sion than place. Within these two are confined, and by the observable parts of them are measured and determined, the particular time or duration, and the particular extension and place, of all corporeal beings.

7. Sometimes for so much of either, as we design by measures taken from the bulk or motion of bodies. Secondly, Sometimes the word time is used in a larger sense, and is applied to parts of that infinite duration, not that were really distinguished and measured out by this real existence, and periodical motions of bodies, that were appointed from the beginning to be for signs and for seasons, and for days and years, and are accordingly our measures of time; but such other portions too of that infinite uniform duration, which we, upon any occasion, do suppose equal to certain lengths of measured time; and so consider them as bounded and determined. For if we should suppose the creation, or fall, of the angels, was at the beginning of the Julian period, we should speak properly enough; and should be understood, if we said, it is a longer time since the creation of angels, than the creation of the world, by seven thousand, six hundred, and forty years: whereby we would mark out so much of that distinguished duration, as we suppose equal to, and would have admitted, seven thousand, six hundred, and forty annual revolutions, of the sun, moving at the rate it now does. And thus likewise we sometimes speak of place, distance, or bulk, in the great inane beyond the confines of the world, when we consider so much of that space as is equal to, or capable to, receive a body of any assigned dimensions, as a cubic foot; or do suppose a point in it, at such a certain distance from any part of the universe.

§ 8. They belong to all beings.—Where and when are questions belonging to all finite existences, and are by us always reckoned from some known parts of this sensible world, and from some certain epochs marked out to us by the motions observable in it. Without some such fixed parts or periods, the order of things would be lost to our finite understandings, in the boundless invariable oceans of duration and expansion; which comprehend in them all finite beings, and in their full extent, belong only to the Deity. And, therefore, we are not to wonder, that we comprehend them not, and do so often find our thoughts at a loss, when we would consider them, either abstractly in themselves, or as any way attributed to the first incomprehensible being. But when applied to any particular finite beings, the extension of any body is so much of that infinite space, as the bulk of the body takes up. And place is the position of any body, when considered at a certain distance from some other. As the 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 shews 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 shews the distance of it in place, or existence, from other fixed points of space of duration; as that it was in the middle of Lincoln's Inn Fields, or the first degree of Taurus, and in the year of our Lord, 1671, or the 1000 year of the Julian period: all which distances we measure by precon

ceived ideas of certain lengths of space and duration, as inches, feet, miles, and degrees; and in the other, minutes, days, and years.

§ 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 nature 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

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 eleventh chapter of the second book, where he begins to speak of simple ideas, an exact definition of what he understands by the word 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 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 second 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 idea of the mind. But if this is not sufficient to clear the difficulty, Mr. Locke hath nothing more to add, but that 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, doctrinæ causa; but after all, several things will not be bundled up together under our terms and ways of speaking.

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 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 and 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 of 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 a 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 other 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, and 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 length 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 to 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 any 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.

12. Duration has never two parts together, expansion altogether.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 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 passed, 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, bring 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; but 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 numbers 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 others, even those that approach nearest, makes me apt to think, that demonstrations in numbers, if they are not more evident and exact than in extension, yet they are more general in their use, and more determinate in their application. Because the ideas of numbers are more precise and distinguishable than in extension, where every equality are excess are not so easy to be observed or measured; because our thoughts cannot in space arrive at any determined smallness, beyond which it cannot go, as an unit; and, therefore, the quantity or proportion of any the least excess cannot be discovered: which is clear otherwise in number; where, as has been said, ninety-one is as distinguishable from ninety, as from nine thousand, though ninety-one be the next immediate excess to ninety. But it is not so in extension, where whatsoever is more than just a foot, or an inch, is not distinguishable 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 assign an angle, which shall be the next biggest to a right one.

§5. Names necessary to numbers.-By the repeating, as has been said, of the idea of an unit, and joining it to another unit, we make thereof one collective idea, marked by the name two. And whosoever

can do this, and proceed on, still adding one more to the last collective idea which he had of any number, and give a name to it, may count, or have ideas for, several collections of units, distinguished one from another, as far as he hath a series of names for following numbers, and a memory to retain that series, with their several numbers; all numeration being but still the adding of one unit more, and giving to the whole together, as comprehended in one idea, a new or distinct name or sign, whereby to know it from those before and after, and distinguish it from every smaller or greater multitude of units. So that he can add one to one, and so to two, and so go on with his tale, taking still with him the distinct names belonging to every progression; and so again, by subtracting an unit from each collection, retreat and lessen them, is capable of all the ideas of numbers within the compass of his language,