ufe, I fay, of such ideas as thefe, as fimple ones; and thefe are the component parts of larger ideas, which the mind, upon occafion, makes by the addition of fuch known lengths which it is acquainted with. On the other fide, the ordinary smallest measure we have of either, is looked on as an unit in number, when the mind by divifion would reduce them into lefs fractions; though on both fides, both in addition and divifion, either of space or duration, when the idea under confideration becomes very big or very fmall, its precise bulk becomes very obfcure and confused; and it is the number of its repeated additions or divifions, that alone remains clear and diftinct, as will eafily appear to any one who will let his thoughts loofe in the vast expanfion of space, or divifibility of matter. Every part of duration, is duration too; and every part of extenfion, is extenfion, both of them capable of addition or divifion in infinitum. But the leaft portions of either of

fimple idea; because the idea of having partes extra partes, cannot be refolved into two other ideas. For the remainder of the objection made to Mr. Locke, with refpect to the nature of extenfion, Mr. Locke was aware of it, as may be feen in § 9. chap. 15. of the 2d book, where he fays, that the leaft portion of space or extenfion, whereof we have a clear and diftinct idea, may perhaps be the fitteft to be confidered by us as a simple idea of that kind, out of which our complex modes of fpace and extenfion are made up. So that, according to Mr. Locke, it may very fitly be called a fimple idea, fince it is the leaft idea of space that the mind can form to itself, and that cannot be divided by the mind into any lefs, whereof it has in itself any determined perception. From whence it follows, that it is to the mind one fmple idea; and that is fufficient to take away this objection; for it is not the design of Mr. Locke, in this place, to difcourfe of any thing but concerning the ideas of the mind. But if this is not fufficient to clear the difficulty, Mr. Locke hath nothing more to add, but that if the idea of extenfion is fo peculiar, that it cannot exactly agree with the definition that he has given of thefe fimple ideas, fo that it differs in fome manner from all others of that kind, he thinks it is better to leave it there expofed to this difficulty, than to make a new divifion in his favour. It is enough for Mr. Locke, that his meaning can be underflood. It is very common to obferve intelligible difcourfes fpoiled by too much fubtilty in nice divifions: We ought to put things together as well as we can, doctrina caufâ¡ but after all, feveral things will not be bundled up together under our terms, and ways of speaking.

them, whereof we have clear and diftinct ideas, may perhaps be fitteft to be confidered by us as the fimple ideas of that kind out of which our complex modes of fpace, 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 sharpeft eyes feldom lefs than thirty feconds of a circle, whereof the eye is the

centre.

$10. Their Parts infeparable.

EXPANSION and duration have this farther agreement, that though they are both 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 meafure 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 feparated, as the one is often by reft, and the other is by fleep, which we call reft

too.

§ 11. Duration is as a Line, Expanfion as a Solid. BUT yet 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 thickness; 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 meafure of all exiftence whatsoever, wherein all things, whilft they exist, equally partake, for this present 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 of expanfion, is beyond my comprehen

fion; 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 exiftence, or to have an idea of any real being, with a perfect negation of all manner of expanfion, 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. poflefs its proper portion of it according to the extent of its folid parts, and thereby exclude all other bodies from having any fhare in that particular portion of space whilft it remains there.

§ 12. Duration has never two Parts together, ExpanSion all together.

DURATION, and time which is a part of it, is the idea we have of perishing diftance, of which no two parts exift together, but follow each other in fucceffion, as expanfion is the idea of lafting diflance, 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 past 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 recal, and what is yet to come he can never make prefent. What I fay 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 meaneft 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 paft and to come; and they

are no more distant 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 existence of all things depending upon his good pleasure, all things exist 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 duration, and every part of duration in every part of expanfion. Such a combination of two diftinct ideas is, I fuppose, scarce to be found in all that great variety we do or can conceive, and may afford matter to farther fpe

culation.

CHAP. XVI.

OF NUMBER.

A

It has

§1. Number the fimpleft and most universal 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. no fhadow of variety or compofition in it; every object our fenfes are employed about, every idea in our underftandings, 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. 2. Its Modes made by Addition

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 of a fcore, or a million, or any other number.

$3. Each Mode diftin&t.

THE fimple modes of number are of all other the most di1 ftinct, every the 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 easy, 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?

§4. Therefore Demonftrations in Numbers the most

precife.

THE clearness and diftinctness of each mode of number from all others, even those that approach nearest, makes me apt to think that demonftrations in numbers, if they are not more evident and exact than in extenfion, yet they are more general in their use, and more determinate in their application, because the ideas of numbers are more precife and distinguishable than in extenfion, where every equality and excefs 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 excefs cannot be difcovered; which is clear otherwife in number, where, as has been faid, 91 is as diftinguishable from 90 as from 9000, though 91 be the next immediate excess to 90. But it is not fo in extenfion, where whatsoever is more than juft a foot or an inch, is not diftinguishable from the ftandard 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 fhall be the next biggeft to a right one.

I