multiply them in our thoughts as far as we can, with all the infinity of endlefs number. I do not pretend to say how these attributes are in God, who is infinitely beyond the reach of our narrow capacities. They do, without doubt, contain in them all poffible perfection: but this, I fay, is our way of conceiving them, and these our ideas of their infinity.

The idea of finite cafily

got.

As for The ob

§. 2. Finite then, and infinite, being by the mind looked on as modifications of expanfion and duration, the next thing to be confidered, is, how the mind comes by them. the idea of finite, there is no great difficulty. vious portions of extenfion that affect our fenfes, carry with them into the mind the idea of finite: and the ordinary periods of fucceffion, whereby we measure time and duration, as hours, days, and years, are bounded lengths. The difficulty is, how we come by those boundlefs ideas of eternity and immenfity, fince the objects we converfe with, come fo much fhort of any approach or proportion to that largeness.

How we come by the idea of infinity.

on, with

§. 3. Every one that has any idea of any ftated lengths of space, as a foot, finds that he can repeat that idea; and, joining it to the former, make the idea of two feet; and by the addition of a third, three feet; and fo out ever coming to an end of his addition, whether of the fame idea of a foot, or if he pleases of doubling it, or any other idea he has of any length, as a mile, or diameter of the earth or of the orbis magnus: for whichfoever of these he takes, and how often foever he doubles, or any otherwife multiplies it, he finds that after he has continued his doubling in his thoughts, and enlarged his idea as much as he pleases, he has no more reason to stop, nor is one jot nearer the end of fuch addition, than he was at first fetting out. The power of enlarging his idea of space by farther additions remaining ftill the fame, he hence takes the idea of infinite space.

§. 4. This, I think, is the way whereby the mind gets the idea of infinite space. It is a quite different confideration, to examine whether the mind has the idea of fuch

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our idea of fpace boundlefs.

a bound

a boundless space actually exifting, fince our ideas are not always proofs of the existence of things; but yet, fince this comes here in our way, I fuppofe I may fay, that we are apt to think that space in itself is actually boundless; to which imagination, the idea of space or expanfion of itself naturally leads us. For it being confidered by us, either as the extenfion of body, or as exifting by itself, without any folid matter taking it up (for of fuch a void space we have not only the idea, but I have proved as I think, from the motion of body, its neceffary exiftence) it is impoffible the mind fhould be ever able to find or fuppofe any end of it, or be stopped any where in its progrefs in this space, how far foever 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 fpace and extenfion, that it rather facilitates and enlarges it; for fo 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 ftop, and fatisfy the mind that it is at the end of fpace, when it perceives that it is not; nay, when it is fatisfied that body itself can move into it? For if it be neceffary for the motion of body, that there should be an empty space, though ever fo little, here amongst '. bodies; and if it be poffible for body to move in or through that empty space; nay it is impoffible for any particle of matter to move but into an empty space; - the fame poffibility of a body's moving into a void fpace, beyond the utmost bounds of body, as well as into a void fpace interfperfed amongst bodies, will always remain clear and evident: the idea of empty pure fpace, whether within or beyond the confines of all bodies, being exactly the fame, differing not in nature, though in bulk; and there being nothing to hinder body from moving into it. So that wherever the mind places itfelf 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 fo muft neceffarily conclude it, by the very nature and idea of cach part of it, to be actually infinite,

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And fo of

duration.

S. 5. As by the power we find in ourfelves of repeating, as often as we will, any idea of fpace, we get the idea of immen-.. fity; fo, 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 fuch repeated ideas, than we can come to the end of number, which every one perceives he cannot. But here again it is another queftion, quite different from our having an idea of eternity, to know whether there were any real being, whofe duration has been eternal. And as to this, I fay, he that confiders fomething now exifting, muft neceffarily come to fomething eternal. But having spoke of this in another place, fhall fay here no more of it, but proceed on to fome other confidera, tions of our idea of infinity.

Why other

ideas are not capable of infinity.

§. 6. If it be fo, that our idea of infinity be got from the power we obferve in our felves of repeating without end our own ideas; it may be demanded, "why we do "not attribute infinite to other ideas, as well as thofe "of space and duration;" fince they may be as easily and as often repeated in our minds, as the other; and yet no-body ever thinks of infinite sweetness, or infinite whitenefs, though he can repeat the idea of fweet or white, as frequently as thofe of a yard, or a day? To which I answer, all the ideas that are confidered as hav ing parts, and are capable of increase by the addition of any equal or lefs parts, afford us by their repetition the idea of infinity; becaufe with this endless repetition, there is continued an enlargement, of which there can be no end. But in other ideas it is not fo; for to the largest idea of extenfion or duration that I at present have, the addition of any the leaft part makes an increase; but to the perfecteft idea I have of the whiteft whiteness, if I add another of a lefs 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 whitenefs, &c. are called degrees. For those ideas that confist of parts are capa

ble of being augmented by every addition of the leaft part; but if you take the idea of white, which one parcel of fnow yielded yesterday to our fight, and another idea of white from another parcel of fnow you fee 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 lefs degree of whiteness to a greater, we are so far from increafing that we diminish it. Thofe ideas that confift not of parts cannot be augmented to what proportion men please, or be stretched beyond what they have received by their fenfes; but space, duration, and number, being capable of increafe 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 progreffion, and fo those ideas alone lead our minds towards the thought of infinity.

Difference

between infi

nity of fpace, and space in

finite.

S. 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 caufe great confufion in our thoughts, when we join infinity to any fuppofed idea of quantity the mind can be thought to have, and fo difcourfe or reafon about an infinite quantity, viz. an infinite space, or an infinite duration. For our idea of infinity being as I think, an endlefs 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 ftanding meafure to a growing bulk; and therefore I think it is not an infignificant fubtilty, if I fay that we are carefully to diftinguish, between the idea of the infinity of space, and the idea of a fpace infinite: the first is nothing but a fuppofed endlefs progreffion of the mind, over what repeated ideas of space it pleafes; but to have actually in the mind the idea of a fpace infinite, is to fuppofe the mind already paffed over, and actually to have a view of all thofe repeated ideas of fpace, which

an

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

We have no

§. 8. This, perhaps, will be a little plainer, if we confider it in numbers. The idea of infi infinity of numbers, to the end of whofe, nite fpace. addition every one perceives there is no ap

proach, eafily appears to any one that reflects on it: but how clear foever this idea of the infinity of number be, there is nothing yet more evident, than the abfurdity of the actual idea of an infinite number. Whatfoever po fitive ideas we have in our minds of any space, duration, or number, let them be ever fo great, they are still finite; but when we fuppofe an inexhauftible remainder, from which we remove all bounds, and wherein we allow the mind an endless progreffion of thought, without ever compleating the idea, there we have our idea of infinity; which though it seems to be pretty clear when we confider nothing elfe in it but the negation of an end, yet when we would frame in our minds the idea of an infinite fpace or duration, that idea is very obfcure and confufed, because it is made up of two parts, very different, if not inconfiftent. For let a man frame in his mind an idea of any fpace or number, as great as he will it is plain the mind refts and terminates in that idea, which is contrary to the idea of infinity, which confifts in a fuppofed endlefs progreffion. And therefore I think it is, that we are so easily confounded, when we come to argue and reafon about infinite space or duration, &c. Because the parts of fuch an idea not being perceived to be, as they are, inconfiftent, the one fide or other always perplexes, whatever confequences we draw from the other; as an idea of motion not paffing on would perplex any one, who fhould argue from fuch an idea, which is not better than an idea of motion at reft and fuch another feems to me to be the idea of a fpace, or (which is the fame thing) a number infinite, i. e. of a space or number which the mind actually has, and fo views and terminates in; and of a space or number, which in a conftant and endless enlarging and progreffion, it can in thought never attain to. For how large foever an idea of fpace I have in my mind, it is

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