Abstract
In this paper I distinguish interpretations of the question ``How fast does time pass?’’ that are important for the debate over the reality of objective becoming from interpretations that are not. Then I discuss how one theory that incorporates objective becoming—the moving spotlight theory of time—answers this question. It turns out that there are several ways to formulate the moving spotlight theory of time. One formulation says that time passes but it makes no sense to ask how fast; another formulation says that time passes at one second per supersecond; and a third says that time passes at one second per second. I defend the intelligibility of this final version of the theory.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Belief in instants of time seems to imply a belief in a relation of absolute simultaneity, and so to conflict with the theory of relativity. But in this paper I will ignore problems raised by the theory of relativity.
As I have defined “the B-theory,” B-theorists need not believe that there are infinitely many times. So a B-theorist could believe that there is just one time. How, then, does such a B-theorist differ from a presentist, who also believes there is just one time?
Although they have the same ontology, this B-theorist and a presentist have different ideologies: the presentist employs primitive tense operators (like “It will be the case that …”), and the B-theorist does not.
Strictly speaking, a defender of the moving spotlight theory could think that time is discrete (isomorphic to the integers), or that it has a beginning (so is isomorphic to the positive real numbers or the natural numbers) or an end; and there are still other possibilities besides.
On the moving spotlight theory of time, “the NOW” is not a thing, like a rock or a pen or a paperclip, that is located first at one time, and then at another. I will, however, sometimes talk as if it is, because it allows me to abbreviate what would otherwise be more complicated sentences. All this talk, though, is just a shorter way to talk about changing facts about which time instantiates the property of being present.
I have changed the name of the argument and the wording of the first premise. Markosian calls this argument “The Second Rate of Passage Argument.”
In fact Markosian proposes the rate of passage argument as an interpretation of (one of) Smart’s arguments in this passage.
I have been asked: if tomorrow I run 8 miles in an hour, will that be because I will be running faster tomorrow than I did today, or because time will be passing more slowly tomorrow than it did today? On the present way of understanding our question, the answer is “both.” That may sound odd; but since this rate is not a rate of objective becoming, it should not worry us.
Markosian’s defense of objective becoming is actually more subtle. He does not endorse the response I have discussed. Instead he includes it in a list of several possible responses, and does not choose one of them as his preferred response.
Strictly speaking, distance in supertime and distance in time are incommensurable on this theory. So saying that the temporal distance between t1 and t2 is equal to the supertemporal distance between s1 and s2 is like saying that my height is equal to my age. (Both are nonsense.) For simplicity I ignore this problem in the text. One way to solve the problem is to pick special units: even though it makes no sense to say that my height is equal to my age, it does make sense to say that my height in meters is equal to my age in decades. So we could say that (*) is true when supertemporal distances are specified in superseconds and temporal distances in seconds. That is how I will understand (*).
(A similar solution that does not depend on any particular unit of measurement is to state (*) using distance ratios rather than distances. These ratios are dimensionless—the same no matter what units we use to measure distances in time and supertime.).
If we formulate (*) along the lines mentioned in footnote 10, then it will not follow from (*) that the answer is “one second per supersecond.” In that case, the NOW’s rate in seconds per supersecond will depend on just how we define “supersecond.” But however we define it, its rate of motion will be constant.
It is not enough to say that it will be the case that (exactly one time is NOW). Intuitively, that only forces there to be one future point in supertime at which exactly one time is NOW. We want to force it to be the case that at every future point in supertime, exactly one time is NOW. (Of course, the tense operators are not to be understood as quantifiers over points in supertime; the supertime talk here is just an aid to understanding.).
Markosian (1993) proposes alternative grounds on which a believer in objective becoming may reject (P1).
Ever since Kaplan’s work in semantics, B-theorists have stopped defending the claim that “It will be the case in five seconds that P” is synonymous with “At the time five seconds after t, P” (where t names the time of the utterance). They say instead that in any context these two sentences express the same proposition. (See the papers in Oaklander and Smith (1994).) That is what I mean by “have the same truth-conditions.”
See Maudlin (2007) for a different response to this argument.
References
Fine, K. (1994). Essence and modality. In J. Tomberlin (Ed.), Philosophical perspectives 8: Logic and language (pp. 1–16). Atascadero: Ridgeview.
Markosian, N. (1993). How fast does time pass? Philosophy and Phenomenological Research, 53, 829–844.
Maudlin, T. (2007). On the passing of time. In The metaphysics within physics (Chap. 4). New York: Oxford University Press.
McTaggart, J. M. E. (1908). The unreality of time. Mind, 17, 457–474.
Oaklander, N., & Smith, Q. (Eds.). (1994). The new theory of time. New Haven: Yale University Press.
Olson, E. T. (2009). The rate of time’s passage. Analysis, 61, 3–9.
Price, H. (1996). Time’s arrow and Archimedes’ point. New York: Oxford University Press.
Prior, A. N. (1958). Time after time. Mind, 67, 244–246.
Smart, J. J. C. (1949). The river of time. Mind, 58, 483–494.
Smart, J. J. C. (1953). The moving ‘now’. Australasian Journal of Philosophy, 31, 184–187.
Smart, J. J. C. (1980). Time and becoming. In P. van Inwagen (Ed.), Time and cause: Essays presented to Richard Taylor (pp. 3–15). Dordrecht, the Netherlands: D. Reidel Publishing Company.
van Inwagen, P. (2002). Metaphysics (2nd ed.). Boulder, CO: Westview Press.
Acknowledgment
Thank you to Phil Bricker, Fred Feldman, Ned Markosian, Kris McDaniel, Agustin Rayo, Ted Sider, Stephen Yablo, the audience at the 2010 Pacific APA meeting, and referees at Philosophy and Phenomenological Research for their comments. It was comments by Sider on another paper of mine that got me thinking about MST-TST. And I owe a special debt of gratitude to Markosian for his comprehensive responses to an earlier draft of this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Skow, B. On the meaning of the question “How fast does time pass?”. Philos Stud 155, 325–344 (2011). https://doi.org/10.1007/s11098-010-9575-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11098-010-9575-3