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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.
According to McTaggart, there are two distinct modes in which all events can be ordered in time. In the first mode, events are ordered as future, present, and past. Futurity and pastness allow of degrees, while the present does not. 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 correspond to the temporal perspective of the person who utters them. This is the A series of temporal events.
Although originally McTaggart defined tenses as relational qualities, i.e. qualities that events possess by standing in a certain relations to something outside of time, something that does not change its position in time, then today it is popularly believed that he treated tenses as monadic properties. As R. D. Ingthorsson notes, this is probably because later philosophers have independently inferred that this is how McTaggart must have understood tense merely because tenses are normally expressed in ordinary English by non-relational singular predicates "is past", "is present" and "is future".
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: "earlier than" (or precedes) and "later than" (or follows). An important difference between the two series is that while events continuously change their position in the A series, their position in the B series does not. If an event ever is earlier than some events and later than the rest, it is always earlier than and later than those very events. Furthermore, while events acquire their A series determinations through a relation to something outside of time, their B series determinations hold between the events that constitutes the B series. 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 A series is tensed and the B series is tenseless. For example, the assertion "today it is raining" is a tensed assertion because it depends on the temporal perspective—the present—of the person who utters it, while the assertion "It rained on 1 April 2020" is tenseless 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 1 April 2020. 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.
The debate between A-theorists and B-theorists is a continuation of a metaphysical dispute reaching back to the ancient Greek philosophers Heraclitus and Parmenides. Parmenides thought that reality is timeless and unchanging. Heraclitus, in contrast, believed that the world is a process of ceaseless change, flux and decay. Reality for Heraclitus is dynamic and ephemeral. Indeed, the world is so fleeting, according to Heraclitus, that it is impossible to step twice into the same river. The metaphysical issues that continue to divide A-theorists and B-theorists concern the reality of the past, the reality of the future, and the ontological status of the present.
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.
It seems quite clear to me that [tenses] are not qualities but relations, though of course, like other relations, they will generate relational qualities in each of their terms