CHAP. XXIX. of those numbers. Such a degree of smallness is not un- BOOK II. reasonable 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, CHAP. XXIX. BOOK II. 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 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 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 1. 1 The complex ideas of infinity in space and time, 'substance in general,' power and causation, personality and its identity-which Locke uses as crucial instances in support of his fundamental principle of the dependence of all our ideas of things upon data of experience-are also illustrations of the inevitable obscurity and indistinctness which a human under. standing, measured by sense, finds itself enveloped in, when it tries to think them out, and finds that at last omnia exeunt in mysteria. CHAPTER XXX. OF REAL AND FANTASTICAL IDEAS. CHAP. 1. BESIDES what we have already mentioned concerning BOOK II. ideas, other considerations belong to them, in reference to things from whence they are taken, or which they may be supposed to represent1; and thus, I think, they may come Ideas conunder 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 2. If we examine 1 In this and the two next chapters our ideas are considered in their possible relation to what really exists. Hitherto, for the most part (except in chap. viii.), the inquiry has been confined to ideas per se; they have been viewed in abstraction from their reality, adequacy, and truth, and thus from the propositions into which they enter, or which are presupposed in them. Locke here approaches those considerations and so prepares for the questions about knowledge that belong to the fourth Book. Cf. Bk. IV. chh. iii, iv, ix, x, xi. VOL. I. ''Nothing,' says Berkeley, 'seems of more importance towards erecting a firm system of sound and real knowledge than to lay the beginning in a distinct explication of what is meant by thing, reality, existence; for in vain shall we dispute concerning the real existence of things, or pretend to any knowledge thereof, so long as we have not fixed the meaning of these words.' (Principles, § 89.) In the analysis of our ideas, in the second Book, Locke has not included the idea of reality. He refers to it here, but without inquiring K k XXX. sidered in reference to their Arche types. BOOK II. the several sorts of ideas before mentioned, we shall find СНАР. XXX. Simple Ideas are all real appear ances of things. that, 2. 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 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 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 2, 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. whether it implies dependence on That the ultimate intelligibility of things is the test of their reality is the conception of the real, opposed to this of Hume, by Hegel. 1 As the secondary qualities of bodies are supposed to do. 2 As the primary qualities of bodies are supposed to be. * In the 'simple ideas of sensation and reflection,' reality, he implies, manifests itself to us; either directly, as in the primary or real qualities of matter, and in the operations of our XXX. Ideas are tions. 3. Though the mind be wholly passive in respect of its simple BOOK II. ideas; yet, I think, we may say it is not so in respect of its СНАР. complex ideas. For those being combinations of simple ideas put together, and united under one general name, it is plain Complex that the mind of man uses some kind of liberty in forming voluntary those complex ideas: how else comes it to pass that one Combinaman'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 not1? 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, Modes and consistent 4. Secondly, Mixed modes and relations, having no other Mixed reality but what they have in the minds of men, there is Relations, nothing more required to this kind of ideas to make them real, made of but that they be so framed, that there be a possibility of Ideas, are existing conformable to them. These ideas themselves, being real. archetypes, cannot differ from their archetypes, and so cannot self-conscious spirits, or indirectly in the sensations which, as secondary qualities, we 'impute' to bodies. It is, he maintains, in the simple ideas, or appearances which the real thus presents that all our complex ideas 'terminate,' including those of relation. Hence the momentous import of sense-perception with Reid and his followers; as against the extremes of nihilism and pure idealism. In its primary application, the real means something apprehended as existing in opposition to that which is not so apprehended, or in opposition to the absence of any appearance whatever. In the earliest conceivable form of perception there is something apprehended—not nothing; and we mean by the real at first, the appearance, percept, impression ['simple idea' of Locke], whatever we come to call it, which is known to consciousness, as opposed to the blank or negation of it; we call the impression real; we speak of the absence of impression as the unreal. .. Unless this form of reality is given to us, we are powerless to think |