PHYSICS movement from A to A But it does not follow from that that no object can be moving at an instant, any more than that no object can be moving at a point Aristotle, however, is not just making a fallacious inference from one acceptation of the Greek present tense to another; as we have seen, he is well capable of steering his way through any possible semantic confusion of this kind He oVers an argument for the stronger conclusion, based on the premiss we have already seen: that whatever is moving has already been moving But the correct conclusion to draw from this argument is not that nothing can be moving at a moment, but that nothing can be moving for a single moment only The truth that lies behind Aristotle’s claim is that we can only talk of X moving at time t if t is a moment within a period of time, t0 to t00 , during which X is in movement; just as we can only talk of X moving at point p if p is a point on a track between p0 and p00 along which X is in movement The notion of velocity at a point is then a derivative (which may be simple or complex, depending on the movement’s uniformity or lack of it) from the length of time, t0 to t00 , that X takes to get from p0 to p00 Aristotle on Causation and Change In his philosophical lexicon in Metaphysics D, and also in Physics (194b16–195b30), Aristotle distinguishes four types of cause, or explanation First, he says, there is that of which and out of which a thing is made, such as the bronze of a statue and the letters of a syllable This is called the material cause Secondly, he says, there is the form and pattern of a thing, which may be expressed in its deWnition: his example is that the proportion of the length of two strings in a lyre is the cause of one note being an octave away from the other The third type of cause is the origin of a change or state of rest in something; Aristotle’s followers often called it the ‘eYcient cause’ Aristotle gives as examples a person reaching a decision, a father who begets a child, a sculptor carving a statue, a doctor healing a patient, and in general anyone who makes a thing or changes a thing The fourth and last type of cause is the end or goal, that for the sake of which something is done; it is the type of explanation we give if someone asks us why we are taking a walk, and we reply ‘In order to keep healthy’ This last kind of cause became known as the ‘Wnal cause’ 189