afforded so much speculation to philosophers. The abstract idea of a man represents men of all sizes and all qualities; which ’tis concluded it cannot do, but either by representing at once all possible sizes and all possible qualities, or by representing no particular one at all. Now it having been esteemed absurd to defend the former proposition, as implying an infinite capacity in the mind, it has been commonly infer’d in favour of the latter; and our abstract ideas have been suppos’d to represent no particular degree either of quantity or quality. But that this inference is erroneous, I shall endeavour to make appear, first, by proving, that ’tis utterly impossible to conceive any quantity or quality, without forming a precise notion of its degrees: And secondly by showing, that tho’ the capacity of the mind be not infinite, yet we can at once form a notion of all possible degrees of quantity and quality, in such a manner at least, as, however imperfect, may serve all the purposes of reflexion and conversation.
To begin with the first proposition, that the mind cannot form any notion of quantity or quality without forming a precise notion of degrees of each; we may prove this by the three following arguments. First, We have observ’d, that whatever objects are different are distinguishable, and that whatever objects are distinguishable are separable by the thought and imagination. And we may here add, that these propositions are equally true in the inverse, and that whatever objects are separable are also distinguishable, and that whatever objects are distinguishable are also different. For how is it possible we can separate what is not distinguishable, or distinguish what is not different? In order therefore to know, whether abstraction implies a separation, we need only consider it in this view, and examine, whether all the circumstances, which we abstract from in our general ideas, be such as are distinguishable and different from those, which we retain as essential parts of them. But ’tis evident at first sight, that the precise length of a line is not different nor distin-