The Nature of Time: Reflections on A-Series and B-Series

I am currently taking a course on contemporary analytic metaphysics. For those who do not know what these three terms mean when used in conjunction, it is the study of the existence claims that current analytic philosophers have made and why. The most recent topic of discussion in the class is the quest 'What is the nature of time?' In reading about the current debate on the topic, I found myself intellectually revolted by the point of departure that modern discussion has taken on the issue. I find it amazing that the debate has been structured in the way it has been for so long. Essentially, I think there is a major problem with the way this issue has been structured, so I have decided to restructure the concept myself.

McTaggart's Argument:

The argument is composed a distinction and three logical steps based on the distinction. The distinction is between two different concepts of time, named A-series and B-series. McTaggart claims that: (1) B-series actually presupposes A-series, (2) A-series entails contradiction, (3) therefore both concepts are meaningless and there is no such thing as time.

The starting point of the debate is an argument formulated by John McTaggart. McTaggart sets up the argument by identifying two conceptions of time. First, there is B-series, which is time as composed of points which either precede or succeed each other. This conception in terms of succession is considered to be a static model in which every point along the dimension of time really exists just as much as any other point. Then there is A-series, which is time as composed of three distinct groupings: past, present and future. However, these groupings change as the future flows through the present into the past. Thus, this is a dynamic conception of time.

With these two distinct conceptions of time in the background, McTaggart observes that time presupposes change. But what does change mean? For Michael Loux, in the metaphysics intro we are reading (Metaphysics: A Contemporary Introduction, 3rd ed., New York and London: Routledge, 2006), "at the very least change involves a variation in the way things are" (208). This seems to be true, but for whatever reason, McTaggart defines change in a much stronger way. We will, therefore, come back to this weak definition of change later. For McTaggart, change in "the way things are" is determined by the events that take place and how they come to be. Every change is an event, so it is the events that change over the course of time.

If time occurs in events, then events that are no longer happening must cease to be events and new events become. But this fact about time is incompatible with B-series, because the static nature of the conception prevents things from coming into being or ceasing to be. Therefore, if we are to speak temporally when we speak of time as a B-series, the temporal conception must be entirely appropriated from A-series. This is so because the concept of change fundamental to temporality is a dynamic concept of change, not a static one. In B-series, a thing's properties are fixed at every point in space-time, so there is simply no possibility of change. All speech about time, then, is only meaningful in terms of A-series, and B-series treats time in an artificial manner which presupposes A-series.

With step (1) accomplished, Mctaggart moves on to step (2). Because time is composed of the changing of events, it turns out that at some point in their career all events must be all three of past, present and future. This seems like contradiction. A supporter of A-series (an A-theorist) might respond that no event exemplifies all three properties simultaneously, so there is no contradiction. McTaggart, however, anticipates this objection by observing that when we say a thing x has a property P or 'x is p', the tenseless translation of what we are saying is 'in the present x is P'. Similarly, in the future, when x no longer has P, the translation of 'x was P' is 'in the future x is not P'; and in the past 'x will be P' becomes 'in the past, x is not P'. The problem, for McTaggart, every past and future moment was once a present moment, so each moment, past and future ascriptions can be made about x. These ascriptions, when broken down into tenseless language, differ. Therefore, we are ascribing contradictory properties to x.

Given these two steps, McTaggart decides that because his decriptions of time exhaust the possibilities of description of time (or so he thinks), time must not exist.

Evaluation of McTaggart's Argument:

I don't think I have ever seen a worse argument that has received as much attention as McTaggart's has. To be fair, the literature that the argument has produced is almost entirely critical -- no one actually believes that time does not exist except McTaggart. However, most of the responses serve to defend one of either A-series or B-series from attack, which has resulted in the fact that the overarching conception that McTaggart has imposed onto the debate does not receive a criticism. This overarching conception will be my target, and I will consider the claims of A-theory and B-theory as the bear on this goal.

I will accept McTaggart's distinction between A-series and B-series, because I think it is the best thing he wrote on the matter (even though these distinctions do not originate with him). Also, relinquishing these definitions would not mean that I do not take him seriously. What I want to question, first, is his claim that change must be defined in terms of events, because only events change. This claim is very strong and completely unwarranted. As a matter of fact, it commits us to a strange ontology of events. McTaggart, in assuming that time describes the change of events, also assumes the unity and identity of events themselves. That is, McTaggart must take as his most fundamental principle about time the concept that events exist as distinct from each other in a way described by identity. In other words, events can have names.

The assumption that events are fundamentally unified does not need to be made, though. In fact, change can be defined as the differences in spatial configuration that obtain between temporally contiguous moments. That is, change is the mere fact that at different points along the temporal axis, the matter scattered throughout space is arranged differently. The change is a discription of the differences between moments as a smooth function. This concept of change seems to me to be both scientifically sound and deeply intuitive. We often say that a surface changes, for example when I describe the topology of Louisiana, I can observe that the landscape changes from south Louisiana to north Louisiana such that the ground goes from soft and marshy to firm and hilly. This description of change is true even if time does not exist. Therefore, change is not a purely temporal term, and it is inappropriate to define it in terms of events which are purely temporal.

In fact, the difference between these two concepts of change is the difference between A-series and B-series. In A-series, time is conceived as events; and in B-series, time is conceived as a smooth spatial function over the dimension of time. But the differences between A-series and B-series go deeper than this. In fact, both series are a description of the things in time and a description of the context of these things (viz., time itself). For A-series, the things that exist in time are events and objects. Each event and each object has an identity that is maintained as unchanging, while the context is held variable: a single event can be spoken of as past, present or future. The only way that this can work is if events and objects are treated as fixed in the same way that a moving body can be treated as fixed in physics.

It is evident, now, that the reverse will be true of B-series. B-series holds the background dimensions fixed, and the objects and events that occur in this background are treated as varied and changing. Thus, for a B-theorist, when I refer to an object or an event, I am actually referring to a particular configuration of matter in occupying a finite space and a finite time. In other words, the B-theorist will bracket off a piece of space-time and refer to that piece as an event or an object. Here, we find that the physical matter and its dimensions are taken as fundamental, rather than the unitied objects and events that the matter comprises.

Now we must remember that events and objects are complex metaphysical concepts about which there is much debate. However, that debate essentially characterizes them in one of the two ways described above, so this cartoon representation of them will suffice as a sketch. A-theory and B-theory, then, is an extension of the nominalist/realist debate. The realist will typically claim that objects and events are fundamental and that time is inherently tensed and dynamic. The nominalist will typically claim that the concrete particulars that occupy space-time are fundamental and that time is inherently a static dimension. Both conceptions of time want to account for events and objects in time. This means that something must be held static and something must be allowed to vary. For B-theory what is held static is the dimension of time, and the objects and events are allowed to vary (we can take any grouping we want and call it an object or event). For A-theory what is held static is the objects and events, and the dimension of time is allowed to vary (we can refer to the same object or event in different tenses).

Responses to McTaggart's argument should be relatively evident at this point. His reduction of B-series temporality to A-series temporality simply does not work, because we have seen that there is a second perfectly good description of time to be had. His claim that A-theory entails a contradiction also does not succeed. McTaggart has not respected the fact that something must be allowed to vary if change is to be accounted for. He wants objects and events to be held static for A-series, but he also wants to be able to speak about time staticly (i.e. tenselessly). Of course, even if these first two logical steps could be made soundly, his conclusion would still not follow, because he has not exhausted the different conceptions of time. Without doing this, he cannot claim that time does not exist.

I do not find either A-theory or B-theory to be superior to the other. Both of them do a good job of describing time, but both are subject to temporal descriptions that the other has difficulty accounting for. Descriptions of events are very difficult in B-series, because places (where events occur) are difficult to define in sheer materialist terms. Similarly, descriptions of science are very difficult in A-series, because they are conceived in B-series (and probably necessarily so). What this means is that both theories have something to offer concerning time, but which one obtains (if only one does) will depend entirely on the metaphysical debate (concerning event and object identity) which underlies the two conceptions.

It seems to me that we ought to retain both conceptions, because, at least as far as human thought is concerned, they provide two different descriptions of the same thing, and each description states something true. The relevant way in which time is dynamic is that it always appears to be so to a human intelligence. The reason is that awareness is a fundamentally present-tense event. We are never aware of existing except in the present, and in the present, we can contemplate the future and the past, but to occupy the future or the past would be to make them present. Thus, time is dynamic at least for human awareness. Time is also static, however. This is so because scientific description of the world is inherently tenseless. Though it may be that only one theory is true of both the world and the entities that have awareness within it, it may also be that A-series is true of us, and B-series is true of the world.

-Priam's Pride