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have not, nor can have any idea of infinite space. The reason of which mistake I suppose to be this, that finding by a due contemplation of causes and effects, that it is necessary to admit some eternal being, and so to consider the real existence of that being, as taken up and commensurate to their idea of eternity ; but, on the other side, not finding it necessary, but on the contrary apparently absurd, that body should be infinite; they forwardly conclude, that they 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 any thing 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 space; yet those philosophers who are of opinion that infinite space is possessed by God's infinite omnipresence, as well as infinite duration by his external 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 idea 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.
$ 21. But yet after all this, there being Supposed men who persuade themselves that they positive have clear positive comprehensive ideas of
ideas of infi
nity, cause infinity, it is fit they enjoy their privilege: of mistakes. and I should be 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. All these $ 22. If I have dwelt pretty long on ideas from
the consideration of duration, space, and sensation and reflec ca number, and what arises from the contion.
templation of them, infinity ; it is possibly no more than the matter requires, there being few simple ideas whose modes give more exercise to the thoughts of men than these do. I pretend not to treat of them in their full latitude; it suffices to my design to show how the mind receives them, such as they are, from sensation and reflection; and how even the 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. 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 infinity from sensation and reflection, in the method we have here set down.
Of other Simple Modes. Modes of $ 1. Though I have in the foregoing motion. chapters shown how from simple ideas, taken in by sensation, the mind comes to extend itself even to infinity; which however it may, of all others, seem most remote from any sensible perception, yet at last hath nothing in it 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
even to infinitisation, the mind w from si
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.
S 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 of time and space put together; so they are complex ideas comprehending time and space with motion.
S 3. The like variety have we in sounds. Modes of Every articulate word is a different modi. sounds. fication of sound : by which we see, that from the sense of hearing, by such modifications, the mind may be furnished with distinct ideas to almost an infinite number. Sounds also, besides the distinct cries of birds and beasts, are modified by diversity of notes of different length put together, which make that complex idea called a tune, which a musician may have in his mind when he hears or makes no sound at all, by reflecting on the ideas of those sounds so put together silently in his own fancy.
4. Those of colours are also very vari. Modes of ous: some we take notice of as the different colours. degrees, or, as they are termed, shades of the same colour. But since we very seldom make assemblages of colours either for use or delight, but figure is taken in also and has its part in it, as in painting, weaving, needle-works, &c. those which are taken notice of do most commonly belong to mixed modes, as being made up of ideas of divers kinds, viz. figure and colour, such as beauty, rainbow, &c.
§ 5. All compounded tastes and smells Modes of are also modes made up of the simple ideas taste. of those senses. But they being such as generally we
our idea of think of infinite space or duration, we at infinite. first step usually make some very large idea, as perhaps of millions of ages, or miles, which possibly we double and multiply several times. All that we thus amass together in our thoughts is positive, and the assemblage of a great number of positive ideas of space or duration. But what still remains beyond this, we have no more a positive distinct notion of, than a mariner has of the depth of the sea; where, having let down a large portion of his sounding-line, he reaches no bottom : whereby he knows the depth to be so many fathoms, and more; but how much the more is he hath no distinct notion at all: and could he always supply new line, and find the plummet always sink, without ever stopping, he would be something in the posture of the mind reaching after a complete and positive idea of infinity. In which case let this line be ten, or one thousand fathoms long, it equally discovers what is beyond it; and gives only this confused and comparative idea, that this is not all, but one may yet go farther. So much as the mind comprehends of any space, it has a positive idea of; but in endeavouring to make it infinite, it being always enlarging, always advancing, the idea is still imperfect and incomplete. So much space as the mind takes a view of in its contemplation of greatness, is a clear picture, and positive in the understanding: but infinite is still greater. 1. Then the idea of so much is positive and clear. 2. The idea of greater is also clear, but it is but a comparative idea, viz. the idea of so much greater as cannot be comprehended; and this is plainly negative, not positive. For he has no positive clear idea of the largeness of any extension (which is that sought for in the idea of infinite), that has not a comprehensive idea of the dimensions of it; and such nobody, I think, pretends to in what is infinite. For to say a man has a positive clear idea of any quantity, without knowing how great it is, is as reasonable as to say, he has the positive clear idea of