187 idea of the particular duration of any thing is an idea of that portion of infinite duration, which passes during the existence of that thing; so the time when the thing existed is the idea of that space of duration which passed between some known and fixed period of duration, and the being of that thing. One shows the distance of the extremities of the bulk or existence of the same thing, as that it is a foot square, or lasted two years; the other shows the distance of it in place, or existence, from other fixed points of space or duration, as that it was in the middle of Lincolns-InnFields, or the first degree of Taurus, and in the year of our Lord 1671, or the 1000th year of the Julian period: all which distances we measure by preconceived ideas of certain lengths of space and duration, as inches, feet, miles, and degrees; and in the other, minutes, days, and years, &c.

§ 9. All the parts of extension, are extension; and all the parts of duration, are duration.

THERE is one thing more wherein space and duration have a great conformity; and that is, though they are justly reckoned amongst our simple ideas, yet none of the distinct ideas we have of either is without all manner of composition ;* it is the very na

* It has been objected to Mr. Locke, that if space consists of parts, as it is confessed in this place, he should not have reckoned it in the number of simple ideas; because it seems to be inconsistent with what he says elsewhere, that a simple idea is uncompounded, and contains in it nothing but one uniform appearance or conception of the mind, and is not distinguishable into different ideas. It is farther objected, that Mr. Locke has not given in the 11th chapter of the 2d book, where he begins to speak of simple ideas, an exact definition of what he understands by the words simple ideas. To these difficulties Mr. Locke answers thus: to begin with the last, he declares, that he has not treated his subject in an order perfectly scholastic, having not had much familiarity with those sort of books during the writing of his, and not remembering at all the method in which they are written; and therefore his readers ought not to expect definitions regularly placed at the beginning of each new subject. Mr. Locke contents himself to employ the principal terms that he uses; so that, from his use of them, the reader may easily comprehend what he means by them. But with respect to the term simple idea, he has had the good luck to define that in the place cited in the objection; and therefore there is no reason to supply that defect. The question then is to know, whether the idea of extension agrees with this definition? Which will effectually agree to it, if it be understood in the sense which Mr. Locke had principally in his view; for that composition which he designed to exclude in that definition, was a composition of different ideas in the mind, and not a composition of the same kind in a thing whose essence consists in having parts of the same kind, where you can never come to a part entirely exempted from

ture of both of them to consist of parts: but their parts being all of the same kind, and without the mixture of any other idea, hinder them not from having a place amongst simple ideas. Could the mind, as in number, come to so small a part of extension or duration, as excluded divisibility, that would be, as it were the indivisible unit, or idea; by repetition of which it would make its more enlarged ideas of extension and duration. But since the mind is not able to frame an idea of any space without parts; instead thereof it makes use of the common measures; which by familiar use, in each country, have imprinted themselves on the memory, (as inches and feet; or cubits and parasangs; and so seconds, minutes, hours, days, and years in duration :) the mind makes use, I say, of such ideas as these, as simple ones; and these are the component parts of larger ideas, which the mind, upon occasion, makes by the addition of such known lengths which it is acquainted with. On the other side, the ordinary smallest measure we have of either is looked on as an unit in number, when the mind by division would reduce them into less fractions. Though on both sides, both in addition and division, either of

this composition. So that if the idea of extension consists in having partes extra partes (as the schools speak) it is always in the sense of Mr. Locke, a simple idea; because the idea of having partes extra partes, cannot be resolved into two other ideas. For the remainder of the objection made to Mr. Locke, with respect to the nature of extension, Mr. Locke was aware of it, as may be seen in § 9. chap. 15. of the 2d book, where he says, that the least portion of space or extension, whereof we have a clear and distinct idea, may perhaps be the fittest to be considered by us as a simple idea of that kind, out of which our complex modes of space and extension are made up. So that, according to Mr. Locke, it may very fitly be called a simple idea, since it is the least idea of space that the mind can form to itself, and that cannot be divided by the mind into any less, whereof it has in itself any determined perception. From whence it follows, that it is to the mind one simple idea; and that is sufficient to take away this objection: for it is not the design of Mr. Locke, in this place, to discourse of any thing but concerning the ideas of the mind. But if this is not sufficient to clear the difficulty, Mr. Locke hath nothing more to add, but that if the idea of extension is so peculiar, that it cannot exactly agree with the definition that he has given of those simple ideas, so that it differs in some manner from all others of that kind, he thinks it is better to leave it there exposed to this difficulty, than to make a new division in his favour. It is enough for Mr. Locke, that his meaning can be understood. It is very common to observe intelligible discourses spoiled by too much subtilty in nice divisions. We ought to put things together as well as we can, doctrine causâ; but, after all, several things will not be bundled up together under our terms, and ways of speaking.

space or duration, when the idea under consideration becomes very big or very small, its precise bulk becomes very obscure and confused; and it is the number of its repeated additions or divisions, that alone remains clear and distinct, as will easily appear to any one who will let his thoughts loose in the vast expansion of space, or divisibility of matter. Every part of duration is duration too; and every part of extension is extension, both of them capable of addition or division in infinitum. But the least portions of either of them, whereof we have clear distinct ideas, may perhaps be fittest to be considered by us, as the simple ideas of that kind, out of which our complex modes of space, extension, and duration, are made up, and into which they can again be distinctly resolved. 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 succession there. The other, wanting a proper name, I know not whether I may be allowed to call a sensible point, meaning thereby the least particle of matter or space we can discern, which is ordinarily about a minute, and to the sharpest eyes seldom less than thirty seconds of a circle, whereof the eye is the centre.

§ 10. Their parts inseparable.

EXPANSION and duration have this farther agreement, that though they are both considered by us as having parts, yet their parts are not separable 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 succession 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 rest, and the oth er is by sleep, which we call rest too.

§ 11. Duration is as a line, expansion as a solid.

BUT yet there is this manifest difference between them, that the ideas of length, which we have of expansion, are turned every way, and so make figure, and breadth, and thickness; but duration is but as it were the lengh of one straight line, extended in infinitum, not capable of multiplicity, variation, or figure; but is one common measure of all existence whatsoever, wherein all things, whilst 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 single being; and we may truly say, they all exist in the same moment of time. Whether angels and spirits have any analogy

to this, in respect of expansion, is beyond my comprehension: and perhaps for us, who have understandings and comprehensions suited to our own preservation, 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 expansion, as it is to have the idea of any real existence, with a perfect negation of all manner of duration and therefore what spirits have to do with space, or how they communicate in it, we know not. All that we know is, that bodies do each singly possess its proper portion of it, according to the extent of solid parts; and thereby exclude all other bodies from having any share in that particular portion of space, whilst it remains there. 1

§ 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 distance, of which no two parts exist together, but follow each other in succession; as expansion is the idea of lasting distance, all whose parts exist together, and are not capable of succession. And therefore though we cannot conceive any duration without succession, nor can put it together in our thoughts, that any being does now exist to-morrow, or possess at once more than the present 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 cannot make present. What I say of man, I say 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 sees all things past and to come; and they are no more distant from his knowledge, no farther removed from his sight than the present: they all lie under the same view; and there is nothing which he cannot make exist each moment he pleases. For the existence of all things depending upon his good pleasure, all things exist every moment that he thinks fit to have them exist. To conclude, expansion 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 expansion. Such a combination of two distinct ideas, is, I suppose, scarce to be found in all that great variety we do or can conceive, and may afford matter to farther speculation.

CHAP. XVI.

OF NUMBER.

§ 1. Number the simplest and most universal idea. AMONGST all the ideas we have, as there is none suggested to the mind by more ways, so there is none more simple than that of unity, or one. It has no shadow of variety or composition in it; every object our senses 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 universal idea we have. For number applies itself to men, angels, actions, thoughts, every thing that either doth exist, 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 so of a score, or a million, or any other number.

§ 3. Each mode distinct.

THE simple modes of number are of all other the most. distinct; every the least 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 distinct from one, as two hundred; and the idea of two as distinct from the idea of three, as the magnitude of the whole earth is from that of a mite. This is not so in other simple modes, in which it is not so easy, nor perhaps possible for us to distinguish 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 distinct ideas of every the least excess in extension?

§ 4. Therefore demonstrations in numbers the most precise. THE clearness and distinctness of each mode of number from all