Motion is impossible, since there's no way to begin a motion.
Motion is nonexistent, since everything is, at every moment, stationary.
Motion cannot be atomic.
Time is not composed of moments.
At the moment you jump off a roof, are you standing on the roof?
No, because if you're still on the roof, you haven't jumped yet.
Yes, because, if you're not standing on the roof any more, you've already jumped.
Moments are a way of talking about the boundaries of changes.
Your jumping of the roof was the beginning of your motion to the ground. But you weren't jumping while you were already moving to the ground. And you weren't jumping before you started moving to the ground.
While we can consider any finite number of moments, by variously describing the world's motions, we cannot coherently consider a series of adjacent moments (what changes would these be based on?)
The continuum is "potentially" but not "actually" infinite.
This resolves the Second Dichotomy Paradox.
But what about the Arrow? Even if time isn't made out of moments, are things really motionless at moments? Constantly starting and stopping?
Is it really true that there is no change during a given moment?
Even if one rejects that time is completely composed of moments (and hence, the inference "¬ϕ is true at every moment ∴ ϕ" is never true), this is still problematic
A general theory of change
There are all sorts of changes:
There are as many types of motion or change as there are meanings of the word "is"
Change involves something that is changed, and a manner in which it is changed
The substratum that persists through a change (e.g. wooden beams, 50 lbs. bronze, Socrates)
the thing that is "added on" or "taken away" by a given change (e.g. "being a house", "being a statue", "sitting")
A finished thing---a substance---will generally consist of a some kind of arrangement (a form) of some stuff (matter). It will also have various subsidiary features (also forms) that aren't part of the main form that makes it what it is.
The stuff (matter) may itself consist of matter arranged in various way. E.g. wooden beams.
Change can be explained in various ways
To exhibit the characteristic features of a state or kind is to be a fully actual example of that state or kind
To be able to exhibit the characteristic features of a state or kind is to be a potential example of that state or kind
Analogy: biological development and gradual actualization of the characteristic form of a living thing.
The potentially to be a fully grown animal of a certain kind is exhibited by a baby animal.
The matter of a thing is responsible for what the thing potentially is
The form of a thing is responsible for what the thing actually is
Actuality and Potentiality are not states or qualities. They're "modifiers" that apply to states and qualities.
You can't just be potentially. You have to be potentially something.
The actuality of a potentiality, qua [insofar as it is] potentiality.
What does this mean?
Well, being potentially something is a state. Hence, we can consider whether it's an actual state, or just dormant, lying in wait.
What's the characteristic activity of something that is potentially on the moon---something it can do, and things that aren't potentially on the moon can't do?
All change is analyzed in the same way, as a type of "motion" towards a final state
Change is inherently directed---it's always change towards something.
Its basic concepts are form and matter, not points and places.
Motion is a higher-order concept---not an ordinary state of a thing, but a feature of a state (whether the states are purely potential, or potential being actualized)