CHAP. BOOK II. though our comparative idea, whereby we can always add to the one, and take from the other, hath no bounds. For that which remains, either great or little, not being comprehended in that positive idea which we have, lies in obscurity; and we have no other idea of it, but of the power of enlarging the one and diminishing the other, without ceasing. A pestle and mortar will as soon bring any particle of matter to indivisibility, as the acutest thought of a mathematician; and a surveyor may as soon with his chain measure out infinite space, as a philosopher by the quickest flight of mind reach it, or by thinking comprehend it; which is to have a positive idea of it. He that thinks on a cube of an inch diameter, has a clear and positive idea of it in his mind, and so can frame one of 1, 1, 1, and so on, till he has the idea in his thoughts of something very little; but yet reaches not the idea of that incomprehensible littleness which division can produce. What remains of smallness is as far from his thoughts as when he first began; and therefore he never comes at all to have a clear and positive idea of that smallness1 which is consequent to infinite divisibility. What is what in our Idea of Infinite. 19. Every one that looks towards infinity does, as I have positive, said, at first glance make some very large idea of that which negative, he applies it to, let it be space or duration; and possibly he wearies his thoughts, by multiplying in his mind that first large idea: but yet by that he comes no nearer to the having a positive clear idea of what remains to make up a positive infinite, than the country fellow had of the water which was yet to come, and pass the channel of the river where he stood: Some 'Rusticus expectat dum defluat amnis, at ille 20. There are some I have met that put so much difference think they between infinite duration and infinite space, that they persuade 1 'smallness'-rather no complete intelligence are incommensurate in the idea of what the intellectual outcome case of infinity, but not in the other would be of the divisibility towards which one is intellectually impelled. 2 'no nearer'-the two states of case. Horat. Epist. I. ii. 42. CHAP. Idea of infinite themselves that they have a positive idea of eternity, but that BOOK II. they have not, nor can have any idea of infinite space. The reason of which mistake I suppose to be this-that finding, XVII. by a due contemplation of causes and effects, that it is neces- have a sary to admit some Eternal Being, and so to consider the real positive existence of that Being as taken up and commensurate to Eternity, their idea of eternity; but, on the other side, not finding it and not of necessary, but, on the contrary, apparently absurd, that body Space. should be infinite, they forwardly conclude that they can have no idea of infinite space, because they can have no idea of infinite matter. Which consequence, I conceive, is very ill collected, because the existence of matter is no ways necessary to the existence of space, no more than the existence of motion, or the sun, is necessary to duration, though duration uses to be measured by it. And I doubt not but that a man may have the idea of ten thousand miles square, without any body so big, as well as the idea of ten thousand years, without any body so old. It seems as easy to me to have the idea of space empty of body, as to think of the capacity of a bushel without corn, or the hollow of a nut-shell without a kernel in it it being no more necessary that there should be existing a solid body, infinitely extended, because we have an idea of the infinity of space, than it is necessary that the world should be eternal, because we have an idea of infinite duration. And why should we think our idea of infinite space requires the real existence of matter to support it, when we find that we have as clear an idea of an infinite duration to come, as we have of infinite duration past? Though I suppose nobody thinks it conceivable that anything does or has existed in that future duration. Nor is it possible to join our idea of future duration with present or past existence, any more than it is possible to make the ideas of yesterday, to-day, and to-morrow to be the same; or bring ages past and future together, and make them contemporary. But if these men are of the mind, that they have clearer ideas of infinite duration than of infinite space, because it is past doubt that God has existed from all eternity, but there is no real matter co-extended with infinite 1 cf. ch. xv. § 4. CHAP. XVII. BOOK II. space; yet those philosophers who are of opinion that infinite space is possessed by God's infinite omnipresence 1, as well as infinite duration by his eternal existence, must be allowed to have as clear an idea of infinite space as of infinite duration; though neither of them, I think, has any positive idea of infinity in either case. For whatsoever positive ideas a man has in his mind of any quantity, he can repeat it, and add it to the former, as easy as he can add together the ideas of two days, or two paces, which are positive ideas' of lengths he has in his mind, and so on as long as he pleases: whereby, if a man had a positive idea of infinite, either duration or space, he could add two infinites together; nay, make one infinite infinitely bigger than another-absurdities too gross to be confuted. Supposed positive Ideas of Infinity, cause of 21. But yet if after all this, there be men who persuade themselves that they have clear positive comprehensive ideas of infinity, it is fit they enjoy their privilege: and I should be Mistakes. very glad (with some others that I know, who acknowledge they have none such) to be better informed by their communication. For I have been hitherto apt to think that the great and inextricable difficulties which perpetually involve all discourses concerning infinity,—whether of space, duration, or divisibility, have been the certain marks of a defect in our ideas of infinity, and the disproportion the nature thereof has to the comprehension of our narrow capacities. For, whilst men talk and dispute of infinite space or duration, as if they had as complete and positive ideas of them as they have of the names they use for them, or as they have of a yard, or an hour, or any other determinate quantity; it is no wonder if the incomprehensible nature of the thing they discourse of, or reason about, leads them into perplexities and contradictions, and their minds be overlaid by an object too large and mighty to be surveyed and managed by them 2. 1 Not that God is extended, as solid and extended things are, but that Divine Reason is everywhere manifested and operative. The expression also suggests Samuel Clarke's attempt to demonstrate, that the existence of God is implied in the necessary infinity of space-which is thus regarded as an attribute of the Divine Being. 2 Are not these 'perplexities and contradictions' evidence of the inadequacy of the supposition that the (unimaginable) Infinite consists of parts, is thus numerable? Leibniz refers to of Ideas Sensation 22. If I have dwelt pretty long on the consideration of BOOK II. duration, space, and number, and what arises from the con- CHAP. templation of them,-Infinity, it is possibly no more than the XVII. matter requires; there being few simple ideas whose modes All these give more exercise to the thoughts of men than those do. I are modes pretend not to treat of them in their full latitude 1. It suffices got from to my design to show how the mind receives them, such as and Rethey are, from sensation and reflection; and how even the flection. idea we have of infinity, how remote soever it may seem to be from any object of sense, or operation of our mind, has, nevertheless, as all our other ideas, its original there 2. Some mathematicians perhaps, of advanced speculations, may have other ways to introduce into their minds ideas of infinity. But this hinders not but that they themselves, as well as all other men, got the first ideas which they had of infinity3 from sensation and reflection, in the method we have here set down. Locke's exposition of them in this chapter, when he writes as follows in 1696:-'Je crois avec M. Locke qu'à proprement parler on peut dire qu'il n'y a point d'espace, de tems, ni de nombre, qui soit infini; mais qu'il est seulement vrai que pour grand que soit un espace, un tems, ou un nombre, il y en a toujours un autre plus grand que lui sans fin ; et qu'ainsi le véritable Infini ne se trouve point dans un tout composé de parties.' (Opera, Erdman, p. 138.) But it is not on that account, he argues, unreal; for we find infinity absolutely in God, without parts, so that the true idea is presupposed in the idea of the finite. Thus with Locke the idea of the Infinite is that of endless increase of a finite positively given in sense; with Leibniz it is rationally given reality, mysteriously limited in our experience, under real relations of space, duration, and number. Not in their full latitude,' but only so far as they admit of being treated according to the 'historical plain method,' which only discovers the 2 In minima tangibilia and visibilia, 'First ideas,' i. e. first occasions of our having those indeterminate, inadequate, mysterious ideas that constitute reason 'first ideas,' so to speak, by which the candle of the Lord' is lighted in man. CHAPTER XVIII. OTHER SIMPLE MODES. BOOK II. СНАР. XVIII. Other simple Modes of simple Ideas of sensation. Simple modes of motion. 1. THOUGH I have, in the foregoing chapters, shown how, from simple ideas taken in by sensation, the mind comes to extend itself1 even to infinity; which, however it may of all others seem most remote from any sensible perception, yet at last hath nothing in it2 but what is made out of simple ideas: received into the mind by the senses, and afterwards there put together, by the faculty the mind has to repeat its own ideas; —Though, I say, these might be instances enough of simple modes of the simple ideas of sensation, and suffice to show how the mind comes by them, yet I shall, for method's sake, though briefly, give an account of some few more, and then proceed to more complex ideas. 2. To slide, roll, tumble, walk, creep, run, dance, leap, skip, and abundance of others that might be named, are words which are no sooner heard but every one who understands English has presently in his mind distinct ideas, which are all but the different modifications of motion. Modes of motion answer those of extension; swift and slow are two different ideas of motion, the measures whereof are made of the distances 1 'extend itself,' i.e. in its complex ideas. 2 i.e. nothing imaginable and immediately useful. Without the data of experience the understanding is empty and dormant; and this is the lesson which the Essay throughout emphasises, in teaching that human knowledge rises from the observation and comparison of concrete things. But it is not less true-this truth is indeed the indispensable ultimate support of human life-that the universe of things and persons, with all its natural and moral laws, is rooted in the Active Reason called God, in whom men and their world of sense have their being. |