extenfion, and duration, are made up, and into which they can again be diftinctly refolved. Such a small part in duration may be called a moment, and is the time of one idea in our minds in the train of their ordinary fucceffion there. The other, wanting a proper name, I know not whether I may be allowed to call a fenfible point, meaning thereby the leaft particle of matter or space we can difcern, which is ordinarily about a minute, and to the fharpeft eyes feldom lefs than thirty fe conds of a circle, whereof the eye is the centre. §. 10. Expansion and duration have this Their parts farther agreement, that though they are both infeparable.. confidered by us as having parts, yet their parts are not feparable one from another, no not even in thought: though the parts of bodies from whence we take our measure of the one, and the parts of motion, or rather the fucceffion of ideas in our minds, from whence we take the measure of the other, may be interrupted and separated; as the one is often by reft, and the other is by fleep, which we call rèft too.

ex

Duration is as a line, panfion as a folid.

§. II. But there is this manifeft difference between them, that the ideas of length, which we have of expanfion, are turned every way, and fo make figure, and breadth, and thicknefs; but duration is but as it were the length of one ftraight line, extended in infinitum, not capable of multiplicity, variation, or figure; but is one common measure of all existence whatsoever, wherein all things, whilft they exift, equally partake. For this prefent moment is common to all things that are now in being, and equally comprehends that part of their existence, as much as if they were all but one fingle being; and we may truly fay, they all exift in the fame moment of time. Whether angels and fpirits have any analogy to this, in refpect to expanfion, is beyond my comprehenfion: and perhaps for us, who have understandings and comprehenfions fuited to our own prefervation, and the ends of our own being, but not to the reality and extent of all other beings; it is near as hard to conceive any existence, or to have an idea of any real being, with a perfect negation of all manner of expan

fion; as it is to have the idea of any real existence, with a perfect negation of all manner of duration; and therefore what fpirits have to do with fpace, or how they communicate in it, we know not. All that we know is, that bodies do each fingly poffefs its proper portion of it, according to the extent of folid parts; and thereby exclude all other bodies from having any fhare in that particular portion of fpace, whilft it remains there.

§. 12. Duration, and time which is a part Duration has of it, is the idea we have of perithing dif

never two

parts together, expanfion all toge ther.

tance, of which no two parts exift toge ther, but follow each other in fucceffion; as expansion is the idea of lafting distance, all whofe parts exift together, and are not capable of fucceffion. And therefore though we cannot conceive any duration without fucceffion, nor can put it together in our thoughts, that any being does now exift to-morrow, or poffefs at once more than the prefent moment of duration; yet we can conceive the eternal duration of the Almighty far different from that of man, or any other finite being. Because man comprehends not in his knowledge, or power, all paft and future things; his thoughts are but of yesterday, and he knows not what to-morrow will bring forth. What is once past he can never recall; and what is yet to come he cannot make prefent. What Ifay of man I fay of all finite beings; who, though they may far exceed man in knowledge and power, yet are no more than the meanest creature, in comparison with God himself. Finite of any magnitude holds not any proportion to infinite. God's infinite duration being accompanied with infinite knowledge, and infinite power, he fees all things past and to come; and they are no more diftant from his knowledge, no farther removed from his fight, than the prefent: they all lie under the fame view; and there is nothing which he cannot make exift each moment he pleafes. For the exiftence of all things depending upon his good-pleasure, all things exift every moment that he thinks fit to have them exift. To conclude, expanfion and duration do mutually embrace and comprehend each other; every part of space being in every part of du

ration,

ration, and every part of duration in every part of expanfion. Such a combination of two diftinct ideas is, I fuppofe, fcarce to be found in all that great variety we do or can conceive, and may afford matter to farther Speculation.

i. A

CHAP. XVI.

Of Number.

Number the

fimpleft and

moft univerfal idea.

MONGST all the ideas we have, as there is none fuggefted to the mind by more ways, fo there is none more fimple, than that of unity, or one. It has no fhadow of variety or compofition in it; every object our fenfes are employed about, every idea in our understandings, every thought of our minds, brings this idea along with it. And therefore it is the most intimate to our thoughts, as well as it is, in its agreement to all other things, the most univerfal idea we have. For number applies itfelf to men, angels, actions, thoughts, every thing that either doth exift, or can be imagined.

Its modes made by ad

dition.

§. 2. By repeating this idea in our minds, and adding the repetitions together, we come by the complex ideas of the modes of it. Thus by adding one to one, we have the complex idea of a couple; by putting twelve units together, we have the complex idea of a dozen; and fo of a score, or a million, or any other number.

§. 3. The fimple modes of numbers are Each mode of all other the moft diftin&t; every the distinct. leaft variation, which is an unit, making each combination as clearly different from that which approacheth nearest to it, as the most remote: two being as diftinct from one, as two hundred; and the idea of two as diftinct from the idea of three, as the magnitude of the whole earth is from that of a mite. This is not fo in other fimple modes, in which it is not fo cafy,

nor

nor perhaps poffible for us to diftinguish betwixt two approaching ideas, which yet are really different. For who will undertake to find a difference between the white of this paper, and that of the next degree to it; or can form diftinct ideas of every the least excefs in extenfion?

Therefore demonftra

tions in numbers the moft precife.

§. 4. The clearnefs and diftinctness of each mode of number from all others, even thofe that approach nearest, makes me apt to think that demonstrations in numbers, if they are not more evident and exact than in extenfion, yet they are more general in their ufe, and more determinate in their application. Because the ideas of numbers are more precife and diftinguishable than in extenfion, where every equality and excess are not so easy to be obferved or measured; because our thoughts cannot in fpace arrive at any determined fmallnefs, beyond which it cannot go, as an unit; and therefore the quantity or proportion of any the leaft excess cannot be difcovered: which is clear otherwife in number, where, as has been faid, ninety-one is as diftinguishable from ninety, as from nine thoufand, though ninety-one be the next immediate excess to ninety. But it is not fo in extenfion, where whatfoever is more than just a foot or an inch, is not diftinguifhable from the standard of a foot or an inch; and in lines which appear of an equal length, one may be longer than the other by innumerable parts; nor can any one affign an angle, which shall be the next biggest to a right one. §. 5. By the repeating, as has been faid, the idea of an unit, and joining it to ano numbers. ther unit, we make thereof one collective idea, marked by the name two. And whofoever can do this, and proceed on ftill, adding one more to the laft collective idea which he had of any number, and give a name to it, may count, or have ideas for feveral collections of units, diftinguished one from another, as far as he hath a series of names for following numbers, and a memory to retain that feries, with their feveral names: all numeration being but ftill the adding of one unit more, and giving to the whole together, as comprehended

Names ne

ceffary to

prehended in one idea, a new or diftinct name or fign, whereby to know it from thofe before and after, and diftinguish it from every fmaller or greater multitude of units. So that he that can add one to one, and fo to two, and fo go on with his tale, taking ftill with him the diftinct names belonging to every progreffion; and fo again, by fubtracting an unit from each collection, retreat and leffen them; is, capable of all the ideas of numbers within the compafs of his language, or for which he hath names, though not perhaps of more. For the feveral fimple modes of numbers, being in our minds but fo many combinations of units, which have no variety, nor are capable of any other difference but more or lefs, names or marks for each diftinct combination feem more neceffary than in any other fort of ideas. For without fuch names or marks we can hardly well make ufe of numbers in reckoning, especially where the combination is made up of any great multitude of units; which put together without a name or mark, to diftinguish that precife collection, will hardly be kept from being a heap in confufión.

§. 6. This I think to be the reason, why fome Americans I have fpoken with, (who were otherwise of quick and rational parts enough) could not, as we do, by any means count to one thoufand; nor had any dif tinct idea of that number,' though they could reckon very well to twenty. Because their language being fcanty, and accommodated only to the few neceffaries of a needy fimple life, unacquainted either with trade or mathematics, had no words in it to ftand for one thoufand; fo that when they were difcourfed with of thofe greater numbers, they would fhow the hairs of their head, to express a great multitude which they could not number: which inability, I fuppofe, proceeded from their want of names. The Tououpinambos had no names for numbers above five; any number beyond that they made out by fhowing their fingers, and the fingers of others who were prefent *. And I doub

+ Hiftoire d'un voyage, fait en la terre du Brafil, par Jean de Lery, 6. 20.497.

not