In Presentism, where only the present exists; the past and future do not - how then does time 'flow'?
To 'flow' requires a motion; for example, in the standard physical presentation of a moving particle, a particle 'moves' into the future.
For Aristotle, change is an aspect of time.
Is it possible then to say things change, but not by moving into the future, but by staying in the immediate present, and changing there?
I doubt that I have read enough on presentism, but from what I can gather, the flow of time is extremely fundamental in presentism. As Ned Markosian wrote in his paper "A Defense of Presentism":
Presentism seems to entail that there is no time except the present time. Thus Presentism also seems to entail that there are no propositions about any non- present times, and that we never say anything about any such times.
An important point to make is that the flow of time as you describe it implicitly refers to an infinitesimally small interval between two points in time. However, the flow of time in presentism works a little differently. Markosian claims that " Times are like worlds" and then goes on to elaborate:
Here’s how times are like worlds. Consider the actual world. There are really two of them. There is the abstract actual world, which is a maximal, consistent proposition. There are many things that are similar to the abstract actual world in being maximal, consistent propositions. Each one is a possible world. The abstract actual world is the only one of all of these possible worlds that happens to be true. And then there is the concrete actual world, which is the sum total of all actual facts. The concrete actual world is the only concrete world that exists, and it is what makes the abstract actual world true.
The Presentist can say that it is the same with the present time. There are really two of them. There is the abstract present time, which is a maximal, consistent proposition. There are many things that are similar to the abstract present time in being maximal, consistent propositions that either will be true, are true, or have been true. Each one is a time. The abstract present time is the only one of all of these abstract times that happens to be true right now. And then there is the concrete present time, which is the sum total of all present facts. It is the only concrete time that exists, and it is what makes the abstract present time true. Talk about non-present times can be understood as talk about maximal, consistent propositions that have been or will be true. For example, the time ten years from now can be identified with the maximal, consistent proposition that will be true in ten years.
As I interpret it, this means that flow really doesn't require motion. Instead, the flow of time is simply a flow between these worlds. The present world isn't a derivative of the past worlds, it simply is what it is. Thus, a particle doesn't move from the past world to the present, it simply exists in the present and ceases to exist in the past.
I cited Ned Markosian's paper a lot here. It's really good and you should read it. It clears up a lot of ambiguities and criticisms of presentism. Here's a link to it.
About Aristotle and motion you may check the notions of ενεργεία and δυνάμει (actuality and potentiality) to get an idea.
(https://en.wikipedia.org/wiki/Potentiality_and_actuality
As presentism rejects the common idea of time he has a great work to do so to clarify what it pursues.
As I understand it, time was historically defined as dependent on motion. Then fine measures were defined. Nevertheless, motion still defines time, so for instance, two particles moving relative to each other in the present are all that is required for time to flow. The intertia of the particles keeps time flowing, but the particles are always (present) in the present.
You are asking about time, a very difficult thing to grasp. According to Einstein it is relative. Your time is not my time, and vica versa. Time seems to depend on the observer... But lets forget about that, to keep things simple.
I think you can compare it to a computer. More and more scientists come to the conclusion that the universe is actually one big computer, E.g. My Big TOE written by Tom Campbell, a former NASA physicist, Programming the Universe by Seth Lloyd who proposed the first feasible quantum computer, and others).
A computer only has it current state. The past states, or possible calculable future states do not exist. The future states only exist in potency but haven't been actualized. And the past states don't exist anymore either. With every CPU tick, its state is altered. Nowadays a computer is very capable of rendering some nice graphics, 3D if you will. A car moving on the screen seems to have motion, yet it's movement exists of a sequence of positions projected on the screen on after the other. If you go along with the universe being one gigantic computer, then particles moving is the same. It is granular, not continious. Hence planck length and planck time are the like the pixels on a computer screen. And the speed of light is the max frequency of the CPU of the computer.
If the computer isn't observed, its state is undetermined, it is a cloud of chance (like Schrodinger's cat, or decaying atoms). When you probe its state, the wave function collapses to a state, which is always in the now, in the present moment, the moment of observation. Hence that is the only state that exists. But as soon as you would be able to observe again, that state is not actual anymore. Because a new state could be determined.
So assuming a computer can only calculate now, it can not calculate in the future nor in the past I would go along with your statement that things change in the now. Maybe that is due to consciousness observes in the now, just like the particle-wave duality double slit experiments.
