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 anything 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 Lincoln's Inn Fields, 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 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,

*

This, as the reader of the Anabasis will remember, is a Persian word, signifying “a league.” (Anab. II. p. 161. Hutchin.) Herodotus, (II. 6, and V. 53,) and Strabo, (XI. t. ii. p. 788,) make use of the word as

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 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 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 further 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

a road measure, of thirty stadia. It is still, Reland observes, in use among the Persians, whose parasang consists of three miles, each 3,000 cubits in length, each cubit of thirty inches, each inch six barleycorns.— ED.

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 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 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 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.

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 can put

*The reader who has any curiosity on this subject, may consult Antoine Le Grand's Principles of the Cartesian Philosophy, in which the whole nature and attributes of angels are made (to borrow the expressive language of Swift) "as clear as mud." (Part III. 110 et seq.) It is lamentable to behold the understanding which was bestowed on man for better purposes wasting itself on useless speculations upon what it can never comprehend.-ED.

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 further 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. 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 further speculation.

CHAPTER XVI.

OF NUMBER.

To

1. Number the simplest and most universal Idea.—AMONGST all the ideas we have, as there is none suggested to the mind

* As the augurs of antiquity were supposed to know by the power of the Divinity, their minds were said to grasp the three divisions of time— the past, the present, and the future-as God does. Thus Homer, speaking of Calchas, οἰωνοπόλων ὄχ ̓ ἄριστος, says,

"Whose comprehensive view;

The past, the present, and the future knew."

as Pope renders the epic line, —

“Ος ἤδη τὰ τ ̓ ἐόντα τά τ ̓ ἐσσόμενα, πρό τ ̓ ἐόντα.”—ED.

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, everything 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 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 and excess are not so easy to be observed or measured; because our thoughts cannot in space arrive at any determined smallness, beyond

The idea of unity enters into our conception of God, "in, whom there is neither variableness nor shadow of turning;" a glorious expression, which possibly suggested the one in the text.-ED.