Clear and Unclear, Distinct and Confused Ideas

1. Ideas, some clear and distinct, others obscure and confused.

1. Some ideas are clear and distinct, while others are unclear and confused.

Having shown the original of our ideas, and taken a view of their several sorts; considered the difference between the simple and the complex; and observed how the complex ones are divided into those of modes, substances, and relations—all which, I think, is necessary to be done by any one who would acquaint himself thoroughly with the progress of the mind, in its apprehension and knowledge of things—it will, perhaps, be thought I have dwelt long enough upon the examination of IDEAS. I must, nevertheless, crave leave to offer some few other considerations concerning them.

I have shown where our ideas come from and reviewed their different kinds. I have considered the difference between simple and complex ideas. I have also noted how complex ideas fall into three groups: modes, substances, and relations. I think all these steps are necessary for anyone seeking to understand fully how the mind comes to grasp and know things. Perhaps readers will therefore think I have spent enough time examining IDEAS. Nevertheless, I must ask permission to offer a few more thoughts about them.

The first is, that some are CLEAR and others OBSCURE; some DISTINCT and others CONFUSED.

The first point is that some are CLEAR and others UNCLEAR. Some are DISTINCT and others CONFUSED.

2. Clear and obscure explained by Sight.

2. Clear and unclear explained through sight.

The perception of the mind being most aptly explained by words relating to the sight, we shall best understand what is meant by CLEAR and OBSCURE in our ideas, by reflecting on what we call clear and obscure in the objects of sight. Light being that which discovers to us visible objects, we give the name of OBSCURE to that which is not placed in a light sufficient to discover minutely to us the figure and colours which are observable in it, and which, in a better light, would be discernible. In like manner, our simple ideas are CLEAR, when they are such as the objects themselves from whence they were taken did or might, in a well-ordered sensation or perception, present them. Whilst the memory retains them thus, and can produce them to the mind whenever it has occasion to consider them, they are clear ideas. So far as they either want anything of the original exactness, or have lost any of their first freshness, and are, as it were, faded or tarnished by time, so far are they obscure. Complex ideas, as they are made up of simple ones, so they are clear, when the ideas that go to their composition are clear, and the number and order of those simple ideas that are the ingredients of any complex one is determinate and certain.

The mind’s perceptions are best explained through words related to sight. So we can best understand CLEAR and OBSCURE ideas by considering what we call clear and obscure in visible objects. Light reveals visible objects to us. We call an object OBSCURE when the light is too weak to reveal its shape and colours in detail. Those details would be visible in better light. Similarly, our simple ideas are CLEAR when they match what the objects they came from presented, or could have presented. This requires sensation or perception to work properly. As long as memory preserves ideas in this form and can recall them whenever needed, they remain clear. To the extent that ideas lack their original accuracy or have lost their initial freshness, they are obscure. Such ideas are, so to speak, faded or tarnished by time. Complex ideas are made up of simple ideas. So complex ideas are clear when their component ideas are clear and those components have a definite, certain number and order.

3. Causes of Obscurity.

3. Causes of Unclear Language.

The causes of obscurity, in simple ideas, seem to be either dull organs; or very slight and transient impressions made by the objects; or else a weakness in the memory, not able to retain them as received. For to return again to visible objects, to help us to apprehend this matter. If the organs, or faculties of perception, like wax over-hardened with cold, will not receive the impression of the seal, from the usual impulse wont to imprint it; or, like wax of a temper too soft, will not hold it well, when well imprinted; or else supposing the wax of a temper fit, but the seal not applied with a sufficient force to make a clear impression: in any of these cases, the print left by the seal will be obscure. This, I suppose, needs no application to make it plainer.

The causes of unclear simple ideas seem to be either unresponsive sense organs, faint and brief impressions from objects, or weak memory. A weak memory cannot preserve impressions as they were received. Let us return to visible objects to help us understand this point. Suppose our organs or powers of perception are like wax made too hard by cold. They cannot receive the seal’s impression from the usual pressure that would leave a mark. Or suppose they are like wax that is too soft. They cannot hold the impression well, even when the seal has made a clear mark. Or suppose the wax has the right firmness, but the seal is not pressed hard enough to leave a clear impression. In any of these cases, the mark left by the seal will be unclear. I suppose there is no need to explain how this comparison applies.

4. Distinct and confused, what.

4. What “distinct” and “confused” mean.

As a clear idea is that whereof the mind has such a full and evident perception, as it does receive from an outward object operating duly on a well-disposed organ, so a DISTINCT idea is that wherein the mind perceives a difference from all other; and a CONFUSED idea is such an one as is not sufficiently distinguishable from another, from which it ought to be different.

A clear idea is one the mind perceives as fully and plainly as it perceives an external object through a properly functioning sense organ. A DISTINCT idea, in turn, is one the mind perceives as different from all other ideas. A CONFUSED idea is one not clearly enough distinguished from another idea from which it ought to differ.

5. Objection.

5. Objection.

If no idea be confused, but such as is not sufficiently distinguishable from another from which it should be different, it will be hard, may any one say, to find anywhere a CONFUSED idea. For, let any idea be as it will, it can be no other but such as the mind perceives it to be; and that very perception sufficiently distinguishes it from all other ideas, which cannot be other, i.e. different, without being perceived to be so. No idea, therefore, can be undistinguishable from another from which it ought to be different, unless you would have it different from itself: for from all other it is evidently different.

Suppose an idea is confused only when it cannot be clearly distinguished from another idea it should differ from. Someone may then say that finding a CONFUSED idea anywhere will be hard. For whatever an idea may be, it can only be what the mind perceives it to be. And that very perception sufficiently distinguishes the idea from all other ideas. Those other ideas cannot be different without being perceived as different. So no idea can be indistinguishable from another idea it ought to differ from, unless you expect it to differ from itself. For it is clearly different from all other ideas.

6. Confusion of Ideas is in Reference to their Names.

6. Confusion about ideas relates to the names given to those ideas.

To remove this difficulty, and to help us to conceive aright what it is that makes the confusion ideas are at any time chargeable with, we must consider, that things ranked under distinct names are supposed different enough to be distinguished, that so each sort by its peculiar name may be marked, and discoursed of apart upon any occasion: and there is nothing more evident, than that the greatest part of different names are supposed to stand for different things. Now every idea a man has, being visibly what it is, and distinct from all other ideas but itself; that which makes it confused, is, when it is such that it may as well be called by another name as that which it is expressed by; the difference which keeps the things (to be ranked under those two different names) distinct, and makes some of them belong rather to the one and some of them to the other of those names, being left out; and so the distinction, which was intended to be kept up by those different names, is quite lost.

To resolve this difficulty, we must consider what makes ideas confused at any given time. Things grouped under different names are assumed to differ enough for us to tell them apart. Each kind can then be identified by its own name and discussed separately whenever needed. Nothing is more obvious than that most different names are assumed to stand for different things. Now, every idea a person has is plainly what it is, distinct from every other idea. An idea becomes confused when another name fits it just as well as the name used to express it. This happens when the idea leaves out the difference between the things grouped under those two names. That difference keeps the groups distinct, making some things belong under one name rather than the other. Without that difference, the distinction those different names were meant to preserve is completely lost.

7. Defaults which make this Confusion.

7. Flaws that cause this confusion.

The defaults which usually occasion this confusion, I think, are chiefly these following:

I think the main faults that usually cause this confusion are the following:

First, complex ideas made up of too few simple ones.

First, complex ideas made up of too few simple ideas.

First, when any complex idea (for it is complex ideas that are most liable to confusion) is made up of too small a number of simple ideas, and such only as are common to other things, whereby the differences that make it deserve a different name, are left out. Thus, he that has an idea made up of barely the simple ones of a beast with spots, has but a confused idea of a leopard; it not being thereby sufficiently distinguished from a lynx, and several other sorts of beasts that are spotted. So that such an idea, though it hath the peculiar name leopard, is not distinguishable from those designed by the names lynx or panther, and may as well come under the name lynx as leopard. How much the custom of defining of words by general terms contributes to make the ideas we would express by them confused and undetermined, I leave others to consider. This is evident, that confused ideas are such as render the use of words uncertain, and take away the benefit of distinct names. When the ideas, for which we use different terms, have not a difference answerable to their distinct names, and so cannot be distinguished by them, there it is that they are truly confused.

First, a complex idea may contain too few simple ideas, all of them shared by other things. Complex ideas are the most likely to be confused. Such an idea leaves out the differences that justify giving it a different name. For example, someone whose idea of a leopard is simply a spotted animal has only a confused idea of a leopard. That idea does not sufficiently distinguish a leopard from a lynx or several other kinds of spotted animals. So, although the idea has the specific name leopard, it cannot be distinguished from ideas called lynx or panther. The idea could just as well be called lynx as leopard. I leave others to consider how much defining words in general terms makes the ideas we express confused and imprecise. But one thing is clear: confused ideas make the use of words uncertain and remove the benefit of distinct names. When we use different terms for ideas, the ideas must differ in ways that match their different names. If the ideas lack those differences, so that the names cannot distinguish them, the ideas are truly confused.

8. Secondly, or their simple ones jumbled disorderly together.

8. Secondly, or their simple ones mixed together without order.

Secondly, Another fault which makes our ideas confused is, when, though the particulars that make up any idea are in number enough, yet they are so jumbled together, that it is not easily discernible whether it more belongs to the name that is given it than to any other. There is nothing properer to make us conceive this confusion than a sort of pictures, usually shown as surprising pieces of art, wherein the colours, as they are laid by the pencil on the table itself, mark out very odd and unusual figures, and have no discernible order in their position. This draught, thus made up of parts wherein no symmetry nor order appears, is in itself no more a confused thing, than the picture of a cloudy sky; wherein, though there be as little order of colours or figures to be found, yet nobody thinks it a confused picture. What is it, then, that makes it be thought confused, since the want of symmetry does not? As it is plain it does not: for another draught made barely in imitation of this could not be called confused. I answer, That which makes it be thought confused is, the applying it to some name to which it does no more discernibly belong than to some other: v.g. when it is said to be the picture of a man, or Caesar, then any one with reason counts it confused; because it is not discernible in that state to belong more to the name man, or Caesar, than to the name baboon, or Pompey: which are supposed to stand for different ideas from those signified by man, or Caesar. But when a cylindrical mirror, placed right, had reduced those irregular lines on the table into their due order and proportion, then the confusion ceases, and the eye presently sees that it is a man, or Caesar; i.e. that it belongs to those names; and that it is sufficiently distinguishable from a baboon, or Pompey; i.e. from the ideas signified by those names. Just thus it is with our ideas, which are as it were the pictures of things. No one of these mental draughts, however the parts are put together, can be called confused (for they are plainly discernible as they are) till it be ranked under some ordinary name to which it cannot be discerned to belong, any more than it does to some other name of an allowed different signification.

Secondly, another fault makes our ideas confused. An idea may contain enough details, yet those details may be so jumbled that its proper name is unclear. We cannot easily tell whether the idea belongs under its given name rather than some other name. Nothing illustrates this confusion better than certain pictures often displayed as remarkable works of art. The colors painted on the surface form very strange, unusual shapes, with no clear order in their arrangement. Such a picture, whose parts show no symmetry or order, is no more confused in itself than a cloudy sky. A picture of a cloudy sky may show just as little order in its colors or shapes. Yet nobody considers that picture confused. What, then, makes the first picture seem confused, since a lack of symmetry does not? Clearly, a lack of symmetry is not the cause. Another picture made simply to copy the first could not be called confused. My answer is that the confusion comes from giving the picture a name. The picture does not clearly belong under that name any more than under another. For example, suppose someone calls the picture a man, or Caesar. Anyone would reasonably consider the picture confused. In its present state, the picture no more clearly represents a man or Caesar than a baboon or Pompey. Yet baboon and Pompey are understood to stand for ideas different from those represented by man and Caesar. But place a cylindrical mirror correctly, and the mirror brings those irregular lines into their proper order and proportion. Then the confusion disappears, and the eye immediately recognizes a man or Caesar. In other words, the picture belongs under those names. The picture is also clearly distinguishable from a baboon or Pompey, meaning the ideas represented by those names. Exactly the same is true of our ideas, which are, in a sense, pictures of things. No such mental picture can be called confused merely because of how its parts are arranged. We can plainly distinguish these mental pictures as they are. Confusion arises only when we place a mental picture under an ordinary name without clearly distinguishing why it belongs there. It belongs no more clearly under that name than under another name whose meaning is recognized as different.

9. Thirdly, or their simple ones mutable and undetermined.

9. Thirdly, or their simple ones are changeable and not clearly defined.

Thirdly, A third defect that frequently gives the name of confused to our ideas, is, when any one of them is uncertain and undetermined. Thus we may observe men who, not forbearing to use the ordinary words of their language till they have learned their precise signification, change the idea they make this or that term stand for, almost as often as they use it. He that does this out of uncertainty of what he should leave out, or put into his idea of CHURCH, or IDOLATRY, every time he thinks of either, and holds not steady to any one precise combination of ideas that makes it up, is said to have a confused idea of idolatry or the church: though this be still for the same reason as the former, viz. because a mutable idea (if we will allow it to be one idea) cannot belong to one name rather than another, and so loses the distinction that distinct names are designed for.

Thirdly, another flaw often leads us to call our ideas confused: an idea may be uncertain and undefined. We can observe people using ordinary words in their language before learning their precise meanings. These people change the idea a word stands for almost every time they use the word. Someone may be unsure what to include in or leave out of their idea of CHURCH or IDOLATRY. Each time they think of either, they fail to keep the same precise combination of ideas. Such a person is said to have a confused idea of idolatry or the church. Yet the reason is still the same as before. A changing idea cannot belong to one name rather than another, if we can call it one idea at all. So the changing idea loses the distinction that different names are meant to provide.

10. Confusion without Reference to Names, hardly conceivable.

10. Confusion without reference to names is hard to imagine.

By what has been said, we may observe how much NAMES, as supposed steady signs of things, and by their difference to stand for, and keep things distinct that in themselves are different, are the occasion of denominating ideas distinct or confused, by a secret and unobserved reference the mind makes of its ideas to such names. This perhaps will be fuller understood, after what I say of Words in the third Book has been read and considered. But without taking notice of such a reference of ideas to distinct names, as the signs of distinct things, it will be hard to say what a confused idea is. And therefore when a man designs, by any name, a sort of things, or any one particular thing, distinct from all others, the complex idea he annexes to that name is the more distinct, the more particular the ideas are, and the greater and more determinate the number and order of them is, whereof it is made up. For, the more it has of these, the more it has still of the perceivable differences, whereby it is kept separate and distinct from all ideas belonging to other names, even those that approach nearest to it, and thereby all confusion with them is avoided.

From what has been said, we can see how much NAMES influence whether we call ideas distinct or confused. Names are assumed to be stable signs of things. Different names are supposed to represent different things and keep them separate. The mind silently and unknowingly connects its ideas with these names, leading us to call the ideas distinct or confused. Perhaps this connection will be better understood after reading and considering what I say about Words in the third Book. But without recognizing this connection between ideas and distinct names, understood as signs of distinct things, explaining a confused idea is difficult. So, suppose someone uses a name to identify a kind of thing, or one particular thing, as distinct from all others. The complex idea attached to that name becomes more distinct as its component ideas become more specific. The complex idea also becomes more distinct as the number and order of its components become greater and more definite. For the more of these features the complex idea has, the more noticeable differences it contains. These differences keep the complex idea separate and distinct from all ideas belonging to other names, even the most similar. In this way, all confusion with those other ideas is avoided.

11. Confusion concerns always two Ideas.

11. Confusion always involves two ideas.

Confusion making it a difficulty to separate two things that should be separated, concerns always two ideas; and those most which most approach one another. Whenever, therefore, we suspect any idea to be confused, we must examine what other it is in danger to be confounded with, or which it cannot easily be separated from; and that will always be found an idea belonging to another name, and so should be a different thing, from which yet it is not sufficiently distinct: being either the same with it, or making a part of it, or at least as properly called by that name as the other it is ranked under; and so keeps not that difference from that other idea which the different names import.

Confusion makes it difficult to separate two things that should be kept apart, so it always involves two ideas. The most similar ideas are the most likely to be confused. So whenever we suspect an idea is confused, we must ask what other idea it risks being confused with. Or we must ask what other idea is difficult to separate from it. That other idea will always have a different name and should therefore be a different thing. Yet the suspected idea is not distinct enough from the other idea. The suspected idea is either identical to the other idea or forms part of it. Or at least, the other idea’s name fits the suspected idea just as well as its current name does. So the two ideas lack the distinction that their different names imply.

12. Causes of confused Ideas.

12. Causes of unclear ideas.

This, I think, is the confusion proper to ideas; which still carries with it a secret reference to names. At least, if there be any other confusion of ideas, this is that which most of all disorders men’s thoughts and discourses: ideas, as ranked under names, being those that for the most part men reason of within themselves, and always those which they commune about with others. And therefore where there are supposed two different ideas, marked by two different names, which are not as distinguishable as the sounds that stand for them, there never fails to be confusion; and where any ideas are distinct as the ideas of those two sounds they are marked by, there can be between them no confusion. The way to prevent it is to collect and unite into one complex idea, as precisely as is possible, all those ingredients whereby it is differenced from others; and to them, so united in a determinate number and order, apply steadily the same name. But this neither accommodating men’s ease or vanity, nor serving any design but that of naked truth, which is not always the thing aimed at, such exactness is rather to be wished than hoped for. And since the loose application of names, to undetermined, variable, and almost no ideas, serves both to cover our own ignorance, as well as to perplex and confound others, which goes for learning and superiority in knowledge, it is no wonder that most men should use it themselves, whilst they complain of it in others. Though I think no small part of the confusion to be found in the notions of men might, by care and ingenuity, be avoided, yet I am far from concluding it everywhere wilful. Some ideas are so complex, and made up of so many parts, that the memory does not easily retain the very same precise combination of simple ideas under one name: much less are we able constantly to divine for what precise complex idea such a name stands in another man’s use of it. From the first of these, follows confusion in a man’s own reasonings and opinions within himself; from the latter, frequent confusion in discoursing and arguing with others. But having more at large treated of Words, their defects, and abuses, in the following Book, I shall here say no more of it.

This, I think, is the kind of confusion that belongs to ideas. It always involves an unspoken reference to names. At least, if ideas can be confused in other ways, this kind most disrupts people’s thinking and discussion. People mostly reason privately about ideas grouped under names, and they always use such ideas when communicating with others. So confusion always arises when two supposedly different ideas have different names but are less distinguishable than those names’ sounds. But if the ideas are as distinct as our ideas of those two sounds, no confusion between them is possible. To prevent confusion, gather and combine into one complex idea all the features that distinguish it from other ideas. Do this as precisely as possible. Then consistently apply the same name to those features, combined in a fixed number and order. But such precision does not suit people’s love of ease or their vanity. Nor does it serve any purpose except plain truth, which is not always their aim. So such precision is more to be wished for than expected. Applying names loosely to undefined, changing ideas, or almost no ideas at all, helps conceal our own ignorance. It also helps bewilder and confuse others, which passes for learning and superior knowledge. So it is no wonder that most people use this practice themselves while complaining about it in others. I think care and ingenuity could prevent a considerable share of the confusion in people’s ideas. Still, I am far from concluding that this confusion is always deliberate. Some ideas are so complex and contain so many parts that memory struggles to retain their exact combination. We cannot easily keep precisely the same combination of simple ideas under one name. Still less can we always guess precisely what complex idea another person means by that name. The first difficulty causes confusion in a person’s own reasoning and opinions. The second causes frequent confusion when people discuss and argue with others. But I discuss words, their defects, and their misuse more fully in the following Book. So I will say no more about them here.

13. Complex Ideas may be distinct in one Part, and confused in another.

13. Complex ideas may be clear in one part and unclear in another.

Our complex ideas, being made up of collections, and so variety of simple ones, may accordingly be very clear and distinct in one part, and very obscure and confused in another. In a man who speaks of a chiliaedron, or a body of a thousand sides, the ideas of the figure may be very confused, though that of the number be very distinct; so that he being able to discourse and demonstrate concerning that part of his complex idea which depends upon the number of thousand, he is apt to think he has a distinct idea of a chiliaedron; though it be plain he has no precise idea of its figure, so as to distinguish it, by that, from one that has but 999 sides: the not observing whereof causes no small error in men’s thoughts, and confusion in their discourses.

Our complex ideas are collections of various simple ideas. So they may be very clear and distinct in one part, yet very vague and confused in another. A man may speak of a chiliaedron, or a solid with a thousand sides. His idea of its shape may be very confused, though his idea of the number is very distinct. He can therefore discuss and prove things about the part of his complex idea involving the number one thousand. Because of this ability, he is likely to think he has a distinct idea of a chiliaedron. Yet clearly, his idea of its shape is not precise enough to distinguish it from a solid with 999 sides. Failing to notice this difference causes considerable error in people's thinking and confusion in their discussions.

14. This, if not heeded, causes Confusion in our Arguings.

14. If we ignore this, it causes confusion in our reasoning.

He that thinks he has a distinct idea of the figure of a chiliaedron, let him for trial sake take another parcel of the same uniform matter, viz. gold or wax of an equal bulk, and make it into a figure of 999 sides. He will, I doubt not, be able to distinguish these two ideas one from another, by the number of sides; and reason and argue distinctly about them, whilst he keeps his thoughts and reasoning to that part only of these ideas which is contained in their numbers; as that the sides of the one could be divided into two equal numbers, and of the others not, &c. But when he goes about to distinguish them by their figure, he will there be presently at a loss, and not be able, I think, to frame in his mind two ideas, one of them distinct from the other, by the bare figure of these two pieces of gold; as he could, if the same parcels of gold were made one into a cube, the other a figure of five sides. In which incomplete ideas, we are very apt to impose on ourselves, and wrangle with others, especially where they have particular and familiar names. For, being satisfied in that part of the idea which we have clear; and the name which is familiar to us, being applied to the whole, containing that part also which is imperfect and obscure, we are apt to use it for that confused part, and draw deductions from it in the obscure part of its signification, as confidently as we do from the other.

Anyone who thinks he has a distinct idea of a chiliaedron, a solid with a thousand faces, should try this experiment. Take another piece of the same uniform material, gold or wax, of equal volume. Shape the second piece into a solid with 999 faces. He will, I have no doubt, distinguish the two ideas by their number of faces. He can reason and argue clearly about them, as long as he considers only the numbers involved. For example, the faces of one can be divided into two equal groups, but those of the other cannot. But when he tries to distinguish the two solids by shape, he will immediately be at a loss. I think he cannot form two distinct mental images based on the shapes of these two pieces of gold alone. He could do so if the same pieces formed a cube and a solid with five faces. With such incomplete ideas, we are very likely to deceive ourselves and argue with others, especially when the ideas have familiar, specific names. We are satisfied with the part of the idea we understand clearly. And we apply the familiar name to the whole idea, including the part that remains incomplete and obscure. So we tend to use the name for the confused part as well. We draw conclusions from the obscure part of its meaning as confidently as we do from the clear part.

15. Instance in Eternity.

15. Eternity as an Example.

Having frequently in our mouths the name Eternity, we are apt to think we have a positive comprehensive idea of it, which is as much as to say, that there is no part of that duration which is not clearly contained in our idea. It is true that he that thinks so may have a clear idea of duration; he may also have a clear idea of a very great length of duration; he may also have a clear idea of the comparison of that great one with still a greater: but it not being possible for him to include in his idea of any duration, let it be as great as it will, the WHOLE EXTENT TOGETHER OF A DURATION, WHERE HE SUPPOSES NO END, that part of his idea, which is still beyond the bounds of that large duration he represents to his own thoughts, is very obscure and undetermined. And hence it is that in disputes and reasonings concerning eternity, or any other infinite, we are very apt to blunder, and involve ourselves in manifest absurdities.

Because we often speak of Eternity, we tend to think we have a definite, complete idea of it. That would mean our idea clearly includes every part of that duration. Someone who thinks so may indeed have a clear idea of duration. They may also have a clear idea of a very long duration. They may also clearly understand how that long duration compares with an even longer one. But no matter how long a duration they imagine, they cannot grasp THE WHOLE EXTENT AT ONCE OF A DURATION THEY SUPPOSE HAS NO END. Whatever lies beyond the limits of the long duration they picture remains very unclear and undefined in their idea. This is why, when debating and reasoning about eternity or anything else infinite, we so easily make mistakes. We become entangled in obvious absurdities.

16. Infinite Divisibility of Matter.

16. Matter Can Be Divided Endlessly.

In matter, we have no clear ideas of the smallness of parts much beyond the smallest that occur to any of our senses: and therefore, when we talk of the divisibility of matter IN INFINITUM, though we have clear ideas of division and divisibility, and have also clear ideas of parts made out of a whole by division; yet we have but very obscure and confused ideas of corpuscles, or minute bodies, so to be divided, when, by former divisions, they are reduced to a smallness much exceeding the perception of any of our senses; and so all that we have clear and distinct ideas of is of what division in general or abstractedly is, and the relation of TOTUM and PARS: but of the bulk of the body, to be thus infinitely divided after certain progressions, I think, we have no clear nor distinct idea at all. For I ask any one, whether, taking the smallest atom of dust he ever saw, he has any distinct idea (bating still the number, which concerns not extension) betwixt the 100,000th and the 1,000,000th part of it. Or if he think he can refine his ideas to that degree, without losing sight of them, let him add ten cyphers to each of those numbers. Such a degree of smallness is not unreasonable to be supposed; since a division carried on so far brings it no nearer the end of infinite division, than the first division into two halves does. I must confess, for my part, I have no clear distinct ideas of the different bulk or extension of those bodies, having but a very obscure one of either of them. So that, I think, when we talk of division of bodies in infinitum, our idea of their distinct bulks, which is the subject and foundation of division, comes, after a little progression, to be confounded, and almost lost in obscurity. For that idea which is to represent only bigness must be very obscure and confused, which we cannot distinguish from one ten times as big, but only by number: so that we have clear distinct ideas, we may say, of ten and one, but no distinct ideas of two such extensions. It is plain from hence, that, when we talk of infinite divisibility of body or extension, our distinct and clear ideas are only of numbers: but the clear distinct ideas of extension, after some progress of division, are quite lost; and of such minute parts we have no distinct ideas at all; but it returns, as all our ideas of infinite do, at last to that of NUMBER ALWAYS TO BE ADDED; but thereby never amounts to any distinct idea of ACTUAL INFINITE PARTS. We have, it is true, a clear idea of division, as often as we think of it; but thereby we have no more a clear idea of infinite parts in matter, than we have a clear idea of an infinite number, by being able still to add new numbers to any assigned numbers we have: endless divisibility giving us no more a clear and distinct idea of actually infinite parts, than endless addibility (if I may so speak) gives us a clear and distinct idea of an actually infinite number: they both being only in a power still of increasing the number, be it already as great as it will. So that of what remains to be added (WHEREIN CONSISTS THE INFINITY) we have but an obscure, imperfect, and confused idea; from or about which we can argue or reason with no certainty or clearness, no more than we can in arithmetic, about a number of which we have no such distinct idea as we have of 4 or 100; but only this relative obscure one, that, compared to any other, it is still bigger: and we have no more a clear positive idea of it, when we [dropped line*] than if we should say it is bigger than 40 or 4: 400,000,000 having no nearer a proportion to the end of addition or number than 4. For he that adds only 4 to 4, and so proceeds, shall as soon come to the end of all addition, as he that adds 400,000,000 to 400,000,000. And so likewise in eternity; he that has an idea of but four years, has as much a positive complete idea of eternity, as he that has one of 400,000,000 of years: for what remains of eternity beyond either of these two numbers of years, is as clear to the one as the other; i.e. neither of them has any clear positive idea of it at all. For he that adds only 4 years to 4, and so on, shall as soon reach eternity as he that adds 400,000,000 of years, and so on; or, if he please, doubles the increase as often as he will: the remaining abyss being still as far beyond the end of all these progressions as it is from the length of a day or an hour. For nothing finite bears any proportion to infinite; and therefore our ideas, which are all finite, cannot bear any. Thus it is also in our idea of extension, when we increase it by addition, as well as when we diminish it by division, and would enlarge our thoughts to infinite space. After a few doublings of those ideas of extension, which are the largest we are accustomed to have, we lose the clear distinct idea of that space: it becomes a confusedly great one, with a surplus of still greater; about which, when we would argue or reason, we shall always find ourselves at a loss; confused ideas, in our arguings and deductions from that part of them which is confused, always leading us into confusion.

In matter, we have no clear ideas of parts much smaller than the smallest our senses can detect. So consider what we mean when we speak of dividing matter WITHOUT END. We have clear ideas of division and divisibility. We also have clear ideas of parts separated from a whole by division. Yet our ideas of the tiny bodies being divided become very obscure and confused. This happens when repeated division makes those bodies far too small for any of our senses to detect. So our clear and distinct ideas concern only division in general, considered abstractly, and the relationship between WHOLE and PART. But I think we have no clear or distinct idea of a body's size after certain stages of this endless division. I ask anyone to consider the smallest speck of dust they have ever seen. Can they clearly distinguish its 100,000th part from its 1,000,000th part in their minds? Set aside the numbers themselves, since numbers do not concern size in space. If anyone thinks they can make their ideas so precise without losing sight of them, let them go further. Let them add ten zeros to each of those numbers. There is nothing unreasonable about supposing such smallness. Division carried that far brings us no closer to the end of infinite division than the first division into halves. For my part, I must admit that I have no clear, distinct ideas of those bodies' different sizes in space. My idea of either body is very obscure. So I think our ideas of bodies' distinct sizes soon become confused and almost disappear into obscurity during endless division. Yet those sizes are the subject and foundation of division. An idea meant to represent size alone must be very obscure and confused under the following condition: we cannot distinguish that size from one ten times larger except by number. So we may say that we have clear, distinct ideas of ten and one. But we have no distinct ideas of two sizes like these. From this, it is plain what happens when we discuss the infinite divisibility of bodies or their size in space. Our clear and distinct ideas concern only numbers. After division has gone some way, our clear and distinct ideas of size in space are completely lost. We have no distinct ideas at all of such tiny parts. Instead, as with all our ideas of infinity, we return at last to NUMBER THAT CAN ALWAYS BE INCREASED. But this never gives us a distinct idea of ACTUALLY INFINITE PARTS. It is true that we have a clear idea of division whenever we think about division. But this gives us no clear idea of infinitely many actual parts in matter. Similarly, being able to add new numbers to any given number gives us no clear idea of an infinite number. Endless divisibility gives us no clear and distinct idea of actually infinite parts. Nor does endless addibility, if I may use that word, give us such an idea of an actually infinite number. Both amount only to the continuing ability to increase a number, however great that number already is. So our idea of what remains to be added (WHICH IS WHERE THE INFINITY LIES) is obscure, incomplete, and confused. We cannot reason about that remainder with any certainty or clarity. We are no better placed than in arithmetic when reasoning about a number we cannot distinctly conceive. We have no idea of that number comparable to our distinct ideas of 4 or 100. We have only this obscure, relative idea: compared with any other number, the number is still larger. And we have no clearer, definite idea of that number when we [dropped line*] than when we say it exceeds 40 or 4. For 400,000,000 is no closer to the end of addition or number than 4. Someone who repeatedly adds 4 to 4 will reach the end of all addition just as soon as someone adding 400,000,000 to 400,000,000. The same holds for eternity. Someone with an idea of only four years has as definite and complete an idea of eternity as someone imagining 400,000,000 years. What remains of eternity beyond either number of years is equally clear to both people. That is, neither person has any clear, definite idea of that remainder at all. Someone who repeatedly adds 4 years to 4 will reach eternity just as soon as someone repeatedly adding 400,000,000 years. The second person may even double each increase as often as they please. The remaining abyss is still just as far beyond all these successive increases as beyond a day or an hour. For nothing finite bears any proportion to the infinite. Therefore, our ideas, which are all finite, cannot bear any proportion to the infinite either. The same holds when we increase our idea of size in space by addition, rather than diminish it by division. We try in this way to extend our thoughts to infinite space. We begin with the largest ideas of space we are accustomed to having. After a few doublings, we lose our clear, distinct idea of that space. Our idea becomes one of confused greatness, with something still greater beyond it. Whenever we try to reason about that confused idea, we will find ourselves at a loss. For reasoning and drawing conclusions from the confused part of an idea always leads us into confusion.