## Thursday, December 11, 2008

### A really weird A-ish theory of time

Start with the following fairly normal A-theory. There is an A-timeline, and it is logically primary. It is marked: "... -5yr -4yr -3yr -2yr -1yr now 1yr 2yr 3yr 4yr 5yr ..." with inbetween markings. Markings on the A-timeline are called "A-times". They are the only real, ontologically basic times. 193 years ago, it was the case that the Battle of Waterloo is (was?) near the "now" marking. Now the Battle of Waterloo is near the "-193yr" marking. It moved--it moved from now to -193yr. The phrase "the present" is ambiguous. Sometimes it means "now"--call that "present1". In that sense, 193y ears ago, the Battle of Waterloo was at the present1, but no longer is. Sometimes "the present" is the changing descriptor: "the A-time of the occurrence of dthose events which are present1" (where "dthose" is Kaplan's rigidifying operator). This is "present2". In that sense, when the Battle of Waterloo took place, it was 193 years before the present2. The present2 keeps on moving through the A-timeline.

If we need B-times like 2008, we have to identify them with sets of simultaneous events or something like that, and then we need acounterpart theory for identifying B-times across worlds. (I actually do myself think we need a counterpart theory for identifying B-times across worlds, because I am a relationalist about times.) Thus, while the real, genuine, rock-bottom time of the Battle of Waterloo keeps on changing (it keeps on getting more negative), the B-time of the Battle of Waterloo is fixed. But it's not an ontologically interesting time. It's the A-times that have ontological significance. This is a genuine A-theory. It requires, as primitives, a number-line of times, with (a) a distinguished direction (from minus to plus), (b) a distinguished origin (zero), and (c) a distinguished equidistance ternary relation--abEcd iff a is the same distance and direction fromb as c is from d and satisfying appropriate axioms. Call this a "moving event" theory, because events move relative to the timeline.

Now, for the really weird A-ish theory of time. One takes the moving event theory, but one impoverishes it by throwing out the distinguished origin, while keeping the distinguished direction and the distinguished equidistance relation. Basically, the idea is that we erase the contentful "... -5yr ... now ... 5yr ..." labels on the A-timeline, and replace them with something completely non-contentful, like "... t81 ... t124 ...t441 ...", albeit still with a direction and an equidistance operation. We then add the following semantic claim: We've (as far as the theory is concerned, arbitrarily) settled on calling t124 "the present1". But t124's difference from t81 and t441is merely numerical (just as on a substantivalist B-theory, the year 2008 only differs numerically from 2007). Still, we call t124 "the present1". Let's say t7 is 193 years before t124. Then, at t7, i.e., 193years ago, it was the case that the Battle of Waterloo is occurring at t124. Currently, at t124, it is the case that the Battle of Waterloo is occurring at t7. Thus, we have a moving event theory, but no distinguished present.

This is a really crazy theory. It is a "dynamic" theory of time in the sense in which the A-theory is "dynamic": events acquire new objective temporal properties as time progresses. (I actually think this is a mistaken understanding of what "dynamism" is, but that's a different story.) But unlike the A-theory, the past, present and future are all ontologically on par, and the distinction between them is ontologically insignificant.

It may seem like this theory has all the disadvantages of the A- and B-theories combined. But not quite. It has the advantage that it escapes this argument against the A-theory. But then so does the B-theory, and it's simpler to opt for the B-theory.