A-series and B-series

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This article is about philosophical terms. For the motor vehicle engines see BMC A-Series engine & BMC B-Series engine.

A-series and B-series are terms introduced by the Scottish idealist philosopher John McTaggart in 1908 which have become classic terms of reference in modern discussions of the philosophy of time, even outside the analytic tradition.

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.

The logic and the linguistic expression of the two series are radically different. The first is tensional and the second is non-tensional. For example, the assertion "today it is raining" is a temporal assertion because it depends on the temporal perspective -- the present -- of the person who utters it, while the assertion "It rained on the 15th of June, 1996" is non-tensional because it does not so depend. It should be obvious that, 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 June 15th, 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.

[edit] References

McTaggart, J.E., The Unreality of Time, in "Mind" , 1908.
McTaggart, J.E.,The Nature of Existence, vol. 1-2, Cambridge University Press, Cambridge, 1968.
Bradley, F.H., The Principles of Logic, Oxford University Press, Oxford, 1922.