Here's a quick argument I thought up. I don't really know whether it is a good one or not, so I hope if there's something wrong, someone who reads this will point it out to me. So here's the argument:

1. If time is dense, for any distinct given moments m1 and m3, there is a further distinct moment m2 that is between m1 and m3.

2. If a moment m3 is the next moment after a moment m1 then there is no further distinct moment m2 between them.

3. So, if time is dense, for any moment m1 there is no next moment.

4. If presentism is true, time irreducibly tensedly passes only if either first some moment m1 is present and then the next moment m2 is present or temporal passage proceeds in a non-continuous manner.

5. So if time is dense and presentism is true then either time does not irreducibly tensedly pass or temporal passage proceeds in a non-continuous manner.

6. Presentism is true only if time irreducibly tensedly passes.

7. So if presentism is true, time is not dense or temporal passage proceeds in a non-continuous manner.

I'm not sure of the mathematics, but I think if time isn't in fact dense, temporal passage will have to be non-continuous here too - in which case, it would follow that if presentism is true, temporal passage proceeds in a non-continuous manner. That is, there are going to have to be something like chronons for the presentist - smallest units of temporal passage with non-zero duration (that is, if the duration of the time segment which is present stays constant - otherwise we might have strange things like first one duration of 5 hours being present, then 1 minute, then 3 years, etc., which would be highly strange and hard to motivate). So the presentist is then, perhaps, committed to a temporally thick present which may be troublesome for some of the motivations that have been offered in its favor. In addition, we would need to come up with some non-arbitrary way of specifying the exact length of said interval, which may or may not cause trouble.

1. If time is dense, for any distinct given moments m1 and m3, there is a further distinct moment m2 that is between m1 and m3.

2. If a moment m3 is the next moment after a moment m1 then there is no further distinct moment m2 between them.

3. So, if time is dense, for any moment m1 there is no next moment.

4. If presentism is true, time irreducibly tensedly passes only if either first some moment m1 is present and then the next moment m2 is present or temporal passage proceeds in a non-continuous manner.

5. So if time is dense and presentism is true then either time does not irreducibly tensedly pass or temporal passage proceeds in a non-continuous manner.

6. Presentism is true only if time irreducibly tensedly passes.

7. So if presentism is true, time is not dense or temporal passage proceeds in a non-continuous manner.

I'm not sure of the mathematics, but I think if time isn't in fact dense, temporal passage will have to be non-continuous here too - in which case, it would follow that if presentism is true, temporal passage proceeds in a non-continuous manner. That is, there are going to have to be something like chronons for the presentist - smallest units of temporal passage with non-zero duration (that is, if the duration of the time segment which is present stays constant - otherwise we might have strange things like first one duration of 5 hours being present, then 1 minute, then 3 years, etc., which would be highly strange and hard to motivate). So the presentist is then, perhaps, committed to a temporally thick present which may be troublesome for some of the motivations that have been offered in its favor. In addition, we would need to come up with some non-arbitrary way of specifying the exact length of said interval, which may or may not cause trouble.

## 4 comments:

I believe that there is some controversy hidden within your premise 4. There seems to be a hidden assumption that isn't really made explicit. I would rather have it as:

P4. If presentism is true, every moment m1 must have a well defined next moment m2.

Of course this premise is problematic if we accept that time is continuous in that it consists of an infinity of points. But there doesn't seem to be much of a problem with points on a line having no "next point" or "previous point", so P4. may not hold.

In fact, we can draw a parallel with Zeno's paradoxes, in particulr the reverse dichotomy paradox, which states that since there is no "first point" in which Achilles runs, then he cannot reach the finish line. But apparently, Zeno does pass the finish line and thus all the points between him and the goal line, so perhaps we are placing an unnecessary restriction on continuous motion. The same can be said about the continuous flow of time as well.

One may also go against P4.by saying that it is wrongheaded description of the process of flow (for objects may just evolve in time), but I will not go further on that.

I agree that this is similar to Zeno's paradoxes, but I take it that what makes them solvable is that continuous motion involves changing values of continuous space over values of continuous time. For presentism, only one time is present, period. For time to flow, there needs to be a new moment arising out of the present one which itself is the new present one. This does not seem analogous to Zeno's paradoxes since those involve a coordination of two existing coordinate systems. There is no other coordinate system here to rely on, at least on standard versions of presentism - which time is present is not relative to a time, since there is only one time on this view. Without a well-defined next moment, there does not seem to anywhere for the presentness of the present time to go.

I'm not sure any of that made any sense (I'm a bit tired at the moment), but there you go.

Another random thought that may or may not help: For time t1 to be present after t0 is present, this presentness must, if time is continuous, traverse an infinite number of times. But time flow seems to require time to move one moment at a time. Only one moment can be present. So such a series is never completed. Unlike in the case of motion over space, since the infinite number of points traversed does involve an infinite number of points of time. Again, I'm probably not stating that very clearly, but that's more food for thought.

Your second post sounds much like what Zeno would've said about the continuum, which assumes that supertasks, by their very nature, are impossible. But nowadays not many would agree that supertasks (probably with a couple specific exceptions) are a logical impossibility.

That said, though I still don't know if I would agree that time necessarily requires a defined next moment in order to flow.

-- Andrew (Anonymous)

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