lour, 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 sorts 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.

Relation.

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

order:

The abstrusest ideas from the

two sources.

§. 8. 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 re flection, 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 those even large and abstract ideas are derived from sensation or reflection, being no other than what the mind, by the ordi nary use of its own faculties, employed about ideas received from objects of sense, or from the operations it observes in itself about them, may and does attain unto. This I shall endeavour to show 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. THOUGH in the foregoing part I Simple
have often mentioned simple ideas, which Modes.
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 con-
sideration, and examine those different modifications
of the same idea: which the mind either finds in
things existing, or is able to make within itself, with-
out 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. I shall begin with the simple idea of space. I have showed above, chap. 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. This space considered barely in length between any two beings, without considering any thing else between them,

Idea of

space.

Space and extension.

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.

Immensity. §. 4. 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 ideas 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. Figure.

§. 5. 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. For the mind having a power to Figure. 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, till it has wholly inclosed 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. Another idea coming under this Place. 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 its 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 hath 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 determined 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;