Wiliams on the Passage of Time

I. Introduction

In his paper “The Myth of Passage,” Donald C. Williams argues against the passage of time as it is understood by many proponents of the A-theory of time.[1] One argument in particular that Williams offers is that there is no sense to be made of the notion that time itself moves. Given this, Williams argues that there is no such thing as the passage of time. He further argues that if the A-series of time exists, then there is the passage of time. He concludes that the A-series does not exist. In this post, I will give a reconstruction of Williams’ argument and offer an evaluation of it. In particular, I will offer criticisms of Williams’ argument as well as ways in which Williams can respond to such criticisms. Ultimately, however, I conclude that Williams’ argument does not succeed.

 

II. Summary of Williams’ Argument Against Temporal Passage

To begin, Williams understands the ‘passage of time’ to consist in the ever-moving (and absolute, i.e., non-indexical) ‘now’ of time in the way in which, for instance, ‘presentness’ dynamically runs along McTaggart’s A-series.[2] For example, if there is a series of (strictly partially ordered) times … t_i, t_j, t_k, …, then ‘presentness’ runs along the series of times so that each moment of time comes to successively have the property of presentness.[3] In this way, presentness moves along the series of times. It is precisely this notion of temporal movement that Williams ultimately finds unintelligible. For if time moves, then there must be some rate at which it moves. But, Williams argues, there is no tenable answer that can be given to the question ‘At what rate does time move?’ Consequently, time does not move and hence the passage of time is—as per the title of Williams’ paper—a myth. A corollary of this that is implicit in the text of Williams’ paper is that the A-series does not exist since its existence implies the passage of time. We can thus formulate Williams’ argument against the passage of time (as well as the existence of the A-series) as follows:

1. If there is the passage of time, then time moves (premise).
2. If time moves, then there must be some rate at which time moves (premise).
3. There cannot be a rate at which time moves (premise).
4. If there is no passage of time, then the A-series does not exist (premise).
5. Therefore, time does not move (2, 3).
6. Therefore, there is no passage of time (1, 5).
7. Therefore, the A-series does not exist (4, 6).

With the argument now having been laid out, I turn to a critical evaluation of it.

 

III. Evaluation of Williams’ Argument

In my view, the most important (and contentious) premise is (3). Williams argues that if time (or the present) moves, then it takes a certain amount of time for it to move a certain amount. This necessitates, Williams argues, that it takes a certain amount of second-order time in order for a certain amount of first-order time to move. But this second-order time also moves. After all, if passage is of the nature of time, then surely second-order time moves just as first-order time moves. As such, it must take a certain amount of third-order time in order for a certain amount of second-order time to move. This in turn will generate a fourth-order time and so on ad infinitum. This regress appears to be vicious. Thus, there cannot be a rate at which time moves.[4] The truth of (3) is thereby established.

In my view, there are important weaknesses in this argumentation. One possibility that Williams overlooks that the defender of temporal passage could appeal to, for instance, is that first-order time passes at a rate of one second (of first-order time) per second (of first-order time). Higher-order times are therefore not needed and the regress that Williams identifies is avoided. In response to this suggestion, Williams can argue as follows. A rate is defined as some number of units of such-and-such per some number of units of time. A ‘rate’ of one second per second is mathematically simply equal to one, a pure (i.e., unitless) number (since the units of the numerator and denominator are the same and thus cancel out). But a pure number is surely not a rate of motion. If one asks what the rate at which something moves is, ‘one’ is not a valid answer.[5] Consequently, the suggestion that time moves at a ‘rate’ of one second per second is bogus.

It seems to me, however, that the defender of temporal passage can muster an alternative response. The Aristotelian view of time is that time is the measure of change with respect to succession.[6] Time measures change. If time itself changes, therefore, then we can say that time measures itself, i.e., it is its own measure. This does not seem incoherent. In a similar way, we can say that the standard meter measures distance and so also measures itself with respect to distance (the standard meter is one meter in distance). But this suggestion does not seem to be sufficient to secure a sensible answer to the question of what rate time moves at. One might say that since time is its own measure with respect to succession of change, time moves at the rate of itself, but Williams can respond by insisting that this is an uninformative tautology that does not really answer the question.

A better suggestion is that if time is the measure of change (so that time supervenes on change), we can answer the question of the rate of time by finding a regular process of change in the world and defining the rate of time’s passage relative to that. For example, we can say that time moves at the rate of one day per rotation of the earth on its axis. This seems like a sensible answer to the rate question. Indeed, mathematically speaking, a rate needn’t have units of time in the dominator as was suggested when arguing on Williams’ behalf above. Rather, a rate is simply any ratio of two quantities with (we can allow for Williams’ sake) different units of measurement. This is exactly what we have in this case, and so it seems that it is possible for the passage of time to have a sensible rate.[7] Consequently, (3) seems to be false. Thus, Williams’ argument has a false premise and is therefore unsound. As such, the inferences from the premises to (6) as well as to (7) are blocked. Therefore, both the reality of the passage of time and the existence of the A-series are unfalsified by Williams’ argument.

 

References

Aristotle. (1995). Aristotle: Selections (T. Irwin & G. Fine, Eds.). Hackett Publishing Company, Inc.

Freeman, E. (2010). On McTaggart’s Theory of Time. History of Philosophy Quarterly, 27(4), 389–401. https://doi.org/https://www.jstor.org/stable/25762149

McTaggart, J. E. (1908). The Unreality of Time. Mind, XVII(4), 457–474.     https://doi.org/10.1093/mind/xvii.4.457

van Inwagen, P. (2015). Metaphysics (4th ed.). Westview Press.

Williams, D. C. (1951). The Myth of Passage. Journal of Philosophy, 48(15), 457–472. https://doi.org/10.2307/2021694

 

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[1] Williams (1951).

[2] Ibid., pp. 460-461; cf. McTaggart (1908).

[3] I will leave aside the debate over whether ‘presentness’ for McTaggart is a monadic property or a relation. For discussion of this debate, see, e.g., Freeman (2010), pp. 395.

[4] Cf. Williams (1951), pp. 463-464.

[5] Cf. van Inwagen (2015), pg. 75.

[6] Cf. Aristotle, Physics IV.11; Irwin & Fine (1995).

[7] Williams might object to this by insisting that a rate of motion specifically must have units of time in the dominator. In response, this does not seem obviously true to me, and in any case, it should hardly be surprising that what might be true of motion in general might not be true of temporal motion in particular. Temporal motion is plausibly a sui generis kind of motion perhaps in a similar way that the expansion of space itself (as contemporary cosmology holds is a real phenomenon) is a sui generis kind of expansion. Expansion in general involves the enlargement of something in space, but the expansion of space itself evidently cannot be expansion in quite the same way. Nevertheless, the expansion of space can be coherently understood in terms of changing spatial objects/points, and I am suggesting similarly that temporal motion can be coherently understood in terms of temporal (and changing) objects/processes.