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fore when a man designs, by any name, a sort of things, or any one particular thing, distinct from all others; the complex idea he annexes to that name is the more distinct, the more particular the ideas are, and the greater and more determinate the number and order of them is, whereof it is made up. For the more it has of these, the more it has still of the perceivable differences, whereby it is kept separate and distinct from all ideas belonging to other names, even those that approach nearest to it; and thereby all confusion with them is avoided.
§ 11. Confusion, making it a difficulty to separate two things that should be separated, concerns always two ideas; and those most, which most approach one another. Whenever therefore we suspect any idea to be confused, we must examine what other it is in danger to be confounded with, or which it cannot easily be separated from; and that will always be found an idea belonging to another name, and so should be a different thing, from which yet it is not sufficiently distinct; being either the same with it, or making a part of it, or at least as properly called by that name, as the other it is ranked under; and so keeps not that difference from that other idea, which the different names import.
§ 12. This, I think, is the confusion confusion. proper to ideas, which still carries with it a secret reference to names. At least, if there be any other confusion of ideas, this is that which most of all disorders men's thoughts and discourses: ideas, as ranked under names, being those that for the most part men reason of within themselves, and always those which they commune about with others. And therefore where there are supposed two different ideas marked by two different names, which are not as distinguishable as the sounds that stand for them, there never fails to be confusion; and where any ideas are distinct, as the ideas of those two sounds they are
concerns always two
marked by, there can be between them no confusion The way to prevent it is to collect and unite into our complex idea, as precisely as is possible, all those ingredients whereby it is differenced from others; and to them, so united in a determinate number and order, apply steadily the same name. But this neither accommodating men's ease or vanity, or serving any design but that of naked truth, which is not always the thing aimed at, such exactness is rather to be wished than hoped for. And since the loose application of names to undetermined, variable, and almost no ideas, serves both to cover our own ignorance, as well as to perplex and confound others, which goes for learning and superiority in knowledge, it is no wonder that most men should use it themselves, whilst they complain of it in others. Though, I think, no small part of the confusion to be found in the notions of men might by care and ingenuity be avoided, yet I am far from concluding it every where wilful. Some ideas are so complex, and made up of so many parts, that the memory does not easily retain the very same precise combination of simple ideas under one name; much less are we able constantly to divine for what precise complex idea such a name stands in another man's use of it. From the first of these, follows confusion in a man's own reasonings and opinions within himself; from the latter, frequent confusion in discoursing and arguing with others. But having more at large treated of words, their defects and abuses, in the following book, I shall here say no more of it. § 13. Our complex ideas being made up of collections, and so variety of simple ones, may accordingly be very clear and clear and distinct in one part, and very obscure and confused in another. In a man who speaks of a chiliædron, or a body of a thousand sides, the ideas of the figure may be very confused, though that of the number be very distinct; so that he being able to discourse and demonstrate
ideas may distinct in
one part, and confused in another.
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 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.
This, if not heeded,
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 any 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