COMPLEX IDEAS OF SIMPLE MODES: — AND FIRST, OF THE SIMPLE MODES OF IDEA OF SPACE.
1. Simple modes of simple ideas.
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. Simple Modes of Idea of Space.
2. Idea of Space.
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. Space and Extension.
This space, considered barely in length between any two beings, without considering anything else between them, is called DISTANCE: if considered in length, breadth, and thickness, I think it may be called CAPACITY. When considered between the extremities of matter, which fills the capacity of space with something solid, tangible, and moveable, it is properly called EXTENSION. And so extension is an idea belonging to body only; but space may, as is evident, be considered without it. At lest I think it most intelligible, and the best way to avoid confusion, if we use the word extension for an affection of matter or the distance of the extremities of particular solid bodies; and space in the more general signification, for distance, with or without solid matter possessing it.
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 having, by accustoming themselves to stated lengths of space, which they use for measuring other distances — as a foot, a yard or a fathom, a league, or diameter of the earth — made those ideas familiar to their thoughts, can, in their minds, repeat them as often as they will, without mixing or joining to them the idea of body, or anything 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.
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. Endless variety of figures.
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, 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 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.