Zeno’s utterances are to be looked at from this point of view, not as being directed against the reality of motion, as would at first appear, but as pointing out how movement must necessarily be determined, and showing the course which must be taken. Zeno now brings forward four different arguments against motion; the proofs rest on the infinite divisibility of space and time. (a) This is his first form of argument:—“Movement has no truth, because what is in motion must first reach the middle of the space before arriving at the end.” Aristotle expresses this thus shortly, because he had earlier treated of and worked out the subject at length. This is to be taken as indicating generally that the continuity of space is presupposed. What moves itself must reach a certain end, this way is a whole. In order to traverse the whole, what is in motion must first pass over the half, and now the end of this half is considered as being the end; but this half of space is again a whole, that which also has a half, and the half of this half must first have been reached, and so on into infinity. Zeno here arrives at the infinite divisibility of space; because space and time are absolutely continuous, there is no point at which the division can stop. Every dimension (and every time and space always have a dimension) is again divisible into two halves, which must be measured off; and however small a space we have, the same conditions reappear. Movement would be the act of passing through these infinite moments, and would therefore never end; thus what is in motion cannot reach its end. It is known how Diogenes of Sinope, the Cynic, quite simply refuted these arguments against movement; without speaking he rose and walked about, contradicting them by action.[60] But when reasons are disputed, the only valid refutation is one derived from reasons; men have not merely to satisfy themselves by sensuous assurance, but also to understand. To refute objections is to prove their non-existence, as when they are made to fall away and can hence be adduced no longer; but it is necessary to think of motion as Zeno thought of it, and yet to carry this theory of motion further still.