AvastYou're arguing it from a scientific and not a philosophic point of view.
You think these Greeks knew what a fucking Planck Length was. In fact even from a mathematical point of view the paradox doesn't really hold as it would be what is considered a series and would converge meaning it isn't infinite.
But in reality if you think about it you do in fact meet an infinite number of half-way points while walking a distance, but since you cannot ever reach infinity then movement is in of itself a paradox that cannot be completed.
The point of philosophy is to examine the nature of our world and if it makes you sense and here you are bringing quantum physics into it smh. Just have some fun and think about it.
You don't just make things up in philosophy, it has to be supported by logical thought, in this case validity and soundness aren't both being reached. The statement basically says:
if all movement is infinite stages, then movement is impossible
movement is infinite stages
therefore, movement is impossible - by modus ponens
The conclusion is provably valid because the premise reaches that logically. We can prove the premise isn't true, so that makes the conclusion not sound.
if all movement is infinite stages, then movement is impossible -- given premise
movement is not impossible -- observable premise, so this is a universal truth
therefore, movement is not infinite stages - by modus tollens
This conclusion is both valid and sound, unless the premise given from the first logic test isn't true, in which case it isn't a sound conclusion (referring to the first statement) anyway since both premises need to be true, so it doesn't matter.
In case anyone's wondering, this logic is provable, you can find a proof if you google 'modus ponens proof' and 'modus tollens proof' probably.
I guess it's all pretty irrelevant if the philosophical exercise is just that perception doesn't always equal fact