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76. A REFUTATION OF HUME'S THEORY OF CAUSALITY1 Given Hume's conceptions of space and time, which I take to be fundamental to his theory of causality, it is not always possible to meet all of those conditions definitive of the cause-effect relation, i.e. , those "general rules, by which we may know when" objects really 2 are "causes or effects to each other" (T. 173). To show this, it will be necessary, first, to give a very brief exposition of Hume's conceptions of space and time, with regard chiefly to their implications for the nature of motion. Then, after briefly summarizing his views on the nature of the cause-effect relation, I shall proceed immediately to my objection. It should be noted first, however, that, if one instance of a cause-effect relation can be found to which Hume's analysis will not apply, that, presumably, would be sufficient to refute his theory. I shall not here repeat all of Hume's arguments for the indivisibility of space and time. Suffice it to say, he takes it to be fairly obvious that each must consist of a finite number of indivisible points or moments, each of which is distinct, and therefore separate, from every other, and, in the case of time, none of which ever "co-exist." Only one of his arguments for the indivisibility of space need concern us here. The argument is brief: The infinite divisibility of space implies that of time, as is evident from the nature of motion. If the latter, therefore, be impossible, the former must be equally so. (T. 31) The argument here seems, roughly, to be this: the motion of an object can be described only by giving its positions at various times (the nature of motion) . If, therefore, an object, such as a ball moving along a line AB, can be assigned an infinite number of positions taken between A and B (the infinite divisibility of space) , 77. the time taken to traverse AB must also be infinite, i.e. , must consist of an infinite number of instants. But the finite time taken to traverse the distance AB is not infinitely divisible; therefore, neither is the line AB. This argument, of course, relies upon the assumption that, in traversing the line AB, the ball will occupy each of the points (whether finite or infinite) of which it consists . The argument can also be turned around so as to derive the finite divisibility of time from that of space. Here, too, it must be assumed that the ball occupies each of those instants which constitute the time taken to traverse the line AB. It thus seems clear that, on Hume's view, the ball's motion can be neither more nor less divisible than the space and time it takes to move. x In its motion from A to B, then, the ball will occupy first one, then another of the points lying between A and B until finally it has occupied them all and has moved from A to B. But, in saying that it will occupy first one and then another, we are saying nothing more than that it successively occupies a series of points, and, insofar as its occupation of these different points is successive, it takes time. We are in a position, then, to define motion (at least motion along a straight line) as "the successive occupation of adjacent, linearly ordered points or places." Now, this is very different from the usual conception of motion. The ball's motion between any two adjacent points is not a moving from one to the other. It is simply its being in the one place at one instant and its being in the other place at the next. It is not a continuous motion, but the occupation of discrete places at different times. It is, as it were, a series of instantaneous leaps. This interpretation, if it is accurate, may also serve to account for Hume's ill-understood propensity for 78. referring to cause and effect as objects rather than as events. Events must, on Hume's view of time at least, be essentially static. Unlike those...