# An Essay Concerning Human Understanding/Book II/Chapter XIII

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.
2. Idea of Space. I shall begin with the simple idea of space. I have showed above, chap. V, 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. (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 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.
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. 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.
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 anything, 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 anything 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. Place relative to particular bodies. 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 chessmen ; 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. Place relative to a present purpose. 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 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 anything 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 part 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 answer would be, that these verses were about the middle of the ninth book of his AEneids, and that they have been always constantly in the same place ever since Virgil was printed : which is true, though the book itself hath moved a thousand times, the use of the idea of place here being, to know in what part of the book that story is, that so, upon occasion, we may know where to find it, and have recourse to it for use.
10. Place of the universe. That our idea of place is nothing else but such a relative position of anything as I have before mentioned, I think is plain, and will be easily admitted, when we consider that we can have no idea of the place of the universe, though we can of all the parts of it ; because beyond that we have not the idea of any fixed, distinct, particular beings, in reference to which we can imagine it to have any relation of distance ; but all beyond it is one uniform space or expansion, wherein the mind finds no variety, no marks. For to say that the world is somewhere, means no more than that it does exist ; this, though a phrase borrowed from place, signifying only its existence, not location : and when one can find out, and frame in his mind, clearly and distinctly, the place of the universe, he will be able to tell us whether it moves or stands still in the undistinguishable inane of infinite space : though it be true that the word place has sometimes a more confused sense, and stands for that space which anybody takes up ; and so the universe is in a place.
The idea, therefore, of place we have by the same means that we get the idea of space, (whereof this is but a particular limited consideration,) viz, by our sight and touch ; by either of which we receive into our minds the ideas of extension or distance.
11. Extension and body not the same. There are some that would persuade us, that body and extension are the same thing, who either change the signification of words, which I would not suspect them of, – they having so severely condemned the philosophy of others, because it hath been too much placed in the uncertain meaning, or deceitful obscurity of doubtful or insignificant terms. If, therefore, they mean by body and extension the same that other people do, viz. by body something that is solid and extended, whose parts are separable and movable different ways ; and by extension, only the space that lies between the extremities of those solid coherent parts, and which is possessed by them, – they confound very different ideas one with another ; for I appeal to every man’s own thoughts whether the idea of space be not as distinct from that of solidity, as it is from the idea of scarlet colour ? It is true, solidity cannot exist without extension, neither can scarlet colour exist without extension, but this hinders not, but that they are distinct ideas. Many ideas require others, as necessary to their existence or conception, which yet are very distinct ideas. Motion can neither be, nor be conceived, without space ; and yet motion is not space, nor space motion ; space can exist without it, and they are very distinct ideas ; and so, I think, are those of space and solidity. Solidity is so inseparable an idea from body, that upon that depends its filling of space, its contact, impulse, and communication of motion upon impulse. And if it be a reason to prove that spirit is different from body, because thinking includes not the idea of extension in it ; the same reason will be as valid, I suppose, to prove that space is not body, because it includes not the idea of solidity in it ; space and solidity being as distinct ideas as thinking and extension, and as wholly separable in the mind one from another. Body then and extension, it is evident, are two distinct ideas. For,
12. Extension not solidity. First, Extension includes no solidity, nor resistance to the motion of body, as body does.
13. The parts of space inseparable, both really and mentally. Secondly, The parts of pure space are inseparable one from the other ; so that the continuity cannot be separated, neither really nor mentally. For I demand of any one to remove any part of it from another, with which it is continued, even so much as in thought. To divide and separate actually is, as I think, by removing the parts one from another, to make two superficies, where before there was a continuity : and to divide mentally is, to make in the mind two superficies, where before there was a continuity, and consider them as removed one from the other ; which can only be done in things considered by the mind as capable of being separated ; and by separation, of acquiring new distinct superficies, which they then have not, but are capable of But neither of these ways of separation, whether real or mental, is, as I think, compatible to pure space.
It is true, a man may consider so much of such a space as is answerable or commensurate to a foot, without considering the rest, which is, indeed, a partial consideration, but not so much as mental separation or division ; since a man can no more mentally divide, without considering two superficies separate one from the other, than he can actually divide, without making two superficies disjoined one from the other : but a partial consideration is not separating. A man may consider light in the sun without its heat, or mobility in body without its extension, without thinking of their separation. One is only a partial consideration, terminating in one alone ; and the other is a consideration of both, as existing separately.
14. The parts of space, immovable. Thirdly, The parts of pure space are immovable, which follows from their inseparability ; motion being nothing but change of distance between any two things ; but this cannot be between parts that are inseparable, which, therefore, must needs be at perpetual rest one amongst another.
Thus the determined idea of simple space distinguishes it plainly and sufficiently from body ; since its parts are inseparable, immovable, and without resistance to the motion of body.
15. The definition of extension explains it not. If any one ask me what this space I speak of is, I will tell him when he tells me what his extension is. For to say, as is usually done, that extension is to have partes extra partes, is to say only, that extension is extension. For what am I the better informed in the nature of extension, when I am told that extension is to have parts that are extended, exterior to parts that are extended, i.e. extension consists of extended parts ? As if one, asking what a fibre was, I should answer him, – that it was a thing made up of several fibres. Would he thereby be enabled to understand what a fibre was better than he did before ? Or rather, would he not have reason to think that my design was to make sport with him, rather than seriously to instruct him?
16. Division of beings into bodies and spirits proves not space and body the same. Those who contend that space and body are the same, bring this dilemma : – either this space is something or nothing ; if nothing be between two bodies, they must necessarily touch ; if it be allowed to be something, they ask, Whether it be body or spirit ? To which I answer by another question, Who told them that there was, or could be, nothing but solid beings, which could not think, and thinking beings that were not extended ? – which is all they mean by the terms body and spirit.
17. Substance which we know not, no proof against space without body. If it be demanded (as usually it is) whether this space, void of body, be substance or accident, I shall readily answer I know not ; nor shall be ashamed to own my ignorance, till they that ask show me a clear distinct idea of substance.
18. Different meanings of substance. I endeavour as much as I can to deliver myself from those fallacies which we are apt to put upon ourselves, by taking words for things. It helps not our ignorance to feign a knowledge where we have none, by making a noise with sounds, without clear and distinct significations. Names made at pleasure, neither alter the nature of things, nor make us understand them, but as they are signs of and stand for determined ideas. And I desire those who lay so much stress on the sound of these two syllables, substance, to consider whether applying it, as they do, to the infinite, incomprehensible God, to finite spirits, and to body, it be in the same sense ; and whether it stands for the same idea, when each of those three so different beings are called substances. If so, whether it will thence follow – that God, spirits, and body, agreeing in the same common nature of substance, differ not any otherwise than in a bare different modification of that substance ; as a tree and a pebble, being in the same sense body, and agreeing in the common nature of body, differ only in a bare modification of that common matter, which will be a very harsh doctrine. If they say, that they apply it to God, finite spirit, and matter, in three different significations and that it stands for one idea when God is said to be a substance ; for another when the soul is called substance ; and for a third when body is called so ; – if the name substance stands for three several distinct ideas, they would do well to make known those distinct ideas, or at least to give three distinct names to them, to prevent in so important a notion the confusion and errors that will naturally follow from the promiscuous use of so doubtful a term ; which is so far from being suspected to have three distinct, that in ordinary use it has scarce one clear distinct signification. And if they can thus make three distinct ideas of substance, what hinders why another may not make a fourth ?
19. Substance and accidents of little use in philosophy. They who first ran into the notion of accidents, as a sort of real beings that needed something to inhere in, were forced to find out the word substance to support them. Had the poor Indian philosopher (who imagined that the earth also wanted something to bear it up) but thought of this word substance, he needed not to have been at the trouble to find an elephant to support it, and a tortoise to support his elephant : the word substance would have done it effectually. And he that inquired might have taken it for as good an answer from an Indian philosopher, – that substance, without knowing what it is, is that which supports the earth, as we take it for a sufficient answer and good doctrine from our European philosophers, – that substance, without knowing what it is, is that which supports accidents. So that of substance, we have no idea of what it is, but only a confused, obscure one of what it does.
20. Sticking on and under-propping. Whatever a learned man may do here, an intelligent American, who inquired into the nature of things, would scarce take it for a satisfactory account, if, desiring to learn our architecture, he should be told that a pillar is a thing supported by a basis, and a basis something that supported a pillar. Would he not think himself mocked, instead of taught, with such an account as this ? And a stranger to them would be very liberally instructed in the nature of books, and the things they contained, if he should be told that all learned books consisted of paper and letters, and that letters were things inhering in paper, and paper a thing that held forth letters : a notable way of having clear ideas of letters and paper. But were the Latin words, inhaerentia and substantio, put into the plain English ones that answer them, and were called sticking on and under-propping, they would better discover to us the very great clearness there is in the doctrine of substance and accidents, and show of what use they are in deciding of questions in philosophy.
21. A vacuum beyond the utmost bounds of body. But to return to our idea of space. If body be not supposed infinite, (which I think no one will affirm), I would ask, whether, if God placed a man at the extremity of corporeal beings, he could not stretch his hand beyond his body ? If he could, then he would put his arm where there was before space without body ; and if there he spread his fingers, there would still be space between them without body. If he could not stretch out his hand, it must be because of some external hindrance ; (for we suppose him alive, with such a power of moving the parts of his body that he hath now, which is not in itself impossible, if God so pleased to have it ; or at least it is not impossible for God so to move him) : and then I ask, – whether that which hinders his hand from moving outwards be substance or accident, something or nothing ? And when they have resolved that, they will be able to resolve themselves, – what that is, which is or may be between two bodies at a distance, that is not body, and has no solidity. In the mean time, the argument is at least as good, that, where nothing hinders, (as beyond the utmost bounds of all bodies), a body put in motion may move on, as where there is nothing between, there two bodies must necessarily touch. For pure space between is sufficient to take away the necessity of mutual contact ; but bare space in the way is not sufficient to stop motion. The truth is, these men must either own that they think body infinite, though they are loth to speak it out, or else affirm that space is not body. For I would fain meet with that thinking man that can in his thoughts set any bounds to space, more than he can to duration ; or by thinking hope to arrive at the end of either. And therefore, if his idea of eternity be infinite, so is his idea of immensity ; they are both finite or infinite alike.
22. The power of annihilation proves a vacuum. Farther, those who assert the impossibility of space existing without matter, must not only make body infinite, but must also deny a power in God to annihilate any part of matter. No one, I suppose, will deny that God can put an end to all motion that is in matter, and fix all the bodies of the universe in a perfect quiet and rest, and continue them so long as he pleases. Whoever then will allow that God can, during such a general rest, annihilate either this book or the body of him that reads it, must necessarily admit the possibility of a vacuum. For, it is evident that the space that was filled by the parts of the annihilated body will still remain, and be a space without body. For the circumambient bodies being in perfect rest, are a wall of adamant, and in that state make it a perfect impossibility for any other body to get into that space. And indeed the necessary motion of one particle of matter into the place from whence another particle of matter is removed, is but a consequence from the supposition of plenitude ; which will therefore need some better proof than a supposed matter of fact, which experiment can never make out ; – our own clear and distinct ideas plainly satisfying us, that there is no necessary connexion between space and solidity, since we can conceive the one without the other. And those who dispute for or against a vacuum, do thereby confess they have distinct ideas of vacuum and plenum, i.e. that they have an idea of extension void of solidity, though they deny its existence ; or else they dispute about nothing at all. For they who so much alter the signification of words, as to call extension body, and consequently make the whole essence of body to be nothing but pure extension without solidity, must talk absurdly whenever they speak of vacuum ; since it is impossible for extension to be without extension. For vacuum, whether we affirm or deny its existence, signifies space without body ; whose very existence no one can deny to be possible, who will not make matter infinite, and take from God a power to annihilate any particle of it.
23. Motion proves a vacuum. But not to go so far as beyond the utmost bounds of body in the universe, nor appeal to God’s omnipotency to find a vacuum, the motion of bodies that are in our view and neighbourhood seems to me plainly to evince it. For I desire any one so to divide a solid body, of any dimension he pleases, as to make it possible for the solid parts to move up and down freely every way within the bounds of that superficies, if there be not left in it a void space as big as the least part into which he has divided the said solid body. And if, where the least particle of the body divided is as big as a mustard-seed, a void space equal to the bulk of a mustard-seed be requisite to make room for the free motion of the parts of the divided body within the bounds of its superficies, where the particles of matter are 100,000,000 less than a mustard-seed, there must also be a space void of solid matter as big as 100,000,000 part of a mustard-seed ; for if it hold in the one it will hold in the other, and so on in infinitum. And let this void space be as little as it will, it destroys the hypothesis of plenitude. For if there can be a space void of body equal to the smallest separate particle of matter now existing in nature, it is still space without body ; and makes as great a difference between space and body as if it were mega chasma, a distance as wide as any in nature. And therefore, if we suppose not the void space necessary to motion equal to the least parcel of the divided solid matter, but to 1/10 or 1/1000 of it, the same consequence will always follow of space without matter.
24. The ideas of space and body distinct. But the question being here, – Whether the idea of space or extension be the same with the idea of body ? it is not necessary to prove the real existence of a vacuum, but the idea of it ; which it is plain men have when they inquire and dispute whether there be a vacuum or no. For if they had not the idea of space without body, they could not make a question about its existence : and if their idea of body did not include in it something more than the bare idea of space, they could have no doubt about the plenitude of the world ; and it would be as absurd to demand, whether there were space without body, as whether there were space without space, or body without body, since these were but different names of the same idea.
25. Extension being inseparable from body, proves it not the same. It is true, the idea of extension joins itself so inseparably with all visible, and most tangible qualities, that it suffers us to see no one, or feel very few external objects, without taking in impressions of extension too. This readiness of extension to make itself be taken notice of so constantly with other ideas, has been the occasion, I guess, that some have made the whole essence of body to consist in extension ; which is not much to be wondered at, since some have had their minds, by their eyes and touch, (the busiest of all our senses,) so filled with the idea of extension, and, as it were, wholly possessed with it, that they allowed no existence to anything that had not extension. I shall not now argue with those men, who take the measure and possibility of all being only from their narrow and gross imaginations : but having here to do only with those who conclude the essence of body to be extension, because they say they cannot imagine any sensible quality of any body without extension, – I shall desire them to consider, that, had they reflected on their ideas of tastes and smells as much as on those of sight and touch ; nay, had they examined their ideas of hunger and thirst, and several other pains, they would have found that they included in them no idea of extension at all, which is but an affection of body, as well as the rest, discoverable by our senses, which are scarce acute enough to look into the pure essences of things.
26. Essences of things. If those ideas which are constantly joined to all others, must therefore be concluded to be the essence of those things which have constantly those ideas joined to them, and are inseparable from them ; then unity is without doubt the essence of everything. For there is not any object of sensation or reflection which does not carry with it the idea of one : but the weakness of this kind of argument we have already shown sufficiently.
27. Ideas of space and solidity distinct. To conclude : whatever men shall think concerning the existence of a vacuum, this is plain to me – that we have as clear an idea of space distinct from solidity, as we have of solidity distinct from motion, or motion from space. We have not any two more distinct ideas ; and we can as easily conceive space without solidity, as we can conceive body or space without motion, though it be never so certain that neither body nor motion can exist without space. But whether any one will take space to be only a relation resulting from the existence of other beings at a distance ; or whether they will think the words of the most knowing King Solomon, « The heaven, and the heaven of heavens, cannot contain thee » ; or those more emphatical ones of the inspired philosopher St. Paul, « In him we live, move, and have our being, » are to be understood in a literal sense, I leave every one to consider : only our idea of space is, I think, such as I have mentioned, and distinct from that of body. For, whether we consider, in matter itself, the distance of its coherent solid parts, and call it, in respect of those solid parts, extension ; or whether, considering it as lying between the extremities of any body in its several dimensions, we call it length, breadth, and thickness ; or else, considering it as lying between any two bodies or positive beings, without any consideration whether there be any matter or not between, we call it distance ; – however named or considered, it is always the same uniform simple idea of space, taken from objects about which our senses have been conversant ; whereof, having settled ideas in our minds, we can revive, repeat, and add them one to another as often as we will, and consider the space or distance so imagined, either as filled with solid parts, so that another body cannot come there without displacing and thrusting out the body that was there before ; or else as void of solidity, so that a body of equal dimensions to that empty or pure space may be placed in it, without the removing or expulsion of anything that was there. But, to avoid confusion in discourses concerning this matter, it were possibly to be wished that the name extension were applied only to matter, or the distance of the extremities of particular bodies ; and the term expansion to space in general, with or without solid matter possessing it, – so as to say space is expanded and body extended. But in this every one has his liberty : I propose it only for the more clear and distinct way of speaking.
28. Men differ little in clear, simple ideas. The knowing precisely what our words stand for, would, I imagine, in this as well as a great many other cases, quickly end the dispute. For I am apt to think that men, when they come to examine them, find their simple ideas all generally to agree, though in discourse with one another they perhaps confound one another with different names. I imagine that men who abstract their thoughts, and do well examine the ideas of their own minds, cannot much differ in thinking ; however they may perplex themselves with words, according to the way of speaking to the several schools or sects they have been bred up in : though amongst unthinking men, who examine not scrupulously and carefully their own ideas, and strip them not from the marks men use for them, but confound them with words, there must be endless dispute, wrangling, and jargon ; especially if they be learned, bookish men, devoted to some sect, and accustomed to the language of it, and have learned to talk after others. But if it should happen that any two thinking men should really have different ideas, I do not see how they could discourse or argue with another. Here I must not be mistaken, to think that every floating imagination in men’s brains is presently of that sort of ideas I speak of. It is not easy for the mind to put off those confused notions and prejudices it has imbibed from custom, inadvertency, and common conversation. It requires pains and assiduity to examine its ideas, till it resolves them into those clear and distinct simple ones, out of which they are compounded ; and to see which, amongst its simple ones, have or have not a necessary connexion and dependence one upon another. Till a man doth this in the primary and original notions of things, he builds upon floating and uncertain principles, and will often find himself at a loss.