A-series and B-series
In philosophy, A-series and B-series are two different descriptions of the temporal ordering relation among events. The two series differ principally in their use of tense to describe the temporal relation between events. The terms were introduced by the Scottish idealist philosopher John McTaggart in 1908 as part of his argument for the unreality of time, but since then they have become widely used terms of reference in modern discussions of the philosophy of time.
McTaggart's use of the A-series and B-series
According to McTaggart, there are two distinct modes in which all events can be ordered in time. In the first mode, events are ordered by way of the non-relational singular predicates "is past", "is present" and "is future". When we speak of time in this way, we are speaking in terms of a series of positions which run from the remote past through the recent past to the present, and from the present through the near future all the way to the remote future. The essential characteristic of this descriptive modality is that one must think of the series of temporal positions as being in continual transformation, in the sense that an event is first part of the future, then part of the present, and then past. Moreover, the assertions made according to this modality imply the temporal perspective of the person who utters them. This is the A-series of temporal events.
From a second point of view, one can order events according to a different series of temporal positions by way of two-term relations which are asymmetric, irreflexive and transitive: "comes before" (or precedes) and "comes after" (or follows). This is the B-series, and the philosophy which says all truths about time can be reduced to B-series statements is the B-theory of time.
The logic and the linguistic expression of the two series are radically different. The first is tensed and the second is tenseless. For example, the assertion "today it is raining" is a tensional assertion because it depends on the temporal perspective—the present—of the person who utters it, while the assertion "It rains on 15 June 1996" is non-tensional because it does not so depend. From the point of view of their truth-values, the two propositions are identical (both true or both false) if the first assertion is made on 15 June 1996. The non-temporal relation of precedence between two events, say "E precedes F", does not change over time (excluding from this discussion the issue of the relativity of temporal order of causally disconnected events in the theory of relativity). On the other hand, the character of being "past, present or future" of the events "E" or "F" does change with time. In the image of McTaggart the passage of time consists in the fact that terms ever further in the future pass into the present...or that the present advances toward terms ever farther in the future. If we assume the first point of view, we speak as if the B-series slides along a fixed A-series. If we assume the second point of view, we speak as if the A-series slides along a fixed B-series.
Relation to other ideas in the philosophy of time
There are two principal varieties of the A-theory, Presentism and the growing block universe. Both assume an objective present, but presentism assumes that only present objects exist, while the growing block universe assumes both present and past objects exist, but not future ones. Ideas that assume no objective present, like the B-theory, include eternalism and four-dimensionalism.
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- Presentism and the Space-Time Manifold by Dean Zimmerman, p. 7
- McTaggart, J.E., 'The Unreality of Time', Mind, 1908.
- McTaggart, J.E.,The Nature of Existence, vols. 1-2, Cambridge University Press, Cambridge, 1968.
- Bradley, F.H., The Principles of Logic, Oxford University Press, Oxford, 1922.
- Time---Notes on McTaggart and the Unreality of Time- Trinity College Seminar on Time.
- McTaggart's A-series and B-series entry in the Stanford Encyclopedia of Philosophy