What is Metaphysics?. John Heil
the reader, can say truly that this occurrence is past. For his part, Armstrong, stepping onto the Moon, can say truly of this moment – July 21, 1969, 2:56 UTC – that it is present, and anyone, prior to July 21, 1969, could have said truly that it is in the future. As far as the A series is concerned, it is true of this moment that it is past, present, and future! Were time real, were time “out there,” every moment of time would have to be past, present, and future, and that, McTaggart insisted, makes no sense.
You can see how the argument works by considering a spatial analogue. The A series places you in the boat, a spectator on the passing scene as you float down the river. Upstream, the willow is afore (ahead of you), later it is abeam (directly opposite you), and, still later, abaft (behind you). Its being true of the willow that it is ahead, abeam, and abaft reflects the fact that, in describing the willow as ahead, abeam, or abaft, you are not describing features of the willow. Subtract you from the picture and it would make no sense to say that the willow, or anything else, is ahead, abeam, or abaft.
This leaves us with the B series, which, in effect, places you on the riverbank, adding you to the scene, undermining any sense of temporal passage. The appearance of time’s passing must be in us, a mere appearance with no foundation in reality. So says McTaggart.
2.2 A Fourth Dimension
This talk about the passage of time is all well and good, but if the goal is to understand time, why not ask the experts? Physicists, after all, have had a good deal to say about time. Time, they tell us, is a “spacelike” fourth dimension inextricably bound up with space. The universe is a four-dimensional McTaggartesque block. Its occupants can be at temporal distances from one another analogous to spatial distances. Your passing the willow and subsequently passing a granite outcropping are both there, at a temporal, as well as spatial, distance from one another. You, as you read these words, are really a stage or temporal part of a you extended in both space and time.
This should remind you of McTaggart’s unchanging, B series universe, which lacks the resources to accommodate temporal passage. The passage of time would seem to belong only to the appearances, not to reality.
As McTaggart observed, the thought that things change and objects move from place to place would seem to be at odds with a four-dimensional B series picture. When a tomato ripens, changing from green to red, what you really have are adjacent temporal parts or stages of the tomato. The tomato is analogous to a highway that passes through varied terrain. The highway is shady in some places, bumpy and in need of repair in others. These features of the highway are all there at once. Similarly, one temporal part of the tomato is green, another red. What you do not have is a persisting object that at one time is wholly green and, at a later time, wholly red. The tomato’s changing in color is really a matter of its parts – its temporal parts – being differently colored.
In the same vein, despite appearances, when you walk to the store, there is not a single you fully occupying successive regions of space, leaving behind vacated regions. Instead, stages or temporal parts of you occupy adjacent regions of spacetime. Your temporal parts are strictly analogous to your spatial parts. Just as your right half and left half are distinct spatial parts of you, you yesterday, you today, and you tomorrow are portions of a temporally extended you.
Even if you were sanguine about all this – and few are – you might worry about what happens to free will given a four-dimensional universe. We like to think that we control our destinies, at least up to a point: by acting today, you help make tomorrow what it is. But if a later you is merely a part of the same temporally extended entity that includes an earlier you, in what sense could you affect the future, even a little? You could no more bring it about that your future self is one way rather than another than one segment of a broomstick could bring it about that another segment has the character it does.
This idea is so appalling to some philosophers that they regard it as a reason to rewrite physics. If that strikes you as special pleading, ask yourself how it could be rational for you to plan, as you assuredly do, for a future that is no more subject to your influence than the past is.
Spatial and Temporal Parts
Some philosophers think of spatial and temporal parts as parts of the occupants of space and time. On such a conception, your head and left hand are distinct spatial parts of you. What of your temporal parts? If these were parts of you analogous to your head and hand, you – all of you – would never be anywhere at any given time. The you here now is simply a slender piece of you. Many philosophers reject temporal parts thus conceived.
I prefer to think of spatial and temporal parts differently. Your head and hand are not spatial parts of you, but parts of you that occupy particular regions of space. If you sit down and raise your hand, your head and hand swap their locations. Similarly, a temporal part of you is not a piece of you, but you at any given time.
This way of thinking about spatial and temporal parts can escape notice because we often use locations in space and time to refer to their occupants. When you slice a tomato in half and give me the top half, you are giving me a portion of the tomato that once occupied a spatial region above another spatial region occupied by the bottom half of the tomato.
Analogously, a temporal part of you is not one of a number of parts that make up you; it is you – the whole of you – at any given time.
2.3 Going with the Flow
What are the options? Some philosophers, the presentists, agree with McTaggart that temporal passage requires the A series, but regard this as a feature, not a bug. Only the present is real, the only moments are present moments. The present moment is not something that arrives from the future and recedes into the past. Because the future and past are not on a par with the present, nothing could literally be in the past or future, no moment could be past, present, and future, so there is no incoherence.
Anyone who embraced the four-dimensional block universe would see this kind of response as profoundly inadequate. A proponent of four-dimensionalism could agree with the presentists that McTaggart was right, both in thinking that temporal passage required the A series and thinking that the A series is internally flawed. McTaggart’s mistake was to suppose that, without temporal passage, without the A series, nothing is left deserving to be called time. Four-dimensionalists would respond that, what is unreal, what is a mere appearance, is not time, but the passage of time.
You do not need to be a four-dimensionalist to find temporal passage baffling. If time passes, at what rate does it pass? One second per second? Could time speed up or slow down, or pause, and for how long? If time passes or flows, this would require something for it to flow through. A river flows because the water it comprises moves relative to the terrain through which it flows. What would play the part of the terrain in the case of time?
Space, maybe? Aside from worries about the physics of spacetime, this would seem to be at odds with the conviction that space, and its occupants, are themselves in time, participants in the flowing. If the terrain flowed with the river, however, in what sense would the river flow?
I shall have more to say about the status of time in chapter 7. For the moment – ha! – the discussion will have served its purpose if it has convinced you that the problem of reconciling appearance and reality is inescapable, not something cobbled together by philosophers engaged in unconstrained flights of fancy.
The problem confronts scientists no less than ordinary citizens. Scientists rely on the appearances to build, test, and deploy instruments designed to probe reality. But it is hard to square the universe revealed by those instruments with the appearances. Difficulties we encounter in making sense of the appearance of time’s passing and of accommodating this appearance to the physics of spacetime