HKB
language, they were not reasoning on what they knew; they were not using words as the signs of things signified, but printing unmeaning collections of letters, or uttering senseless sounds.
The system, if it were to be classed under the old metaphysical divisions, was one of nominalism. Such words as shape, colour, hardness, roughness, &c. the author of the Treatise could only admit to have a meaning in as far as they signified ideas in the mind; and these ideas could only be there as the relics of impressions derived through the senses. Thus, general terms, such as the categories of Aristotle, could have no existence except in so far as they represented and called up particulars. Of the abstract term colour, our notion is derived solely from the ideas left in the mind by the actual impressions made through the senses. Heat, cold, and largeness, so far as these words represent what is really in the mind, have no other foundation.
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.