16. Divisibility of matter.-In matter, we have no clear ideas of the smallness of parts much beyond 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 abstractly is, and the relation of totum and pars: 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 will 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 number 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 40 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 400,000,000. And so likewise in eternity, he that has an idea of but 4 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 4 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.

CHAPTER XXX.

OF REAL AND FANTASTICAL IDEAS.

1. Real ideas are conformable to their archetypes.-Besides what we have already mentioned concerning ideas, other considerations belong to them, in reference to 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; and are,

First. Either real or fantastical.

Secondly. Adequate or inadequate.

Thirdly. True or false.

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,

2. Simple ideas all real.-First. Our simple ideas are 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 showed. 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 marks 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 resemblances of something in the things themselves; the reality lying in that steady correspondence they have with the distinct constitutions of real beings. But whether they answer to those constitutions, as to causes or patterns, it matters not; it suffices that they are constantly produced by them. And thus our simple ideas are all real and true, because they answer and agree to those powers of things which produce them in our minds, that being all that is requisite to make them real, and not fictions at pleasure. For in simple ideas, (as has been shown,) the mind is wholly confined to the operation of things upon it, and can make to itself no simple idea, more than what it has received.

3. Complex ideas are voluntary combinations.-Though the mind be wholly passive in respect of its simple ideas, yet, I think, we may say, it is not so in respect of its complex ideas; for, those being combinations of simple ideas put together, and united under one general name, it is plain that the mind of man uses some kind of liberty in forming those complex ideas: how else comes it to pass, that one man's idea of gold or justice is different from another's, but because he has put in or left out of his some simple idea which the other has not? The question then is, Which of these are real, and which barely imaginary, combinations? What collections agree to the reality of things, and what not? And to this, I say, that,

4. Mixed modes made of consistent ideas are real.-Secondly. Mixed modes and relations having no other reality but what they have in the minds of men, there is nothing more required to those kinds of ideas to make them real but that they be so framed that there be a possibility of existing conformable to them. These ideas, being themselves archetypes, cannot differ from their archetypes, and so cannot be chimerical, unless any one will jumble together in them inconsistent ideas. Indeed, as any of them have the names of a known language assigned to them, by which he that has them in his mind would signify them to others, so bare possibility of existing is not enough; they must have a conformity to the ordinary signification of the name that is given them, that they may not be thought fantastical: as if a man would give the name of "justice" to that idea which common use calls "liberality." But this fantasticalness relates more to propriety of speech, than reality of ideas. For a man to be undisturbed in danger, sedately to consider what is fittest to be done, and to execute it steadily, is a mixed mode or a complex idea of an action which may exist.

But to be undisturbed in danger, without using one's reason or industry, is what is also possible to be; and so is as real an idea as the other. Though the first of these, having the name "courage" given to it, may, in respect of that name, be a right or wrong idea: but the other, whilst it has not a common received name of known language assigned to it, is not capable of any deformity,* being made with no reference to any thing but itself.

any

5. Ideas of substances are real, when they agree with the existence of things. Thirdly. Our complex ideas of substances, being made all of them in reference to things existing without us, and intended to be representations of substances as they really are, are no farther real than as they are such combinations of simple ideas as are really united, and co-exist in things without us. On the contrary, those are fantastical which are made up of such collections of simple ideas as were really never united, never were found together in any substance; v. g. a rational creature, consisting of a horse's head, joined to a body of human shape, or such as the centaurs are described: or, a body yellow, very malleable, fusible, and fixed, but lighter than common water: or, an uniform, unorganized body, consisting, as to sense, all of similar parts, with perception and voluntary motion joined to it. Whether such substances as these can possibly exist or no, it is probable we do not know but be that as it will, these ideas of substances being made conformable to no pattern existing that we know, and consisting of such collections of ideas as no substance ever showed us united together, they ought to pass with us for barely imaginary: but much more are those complex ideas so, which contain in them any inconsistency or contradiction of their parts.

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CHAPTER XXXI.

OF ADEQUATE AND INADEQUATE IDEAS.

1. Adequate ideas are such as perfectly represent their archetypes. Of our real ideas, some are adequate, and some are inadequate. Those I call "adequate," which perfectly represent those archetypes which the mind supposes them taken from; which it intends them to stand for, and to which it refers them. Inadequate ideas are such which are but a partial or incomplete representation of those archetypes to which they are referred. Upon which account it is plain,

2. Simple ideas all adequate.-First. That all our simple ideas are adequate. Because being nothing but the effects of certain powers in things, fitted and ordained by God to produce such sensations in us, they cannot but be correspondent and adequate to those powers: and we are sure they agree to the reality of things. For if sugar produce in us the ideas which we call "whiteness," and "sweetness," we are sure there is a power in sugar to produce those ideas in our minds, or else they could not have been produced by it. And so each sensation answering the power that

In more modern language, difformity; in opposition to conformity and conformable in the early part of the paragraph.-EDIT.

operates on any of our senses, the idea so produced is a real idea, (and not a fiction of the mind, which has no power to produce any simple idea,) and cannot but be adequate, since it ought only to answer that power: and so all simple ideas are adequate. It is true, the things producing in us these simple ideas are but few of them denominated by us as if they were only the causes of them; but as if those ideas were real beings in them. For though fire be called "painful to the touch," whereby is signified the power of producing in us the idea of pain; yet it is denominated also "light," and "hot" as if light and heat were really something in the fire more than a power to excite these ideas in us; and therefore are called qualities in or of the fire. But these being nothing, in truth, but powers to excite such ideas in us, I must in that sense be understood when I speak of secondary qualities, as being in things; or of their ideas, as being in the objects that excite them in us such ways of speaking, though accommodated to the vulgar notions, without which one cannot be well understood, yet truly signify nothing but those powers which are in things to excite certain sensations or ideas in us; since, were there no fit organs to receive the impressions fire makes on the sight and touch, nor a mind joined to those organs to receive the ideas of light and heat, by those impressions from the fire or the sun, there would yet be no more light or heat in the world, than there would be pain if there were no sensible creature to feel it, though the sun should continue just as it is now, and Mount Etna flame higher than ever it did. Solidity, and extension, and the termination of it, figure, with motion and rest, whereof we have the ideas, would be really in the world as they are, whether there were any sensible being to perceive them or no: and therefore those we have reason to look on as the real modifications of matter, and such as are the exciting causes of all our various sensations from bodies. But this being an inquiry not belonging to this place, I shall enter no farther into it, but proceed to show what complex ideas are adequate, and what not.

3. Modes are all adequate.-Secondly. Our complex ideas of modes, being voluntary collections of simple ideas which the mind puts together, without reference to any real archetypes or standing patterns existing any where, are and cannot but be adequate ideas. Because they, not being intended for copies of things really existing, but for archetypes made by the mind to rank and denominate things by, cannot want any thing; they having each of them that combination of ideas, and thereby that perfection, which the mind intended they should: so that the mind acquiesces in them, and can find nothing wanting. Thus by having the idea of a figure with three sides meeting at three angles, I have a complete idea, wherein I require nothing else to make it perfect. That the mind is satisfied with the perfection of this its idea, is plain in that it does not conceive that any understanding hath or can have a more complete or perfect idea of that thing it signifies by the word "triangle," supposing it to exist, than itself has in that complex idea of three sides and three angles; in which is contained all that