I've heard the following argument from one professional philosopher about the impossibility of motion (it's a version of Zeno's paradox): Assume that motion is possible. If an object is to move from point A to point B, then it has to move through an infinite number of points to get to B. This means that in order for the object to complete its journey in a FINITE amount of time, at each point the object can only spend ZERO time, since there's an infinite number of points, and anything other than zero multiplied by infinity will give an infinite result. But being at some place for zero time means you haven't been at that place at all (if you were on Mars for zero time yesterday, then that means that you weren't there at all). I.e. the object has not been at any of the points on its trajectory. So, we have a logical contradiction, and therefore motion is impossible. This argument seems like a play on words more than anything else to me, but I'd like to hear your thoughts on this.