and confused, which we cannot diftinguish from one ten times as big, but only by number; fo that we have clear diftinct ideas, we may fay, of ten and one, but no diftinct ideas of two fuch extenfions. It is plain from hence, that when we talk of infinite divifibility of body, or extenfion, our distinct and clear ideas are only of numbers; but the clear diftinct ideas of extension, after fome progrefs of divifion, is quite loft, and of fuch 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 affigned number we have; endlefs divifibility giving us no more a clear and distinct idea of a&ually infinite parts, than endless addibility (if I may fo fpeak) gives us a clear and distinct idea of an actually infinite number; they both being only in a power still increafing the number, be it already as great as it will: So that of what remains to be added (wherein confifts the infinity) we have but an obfcure, imperfect, and confused idea, from or about which we can argue or reafon with no certainty or clearness, no more than we can in arithmetic, about a number of which we have no fuch diftin&t idea as we have of 4 or 100, but only this relative obfcure one, that, compared to any other, it is ftill bigger: And we have no more a clear positive idea of it when we fay or conceive it is bigger, or more than 400,000,000, than if we fhould fay it is bigger than 40 or 4; 400,00o,coo, 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, fhall as foon come to the end of all addition, as he that adds 400,000,000, to 400,000,000. And so likewife in eternity, he that has an idea of but four years, has as much a pofitive complete idea of eternity, as he that has one of 400,000,000 of years; for what remains of eternity beyond either of thefe two numbers of years, is as clear to the one as the other; i. e. neither of them has any clear pofitive idea of it at all: For he that adds only 4 years to 4, and so on, shall as foon reach eternity, as he that adds 400,000,000 of years, and fo on, or if he please, doubles the increase as often as he will; the remaining abyss being ftill as far beyond the end of all thefe progreffions, 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 alfo in our idea of extenfion, when we increase it by addition, as well as when we diminish it by divifion, and would enlarge our thoughts to infinite fpace. After a few doublings of thofe ideas of extenfion, which are the largest we are accustomed to have, we lose the clear diftinct idea of that space; it becomes a confufedly great one, with a furplus of ftill greater; about which, when we would argue or reafon, we shall always find ourselves at a 'lofs; confufed ideas in our arguings and deductions from that part of them which is confused, always leading us into confufion. § 1. B CHAP. XXX. OF REAL AND FANTASTICAL IDEAS. Real Ideas are conformable to their Archetypes. ESIDES what we have already mentioned concerning ideas, other confiderations belong to them, in reference to things from whence they are taken, or which they may be fuppofed to reprefent: and thus, I think, they may come under a threefold diftinction; and are, First, Either real or fantaftical. First, By real ideas, I mean fuch as have a foundation. in nature; fuch as have a conformity with the real being and exiftence of things, or with their archetypes. Fantaftical or chimerical, I call fuch as have no founda tion 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 feveral forts of ideas before mentioned, we fhall find that, § 2. Simple Ideas all real. FIRST, Our fimple ideas are all real, all agree to the reality of things: Not that they are all of them the images or reprefentations of what does exift; the contrary whereof, in all but the primary qualities of bodies, hath been already fhown. But though whitenefs and coldnefs are no more in fnow than the pain is, yet those ideas of whitenefs and coldnefs, pain, &c. being in us the effects of powers in things without us, ordained by our Maker to produce in us fuch fenfations, they are real ideas in us, whereby we diftinguith the qualities that are really in things themselves. For these several appearances being defigned to be the marks whereby we are to know and dif tinguish things which we have to do with, our ideas do as well ferve us to that purpofe, and are as real diftinguishing characters, whether they be only conftant effects, or elfe exact resemblances of fomething in the things themselves; the reality lying in that fteady correfpondence they have with the diftinct conftitutions of real beings. But whether they answer to thofe conftitutions, as to caufes or patterns, it matters not; it fuffices that they are conitantly produced by them. And thus our fimple ideas are all real and true, because they anfwer and agree to thofe powers of things which produce them in our minds, that being all that is requifite to make them real, and not fictions at pleafure. For in fimple ideas (as has been thown) the mind is wholly confined to the operation of things upon it, and can make to itself no fimple idea, more than what it has received. §3. Complex Ideas are voluntary Combinations. THOUGH the mind be wholly paffive, in refpect of its fimple ideas, yet, I think, we may fay it is not so in refpect of its complex ideas; for thofe being combinations of fimple ideas put together, and united under one general name, it is plain that the mind of man uses fome kind of liberty, in forming those complex ideas : How elfe 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 fome fimple idea, which the other has not. The question then is, which of thefe are real, and which barely imaginary combinations? What collections agree to the reality of things, and what not? And to this I fay, That, §4 Mixed Modes, made of confiftent 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 thofe kind of ideas, to make them real, but that they be fo framed, that there be a poffibility of exifting conformable to them. These ideas themselves being archetypes, cannot differ from their archetypes, and fo cannot be chimerical, unless any one will jumble together in them inconfiftent ideas. Indeed, as any of them have the names of a known language affigned to them, by which he that has them in his mind would fignify them to others, fo bare poffibility of exifting is not enough they must have a conformity to the ordinary fignification 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 ufe calls liberality. But this fantasticalnefs relates more to propriety of fpeech than reality of ideas; for a man to be undisturbed in danger, fedately to confider what is fittest to be done, and to execute it steadily, is a mixed mode, or a complex idea of an action which may exift; but to be undisturbed in danger, without ufing one's reason or industry, is what is alfo poffible to be, and fo is as real an idea as the other; though the first of thefe, having the name courage given to it, may, in refpect of that name, be a right or wrong idea; but the other, whilft it has not a common received name of any known language affigned to it, is not capable of any deformity, being made with no reference to any thing but itself. § 5. Ideas of Subftances are real, when they agree with the Existence of Things. THIRDLY, Our complex ideas of fubftances being made all VOL. II. of them in reference to things exifting without us, and intended to be reprefentations of fubftances as they really are, are no farther real than as they are fuch combinations of fimple ideas as are really united, and coexift in things without us. On the contrary, thofe are fantaftical which are made up of fuch collections of fimple ideas as were never really united, never were found together in any substance; v. g. a rational creature, confifting of a horfe's head, joined to a body of human fhape, or fuch as the Centaurs are defcribed; or a body yellow, very malleable, fufible, and fixed, but lighter than common water; or an uniform unorganized body, confifting, as to fenfe, all of fimilar parts, with perception and voluntary motion joined to it. Whether fuch fubftances as thefe can poffibly exift or no, it is probable we do not know; but be that as it will, thefe ideas of fubftances being made conformable to no pattern exifting that we know, and confifting of fuch collections of ideas as no fubftance ever fhowed us united together, they ought to pafs with us for bly imaginary; but much more are thofe complex ideas fo, which contain in them any inconfiftency or contradiction of their parts. CHAP. XXXI. OF ADEQUATE AND INADEQUATE IDEAS. § 1. Adequate Ideas are fuch as perfectly reprefent their Archetypes. F our real ideas, fome are adequate, and fome are inadequate. Thefe I call adequate, which perfectly reprefent thofe archetypes which the mind fuppofes them taken from, which it intends them to ftand for, and to which it refers them. Inadequate ideas are fuch, which are but a partial or incomplete reprefentation of those archetypes to which they are referred. Upon which account it is plain, §2. Simple Ideas all adequate. FIRST, That all our fimple ideas are adequate; because being nothing but the effects of certain powers in hings, |