- Whether an arrow is moving now depends on where it will be in the future.
- If the future is open, there is no fact about where the arrow will be in the future.
- If if whether p depends on how A is, and there is no fact about how A is, then it is not a fact that p.
- So, if the future is open, no arrow is moving now.
Premise 1 is the most controversial one. Suppose that an arrow has been flying for half a second. There are two metaphysically possible worlds. In the first, it continues moving as usual. In the second, its motion instantly reverses after this moment, so that this moment is the furthest point in its flight. In the second world there is no more reason to say that the present moment is the last moment of forward motion than to say that it is the first moment of backward motion. So we shouldn't say the arrow is moving forward in the second world.
Hence there are worlds that differ on whether the arrow moves now and yet that differ only in the future positions of the arrow. That gives us reason to accept 1.
Premise 2 is particularly clear given theism: God can miraculously relocate the arrow if he so chooses. But I think premise 2 is going to be plausible on other views, too.