. If we want to understand motion, then, we must understand time, but our object was the reverse: we were proposing to understand time (or at least its dynamic aspect) in terms of motion (the motion added by the A series). It looks as if the proposal to understand time in terms of motion is at best circular, and moving in circles will get us nowhere. Remember what weʼre doing. We could explain the B series clearly, as in our picture at the beginning of these notes, but it seemed to lack something essential to time, dynamism. We propose to add passage or dynamism to the B series in terms of motion, but now find that motion requires time for its understanding. And all we have in hand to give us this understanding of time is the B series, 11

12 which is precisely what is supposed to be inert and to lack motion. If the B series all by itself could suffice to give us an understanding of motion, then the A series would not (or at least might not) be needed to add motion to it. But we have agreed (so far) that the B series is inert. (Just look at the picture of the B series again. Itʼs still sitting there, unchanged.) When we get desperate enough, perhaps we will revisit this claim. Meanwhile, letʼs try a second way to import temporal dynamism into the B series. Time, as we noted above, is intimately related to change. Let us then suppose that the A determinations that McTaggart speaks of are really properties, like ʻ is presentʼ or ʻ is 10 minutes pastʼ, and so on. Events cannot change their ordinary properties, as we noted above. Take any event--the death of Queen Ann, for example--and consider what change can take place in its characteristics. That it is a death, that it is the death of Ann Stuart, that is has such causes, and that it has such effects--every characteristic of this sort never changes. Before the stars saw one another plain the event in question will still be a death of an English Queen. And in every respect but one it is equally devoid of change. But in one respect it does change. It began by being a future 12

13 event. It became every moment an event in the nearer future. At last it was present. Then it became past, and will always remain so, though every moment it becomes further and further past. (460) This unique respect in which events can change sounds encouragingly like Broadʼs description of the transitory aspect of time. The suggestion is that the transitory aspect is best understood as (1) supposing the existence of a series of A properties and (2) supposing that the passage of time is events constantly changing their A properties or, as McTaggart puts it, A characteristics. The second suggestion to import dynamism into the B series is to understand passage as a kind of qualitative change (or property change). But what is qualitative change. Think of a standard example: a leafʼs changing from green to red. The leaf may be green in July but red in October. It has changed colour. Notice that it is the leaf that has changed its properties. the leaf had one colour in July, but persisted until October, when it had a different colour, red. Persistence--the persistence of the leaf--is persistence through time. Understanding qualitative change involves understanding persistence through time, but what we are trying to do at this point is to understand time (or at least its essential 13

14 dynamic aspect) as a kind of qualitative change. Again we find investigation moving in a circle. In addition, the A properties do seem to appear magically, to be made-up entities. And since the events in our B series are point events, the do not persist the way a leaf does. They occur, and they occur only at or for an instant. They are not good candidates to undergo qualitative change, as McTaggart noted, and it is puzzling how they could undergo the special kind of change that the A properties are supposed to bring in their train. We have now looked at the two traditional ways that philosophers have sought to understand the passage of time. The B series is clear enough, but it does not seem to suffice. Efforts to add to the B series seem to lead to infinite hierarchies, to meaningless statements, or to small circles in our reasoning. Might not a reasonable person then just write off this alleged dynamical aspect of time, its passing, as a myth? If the dynamical aspect of time, its passing, is a myth, then isnʼt time itself a myth, for what is more central to or characteristic of time than passage? McTaggart put it a little more bluntly: Without the A series then, there would be no change, and consequently the B series by itself is 14

15 not sufficient for time,since time involves change. (461) 15