a boundless space actually existing, since our ideas are not always proofs of the existence of things; but yet, since this comes here in our way, I suppose I may say, that we are apt to think that space in itself is actually boundless; to which imagination, the idea of space or expansion of itself naturally leads us. For it being considered by us, either as the extension of body, or as existing by itself, without any solid matter taking it up (for of such a void space we have not only the idea, but I have proved as I think, from the motion of body, its necessary existence) it is impossible the mind should be ever able to find or suppose any end of it, or be stopped any where in its progress in this space, how far soever it extends its thoughts. Any bounds made with body, even adamantine walls, are so far from putting a stop to the mind in its farther progress in space and extension, that it rather facilitates and enlarges it for so far as that body reaches, so far no one can doubt of extension; and when we are come to the utmost extremity of body, what is there that can there put a stop, and satisfy the mind that it is at the end of space, when it perceives that it is not; nay, when it is satisfied that body itself can move into it? For if it be necessary for the motion of body, that there should be an empty space, though ever so little, here amongst bodies; and if it be possible for body to move in or through that empty space; nay it is impossible for any particle of matter to move but into an empty space; the same possibility of a body's moving into a void space, beyond the utmost bounds of body, as well as into a void space interspersed amongst bodies, will always remain clear and evident: the idea of empty pure space, whether within or beyond the confines of all bodies, being exactly the same, differing not in nature, though in bulk: and there being nothing to hinder body from moving into it. So that wherever the mind places: itself by any thought, either amongst or remote from all bodies, it can in this uniform idea of space no-where find any bounds, any end; and so must necessarily conclude it, by the very nature and idea of each part of it, to be actually infinite.

so of

§. 5. As by the power we find in our- And selves of repeating, as often as we will, any duration. idea of space, we get the idea of immensity;

so, by being able to repeat the idea of any length of duration we have in our minds, with all the endless addition of number, we come by the idea of eternity. For we find in ourselves, we can no more come to an end of such repeated ideas, than we can come to the end of number, which every one perceives he cannot. But here again it is another question, quite different from our having an idea of eternity, to know whether there were any real being, whose duration has been eternal. And as to this, I say, he that considers something now existing, must necessarily come to something eternal. But having spoke of this in another place, I shall say here no more of it, but proceed on to some other considerations of our idea of infinity.

§. 6. If it be so, that our idea of infinity Why other be got from the power we observe in our ideas are not selves of repeating without end our own capable of ideas; it may be demanded, "why we do infinity. "not attribute infinite to other ideas, as well as those "of space and duration;" since they may be as easily, and as often repeated in our minds, as the other; and yet nobody ever thinks of infinite sweetness, or infinite whiteness, though he can repeat the idea of sweet or white, as frequently as those of a yard, or a day? To which I answer, all the ideas that are considered as hav ing parts, and are capable of increase by the addition of any equal or less parts, afford us by their repetition the idea of infinity; because with this endless repetition, there is continued an enlargement, of which there can be no end. But in other ideas it is not so; for to the largest idea of extension or duration that I at present have, the addition of any the least part makes an increase; but to the perfectest idea I have of the whitest whiteness, if I add another of a less or equal whiteness, (and of a whiter than I have, I cannot add the idea) it makes no increase, and enlarges not my idea at all: and therefore the different ideas of whiteness, &c. are called degrees. For those ideas that consist of parts are capa

ble of being augmented by every addition of the least part; but if you take the idea of white, which one parcel of snow yielded yesterday to our sight, and another idea of white from another parcel of snow you see to-day, and put them together in your mind, they embody, as it were, and run into one, and the idea of whiteness is not at all increased, and if we add a less degree of whiteness to a greater, we are so far from increasing that we diminish it. Those ideas that consist not of parts cannot be augmented to what proportion men please, or be stretched beyond what they have received by their senses; but space, duration, and number, being capable of increase by repetition, leave in the mind an idea of endless room for more: nor can we conceive any where a stop to a farther addition or progression, and so those ideas alone lead our minds towards the thought of infinity.

Difference between in finity of

space, and

space infinite.

§. 7. Though our idea of infinity arise from the contemplation of quantity, and the endless increase the mind is able to make in

quantity, by the repeated additions of what portions thereof it pleases; yet I guess we cause great confusion in our thoughts, when we join infinity to any supposed idea of quantity the mind can be thought to have, and so discourse or reason about an infinite quantity, viz. an infinite space, or an infinite duration. For our idea of infinity being as I think, an endless growing idea, by the idea of any quantity the mind has, being at that time terminated in that idea, (for be it as great as it will, it can be no greater than it is) to join infinity to it, is to adjust a standing measure to a growing bulk; and therefore I think it is not an insignificant subtilty, if I say that we are carefully to distinguish between the idea of the infinity of space, and the idea of a space infinite: the first is nothing but a supposed endless progression of the mind, over what repeated ideas of space it pleases; but to have actually in the mind the idea of a space infinite, is to suppose the mind already passed over, and actually to have a view of all those repeated ideas of space, which

an endless repetition can never totally represent to it; which carries in it a plain contradiction.

idea of infi

§. 8. This, perhaps, will be a little plainer, if we consider it in numbers. The We have no infinity of numbers to the end of whose nite space. addition every one perceives there is no ap

proach, easily appears to any one that reflects on it: but how clear soever this idea of the infinity of number be, there is nothing yet more evident, than the absurdity of the actual idea of an infinite number. Whatsoever positive ideas we have in our minds of any space, duration, or number, let them be ever so great, they are still finite; but when we suppose an inexhaustible remainder, from which we remove all bounds, and wherein we allow the mind an endless progression of thought, without ever completing the idea, there we have our idea of infinity; which though it seems to be pretty clear when we consider nothing else in it but the negation of an end, yet when we would frame in our minds the idea of an infinite space or duration, that idea is very obscure and confused, because it is made up of two parts, very different, if not inconsistent. For let a man frame in his mind an idea of any space or number, as great as he will: it is plain the mind rests and terminates in that idea, which is contrary to the idea of infinity, which consists in a supposed endless progression. And therefore I think it is, that we are so easily confounded, when we come to argue and reason about infinite space or duration, &c. Because the parts of such an idea not being perceived to be, as they are, inconsistent, the one side or other always perplexes, whatever consequences we draw from the other; as an idea of motion not passing on would perplex any one, who should argue from such an idea, which is not better than an idea of motion at rest and such another seems to me to be the idea of a space, or (which is the same thing) a number infinite, i. e. of a space or number which the mind actually has, and so views and terminates in; and of a space or number, which in a constant and endless enlarging and progression, it can in thought never attain to. For how large soever an idea of space I have in my mind, it is

no larger than it is that instant that I have it, though I be capable the next instant to double it, and so on in infinitum for that alone is infinite which has no bounds; and that the idea of infinity, in which our thoughts can find none.

Number af- §. 9. But of all other ideas it is numfords us the ber, as I have said, which I think furclearest idea nishes us with the clearest and most distinct of infinity. idea of infinity we are capable of. For even in space and duration, when the mind pursues the idea of infinity, it there makes use of the ideas and repetitions of numbers, as of millions and millions of miles, or years, which are so many distinct ideas, kept best by number from running into a confused heap, wherein the mind loses itself; and when it has added together as many millions, &c. as it pleases of known lengths of space or duration, the clearest idea it can get of infinity, is the confused incomprehensible remainder of endless addible numbers, which affords no prospect of stop or boundary.

Our different conception of the

infinity of number, du

ration, and expansion.

A

§. 10. It will, perhaps, give us a little farther light into the idea we have of infinity, and discover to us that it is nothing but the infinity of number applied to determinate parts, of which we have in our minds the distinct ideas, if we consider, that number is not generally thought by us infinite, whereas duration and extension are apt to be so; which arises from hence, that in number we are at one end as it were: for there being in number nothing less than an unit, we there stop, and are at an end; but in addition or increase of number, we can set no bounds. And So it is like a line, whereof one end terminating with us, the other is extended still forwards beyond all that we can conceive; but in space and duration it is otherwise. For in duration we consider it, as if this line of number were extended both ways to an unconceivable, undeterminate, and infinite length; which is evident to any one that will but reflect on what consideration he hath of eternity; which, I suppose, he will find to be nothing else, but the turning this infinity of