§ 7. Difference between Infinity of Space and Space infinite.

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 pleafes, yet I guefs we, cause 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 fpace, or an infinite duration; for our idea of infinity being, as I think, an endless grow→ ing idea, but 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 infignificant fubtilty, if I fay that we are carefully to diftinguish between the idea of the infinity of space and the idea of a space infinite: The first is nothing but a fuppofed endlefs progreffion of the mind over what repeated ideas of fpace it pleases; but to have actually in the mind the idea of a space infinite, is to fuppofe the mind already paffed over, and actually to have a view of all those repeated ideas of space, which an endless repetition can never totally reprefent to it; which carries in it a plain contradiction.

8. We have no Idea of infinite Space.

THIS perhaps will be a little plainer if we confider it in numbers. The infinity of numbers, to the end of whofe addition every one perceives there is no approach, easily 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. Whatsoever pofitive 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 completing the idea, there we have our idea of infini

ty, which, though it feems to be pretty clear when we confider 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 obfcure and confufed, becaufe it is made up of two parts very different, if not inconfiftent. 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 refts and terminates in that idea, which is contrary to the idea of infinity, which confifts in a fuppofed endless progreffion; and therefore I think it is that we are fo eafily confounded when we come to argue or 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 wc 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 reft. And fuch another seems 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 space I have in my mind, it is no larger than it is that inftant that I have it, though I be capable the next inftant 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.

§ 9. Number affords us the clearest Idea of Infinity. Bur of all other ideas, it is number, as I have faid, which I think furnishes us with the clearest and most distinct idea of infinity we are capable of; for even in fpace and duration, when the mind purfues the idea of infinity, it there makes ufe of the ideas and repetitions of numbers, as of millions of millions of miles or years, which are fo many diftinct ideas, kept beft by number from running into a confufed heap, wherein the mind lofes itself; and when it has added together as

many millions, &c. as it pleafes of known lengths of fpace or duration, the cleareft idea it can get of infinity is the confufed incomprehenfible remainder of endless addable numbers, which affords no prospect of stop or boundary.

10. Our different Conception of Infinity, Number, Du

ration, and Expanfion.

Ir will perhaps give us a little farther light into the idea we have of infinity, and difcover to us that it is nothing but the infinity of number applied to determinate parts, of which we have in our minds the diftinct ideas, if we confider that number is not generally thought by us infinite, whereas duration and extenfion 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 ftop, and are at an end; but in addition or increase of number we can set no bounds; and fo it is like a line, whereof one end terminating with us, the other is extended ftill forwards beyond all that we can conceive; but in fpace and duration it is otherwife; for in duration we confider it as if this line of number were extended both ways to an inconceivable, undeterminate, and infinite length; which is evident to any one that will but reflect on what confideration he hath of eternity, which I fuppofe he will find to be nothing else but the turning this infinity of number both ways, à parte ante, and à parte poft, as they fpeak: For when we would confider eternity à parte ante, what do we but, beginning from ourselves and the prefent time we are in, repeat in our minds the ideas of years, or ages, or any other affignable portion of duration paft, with a prospect of proceeding in fuch addition with all the infinity of number? And when we would confider eternity à parte poft, we just, after the fame rate, begin from ourselves, and reckon by multiplied periods yet to come, ftill extending that line of number as before; and thefe two being put together, are that infinite duration we call eternity, which, as we turn our view either way, forwards or backwards, appears infinite, because we still turn that way

the infinite end of number, i. e. the power ftill of adding more.

THE fame happens alfo in space, wherein, conceiving ourselves to be as it were in the centre, we do on all fides pursue those indeterminable lines of number, and reckoning any way from ourselves a yard, mile, diameter of the earth, or orbis magnus, by the infinity of number, we add others to them as often as we will, and having no more reason to set bounds to thofe repeated ideas than we have to fet bounds to number, we have that indeterminable idea of immenfity.

12. Infinite Divifibility.

AND fince in any bulk of matter our thoughts can never arrive at the utmost divisibility, therefore there is an apparent infinity to us alfo in that which has the infinity alfo of number, but with this difference, that in the former confiderations of the infinity of space and duration we only ufe addition of numbers; whereas this is like the divifion of an unit into its fractions, wherein the mind also can proceed in infinitum as well as in the former additions, it being indeed but the addition ftill of new numbers; though in the addition of the one we can have no more the pofitive idea of a fpace infinitely great, than in the divifion of the other we can have the idea of a body infinitely little, our idea of infinity being, as I may so say, a growing and fugitive idea, ftill in a boundless progression, that can stop no where.

13. No pofitive Idea of Infinite. THOUGH it be hard, I think, to find any one fo abfurd as to fay he has the pofitive idea of an actual infinite number, the infinity whereof lies only in a power still of adding any combination of units to any former number, and that as long and as much as one will, the like alfo being in the infinity of space and duration, which power leaves always to the mind room for endless additions, yet there be those who imagine they have positive ideas of infinite duration and fpace. It would, I think, be enough to destroy any fuch pofitive idea of in

finite, to afk him that has it, whether he could add to it or no; which could easily fhow the mistake of fuch a pofitive idea. We can, I think, have no pofitive idea of any space or duration which is not made up of and commenfurate to repeated numbers of feet or yards, or days and years, which are the common measures whereof we have the ideas in our minds, and whereby we judge of the greatness of these fort of quantities; and therefore, fince an idea of infinite space or duration must needs be made up of infinite parts, it can have no other infinity than that of number, capable ftill of farther addition, but not an actual pofitive idea of a number infinite For I think it is evident, that the addition of finite things together (as are all lengths whereof we have the pofitive ideas) can never otherwife produce the idea of infinite than as number does, which, confifting of additions of finite units one to another, fuggefts the idea of infinite, only by a power we find we have of ftill increasing the fum, and adding more of the fame kind, without coming one jot nearer the end of such progreffion.

§ 14.

THEY Who would prove their idea of infinite to be pofitive, feem to me to do it by a pleasant argument, taken from the negation of an end, which being negative, the negation of it is pofitive. He that confiders that the end is in body but the extremity or fuperficies of that body, will not perhaps be forward to grant that the end is a bare negative; and he that perceives the end of his pen is black or white, will be apt to think that the end is fomething more than a pure negation. Nor is it, when applied to duration, the bare negation of existence, but more properly the last moment of it. But if they will have the end to be nothing but the bare negation of exiftence, I am fure they cannot deny but that the beginning is the first inftant of being, and is not by any body conceived to be a bare negation; and therefore, by their own argument, the idea of eternal, à parte ante, or of a duration without a beginning, is but a negative idea.