McTaggart on time

McTaggart is famous for his argument that there is no such thing as time as it is commonly conceived--there is only a sequence with a betweenness relation but no ordering.

The part of the argument that has received most attention is the clever argument that an A-series--the series of times ordered as past, present and future--is incoherent. This argument is that (a) the Battle of Waterloo was exactly the same when it was in the future, then when it was in the present and then when it was in the past, but (b) it was not exactly the same because it changed from being future, to being present to being past. Since (a) and (b) conflict, the notions of pastness, presentness and futurity are incoherent.

What I want to say something about, however, is the second part of McTaggart's argument. The second part of the argument is that a B-series--the series of points in time ordered by an earlier-than relation--cannot do justice to what we mean by "time" because the earlier-than ordering from depends on the A-series. The third part was to note that our perception of time is innately contradictory because of flexibility in the length of the "now".

Crucial to the second part of McTaggart's argument is the idea that the A-series is needed to give a direction to the set of times. Given the set of all times and a betweenness relation on them (time t₁ is between times t₀ and t₂, say), we can get two different orderings compatible with the betweenness relation (e.g., we can take t₀ to be earlier than t₁ and t₁ to be earlier than t₂, or we can take t₂ to be earlier than t₁ and t₁ to be earlier than t₀), and unless we use the A-series to specify that the right ordering is the one that takes the past to be earlier than the future, we have no way of choosing between these two.

But here McTaggart is mistaken in two ways. First, he has given us no reason to think that the earlier-than ordering is supposed to be defined in terms of the A-series concepts of past, present and future, rather than the other way around. For he gives us no reason to suppose that the A-series has any special resources to distinguish between past and future. Granted, we might posit that the distinction is primitive, but we if we do that, we can just as well posit that the choice between one of the two candidates for the earlier-than relation is to be settled by saying that one of them is primitively the right relation for the job. (The growing block theorist does have an answer, but McTaggart's argument against the A-series supposes an eternalist A-series.)

Second, there certainly is candidates for the job of distinguishing the relation. We might, very simply, take a variant of Kant's solution. The earlier-than relation is the one that points in the direction of predominant causation--typically, when A causes B and A and B are non-simultaneous, then A is prior to B. If there are any exceptions to this (cases of prophecy might be such), they seem to be rare. This account has the theoretical advantage that it leaves one less thing to explain--why the earlier-than relation happens to be the direction of predominant causation. Granted, one might explain that through a reductive account of causation where the direction of time is part of the reductive base (e.g., Hume's account), but I don't think any such account is plausible.