CHAP. XII.

OF COMPLEX IDEAS.

§ 1. Made by the mind out of simple ones.-We have hitherto considered those ideas, in the reception whereof the mind is only passive, which are those simple ones received from sensation and reflection before mentioned, whereof the mind cannot make one to itself, nor have any idea which does not wholly consist of them. But as the mind is wholly passive in the reception of all its simple ideas, so it exerts several acts of its own, whereby, out of its simple ideas, as the materials and foundations of the rest, the others are framed. The acts of the mind wherein it exerts its power over its simple ideas, are chiefly these three: 1. Combining several simple ideas into one compound one, and thus all complex ideas are made. 2. The second is bringing two ideas, whether simple or complex, together; and setting them by one another, so as to take a view of them at once, without uniting them into one; by which way it gets all ideas of relations. 3. The third is separating them from all other ideas that accompany them in their real existence; that is called abstraction; and thus all its general ideas are made. This shews man's power, and its way of operation, to be much the same in the material and intellectual world; for the material in both being such as he has no power over, either to make or destroy, all that man can do, is either to unite them together, or to set them by one another, or wholly separate them. I shall here begin with the first of these, in the consideration of complex ideas, and come to the other two, in their due places. As simple ideas are observed to exist in several combinations united together; so the mind has a power to consider several of them united together, as one idea; and that not only as they are united in external objects, but as itself has joined them. Ideas thus made up of several simple ones put together, I call complex; such as are beauty, gratitude, a man, an army, the universe; which, though complicated of various simple ideas, or complex ideas made up of simple ones, yet are, when the mind pleases, considered each by itself, as one entire thing, and signified by one name.

§ 2. Made voluntarily.-In this faculty of repeating and joining together its ideas, the mind has great power in varying and multiplying the objects of its thoughts, infinitely beyond what sensation or reflection furnishes it with; but all this still confined to those simple ideas which it received from those two sources, which are the ultimate materials of all its compositions. For simple ideas are all from things themselves; and of these the mind can have no more, nor other, than what are suggested to it. It can have no other ideas of sensible qualities, than what come from without, by the senses; nor any ideas of other kind of operations of a thinking substance, than what it finds in itself: but when it has once got these simple ideas, it is not confined barely to observation, and what offers itself from without it: it can by its own power, put together those ideas it has, and make new complex ones, which it never received so united.

§ 3. Are either modes, substances, or relations.-Complex ideas, however compounded and decompounded, though their number be infinite, and the variety endless, wherewith they fill and entertain the thoughts of men; yet, I think, they may be all reduced under these three heads: 1. Modes. 2. Substances. 3. Relations.

4. Modes.-First, Modes I call such complex ideas, which, however compounded, contain not in them the supposition of subsisting by themselves, but are considered as dependences on, or affections of, substances; such are ideas signified by the words triangle, gratitude, murder, &c. And if in this I use the word mode in somewhat a different sense from its ordinary signification, I beg pardon; it being unavoidable in discourses differing from the ordinary received notions, either to make new words, or to use old words in somewhat a new signification; the latter whereof, in our present case, is perhaps the most tolerable of the two.

§ 5. Simple and mixed modes. Of these modes there are two sorts, which deserve distinct consideration. First, There are some which are only variations, or different combinations of the same simple idea, without the mixture of any other, as a dozen, or score; which are nothing but the ideas of so many distinct units added together, and these I call simple modes, as being contained within the bounds of one simple idea. Secondly, There are others compounded of simple ideas of several kinds, put together to make one complex one; v. g. beauty, consisting of a certain composition of colour and figure, causing delight in the beholder; theft, which being the concealed change of the possession of any thing, without the consent of the proprietor, contains, as is visible, a combination of several ideas of several kinds: and these I call mixed modes.

§ 6. Substances, single or collective.-Secondly, The ideas of substances are such combinations of simple ideas, as are taken to represent distinct particular things subsisting by themselves; in which the supposed, or confused, idea of substance, such as it is, is always the first and chief. Thus, if to substance be joined the simple idea of a certain dull whitish colour, with certain degrees of weight, hardness, ductility, and fusibility, we have the idea of lead: and a combination of the ideas of a certain sort of figure, with the powers of motion, thought, and reasoning, joined to substance, make the ordinary idea of a man. Now, of substances also, there are two sort of ideas; one of single substances, as they exist separately, as of a man, or a sheep; the other of several of those put together, as an army of men, or flock of sheep; which collective ideas of several substances thus put together, are as much each of them one single idea, as that of a man, or an unit.

§ 7. Relation. Thirdly, The last sort of complex ideas is, that we call relation, which consists in the consideration and comparing one idea with another; of these several kinds we shall treat in their order.

§ 8. The abstrusest ideas from the two sources.-If we trace the progress of our minds, and with attention observe how it repeats, adds together, and unites its simple ideas received from sensation or reflection, it will lead us farther than at first, perhaps, we should have imagined. And, I believe, we shall find, if we warily observe the originals of our

notions, that even the most abstruse ideas, how remote soever they may seem from sense, or from any operations of our own minds, are yet only such as the understanding frames to itself, by repeating and joining together ideas, that it had, either from objects of sense, or from its own operations about them; so that even those large and abstract ideas are derived from sensation or reflection, being no other than what the mind, by the ordinary use of its own faculties, employed about ideas received from objects of sense, or from the operations it observes itself about them, may, and does, attain unto. This I shall endeavour to shew in the ideas we have of space, time, and infinity, and some few others that seem the most remote from those originals.

CHAP. XIII.

OF SIMPLE MODES; AND FIRST, OF THE SIMPLE
MODES OF SPACE.

§ 1. Simple Modes.-Though, in the foregoing part, I have often mentioned simple ideas, which are truly the materials of all our knowledge; yet having treated of them there, rather in the way that they come into the mind, than as distinguished from others more compounded, it will not be, perhaps, amiss to take a view of some of them again under this consideration, and examine those different modifications of the same idea, which the mind either finds in things existing, or is able to make within itself, without the help of any extrinsical object, or any foreign suggestion.

Those modifications of any one simple idea (which, as has been said, I call simple modes) are as perfectly different and distinct ideas in the mind, as those of the greatest distance or contrariety. For the idea of two, is as distinct from that of one, as blueness from heat, or either of them from any number: and yet it is made up only of that simple idea of an unit repeated; and repetitions of this kind joined together, make those distinct simple modes, of a dozen, a gross, a million.

§ 2. Idea of space.-I shall begin with the simple idea of space. I have shewed above, c. 4., that we get the idea of space, both by our sight and touch; which, I think, is so evident, that it would be as needless to go to prove, that men perceive, by their sight, a distance between bodies of different colours, or between the parts of the same body; as that they see colours themselves; nor is it less obvious, that they can do so in the dark by feeling and touch.

§ 3. Space and extension.-This space, considered barely in length between any two beings, without considering any thing else between them, is called distance; if considered in length, breadth, and thickness, I think it may be called capacity; the term extension is usually applied to it in what manner soever considered.

§ 4. Immensity.-Each different distance, is a different modification of space; and each idea of any different distance, or space, is a simple mode of this idea. Men, for the use, and by the custom of measuring, settle in their minds the ideas of certain stated lengths, such as are an inch, foot, yard, fathom, mile, diameter of the earth, &c., which are so many distinct ideas made up only of space. When any such stated

lengths or measures of space are made familiar to men's thoughts, they can, in their minds, repeat them as often as they will, without mixing or joining to them the idea of body, or any thing else; and frame to themselves the idea of long, square, or cubic feet, yards, or fathoms, here amongst the bodies of the universe, or else beyond the utmost bounds of all bodies; and by adding these still one to another, enlarge their ideas of space as much as they please. The power of repeating or doubling any idea we have of any distance, and adding it to the former as often as we will, without being ever able to come to any stop or stint, let us enlarge it as much as we will, is that which gives us the idea of immensity.

§ 5. Figure. There is another modification of this idea, which is nothing but the relation which the parts of the termination of extension, or circumscribed space, have amongst themselves. This the touch discovers in sensible bodies, whose extremities come within our reach; and the eye takes both from bodies and colours, whose boundaries are within its view; where observing how the extremities terminate either in straight lines, which meet at discernible angles; or in crooked lines, wherein no angles can be perceived, by considering these as they relate to one another, in all parts of the extremities of any body or space, it has that idea we call figure, which affords to the mind infinite variety. For besides the vast number of different figures that do really exist in the coherent masses of matter, the stock that the mind has in its power, by varying the idea of space, and thereby making still new compositions, by repeating its own ideas, and joining them as it pleases, is perfectly inexhaustible; and so it can multiply figures in infinitum.

§ 6. Figure. For the mind having a power to repeat the idea of any length directly stretched out, and join it to another in the same direction, which is to double the length of that straight line, or else join another with what inclination it thinks fit, and so make what sort of angle it pleases; and being able also to shorten any line it imagines, by taking from it one half, or one fourth, or what part it pleases, without being able to come to an end of any such divisions, it can make an angle of any bigness; so also the lines that are its sides, of what length it pleases, which joining again to other lines of different lengths, and at different angles, until it has wholly enclosed any space, it is evident that it can multiply figures, both in their shape and capacity, in infinitum; all which are but so many different simple modes of space.

The same that it can do with straight lines, it can also do with crooked, or crooked and straight together; and the same it can do in lines, it can also in superficies; by which we may be led into farther thoughts of the endless variety of figures that the mind has a power to make, and thereby to multiply the simple modes of space.

7. Place. Another idea coming under this head, and belonging to this tribe, is that we call place. As in simple space we consider the relation of distance between any two bodies or points; so in our idea of place, we consider the relation of distance betwixt any thing, and any two or more points, which are considered as keeping the same distance one with another, and so considered as at rest for when we

find any thing at the same distance now, which it was yesterday, from any two or more points, which have not since changed their distance one with another, and with which we then compared it, we say it hath kept the same place: but if it hath sensibly altered its distance with either of those points, we say it hath changed its place: though vulgarly speaking, in the common notion of place, we do not always exactly observe the distance from these precise points; but from larger portions of sensible objects, to which we consider the thing placed to bear relation, and distance from which we have some reason to observe. § 8. Thus, a company of chess-men, standing on the same squares of the chess-board where we left them, we say, they are all in the same place, or unmoved; though perhaps, the chess-board hath been in the mean time carried out of one room into another, because we compared them only to the parts of the chess-board, which keep the same distance one with another. The chess-board, we also say, is in the same place it was, if it remain in the same part of the cabin, though, perhaps, the ship which it is in, sails all the while: and the ship is said to be in the same place, supposing it kept the same distance with the parts of the neighbouring land; though, perhaps, the earth has turned round; and so both chess-men, and board, and ship, have every one changed place, in respect of remoter bodies, which have kept the same distance one with another. But yet the distance from certain parts of the board, being that which determines the place of the chess-men; and the distance from the fixed parts of the cabin (with which we made the comparison) being that which determines the place of the chess-board; and the fixed parts of the earth, that by which we determined the place of the ship, these things may be said to be in the same place, in those respects though their distance from some other things, which, in this matter, we did not consider, being varied, they have undoubtedly changed place in that respect; and we ourselves shall think so, when we have occasion to compare them with those other.

§ 9. But this modification of distance we call place, being made by men for their common use, that by it they might be able to design the particular position of things; where they had occasion for such designation, men consider and determine of this place, by reference to those adjacent things which best served to their present purpose, without considering other things, which, to answer another purpose, would better determine the place of the same thing. Thus, in the chess-board, the use of the designation of the place of each chess-man being determined only within that chequered piece of wood, it would cross that purpose, to measure it by any thing else: but when these very chess-men are put up in a bag, if any one should ask where the black king is, it would be proper to determine the place by the parts of the room it was in, and not by the chess-board; there being another use of designing the place it is now in, than when in play it was on the chess-board, and so must be determined by other bodies. So if any one should ask in what place are the verses which report the story of Nisus and Euryalus, it would be very improper to determine this place, by saying, they were in such a part of the earth, or in Bodley's library; but the right designation of the place would be by the parts of Virgil's works; and the proper an