Thursday, May 15, 2008

Subjective Time and the A-Series

I’ve been lightly dabbling in philosophy of time (not very successfully, if last week’s letter from the APA is any indication) and wanted to throw out a couple of thoughts. The present line is largely in response to Alexander Pruss’s recent post on the famous “Thank goodness that’s over” argument, first formulated by Arthur Prior (no way is that name a coincidence, though perhaps “Paster” would have been more appropriate). Pruss argues, based on time-travel scenarios, that subjective time differs from objective time and then suggests that subjective time is logically primitive. I agree with these points. But then something a bit odd happens: Pruss claims that both subjective and objective time are B-theoretical, which seems to be the opposite of what his conclusions imply.

For those unfamiliar with the distinction, it derives from McTaggart’s “The Unreality of Time” and breaks up theories of time into two possibilities. According to A-theorists, the past, present, and future are real. According to B-theorists, we can arrange all temporal events according to earlier/later relations. B-theorists generally argue that earlier/later relations serve as truth-makers for all superficially A-theoretic claims; A-theorists respond that the B-theory cannot account for temporal indexicals or for the subjective experience of time.

Pruss’s argument, basically, is this: Let’s say that, while suffering from a headache, I go back in time. My headache magically vanishes in the very instant I find myself in the past. In this case, I think that my headache was in the past, but in fact it is clearly in the future. So it is in the future in objective time, but in the past in my subjective time, something we can mark by pointing out that the headache is something I remember, and am glad to have gotten over, but am not anticipating or dreading. The conclusion, then, is that subjective time can differ from objective time. This seems to imply that whatever may be said about objective time, subjective time is A-theoretic, since subjectively my headache is past, even though objectively the event of the onset of my headache may be later than my gladness that the headache is gone. Pruss disagrees, however, on the grounds that the A-theorist must hold that there is an objective present, and the view under cannot give us an objective present—at best, it could only give us a subjective present, and that is something the possibility of which Pruss denies. Before going on to that point, a brief aside about the form of Pruss’s argument.

His suggestion that subjective time is B-theoretic seems to go through the excluded middle. Here's a sloppy schematization (hopefully I have it right):

(1) Time is either A-theoretic or B-theoretic.
(2) A-theorists claim there is an objective present.
(3) Subjective time lacks an objective present.
(4) Subjective time is not A-theoretic. (from 2&3)
(5) Therefore, subjective time is B-theoretic. (from 1&4)
This won't do, since the B-theory is not just the fall-back position for anyone who doesn't think there is an objective present. After all, one can reject the present while still rejecting that all relations between events are reducible to later than/earlier than relations, and someone who rejects this is certainly not a B-theorist. So by the same token, we might argue that a theory that insists on the reality of past and future, even if it leaves out the present, is still an A-theory. At least, it is clearly not a B-theory, and although it differs from most A-theorists in leaving out the present, by insisting on the reality of past and future it retains some A-theoretic status.

But why should we reject the present? One problem, I think, rests on Pruss’s taking subjective time to be a variety of internal time; in fact, he argues that all objects have internal time, and subjective time just seems to be the form of internal time that applies to conscious entities. If we understand subjective time on this model, however, I do not think we are really talking about anything subjective; only something individual. If I pin a chronometer to myself, leave another one on my desk, and then go time traveling (without the desk), then the two chronometers will diverge (if I jump a hundred years into the future, spend five minutes there, and then return to ten minutes after my initial jump, my personal chronometer will have measured five minutes; the one on my desk, on the other hand, will have measured ten; immediately after the first jump, in the future, the chronometer on my desk will show a hundred years, while my personal chronometer will show no time has passed). But neither chronometer, as far as I can tell, is showing subjective time: both show objective time, it’s just that one is measuring objective time relative to my time-traveling body, while the other is measuring objective time relative to the non-time-traveling world. The very distinction between internal and external time, as Pruss presents it, seems to me to collapse: external time just is the internal time of the universe taken as a whole.

My point, then, is that Pruss’s view of subjective time doesn’t seem to be subjective: it seems to be objective time within a frame of reference that is only a part of the universe (my body) rather than the universe itself. It is on these grounds that Pruss thinks that we should reject the notion of the present. His arguments against the idea of a subjective present are, in this regard, very telling. In response to some prodding from Heath White, with whose comments I think I am in agreement, Pruss writes,

Surely the right answer to the question: "At noon, what time is subjectively present to x" is noon. (The subjective present isn't just the time one believes to be present--one can be wrong about what time it is!) What sense could there be in saying that at noon, it is 1 pm for x? Would that mean that x is literally now in the future? No. So, at every time t, the time that is subjectively present to x is t.
And Pruss correctly concludes that this is not a subjective present. But of course if we think of the subjective present in terms of “noon” or “1 pm”, then we’ve already set up the problem in such a way as to exclude the subjective present: after all, clock-time is an intersubjective convention, designed to co-ordinate the activities of human beings according to the regular order of objective time. And so it would not make any sense to speak of a subjective present as involving a point on a clock-face that differs from the objective present point on the clock-face.

But if we stop modeling subjective time on objective time, this difficulty goes away. Pruss grants, after all, that there might still be a subjective past and a subjective future. If so, then clearly we need not dispense with the idea of a subjective present: the standpoint I occupy, from which I have a subjective past and a subjective future, just is my subjective present. I doubt very much that we could have such a subjective present without reference to a subjective past and a subjective future, but this isn’t overly problematic, since “past”, “present”, and “future” are interrelated concepts; they come bundled together. Whenever we correctly apply one of them, we must be able to apply the other two as well. And this is effectively what distinguishes the A-series from the B-series. For on the B-series, no point in time logically implies an earlier or a later point; every point on the timeline has its own independent reality. But on the A-series, every point is interdependent. This, of course, is roughly why McTaggart thought that the A-series could not be real. But his attempt to cleave off the subjective from the real is not one we are bound to accept.

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