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concerning that part of his complex idea which depends upon the number of a thousand, he is apt to think he has a distinct idea of a chiliædron; though it be plain he has no precise idea of its figure, so as to distinguish it by that, from one that has but 999 sides ; the not observing whereof causes no small error in men's thoughts, and confusion in their discourses.
$ 14. He that thinks he has a distinct This, if not heeded, idea of the figure of a chiliædron, let him
for trial sake take another parcel of the fusion in our
same uniform matter, viz. gold or wax, arguings.
of an equal bulk, and make it into a figure of 999 sides : he will, I doubt not, be able to distinguish these two ideas one from another, by the number of sides; and reason and argue distinctly about them, whilst he keeps his thoughts and reasoning to that part only of these ideas which is contained in their numbers; as that the sides of the one could be divided into two equal numbers, and of the others not, &c. But when he goes about to distinguish them by their figure, he will there be presently at a loss, and not be able, I think, to frame in his mind two ideas, one of them distinct from the other, by the bare figure of these two pieces of gold, as he could, if the same parcels of gold were made one into a cube, the other a figure of five sides. In which incomplete ideas we are very apt to impose on ourselves, and wrangle with others, especially where they have particular and familiar names. For being satisfied in that part of the idea, which we have clear,—and the name which is familiar to us being applied to the whole, containing that part also which is imperfect and obscure,—we are apt to use it for that confused part, and draw deductions from it, in the obscure part of its signification, as confidently as we do from the other. Instance in $ 15. Having frequently in our mouths eternity. the name eternity, we are apt to think we have a positive comprehensive idea of it, which is as much as to say that there is no part of that duration
which is not clearly contained in our idea. It is true, that he that thinks so may have a clear idea of duration; he may also have a very clear idea of a very great length of duration; he may also have a clear idea of the comparison of that great one with still a greater : but it not being possible for him to include in his idea of any duration, let it be as great as it will, the whole extent together of a duration, where he supposes no end, that part of his idea, which is still beyond the bounds of that large duration he represents to his own thoughts, is very obscure and undetermined. And hence it is, that in disputes and reasonings concerning eternity, or any other infinite, we are apt to blunder, and involve ourselves in manifest absurdities.
$ 16. In matter we have no clear ideas Divisibility of the smallness of parts much beyond of matter. the smallest that occur to any of our senses; and therefore when we talk of the divisibility of matter in infinitum, though we have clear ideas of division and divisibility, and have also clear ideas of parts made out of a whole by division; yet we have but very obscure and confused ideas of corpuscles, or minute bodies so to be divided, when by former divisions they are reduced to a smallness much exceeding the perception of
of our senses; and so all that we have clear and distinct ideas of, is of what division in general or abstractedly is, and the relation of totum and parts; but of the bulk of the body, to be thus infinitely divided after certain progressions, I think, we have no clear nor distinct idea at all. For I ask any one, whether taking the smallest atom of dust he ever saw, he has any distinct idea (bating still the number, which concerns not extension) betwixt the 100,000th, and the 1,000,000th part of it. Or if he thinks he can refine his ideas to that degree, without losing sight of them, let him add ten cyphers to each of those numbers. Such a degree of smallness is not unreasonable to be supposed, since a division carried on so far brings it no nearer the end of infinite division than the first division into two halves does. I must confess, for my part, I have no clear distinct ideas of the different bulk or extension of those bodies, having but a very obscure one of either of them. So that, I think, when we talk of division of bodies in infinitum, our idea of their distinct bulks, which is the subject and foundation of division, comes, after a little progression, to be confounded and almost lost in obscurity. For that idea, which is to represent only bigness, must be very obscure and confused, which we cannot distinguish from one ten times as big, but only by number; so that we have clear distinct ideas, we may say, of ten and one, but no distinct ideas of two such extensions. It is plain from hence, that when we talk of infinite divisibility of body, or extension, our distinct and clear ideas are only of numbers; but the clear distinct ideas of extension, after some progress of division, are quite lost: and of such minute parts we have no distinct ideas at all; but it returns, as all our ideas of infinite do, at last to that of number always to be added; but thereby never amounts to any
distinct idea of actual infinite parts. We have, it is true, a clear idea of division, as often as we think of it; but thereby we have no more a clear idea of infinite parts in matter, than we have a clear idea of an infinite number, by being able still to add new numbers to any assigned numbers we have: endless divisibility giving us no more a clear and distinct idea of actually infinite parts, than endless addibility (if I may so speak) gives us a clear and distinct idea of an actually infinite number; they both being only in a power still of increasing the number, be it already as great as it will. So that of what remains to be added (wherein consists the infinity), we have but an obscure, imperfect, and confused idea; from or about which we can argue or reason with no certainty or clearness, no more than we can in arithmetic, about a number of which we have no such distinct idea as we
have of 4 or 100; but only this relative obscure one, that compared to any other, it is still bigger; and we have no more a clear positive idea of it when we say or conceive it is bigger, or more than 400,000,000, than if we should say it is bigger than 10, or 4; 400,000,000 having no nearer a proportion to the end of addition or number, than 4. For he that adds only 4 to 4, and so proceeds, shall as soon come to the end of all addition, as he that adds 400,000,000 to 4:00,000,000. And so likewise in eternity, he that has an idea of but four years, has as much a positive complete idea of eternity, as he that has one of 400,000,000 of years : for what remains of eternity beyond either of these two numbers of years is as clear to the one as the other; i. e. neither of them has any clear positive idea of it at all. For he that adds only four years to 4, and so on, shall as soon reach eternity as he that adds 400,000,000 of years, and so on; or, if he please, doubles the increase as often as he will: the remaining abyss being still as far beyond the end of all these progressions, as it is from the length of a day or an hour. For nothing finite bears any proportion to infinite; and therefore our ideas, which are all finite, cannot bear any. Thus it is also in our idea of extension, when we increase it by addition, as well as when we diminish it by division, and would enlarge our thoughts to infinite space. After a few doublings of those ideas of extension, which are the largest we are accustomed to have, we lose the clear distinct idea of that space : it becomes a confusedly great one, with a surplus of still greater; about which, when we would argue or reason, we shall always find ourselves at a loss; confused ideas in our arguings and deductions from that part of them which is confused always leading us into confusion.
Of Real and Fantastical Ideas. Real ideas § 1. Besides what we have already are conform- mentioned concerning ideas, other consiable to their
derations belong to them, in reference to archetypes.
things from whence they are taken, or which they may be supposed to represent: and thus, I think, they may come under a threefold distinction;
First, either real or fantastical.
First, by real ideas, I mean such as have a foundation in nature; such as have a conformity with the real being and existence of things, or with their archetypes. Fantastical or chimerical I call such as have no foundation in nature, nor have any conformity with that reality of being to which they are tacitly referred as to their archetypes. If we examine the several sorts of ideas before-mentioned, we shall find, that, Simple ideas
$ 2. First, our simple ideas are all real, all real. all agree to the reality of things, not that they are all of them the images or representations of what does exist; the contrary whereof, in all but the primary qualities of bodies, hath been already shown. But though whiteness and coldness are no more in snow than pain is, yet those ideas of whiteness and coldness, pain, &c. being in us the effects of powers in things without us, ordained by our Maker to produce in us such sensations; they are real ideas in us, whereby we distinguish the qualities that are really in things themselves.
For these several appearances being designed to be the mark, whereby we are to know and distinguish things which we have to do with, our ideas do as well serve us to that purpose, and are as real distinguishing characters, whether they be only constant effects, or else exact resem