which will always be less than any one whereof we have the positive idea. All our positive ideas of any quantity, whether great or little, have always bounds; 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 our 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,,, 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 smallness, which is consequent to infinite divisibility. po What is §. 19. Every one that looks towards insitive, what finity does, as I have said, at first glance negative, in make some very large idea of that which our idea of he applies it to, let it be space or duration; infinite. 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: Rusticus expectat dum transeat amnis, at ille Some think they have a positive idea of eternity, and not ofin §. 20. There are some I have met with that put so much difference between infinite duration and infinite space that they persuade themselves that they have a positive idea of eternity; but that they have not, finite space. nor can have any idea of ifinnite 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 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 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 mah 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 §. 21. But yet after all this, there being positive men who persuade themselves that they. ideas of infi- have clear positive comprehensive ideas of 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 ob ject too large and mighty to be surveyed and managed by them. All these tion. §. 22. If I have dwelt pretty long on the consideration of duration, space, and num- ideas from ber, and what arises from the contemplation sensation of them, infinity; it is possibly no more than and reflecthe 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. CHAP. XVIII. Of other Simple Modes. §. 1. THOUGH I have in the foregoing Modes of chapters shown, how from simple ideas, motion. 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 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 of time and space put together; so they are complex ideas comprehending time and space with motion. Modes of §. 3. The like variety have we in sounds. sounds. Every articulate word is a different modification 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. colours. Modes of §. 4. Those of colours are also very va rious: some we take notice of as the different 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. Modes of taste. §. 5. All compounded tastes and smells are also modes made up of the simple ideas of those senses. But they being such as generally we have no names for, are less taken notice of, and cannot be set down in writing; and therefore must be left without enumeration to the thoughts and experience of my reader. |