Objection: The B-Series is Not Enough For Change

McTaggart was not satisfied with the В-theory or tenseless theory approach. Many philosophers since McTaggart agree. The problem they see is that it prioritizes the В-series over the A-series. А-series positions are derived from their В-series positions. However, so these objectors claim, this approach has two problems:

  • (1) The В-series does not define real A-series.
  • (2) The В-series has no change in it, and real time needs change.

Objection 1: The B-Series Does Not Provide Real B-Series-a-Series Positions

The В-theory solutions suits any A-series positions that are derived from the B- series. However, such A-series positions are not real A-series positions. These are derivative, indexed A-series positions. Real A-series positions are fundamental. If time is real, then events in it must have real A-series positions. And such real A-series positions are not derived from another series.

Indeed, В-theory does not have a means of picking out a single real A-series from all the others. In В-theory, all A-series positions are equal. They are all derived and not fundamental: they are indexed to different positions in the B- series. Just as no single real “here” or “there” can be picked out by indexing “here” and “there” to different things or points in space, so no “present” and “past” can be picked out by indexing “present” and “past” to different events or В-series positions.

Yet why is this a problem? Why should an A-series be fundamental? Why not have all A-series be indexical, derived from the B-series?

Objection 2: The B-Series Does Not Capture Real Change

The problem, according to McTaggart, is real change. McTaggart’s contemporary Bertrand Russell gave a tenseless theory-like account of change: change is just objects having one property (such as being hot) at one time and lacking that property at a later time.

McTaggart responded:

Mr Russell looks for change, not in the events in the time series, but in the entity to which these events happen ... [I]f my poker, for example, is hot on a particular Monday, and never before or since, the event of the poker being hot does not change. But the poker changes, because there is a time when this event is happening to it, and a time when it is not happening to it. [...] But this makes no change in the qualities of the poker. It is always a quality of that poker that it is hot on that particular Monday... [and always a quality that it] is not hot at any other time ... The fact that it is hot at one point in a series and cold at other points cannot give change, if neither of these facts change—and neither of them does. Nor does any other fact about the poker change unless its presentness, pastness, or futurity changes.

(McTaggart 1927/1991,28)

According to McTaggart, the В-series cannot describe real time because events in the В-series do not change. Real change requires change in positions in time. Events do not change positions in the В-series. They do change positions in the A-series.

Here is an example of the thinking. It is a fact that the sun’s death is later

than your death. Relative to your death, the sun is a future event. Relative to the

sun’s death, your death is a past event. These are all facts that do not change. The sun’s death never changes from being later than (or a future event relative to) your death; your death never changes from being earlier than (or a past event relative to) the sun’s death.

What does change is this: both your death and the death of the sun change А-series positions. They change positions in the А-series in the following order:

  • 1. Your death is future. The sun’s death is much further future.
  • 2. Your death is present. The sun’s death is future.
  • 3. Your death is past. The sun’s death is present.
  • 4. Your death is long past. The sun’s death is past...

For McTaggart, the differences 1-4 capture real change. (Well, except that he denies such change is possible—this is central to his paradox.) Tenseless theorists can account for some kinds of А-series positions by the В-theory. For example, the sun’s death is in the future of your present. But they cannot account for the real change described above.

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