Page - 515 - in The Complete Aristotle

moments: if this assumption is not granted, the conclusion will not follow. The fourth argument is that concerning the two rows of bodies, each row being composed of an equal number of bodies of equal size, passing each other on a race-course as they proceed with equal velocity in opposite directions, the one row originally occupying the space between the goal and the middle point of the course and the other that between the middle point and the starting-post. This, he thinks, involves the conclusion that half a given time is equal to double that time. The fallacy of the reasoning lies in the assumption that a body occupies an equal time in passing with equal velocity a body that is in motion and a body of equal size that is at rest; which is false. For instance (so runs the argument), let A, A… be the stationary bodies of equal size, B, B… the bodies, equal in number and in size to A, A… ,originally occupying the half of the course from the starting-post to the middle of the A’s, and G, G… those originally occupying the other half from the goal to the middle of the A’s, equal in number, size, and velocity to B, B… .Then three consequences follow: First, as the B’s and the G’s pass one another, the first B reaches the last G at the same moment as the first G reaches the last B. Secondly at this moment the first G has passed all the A’s, whereas the first B has passed only half the A’s, and has consequently occupied only half the time occupied by the first G, since each of the two occupies an equal time in passing each A. Thirdly, at the same moment all the B’s have passed all the G’s: for the first G and the first B will simultaneously reach the opposite ends of the course, since (so says Zeno) the time occupied by the first G in passing each of the B’s is equal to that occupied by it in passing each of the A’s, because an equal time is occupied by both the first B and the first G in passing all the A’s. This is the argument, but it presupposed the aforesaid fallacious assumption. Nor in reference to contradictory change shall we find anything unanswerable in the argument that if a thing is changing from not-white, say, to white, and is in neither condition, then it will be neither white nor not- white: for the fact that it is not wholly in either condition will not preclude us from calling it white or not-white. We call a thing white or not-white not necessarily because it is be one or the other, but cause most of its parts or the most essential parts of it are so: not being in a certain condition is different from not being wholly in that condition. So, too, in the case of being and not- being and all other conditions which stand in a contradictory relation: while the changing thing must of necessity be in one of the two opposites, it is never wholly in either. Again, in the case of circles and spheres and everything whose motion is confined within the space that it occupies, it is not true to say the motion can 515