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finite space or duration, that idea is obscure, because made up of two inconsistent parts: therefore we are so easily confounded when we come to argue about infinite space or duration.

Of all other ideas it is number which furnishes us with the clearest idea of infinity. For even in space and duration, when the mind pursues the idea of infinity, it makes use of the repetition of numbers; and when it has added together as many millions as it pleases of known lengths of space and duration, the clearest idea it can get of infinity is the incomprehensible remainder of endless addible numbers.

It will give us a little farther light into the idea we have of infinity, if we consider that number is not generally thought infinite; whereas duration and extension are. In number we are, as it were, at one end, for there being nothing less than a unit, there we stop; but in addition, we can set no bounds. So it is like a line, one end terminating with us, and the other extended beyond all conception. But in duration we consider the line infinitely extended both ways, and which is nothing else but turning this infinity of numbers both ways, a parte ante, and a parte post. For when we consider eternity a parte ante, we begin from the present time, repeating ideas of years and ages with all the infinity of number; and when we consider eternity a parte post, we begin from ourselves, and reckon by periods to come, extending the line of number as before; and these being put together are the infinite duration we call eternity. The same happens in space, wherein, conceiving ourselves in the centre, we on all sides pursue the interminable lines of number; and having no more reason to set bounds to those repeated ideas than we have to set bounds to number, we have the idea of immensity. And since our thoughts can never arrive at the utmost divisibility of matter, there is an infinity in that which has also the infinity of number; but while in

the former considerations we use addition, this is like the division of a unit into fractions, wherein the mind can proceed in infinitum, by the addition, still, of new numbers; though in the one we cannot have the idea of a space infinitely great, nor in the other of a body infinitely little; our idea of infinity being in a boundless progression.

Though no one can be so absurd as to say he has a positive idea of an infinite number, yet there are those who imagine that they have positive ideas of infinite space and duration. But to ask such a one whether he could add to his idea, would show him his mistake. We can have no idea of any space or duration which is not commensurate to repeated numbers of the common measures whereby we judge of the greatness of these quantities; and, therefore, since an idea of infinite space or duration must be made up of infinite parts, it can have no other infinity than that of number still capable of farther addition.

It is a pleasant argument, whereby the idea of infinite is proved to be positive by the negation of an end, which, being negative, the negation of it is positive. But end is not negative. He that perceives that the end of his pen is black or white, will be apt to think that end to be something more than a negation: and when applied to duration, the end is but the last moment of it. But if they will have the end to be a negation, they cannot conceive the beginning to be also a bare negation; and, therefore, their idea of eternal, a parte ante, must be a negative idea.

The idea of infinite has something of positive in the things that we apply to it. When we think of infinite space or duration, we make some large idea, as of millions of miles or ages, and all that we amass together is positive. But of what remains we have no more a positive notion than the mariner has of the depth of the sea when his sounding line reaches not the bottom. He knows the depth to be so many

fathoms; but how much more, he hath no distinct notion. So much as the mind comprehends of any space it has a distinct idea of; but in endeavoring to make it infinite, the idea is imperfect and incomplete. 1. The idea of so much is positive and clear. 2. The idea of greater is also clear, though it is but a comparative idea. 3. The idea of so much greater as cannot be comprehended is plain negative, and not positive. For to say a man can have a positive idea of any quantity without knowing how great it is, is as reasonable as to say that he has a clear idea of the number of the sands on the shore who knows not how many they be, but only that they are more than twenty. So that what lies beyond our positive idea towards infinity, has the confusion of a negative idea; and that is far from a positive idea, whereof the greatest part is left out under the indeterminate intimation of being still greater. For to say, that having in any quantity gone so far, yet you are not at the end, is to say that that quantity is greater, and a total negation of an end is but carrying the idea of greater in all the progressions of your thoughts, and adding the idea of greater to all the ideas you have of quantity. Whether such an idea as that be positive, I leave any one to consider.

I ask those who say they have a positive idea of eternity, whether their idea of duration includes succession or not. If not, they should show the difference of duration as applied to an eternal and to a finite being. If, to avoid succession in eternal existence, they recur to the punctum stans of the schools, they will not thereby help us to a clearer idea of infinite duration. Besides, that punctum stans being not quantum, finite or infinite cannot belong to it. But if we cannot separate succession from duration, our idea of eternity can be only of an infinite succession of moments, and I leave any one to consider whether he has a positive idea of an actual infinite

number. I think it unavoidable for every rational creature to have the notion of an eternal wise Being, who had no beginning. Such an idea of infinite duration I am sure I have; but this negation of a beginning gives me not a positive idea of infinity.

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He that thinks he has a positive idea of infinite space will find that he has no more idea of the greatest than he has of the least space. All our positive ideas of any quantity, whether great or little, have bounds; though our comparative idea, whereby we can add to the one and take from the other, has no bounds. pestle and mortar will as soon bring any particle of matter to indivisibility, as the acutest thought of the mathematician. He that thinks on a cube of an inch diameter has a clear idea of it, and so can frame one of, 4, 1, and so on, till he has the idea of something very little but he reaches not the idea of the incomprehensible littleness which division can pro

duce.

Some persons persuade themselves that they have a positive idea of eternity, but that they have not an idea of infinite space: the reason of which I suppose to be, that finding it necessary to admit some eternal Being, they consider the real existence of that Being, as taking up their idea of eternity; but not finding it necessary that body should be infinite, they conclude they have no idea of infinite space, because they have no idea of infinite matter. But the existence of matter is no more necessary to the existence of space, than the existence of the sun is necessary to duration, though duration be measured by it. It is as easy to have the idea of space empty of body as to think of the capacity of a bushel without corn. And why should we think our idea of space requires the existence of matter, when we have as clear an idea of infinite duration to come as we have of infinite duration past? though nobody conceives that any thing has existed in that future duration. Those philoso

phers who are of opinion that infinite space is possessed by God's 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, but they cannot have a positive idea of infinity in either case. For whatever positive idea a man has of any quantity, he may repeat it; so that if a man had a positive idea either of infinite duration or space, he could add two infinities together, an absurdity too gross to be confuted. I am apt to think that the difficulties, which involve all discourses concerning infinity, are the marks of a defect in our ideas of infinity and the disproportion the nature of it has to our narrow capacities. For while men talk of infinite space or duration, as if they had as positive ideas of them as they have of a yard or an hour, it is no wonder if the incomprehensible nature of the thing they reason about leads them into perplexities and contradictions.

I pretend not to treat of duration, space, number, and infinity, in their full latitude; it suffices to show that the mind receives them from sensation and reflection, and how the idea of infinity, remote as it may seem from any object of sense or operation of the mind, has, as all our other ideas, its original there.

CHAPTER XVIII.

Of other simple Modes.

Though the instances I have given in the foregoing chapters of simple modes of the simple ideas of sensation might suffice to show how the mind comes by them, yet for method's sake I shall briefly give a few

more.

To slide, roll, tumble, walk, &c. are words which present to the mind distinct ideas, which are but the different modifications of motion. Modes of motion answer those of extension. Swift and slow are com

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