The application of this system to the mathematics, and to natural philosophy, was so startling as to afford to some readers almost a _reductio ad absurdum_. The infinite divisibility of matter was arraigned by Hume as so far from being a truth, that it was not even capable of being conceived by the mind, which had never yet received any impressions through the senses corresponding to the expression. Every man had seen matter divided--some into smaller fragments than others; but where our ideas, derived from actual experiment, stopped in minuteness of division, the conception of divisibility stopped also. The truth of geometrical demonstration, as applicable to practice, he did not deny; but he maintained, or rather seemed to maintain, for his reasoning here is of a highly subtle order, that we have a conception of these operations only in as far as they concur with really existing things, or, more properly speaking, with the ideas in the mind conveyed thither by the senses. Of the point, which has no breadth, depth, or length; of the straight line, which is deficient in the first and second, and not in the last of these qualities, he denied that we could have an idea, unless that idea were just as much the representative of an actual existence as any other idea is. Infinity of space was an expression to which he had an objection on similar grounds; it had no idea corresponding to it lodged in the mind. Of space finite in various quantities, the mind possessed ideas stored up from repeated impressions, and by adding these ideas together, more or less vastness in the conception of finite space was afforded. But any thing beyond this definitive increase, attested as it was by the senses, the mind had no means of conceiving. Whatever might be in another intellectual world, there was no idea corresponding to infinity of space in the mind of man. It thence followed, that space unoccupied was a conception of which the mind was incapable, because the impressions originally conveyed to the mind were the medium through which the conception of space existed, and where there were no ideas of such impressions, an aggregate idea of space was wanting. In the same manner it was held, that it was in a succession of impressions, with ideas corresponding, that the conception of time consisted, and that without such a succession, time would be a thing unknown and unconceived. Our ideas of numbers he found to be but the collected ideas of the impressions of the units of which the senses have received distinct impressions; and in confirmation of this he appealed to the distinctness of our notion of small numbers, which our mind has been accustomed to find represented by units, and our imperfect conception of those large numbers, which we have never had presented to us in detail. How readily we have a notion of six, but how imperfectly the mind receives the conception of six millions; how clearly we perceive, in units, the