no larger than it is that inftant that I have it, though I be capable the next inftant to double it, and fo 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 affords us the clearest idea of infinity.

§. 9. But of all other ideas, it is number, as I have faid, which I think furnishes us with the clearest and most diftinct idea of infinity we are capable of. For even in space and duration, when the mind pursues the idea of infinity, it there makes ufe of the ideas and repetitions of numbers, as of millions and millions of miles, or years, which are fo many diftinct ideas, kept beft by number from running into a confused heap, wherein the mind lofes itself; and when it has added together as many millions, &c. as it pleases, of known lengths of fpace or duration, the cleareft idea it can get of infinity, is the confused incomprehenfible remainder of endless addible numbers, which affords no profpect of stop or boundary.

Our different

conception of the infinity of number, duration, and

§. 10. It 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 expanfion. minds the diftinct ideas, if we confider, that number is not generally thought by us infinite, whereas duration and extenfion are apt to be fo; which arifes 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 fet 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 unconceivable, 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

num

number both ways, à parte ante and à parte poft, as they speak. 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 profpect 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 these 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 ftill turn that way the infinite end of number, i. e. the power still of adding more.

§. 11. 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 reafon to fet' bounds to those repeated ideas than we have to fet bounds to number, we have that indeterminable idea of immenfity.

Infinite divi

§. 12. And fince in any bulk of matter our thoughts can never arrive at the utmost fibility. divifibility, therefore there is an apparent infinity to us alfo in that, which has the infinity also of number; but with this difference, that, in the former confiderations of the infinity of. space and duration, we only use addition of numbers; whereas this is like the ' division of an unit into its fractions, wherein the mind alfo can proceed in infinitum, as well as in the former additions; it being indeed but, the addition still of new numbers: Though in the addition of the one we can have no more the pofitive idea of a space 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 fay, a growing or fugitive idea, ftill in a boundless progreffion, that can ftop nowhere.

§. 13.

No pofitive idea of infinity.

§. 13. 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 ftill 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 thofe who imagine they have pofitive ideas of infinite duration and fpace. It would, I think, be enough to deftroy any fuch pofitive idea of infinite, to afk him that has it, whether he could add to it or no; which would easily show 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, and commenfurate to repeated numbers of feet or yards, or days and years, which are the common meafures, whereof we have the ideas in our minds, and whereby we judge of the greatnefs of this fort of quantities. And therefore, fince an infinite idea of fpace or duration muft 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 increafing the fum, and adding more of the fame kind, without coming one jot nearer the end of fuch progreffion.

§. 14. They who would prove their idea of infinite to be pofitive, feem to me to do it by a pleafant 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

nega

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 existence, I am fure they cannot deny but the beginning is the first instant 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.

What is pofitive, what negative, in infinite.

our idea of

§. 15. The idea of infinite has, I confefs, fomething of pofitive in all thofe things we apply to it. When we would think of infinite space or duration, we at first step usually make fome very large idea, as perhaps of millions of ages, or miles, which poffibly we double and multiply feveral times. All that we thus amafs together in our thoughts is pofitive, and the affemblage of a great number of pofitive ideas of space or duration. But what ftill remains beyond this, we have no more a pofitive diftinct notion of, than a mariner has of the depth of the fea; where having let down a large portion of his founding-line, he reaches no bottom: whereby he knows the depth to be fo many fathoms, and more; but how much the more is, he hath no diftinct notion at all: And could he always fupply new line, and find, the plummet always fink without ever stopping, he would be fomething in the posture of the mind reaching after a complete and pofi tive idea of infinity. In which cafe let this line b ten, or one thousand fathoms long, it equally difco. vers what is beyond it; and gives only this confuse, and comparative idea, that this is not all, but one ma yet go farther. So much as the mind comprehend of any space, it has a pofitive idea of; but in endea vouring to make it infinite, it being always enlarging always advancing, the idea is ftill imperfect and incom plete. So much space as the mind takes a view of i its contemplation of greatnefs, is a clear picture, an pofitive in the understanding: but infinite is fti greater. 1. Then the idea of fo much is pofitive ar clear. 2. The idea of greater is alfo clear, but it

!

but a comparative idea, viz. the idea of fo much greater as cannot be comprehended; and this is plainly negative, not pofitive. For he has no pofitive clear idea of the largeness of any extenfion, (which is that sought for in the idea of infinite) that has not a comprehenfive idea of the dimenfions of it; and fuch no-body, I think, pretends to in what is infinite. For to fay a man has a positive clear idea of any quantity, without knowing how great it is, is as reafonable as to fay, he has the positive clear idea of the number of the fands on the fea-fhore, who knows not how many there be; but only that they are more than twenty. For juft fuch a perfect and pofitive idea has he of an infinite fpace or duration, who fays it is larger than the extent or duration of ten, one hundred, one thoufand, or any other number of miles, or years, whereof he has, or can have a positive idea; which is all the idea, I think, we have of infinite. So that what lies beyond our pofitive idea towards infinity, lies in obfcurity; and has the indeterminate confufion of a negative idea, wherein I know I neither do nor can comprehend all I would, it being too large for a finite and narrow capacity: and that cannot but be very far from a pofitive complete idea, wherein the greatest part of what I would comprehend is left out, under the undeterminate intimation of being still greater: for to fay, that having in any quantity measured fo much, or gone fo far, you are not yet at the end; is only to fay, that that quantity is greater. So that the negation of an end in any quantity is, in other words, only to say, that it is bigger: and a total negation of an end is but carrying this bigger ftill with you, in all the progreffions your thoughts fhall make in quantity; and adding this idea of ftill greater, to all the ideas you have, or can be fuppofed to have, of quantity. Now whether such an idea as that be pofitive, I leave any one to confider.

We have no ofitive idea of an infinite luration.

§. 16. I ask thofe who fay they have a pofitive idea of eternity, whether their idea of duration includes in it fucceffion, or not? if it does not, they ought to show he difference of their notion of duration, when ap