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

§ 10. Our different Conception of Infinity, Number, Duration, and Expanfion.

Ir 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 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 ar 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 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 ourfelves, 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, becaufe we ftill turn that way

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

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THE fame happens alfo in fpace, wherein, conceiving ourselves to be as it were in the centre, we do on all fides pursue thofe indeterminable lines of number, and reckoning any way from ourfelves 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 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 divifibility, 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 fpace and duration we only ufe addition of numbers; whereas this is like the divifion 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 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 fo fay, a growing and fugitive idea, ftill in a boundlefs progreffion, that can ftop 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 ftill of adding any combination of units to any former number, and that as long and as much as one will, the l'ke 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 pofitive ideas of infinite duration and space. It would, I think, be enough to deftroy any fuch pofitive idea of in

finite, to ask him that has it, whether he could add to it or no; which could eafily fhow the mistake of such a pofitive idea. We can, I think, have no positive 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 fpace 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 funi, 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 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 laft 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 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, ù parte ante, or of a duration without a beginning, is but a negative idea.

§ 15. What is pofitive, what negative in our Idea of Infinite.

THE idea of infinite has, I confefs, fomething of pofitive in all thofe things we apply to it. When we would think of infinite fpace 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 that more is he hath no diftinct notion at all; and could he always fupply new line, and find the plummet always fink without ever ftopping, he would be fomething in the posture of the mind reaching after a complete and pofitive idea of infinity; in which cafe, let this line be 10 or 10,000 fathoms long, it equally difcovers what is beyond it, and gives only this confufed and comparative idea, that this is not all, but one may yet go farther. So much as the mind comprehends of any fpace, it has a pofitive idea of; but in endeavouring to make it infinite, it being always enlarging, always advancing, the idea is ftill imperfect and incomplete. So much space as the mind takes a view of in its contemplation of greatneis, is a clear picture and pofitive in the understanding; but infinite is ftill greater. 1. Then, the idea of fo much is pofitive and clear. 2. The idea of greater is aljo clear, but it is but a comparative idea. 3. The idea of fo much greater as cannot be comprehended; and this is plain negative, not pofitive; for he has no pofitive clear idea of the largenefs of any extenfion (which is that fought for in the idea of infinite), that has not a comprehenfive idea of the dimenfions of it; and fuch nobody, I think, pretends to in what is infinite; for to fay a man has a pofitive clear idea of any quantity, without knowing

how great it is, is as reasonable as to fay he has the pofitive clear idea of the number of the fands on the feafhore, 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 10, 100, 1000, or any other number of miles or years, whereof, he has or can have a pofitive idea; which is all the idea I think we have of infinite; fo that what lies beyond our politive 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 till 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 the quantity is greater; fo that the negation of an end in any quantity is, in other words, only to fay that it is bigger; and a total negation of an end is but the carrying this bigger ftill with you, in all the progreflions your thoughts fhall make in quantity, and adding this idea of fill greater to all the ideas you have, or can be fuppofed to have of quantity. Now, whether fuch an idea as that be positive, I leave any one to confider.

§ 16. We have no pofitive Idea of an infinite Duration. I ASK those who say they have a pofitive idea of eternity, whether their idea of duration includes in it fuccellion or not? If it does not, they ought to fhow the difference of their notion of duration, when applied to an eternal being and to a finite, fince perhaps there may be others, as well as I, who will own to them their weakness of understanding in this point, and acknow ledge, that the notion they have of duration forces them to conceive, that whatever has duration, is of a longercontinuance to-day than it was yesterday. If to avoidfucceffion in eternal existence, they recur to the punc

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