Causal Approaches to the Direction of Time

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CAUSAL APPROACHES TO THE DIRECTION OF TIME

What account is to be given temporal priority and of the direction of time? One natural view is that no accountis needed (Oaklander 2004), a position that can be defended by arguing, first, that one immediately perceives the succession of events (Bergson 1912), and second, that if one can immediately see that events stand in the relation of temporal priority, then the concept of that relation is primitive and unanalyzable.

There are, however, important objections to this view and to the supporting argument. As regards the latter, the question arises whether perception of change does not turn out, on closer scrutiny, to involve not only a momentary visual state but also short-term memories of immediately preceding visual states. If so, then the acquisition of a belief that something is moving or changing will involve inference, and succession will not be something immediately perceived.

As regards the view itself, one problem is that temporal priority is a relation with certain properties: It is impossible for an event to be earlier than itself; if A is earlier than B, B cannot be earlier than A; and if A is earlier than B, and B earlier than C, then A must be earlier than C. If the concept of the earlier than relation is analytically basic, then no account can be given of these necessary truths: they will have to be treated as synthetic a priori. By contrast, if the idea of temporal priority is analyzable, then it should be possible to show that these necessary truths are analytic.

One can assume, then, that the concept of temporal priority must be analyzable. What are the possibilities? The answer is that three main types of accounts have been offered. First, philosophers who favor a tensed accountof the nature of time often maintain that the tensed properties of pastness, presentness, and future are basic properties and that the tenseless temporal relations of simultaneity and temporal priority are to be analyzed in terms of those tensed properties (e.g., Broad 1933, Sellars 1962, Prior 1967). According to this view, then, the direction of time logically supervenes on the tensed properties of events.

A second approach holds that if events stand in the relation of temporal priority, and if time has a direction, then such facts must be reducible to properties and relations recognized by physics. The idea, accordingly, is to analyze the relation of temporal priority and the direction of time in terms of such things as the direction of increase in entropy, the direction of the expansion of the universe, or the direction of irreversible processes (e.g., Popper 1956; Grünbaum 1971, 1973; Sklar 1974).

A third possibility is a causal approach. Here the idea is, first, that causal processes involve a direction, and, second, that causal facts are more basic than temporal facts, with the result that the direction of time can be analyzed in terms of the direction of causation.

How do these three alternatives fare? As regards the first, there are two crucial objections. First, it is clear that the relation of temporal priority cannot be analyzed in terms of the tensed properties of pastness, presentness, and futurity alone, since one event may be earlier than another, though both have the same tensed property of pastness. One needs, then, to introduce additional tensed concepts, such as those of one event's being more past than, and more future than, another. These latter, however, are not plausible candidates for primitive concepts, since then one would be unable to explain, for example, why event A's being more future than event B entails that A is future and B is future. However, if one attempts to analyze those concepts, the natural way of doing so is in terms of the concept of the past, and the concept of the future, with the concept of temporal priority. Such analyses, however, will make the analysis of temporal priority in terms of tensed concepts implicitly circular.

Second, even the concept of futurity itself is not a plausible candidate for a basic concept, since it is plausible that it is concepts that pick out immediately given properties and relations that are analytically basic, and the concept of the future does not pick out a property of events that can be immediately perceived. However, if the concept of the future must be analyzed, how is this to be done except in terms of the idea of the present with the idea of temporal priority? So, once again, the attempt to analyze the relation of temporal priority in terms of tensed concepts can be seen to be circular.

In the case of the second approachwhich involves analyzing temporal priority in terms of specialized scientific concepts, such as those of entropy and the expansion of the universethere are also two main objections. First, most proposals for a scientific analysis of temporal priority entail that it is possible that the universe might undergo a temporal reversal. For the universe, rather than expanding forever, may stop expanding, and then begin contracting. Moreover, if this were to happen, entropy would at some point stop increasing and begin decreasing. The direction of time cannot be analyzed, therefore, in terms of the direction of increase in entropy or in terms of the direction of the expansion of the universe, since such analyses entail the unacceptable consequence that the resulting contraction of the universe would be earlier than the time at which the universe stopped expanding.

Second, there are logically possible worlds that contain temporally ordered events, but no increase in entropy or expansion of the universe. Consider, for example, two uncharged particles rotating endlessly about one another due to gravitational attraction. Accordingly, the concept of temporal priority cannot be analyzed in terms of such scientific concepts.

The conclusion, therefore, is that the first two approaches to the analysis of the concept of temporal priority appear unsatisfactory. If this is so, one is left with the third alternativethat of analyzing temporal priority in causal terms.

A Causal Theory of the Direction of Time and Temporal Priority

The idea of analyzing the concept of temporal priority in causal terms is not a recent development, since it dates back at least to Gottfried Wilhelm Leibniz (1715/1969) and Immanuel Kant (1781/1961). In more recent years it was advanced by the mathematician Alfred A. Robb (1914, 1921), and by philosophers such as Henryk Mehlberg (1935, 1937), Hans Reichenbach (1956), D. H. Mellor (1981, 1995, 1998), and Michael Tooley (1987, 1997), among others.

Before setting out a causal theory, it will be best to address an initial objection, the thrust of which is that it may well be, as many philosophers and scientists believe (e.g., Lewis 1976), that backward causation is logically possible, and, if this is so, how can the direction of time be defined in terms of the direction of causation?

One response, adopted by some advocates of a causal approach (Mellor 1981, 1995, 1998; Tooley 1987, 1997), is to argue that backward causation is not logically possible. However, a different response is available. For if one considers, for example, Dr. No traveling backward in time, then it is natural to say that the temporal ordering of events inside his time machine is opposite to the temporal ordering of events outside of it. If so, then in a world where there is backward causation, one needs the concept of the local direction of time, which can be defined in terms of the direction of causal processes in that region. One could then go on to introduce the idea of the overall direction of the universe, defined, as David Lewis (1976, 1979) suggests, in terms of the direction of most causal processes.

How can temporal priority be analyzed in causal terms? A natural starting point is the following postulate:
(P ) If A causes B, then A is earlier than B. This gives one a sufficient condition for one event's being earlier than another, but it does not provide a necessary condition. So how can one arrive at necessary and sufficient conditions for one event's being earlier than another?

To arrive at an answer, consider the following two plausible claims:
(Q ) If A is earlier than B, and B is simultaneous with C, then A is earlier than C.
(R ) If A is simultaneous with B, and B is earlier than C, then A is earlier than C.
These two postulates, with (P ), then entail two further, more comprehensive propositions relating causation to temporal priority:
(S ) If A causes B, and B is simultaneous with C, then A is earlier than C ;
(T ) If A is simultaneous with B, and B causes C, then A is earlier than C.

However, in addition, these two conditions, in conjunction with the fact that temporal priority is a transitive relation, entail another, much more encompassing condition:
(U ) If {A 1, A 2, , Ai, , A n1, An } is a set of n instantaneous events such that, for every i < n, either Ai causes Ai +1, or Ai is simultaneous with Ai +1, and if, in addition, there is some i < n such that Ai causes Ai +1, then A 1 is earlier than An.

Principle U, entailing, as it does, principles R, S, and T, and more as well, is a comprehensive principle relating causation to temporal priority, and that it follows from the conjunction of the noncausal principles Q and R with the modest claim involved in P shows how powerful principle P is.

Principle U, of course, still gives one only a sufficient condition for one event's being earlier than another. The idea now, however, is that the sufficient condition that is given by U is also a necessary condition. If this is right, then the relation of temporal priority can be analyzed as follows:
A is earlier than B
means the same as
For some number n, there is a set of n instantaneous events {A 1, A 2, , Ai, , An 1, An } such that, first, A is identical with A 1, and B is identical with An ; second, for every i < n, either Ai causes Ai +1, or Ai is simultaneous with Ai +1; and,
third, there is some i < n such that Ai causes Ai +1.

This proposed analysis does, of course, involve a temporal notionnamely, that of simultaneity. However, that will be an objection to the analysis only if the concept of simultaneity itself has to be analyzed in terms of temporal priority. The latter, however, does not seem likely, since it would seem possible for there to be a world that consists of a single moment, containing states of affairs all of which are simultaneous with each other.

Objections to a Causal Account

Causal analyses of temporal priority are exposed to a number of objections, many of them advanced by J. J. C. Smart (1971). Among the most important are the following. First, given that the laws of physics do not, with one possible exception, involve any asymmetry, is it possible to explain causal priority without appealing to temporal priority? Second, it is surely logically possible for there to be events that have temporal location, but that have neither causes nor effects. However, this would seem to be ruled out by a causal analysis of temporal priority. Third, is it not also logically possible for there to be moments of time at which no events take placeperhaps because the world contains gappy causal laws? But then there would be no way of ordering that moment relative to other moments. Finally, and even more dramatically, is it not logically possible for there to be a spatiotemporal world that contains no events at all? But then there would be no causal relations, and so, according to a causal theory of temporal priority, no ordering of times in such a world.

With regard to the first objection, the answer is that most present-day analyses of causation offer accounts of the direction of causation that do not involve any appeal to temporal priority (Lewis 1973; Tooley 1987, 1997; Mellor 1995). As regards the second objection, it does not tell against the account set out earlier, since an event that does not itself enter into any causal relations may have temporal location by being simultaneous with an event that does enter into causal relations.

The third and fourth objections are more threatening. One way of responding to these objections is by appealing to possible events and causal relations. Here the idea is, in the case of the third objection, that if the world had been different at certain times, there would have been events when, as things stand, there are no events, and that it is those possible causal relations that make it the case that the time when no events occur has a temporal location. Similarly, in the case of the totally empty spatiotemporal world, if there had been events at some times, these would have caused events at other times, and it is those possible causal relations that serve to order moments of time.

The problem with this sort of response is that if temporal order is to be analyzed causally, it seems clear, especially in the case of the totally empty world, that there are no truth makers for counterfactuals concerning such possible events. A different response, however, is available (Tooley 1987, 1997). The basic idea is that if one adopts a realist conception of space-time, then the continued existence of space-time is itself something that requires explanation if it is not to be a cosmic accident. However, what sort of explanation is possible, other than one according to which regions of space-time themselves causally give rise to other regions of space-time? If such immanent causal connections between spatiotemporal regions are possible, then the temporal ordering of different moments of time can, on a causal theory, be given by those causal relations, rather than only by causal relations between events in space-time.

See also Physics and the Direction of Time; Time; Time, Being, and Becoming.

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Michael Tooley (2005)