The Problems of Philosophy

PREFACE

In the pages that follow, I have mostly limited myself to those problems of philosophy about which I thought it possible to say something positive and constructive. Purely negative criticism seemed out of place here. For this reason, this book gives more space to the theory of knowledge than to metaphysics. Some topics that philosophers discuss at length are treated only briefly, and some not at all.

I have received valuable help from the unpublished writings of G. E. Moore and J. M. Keynes. Moore’s work helped me on the relation between sense-data and physical objects, and Keynes’s work helped me on probability and induction. I have also benefited greatly from the criticisms and suggestions of Professor Gilbert Murray.

1912

CHAPTER I. APPEARANCE AND REALITY

Is there any knowledge in the world so certain that no reasonable person could doubt it? At first this question might not seem difficult. In fact, it is one of the most difficult questions that can be asked. Once we have recognized what stands in the way of a straightforward and confident answer, we will be well started in the study of philosophy.

Philosophy is simply the attempt to answer such ultimate questions. In ordinary life, and even in the sciences, we answer them carelessly and dogmatically. Philosophy tries to answer them critically. It does so only after exploring everything that makes such questions puzzling, and after recognizing all the vagueness and confusion that lie beneath our ordinary ideas.

In daily life we take many things as certain. On closer examination, however, these things turn out to be so full of apparent contradictions that only a great deal of thought lets us know what we may really believe.

In the search for certainty, it is natural to begin with our present experiences. In some sense, no doubt, knowledge must come from them. But any statement about what our immediate experiences allow us to know is very likely to be wrong.

It seems to me that I am now sitting in a chair, at a table of a certain shape. On the table I see sheets of paper with writing or print on them. When I turn my head, I see buildings, clouds, and the sun through the window.

I believe that the sun is about ninety-three million miles from the earth. I believe it is a hot globe many times bigger than the earth. I believe that, because the earth rotates, the sun rises every morning, and that it will go on doing so for an indefinite time into the future.

I also believe that if any other normal person comes into my room, he will see the same chairs, tables, books, and papers that I see. And I believe that the table I see is the same table I feel pressing against my arm.

All of this seems so obvious that it hardly seems worth saying, except in reply to someone who doubts whether I know anything at all. Yet all of it can reasonably be doubted. All of it needs careful discussion before we can be sure we have stated it in a form that is entirely true.

To make our difficulties clear, let us focus on the table. To the eye it is oblong, brown, and shiny. To the touch it is smooth, cool, and hard. When I tap it, it makes a wooden sound. Anyone else who sees, feels, and hears the table will agree with this description, so it might seem that no difficulty could arise. But as soon as we try to be more precise, our troubles begin.

I believe that the table is “really” the same colour all over. Yet the parts that reflect the light look much brighter than the other parts, and some parts look white because of reflected light. I know that if I move, different parts will reflect the light, so the apparent distribution of colours on the table will change.

It follows that if several people look at the table at the same moment, no two of them will see exactly the same distribution of colours. No two people can see it from exactly the same point of view, and any change in point of view changes the way the light is reflected.

For most practical purposes these differences do not matter. To the painter, though, they matter enormously. A painter has to unlearn the habit of thinking that things seem to have the colour that common sense says they “really” have. Instead, the painter must learn the habit of seeing things as they appear.

Here we already have the beginning of one of the distinctions that cause the most trouble in philosophy: the distinction between “appearance” and “reality,” between what things seem to be and what they are. The painter wants to know what things seem to be. The practical person and the philosopher want to know what they are.

But the philosopher’s wish to know this is stronger than the practical person’s. It is also more troubled by an awareness of how difficult the question is to answer.

Return to the table. From what we have found, it is clear that no colour stands out as the colour of the table, or even of any one part of it. The table appears to be different colours from different points of view, and there is no reason to regard some of these as more truly its colour than others.

We also know that even from a single point of view, the colour will look different under artificial light, or to a colour-blind person, or to someone wearing blue spectacles. In the dark there will be no colour at all, though the table will feel and sound exactly the same.

So this colour is not something built into the table. It depends on the table, on the person looking, and on the way the light falls on the table. In ordinary life, when we speak of the colour of the table, we mean only the sort of colour it will seem to have to a normal observer, from an ordinary point of view, under usual lighting.

But the other colours that appear under other conditions have just as good a claim to be considered real. To avoid favouritism, then, we are forced to deny that the table, in itself, has any one particular colour.

The same applies to texture. With the naked eye, one can see the grain, but otherwise the table looks smooth and even. Through a microscope we would see roughnesses, hills and valleys, and all sorts of differences that the naked eye cannot detect. Which of these is the “real” table?

We are naturally tempted to say that what we see through the microscope is more real. But that view would in turn be changed by a still more powerful microscope. If we cannot trust what we see with the naked eye, why should we trust what we see through a microscope? Once again, the confidence in our senses with which we began abandons us.

The shape of the table is no better. We are all used to judging the “real” shapes of things, and we do this so automatically that we come to think we actually see the real shapes. But as anyone who tries to draw has to learn, a given thing looks a different shape from every different point of view.

If our table is “really” rectangular, then from almost every point of view it will look as if it had two acute angles and two obtuse angles. If its opposite sides are parallel, they will look as if they converged toward a point away from the viewer. If they are of equal length, the nearer side will look longer.

We do not usually notice any of this when we look at a table. Experience has taught us to construct the “real” shape from the apparent shape, and as practical people, the “real” shape is what interests us. But the “real” shape is not what we see. It is something inferred from what we see.

And what we see keeps changing shape as we move about the room. So here again, the senses seem to give us the truth not about the table itself, but only about the appearance of the table.

Similar difficulties arise with the sense of touch. It is true that the table always gives us a sensation of hardness, and we feel that it resists pressure. But the sensation we get depends on how hard we press the table, and also on which part of the body we press with.

So the various sensations produced by different pressures, or by different parts of the body, cannot be taken to reveal directly any definite property of the table. At most, they are signs of some property that perhaps causes all of the sensations but does not actually appear in any of them. The same applies even more obviously to the sounds we can produce by rapping on the table.

It becomes clear, then, that the real table, if there is one, is not the same as what we immediately experience through sight, touch, or hearing. The real table, if there is one, is not immediately known to us at all. It must be inferred from what is immediately known.

Two very difficult questions therefore arise at once: (1) Is there a real table at all? (2) If so, what sort of object can it be?

In considering these questions, it will help to have a few simple terms with definite and clear meanings. Let us use the name “sense-data” for the things that are immediately known in sensation: colours, sounds, smells, hardnesses, roughnesses, and so on. We will use the name “sensation” for the experience of being immediately aware of these things.

So whenever we see a colour, we have a sensation of the colour, but the colour itself is a sense-datum, not a sensation. The colour is what we are immediately aware of. The awareness itself is the sensation.

Clearly, if we are to know anything about the table, it must be through the sense-data we associate with it: brown colour, oblong shape, smoothness, and so on. But for the reasons already given, we cannot say that the table is the sense-data, or even that the sense-data are directly properties of the table.

This raises a problem about how the sense-data relate to the real table, supposing there is such a thing.

We will call the real table, if it exists, a “physical object.” So we have to consider the relation of sense-data to physical objects. The collection of all physical objects is called “matter.” Our two questions can therefore be restated: (1) Is there any such thing as matter? (2) If so, what is its nature?

The philosopher who first made prominent the reasons for thinking that the immediate objects of our senses do not exist independently of us was Bishop Berkeley (1685–1753). His Three Dialogues between Hylas and Philonous, in Opposition to Sceptics and Atheists sets out to prove that there is no such thing as matter at all, and that the world consists of nothing but minds and their ideas.

In the dialogues, Hylas has always believed in matter, but he is no match for Philonous. Philonous mercilessly drives him into contradictions and paradoxes, and in the end makes his own denial of matter seem almost like common sense.

The arguments Berkeley uses vary greatly in value. Some are important and sound; others are confused or quibbling. But Berkeley still deserves credit for showing two things. First, the existence of matter can be denied without absurdity. Second, if anything exists independently of us, it cannot be the immediate object of our sensations.

When we ask whether matter exists, two different questions are involved, and it is important to keep them distinct. By “matter” we usually mean something opposed to “mind”: something we think of as occupying space and as fundamentally incapable of any kind of thought or consciousness. It is chiefly in this sense that Berkeley denies matter.

He does not deny that the sense-data we usually take as signs of the table’s existence really are signs of something independent of us. What he denies is that this something is non-mental, that is, that it is neither a mind nor ideas held by some mind.

He admits that something must continue to exist when we leave the room or shut our eyes. He grants that what we call seeing the table really does give us reason to believe in something that persists even when we are not seeing it.

But he thinks this something cannot be radically different in nature from what we see. Nor can it be independent of seeing altogether, although it must be independent of our seeing. This leads him to regard the “real” table as an idea in the mind of God.

Such an idea has the required permanence and independence of ourselves. Yet it is not, as matter would otherwise be, something entirely unknowable: something we can only infer, and of which we can never be directly and immediately aware.

Other philosophers since Berkeley have also held that the table does not depend on being seen by me, but does depend on being seen, or otherwise perceived through sensation, by some mind. This need not be the mind of God. More often, it is taken to be the whole collective mind of the universe.

They hold this, as Berkeley does, mainly because they think nothing can be real except minds and their thoughts and feelings, or at least that nothing else can be known to be real. Their argument might be stated roughly like this: “Whatever can be thought of is an idea in the mind of the person thinking of it. Therefore nothing can be thought of except ideas in minds. Therefore anything else is inconceivable, and what is inconceivable cannot exist.”

In my opinion, this argument is fallacious. Of course, those who advance it do not put it so briefly or so crudely. But valid or not, it has been put forward very widely in one form or another. Very many philosophers, perhaps most, have held that nothing is real except minds and their ideas. Such philosophers are called “idealists.”

When idealists come to explain matter, they take one of two routes. Some say, like Berkeley, that matter is really nothing but a collection of ideas. Others say, like Leibniz (1646–1716), that what appears to us as matter is really a collection of more or less rudimentary minds.

These philosophers deny matter in the sense of something opposed to mind. In another sense, however, they still accept it. Recall our two questions: (1) Is there a real table at all? (2) If so, what sort of object can it be? Both Berkeley and Leibniz accept that there is a real table. Berkeley says it is certain ideas in the mind of God; Leibniz says it is a colony of souls.

So both answer our first question with a yes. They depart from the views of ordinary people only in how they answer the second. In fact, nearly all philosophers seem to agree that there is a real table. Our sense-data, such as colour, shape, and smoothness, may depend heavily on us. Even so, philosophers almost all agree that the occurrence of these sense-data is a sign of something that exists independently of us.

This something may be completely different from our sense-data. Even so, it is regarded as causing those sense-data whenever we stand in a suitable relation to the real table.

This point of agreement, that there is a real table whatever its nature may be, is obviously of great importance. Before moving on to the further question of what the real table is like, it is worth considering what reasons there are for believing that it exists at all. Our next chapter will therefore deal with the reasons for supposing that there is a real table.

Before going further, we should pause to consider what we have discovered so far. Take any ordinary object of the kind supposed to be known through the senses. What the senses immediately tell us is not the truth about that object as it is apart from us. They tell us only the truth about certain sense-data, which, as far as we can see, depend on the relations between us and the object.

So what we directly see and feel is merely “appearance,” which we believe to be a sign of some “reality” behind it. But if the reality is not what appears, do we have any way of knowing whether there is any reality at all? And if there is, do we have any way of finding out what it is like?

These questions are bewildering, and it is hard to be sure that even the strangest hypotheses are false. Our familiar table, which until now stirred only the slightest thoughts in us, has become a problem full of surprising possibilities. The one thing we know about it is that it is not what it seems. Beyond this modest result, we are so far completely free to speculate.

Leibniz tells us the table is a community of souls. Berkeley tells us it is an idea in the mind of God. Sober science, hardly less astonishing, tells us it is a vast collection of electric charges in violent motion.

Among these surprising possibilities, doubt suggests that perhaps there is no table at all. Philosophy may not be able to answer as many questions as we would like. But it does at least have the power to ask questions that make the world more interesting. Such questions reveal the strangeness and wonder lying just below the surface of even the most ordinary things in daily life.

CHAPTER II. THE EXISTENCE OF MATTER

In this chapter we must ask whether, in any sense at all, there is such a thing as matter. Is there a table with a certain intrinsic nature, which continues to exist when I am not looking? Or is the table merely a product of my imagination, a dream-table in a very long dream?

This question is of the greatest importance. If we cannot be sure that objects exist independently, we cannot be sure that other people’s bodies exist independently. We can be even less sure of other people’s minds, since our only grounds for believing in their minds come from observing their bodies.

So if we cannot be sure that objects exist independently of us, we will be left alone in a desert. It may be that the whole outer world is nothing but a dream, and that we alone exist. This is an uncomfortable possibility. It cannot be strictly proved false, but there is not the slightest reason to think it true. In this chapter we must see why this is so.

Before we set out into doubtful territory, let us try to find a more or less fixed point to start from. Although we are doubting the physical existence of the table, we are not doubting the existence of the sense-data that made us think there was a table. We do not doubt that, while we look, a certain colour and shape appear to us, and that, while we press, we experience a certain sensation of hardness.

None of this, which is psychological, is in question. In fact, whatever else may be doubtful, at least some of our immediate experiences seem absolutely certain.

Descartes (1596–1650), the founder of modern philosophy, invented a method that can still be used with profit: the method of systematic doubt. He resolved to believe nothing that he did not see quite clearly and distinctly to be true. Whatever he could bring himself to doubt, he would doubt, until he saw reason not to. By applying this method, he gradually became convinced that the only existence he could be quite certain of was his own.

He imagined a deceitful demon who presented unreal things to his senses in an endless parade of illusions. It might be very unlikely that such a demon existed, but it was still possible. Therefore it was possible to doubt the things perceived by the senses.

But Descartes could not doubt his own existence, because if he did not exist, no demon could deceive him. If he doubted, he must exist. If he had any experiences whatever, he must exist. His own existence was therefore absolutely certain to him. “I think, therefore I am,” he said (Cogito, ergo sum).

On the basis of this certainty, he set to work to rebuild the world of knowledge that his doubt had reduced to ruins. By inventing the method of doubt, and by showing that subjective things are the most certain, Descartes did philosophy a great service. That service still makes him useful to every student of the subject.

But Descartes’ argument needs to be used with some care. “I think, therefore I am” says somewhat more than is strictly certain. It might seem that we are quite sure of being the same person today as we were yesterday, and in some sense this is no doubt true. But the real Self is as hard to reach as the real table. It does not seem to have the absolute, convincing certainty that belongs to particular experiences.

When I look at my table and see a certain brown colour, what is immediately and fully certain is not “I am seeing a brown colour,” but rather “a brown colour is being seen.” This does involve something, or somebody, that sees the brown colour. But it does not by itself involve the more or less permanent person we call “I.”

As far as immediate certainty goes, the something that sees the brown colour might be quite momentary. It might not be the same as the something that has a different experience the next moment.

So it is our particular thoughts and feelings that have primitive certainty. This holds for dreams and hallucinations as well as for normal perceptions. When we dream or see a ghost, we certainly do have the sensations we think we have, though for various reasons it is held that no physical object corresponds to them.

The certainty of our knowledge of our own experiences therefore does not need to be limited in any way to allow for exceptional cases. Here, then, for what it is worth, we have a solid basis from which to begin our pursuit of knowledge.

The problem we must consider is this. Granted that we are certain of our own sense-data, do we have any reason to regard them as signs that something else exists, something we can call the physical object? Once we have listed all the sense-data we would naturally connect with the table, have we said everything there is to say about it? Or is there something more, something that is not a sense-datum and that persists when we leave the room?

Common sense answers without hesitation that there is. Something that can be bought and sold, pushed about, and covered with a cloth cannot be a mere collection of sense-data. If the cloth completely hides the table, we receive no sense-data from the table. If the table were nothing but sense-data, it would then have ceased to exist.

The cloth would be hanging in empty air, resting by a miracle in the place where the table used to be. This seems plainly absurd. But anyone who wants to become a philosopher must learn not to be frightened by absurdities.

One major reason we feel we must secure a physical object in addition to sense-data is that we want the same object for different people. When ten people sit around a dinner table, it seems ridiculous to claim that they are not seeing the same tablecloth, the same knives, forks, spoons, and glasses.

But sense-data are private to each person. What is immediately present to one person’s sight is not immediately present to another’s. They all see things from slightly different points of view, and therefore see them slightly differently.

So if there are to be public, neutral objects that many different people can in some sense know, there must be something beyond the private, particular sense-data that appear to each of them. What reason, then, do we have for believing that such public, neutral objects exist?

The first answer that naturally comes to mind is this. Although different people may see the table slightly differently, they all see more or less similar things when they look at it. The variations in what they see follow the laws of perspective and of the reflection of light. It is therefore easy to arrive at a permanent object underlying all these different people’s sense-data.

I bought my table from the former occupant of my room. I could not buy his sense-data, which died when he went away. But I could buy, and did buy, the confident expectation of more or less similar sense-data.

So two facts lead us to suppose that there is something more than sense-data. Different people have similar sense-data, and one person in a given place has similar sense-data at different times. From these facts we suppose that there is a permanent public object that underlies or causes the sense-data of various people at various times.

These considerations depend partly on supposing that there are other people besides ourselves. To that extent, they assume the very point in question. Other people are represented to me by certain sense-data, such as the sight of them or the sound of their voices. If I had no reason to believe in physical objects independent of my sense-data, I would have no reason to believe that other people exist except as part of my dream.

So when we try to show that there must be objects independent of our own sense-data, we cannot appeal to the testimony of other people. Their testimony itself consists of sense-data. It does not reveal other people’s experiences unless our own sense-data are signs of things that exist independently of us.

We must therefore try, if possible, to find features within our own purely private experiences that show, or tend to show, that the world contains things other than ourselves and our private experiences.

In one sense, we have to admit that we can never prove the existence of things other than ourselves and our experiences. No logical absurdity follows from the hypothesis that the world consists of myself and my thoughts, feelings, and sensations, and that everything else is mere imagination.

In dreams, a very complicated world may seem to be present, and yet on waking we find it was a delusion. That is, we find that the sense-data in the dream do not seem to have corresponded to the physical objects we would naturally infer from them.

It is true that, once we assume a physical world, we can find physical causes for the sense-data in dreams. A banging door, for instance, may cause us to dream of a naval battle. In that case there is a physical cause for the sense-data. But there is no physical object corresponding to them in the way an actual naval battle would correspond.

There is nothing logically impossible in supposing that the whole of life is a dream, in which we ourselves create all the objects that come before us. But although this is not logically impossible, there is no reason whatever to suppose it is true.

In fact, as a way of accounting for the facts of our own life, it is a less simple hypothesis than the common-sense one: that there really are objects independent of us, and that their action on us causes our sensations.

It is easy to see how supposing that physical objects really exist makes things simpler. If the cat appears at one moment in one part of the room, and at another moment in another part, it is natural to suppose that it moved from one place to the other, passing through a series of positions in between.

But if the cat is merely a set of sense-data, it can never have been in any place where I did not see it. We would then have to suppose that it did not exist at all while I was not looking, and that it suddenly sprang into being in a new place.

If the cat exists whether I see it or not, my own experience lets me understand how it gets hungry between one meal and the next. But if it does not exist when I am not seeing it, it seems odd that its appetite should grow during its non-existence just as fast as during its existence.

And if the cat consists only of sense-data, it cannot be hungry at all, since no hunger except my own can be a sense-datum to me. The behaviour of the sense-data that represent the cat to me seems quite natural when I regard it as an expression of hunger.

Regarded instead as mere movements and changes of patches of colour, the same behaviour becomes utterly inexplicable. Patches of colour are as incapable of hunger as a triangle is of playing football.

The difficulty with the cat, however, is nothing compared to the difficulty with human beings. When people speak, we hear certain noises that we associate with ideas, and at the same time we see certain movements of lips and expressions of face.

In that situation, it is very hard to suppose that what we hear is not the expression of a thought. We know it would be an expression of thought if we ourselves made the same sounds.

Of course, similar things happen in dreams, where we are mistaken about the existence of other people. But dreams are more or less suggested by what we call waking life. And if we assume that there really is a physical world, dreams can be more or less explained on scientific principles.

Every principle of simplicity therefore urges us to adopt the natural view. There really are objects other than ourselves and our sense-data, and their existence does not depend on our perceiving them.

Of course, we do not originally arrive at our belief in an independent external world by argument. We find this belief already present in ourselves as soon as we begin to reflect. It is what we might call an instinctive belief.

We would never have been led to question this belief except for one fact. At least in the case of sight, we seem to believe instinctively that the sense-datum itself is the independent object. Argument shows, however, that the object cannot be identical with the sense-datum.

This discovery is not at all paradoxical in the case of taste, smell, and sound, and only slightly so in the case of touch. In any case, it leaves our instinctive belief that there are objects corresponding to our sense-data completely intact.

This belief leads to no difficulties. On the contrary, it tends to simplify and systematize our account of our experiences. So there seems to be no good reason for rejecting it.

We may therefore accept, though with a slight doubt arising from dreams, that the external world really exists, and that its existence does not wholly depend on our continuing to perceive it.

The argument that has led us to this conclusion is no doubt weaker than we could wish. But it is typical of many philosophical arguments, so it is worth briefly considering its general character and validity.

All knowledge, we find, must be built on our instinctive beliefs. If these are rejected, nothing is left. But some of our instinctive beliefs are much stronger than others.

Many of them have also become tangled, through habit and association, with other beliefs that are not really instinctive but are wrongly supposed to be part of what we believe instinctively.

Philosophy should show us the hierarchy of our instinctive beliefs, beginning with those we hold most strongly. It should present each one as isolated as possible and as free as possible from irrelevant additions.

It should also take care to show that, in the form in which they are finally stated, our instinctive beliefs do not clash but form a harmonious system. The only possible reason for rejecting one instinctive belief is that it clashes with others. So if they are found to fit together, the whole system becomes worthy of acceptance.

Of course, it is possible that any or all of our beliefs are mistaken. All of them should therefore be held with at least a slight element of doubt. But we can never have reason to reject a belief except on the basis of some other belief.

So we can organize our instinctive beliefs and their consequences, and consider which of them could most easily be modified or abandoned if necessary. In this way, accepting only what we instinctively believe as our data, we can arrive at an orderly, systematic organization of our knowledge.

In such a system the possibility of error remains. But its likelihood is reduced by the way the parts support one another, and by the critical examination that came before we accepted them.

This function, at least, philosophy can perform. Most philosophers, rightly or wrongly, believe that philosophy can do much more. They think it can give us knowledge, not attainable in any other way, about the universe as a whole and about the nature of ultimate reality.

Whether or not that is so, philosophy can certainly perform the more modest function we have described. For anyone who has once begun to doubt whether common sense is adequate, that function is enough to justify the hard and demanding work that philosophical problems involve.

CHAPTER III. THE NATURE OF MATTER

In the previous chapter we agreed, though without finding conclusive proof, that it is rational to believe that our sense-data are really signs of something that exists independently of us and our perceptions. The sense-data we associate with my table are an example.

That is, over and above the sensations of colour, hardness, noise, and so on, which make up the table’s appearance to me, I assume that there is something else, of which these things are appearances.

The colour stops existing if I shut my eyes. The sensation of hardness stops existing if I take my arm off the table. The sound stops existing if I stop rapping the table with my knuckles. But I do not believe that the table stops existing when all these things stop.

On the contrary, I believe that all these sense-data will reappear when I open my eyes, put my arm back, and start rapping with my knuckles again, precisely because the table exists continuously.

The question for this chapter is this: what is the nature of this real table, which persists independently of my perception of it?

Physical science offers an answer. It is admittedly somewhat incomplete, and in part still very hypothetical, but as far as it goes it deserves respect.

Physical science has drifted, more or less unconsciously, into the view that all natural phenomena should be reduced to motions. Light, heat, and sound are all due to wave-motions. These travel from the body that emits them to the person who sees the light, feels the heat, or hears the sound.

What carries the wave-motion is either the aether or “gross matter.” In either case it is what a philosopher would call matter.

The only properties science assigns to this matter are position in space and the power to move according to the laws of motion. Science does not deny that it may have other properties. But if it does, those properties are of no use to the scientist and do nothing to help explain the phenomena.

People sometimes say that “light is a form of wave-motion,” but this is misleading. The light we immediately see, which we know directly through our senses, is not a form of wave-motion. It is something quite different.

Everyone who is not blind knows this light. Yet we cannot describe it in a way that would convey our knowledge to someone who is blind.

A wave-motion, by contrast, could easily be described to a blind person. He can gain a knowledge of space through the sense of touch, and he can experience a wave-motion on a sea voyage almost as well as we can.

But what a blind person can understand in this way is not what we mean by light. By light we mean precisely what a blind person can never understand, and what we can never describe to him.

According to science, this thing that all sighted people know is not really found in the outer world. It is something caused by the action of certain waves on the eyes, nerves, and brain of the person who sees the light.

When we say that light is waves, what we really mean is that waves are the physical cause of our sensations of light. But science does not suppose that light itself, the thing sighted people experience and blind people do not, is part of the world that exists independently of us and our senses. Very similar points would apply to other kinds of sensation.

Colours, sounds, and the like are not the only things missing from the scientific world of matter. Space as we get it through sight or touch is missing too.

Science requires that its matter exist in a space. But the space it exists in cannot be exactly the space we see or feel.

To begin with, space as we see it is not the same as space as we get it through touch. Only through experience in infancy do we learn how to touch the things we see, or how to catch sight of the things we feel touching us.

The space of science, however, is neutral between touch and sight. So it cannot be either the space of touch or the space of sight.

Again, different people see the same object as having different shapes, depending on their point of view. A circular coin, for example, looks oval unless we are directly in front of it, even though we would always judge it to be circular.

When we judge that the coin is circular, we are judging that it has a real shape that differs from its apparent shape. This real shape belongs to the coin in itself, apart from how it appears.

But this real shape, which is what science cares about, must exist in a real space. That space is not the same as anyone’s apparent space. The real space is public, while apparent space is private to the person perceiving.

In different people’s private spaces, the same object seems to have different shapes. So the real space, in which the object has its real shape, must be different from these private spaces.

The space of science, then, is connected with the spaces we see and feel, but it is not identical with them. How exactly it is connected to them needs to be investigated.

We agreed provisionally that physical objects cannot be exactly like our sense-data, but that they may be regarded as causing our sensations. These physical objects are in the space of science, which we may call “physical” space.

It is important to notice that, if physical objects are to cause our sensations, there must be a physical space that contains these objects along with our sense-organs, nerves, and brain.

We get a sensation of touch from an object when we are in contact with it. That is, we feel it when some part of our body occupies a place in physical space very close to the space the object occupies.

Roughly speaking, we see an object when no opaque body lies between it and our eyes in physical space. Similarly, we hear, smell, or taste an object only when we are close enough to it, or when it touches the tongue, or when it has some suitable position in physical space relative to our body.

We cannot even begin to say what different sensations we will get from a given object under different circumstances unless we treat the object and our body as both being in one physical space. It is mainly the relative positions of the object and our body that determine what sensations we will get from the object.

Our sense-data are located in our private spaces: the space of sight, the space of touch, or the vaguer spaces that other senses may give us. Science and common sense assume that there is one public, all-embracing physical space containing physical objects. If so, the relative positions of objects in physical space must more or less correspond to the relative positions of sense-data in our private spaces.

There is no difficulty in supposing this to be the case. If we see one house on a road nearer to us than another, our other senses will confirm that it is nearer. For example, we will reach it sooner if we walk along the road. Other people will agree that the house that looks nearer is nearer, and the ordnance map, the official survey map, will take the same view.

Everything therefore points to a spatial relation between the houses that corresponds to the relation between the sense-data we see when we look at them. So we may assume that there is a physical space in which physical objects have spatial relations corresponding to those their sense-data have in our private spaces. This physical space is the one studied in geometry and assumed in physics and astronomy.

Assuming that physical space exists and corresponds to private spaces in this way, what can we know about it? We can know only what is required to secure the correspondence. We can know nothing about what it is like in itself. But we can know the kind of arrangement of physical objects that results from their spatial relations.

For example, we can know that the earth, moon, and sun lie in one straight line during an eclipse. Yet we cannot know what a physical straight line is in itself, in the way we know the look of a straight line in our visual space.

So we come to know much more about the relations between distances in physical space than about the distances themselves. We may know that one distance is greater than another, or that it lies along the same straight line as another. But we cannot have the immediate acquaintance with physical distances that we have with distances in our private spaces, or with colours, sounds, and other sense-data.

We can know everything about physical space that a man born blind might learn from other people about the space of sight. But the kinds of things a man born blind could never know about the space of sight, we likewise cannot know about physical space. We can know the properties of the relations needed to preserve the correspondence with sense-data. We cannot know the nature of the terms between which those relations hold.

With regard to time, our feeling of duration, our sense of time passing, is notoriously unreliable as a guide to how much time has passed by the clock. Time passes slowly when we are bored or in pain. It passes quickly when we are pleasantly occupied. When we are asleep, it passes almost as if it did not exist.

So, insofar as time consists of duration, we must distinguish a public time from a private time, just as we did with space. But insofar as time consists of an order of before and after, no such distinction is needed. As far as we can tell, the time-order that events seem to have is the same as the time-order they actually have. At any rate, no reason can be given for supposing that the two orders differ.

The same is usually true of space. If a regiment of soldiers marches along a road, its shape will look different from different points of view, but the men will appear arranged in the same order from every point of view. We therefore regard the order as true in physical space as well. The shape, by contrast, is only supposed to correspond to physical space as far as is needed to preserve the order.

In saying that the apparent time-order of events matches their real time-order, we must guard against a possible misunderstanding. We must not suppose that the various states of different physical objects have the same time-order as the sense-data that make up our perceptions of those objects.

Considered as physical objects, thunder and lightning are simultaneous. That is, the lightning is simultaneous with the disturbance of the air at the place where the disturbance begins, namely where the lightning is. But the sense-datum we call hearing the thunder does not occur until that disturbance of the air has travelled all the way to where we are.

Similarly, the sun’s light takes about eight minutes to reach us, so when we see the sun, we are seeing the sun of eight minutes ago. Insofar as our sense-data provide evidence about the physical sun, they provide evidence about the physical sun of eight minutes ago.

If the physical sun had ceased to exist within the last eight minutes, that would make no difference to the sense-data we call ‘seeing the sun’. This is a fresh illustration of why we must distinguish sense-data from physical objects.

What we have found about space is much the same as what we find about how sense-data correspond to their physical counterparts. If one object looks blue and another red, we may reasonably presume some corresponding difference between the physical objects. If two objects both look blue, we may presume a corresponding similarity. But we cannot hope to be directly acquainted with the quality in the physical object that makes it look blue or red.

Science tells us that this quality is a certain kind of wave-motion. That sounds familiar, because we picture wave-motions in the space we see. But the wave-motions must really be in physical space, with which we have no direct acquaintance. So the real wave-motions are not as familiar as we might have supposed. And what holds for colours holds in much the same way for other sense-data.

We find, then, that the relations between physical objects have all sorts of knowable properties, derived from their correspondence with the relations between sense-data. But the physical objects themselves remain unknown in their intrinsic nature, at least as far as the senses can discover. The question remains whether there is any other way to discover the intrinsic nature of physical objects.

The most natural hypothesis to adopt at first, at least for visual sense-data, though not ultimately the most defensible, would be this. Physical objects cannot be exactly like sense-data, for the reasons we have been considering, but they may be more or less like them. On this view, physical objects really do have colours, and with luck we might see an object in the colour it really has.

The colour an object seems to have at any given moment will generally be very similar, though not identical, from many different points of view. We might therefore suppose that its ‘real’ colour is a kind of medium colour, intermediate between the various shades that appear from the different viewpoints.

This theory perhaps cannot be definitely refuted, but it can be shown to have no basis. To begin with, the colour we see clearly depends only on the nature of the light-waves that strike the eye. It is therefore altered by the medium between us and the object, and by the way light is reflected from the object toward the eye. The air in between alters colours unless it is perfectly clear, and any strong reflection will change them completely.

So the colour we see is a result of the ray as it reaches the eye, not simply a property of the object the ray comes from. It follows that, provided certain waves reach the eye, we will see a certain colour whether or not the object they start from has any colour. Supposing that physical objects have colours is therefore entirely gratuitous, and there is no justification for it. Exactly similar arguments apply to other sense-data.

It remains to ask whether any general philosophical arguments allow us to say that, if matter is real, it must have some particular nature. As explained above, very many philosophers, perhaps most, have held that whatever is real must be in some sense mental. Or at least they have held that whatever we can know anything about must be in some sense mental. Such philosophers are called ‘idealists’.

Idealists tell us that what appears as matter is really something mental. It is either more or less rudimentary minds, as Leibniz held, or ideas in the minds that, as we would normally say, ‘perceive’ the matter, as Berkeley argued. Idealists therefore deny that matter exists as something intrinsically different from mind. They do not, however, deny that our sense-data are signs of something that exists independently of our private sensations.

In the next chapter we will briefly consider the reasons idealists offer in favour of their theory, reasons that are, in my opinion, fallacious.

CHAPTER IV. IDEALISM

The word ‘idealism’ is used by different philosophers in somewhat different senses. We will take it to mean the doctrine that whatever exists, or at least whatever can be known to exist, must be in some sense mental. This doctrine is very widely held among philosophers. It takes several forms and is defended on several different grounds.

Because the doctrine is so widely held, and so interesting in itself, even the briefest survey of philosophy must give some account of it.

People unaccustomed to philosophical speculation may be inclined to dismiss such a doctrine as obviously absurd. Common sense certainly regards tables, chairs, the sun, the moon, and material objects generally as radically different from minds and their contents. It treats them as having an existence that could continue even if minds ceased to exist.

We think of matter as having existed long before there were any minds, and it is hard to think of it as a mere product of mental activity. But whether idealism is true or false, it should not be dismissed as obviously absurd.

We have seen that even if physical objects do exist independently, they must differ very widely from sense-data. They can only correspond to sense-data in the way a catalogue corresponds to the things listed in it. Common sense therefore leaves us completely in the dark about the true intrinsic nature of physical objects.

So if there were good reason to regard physical objects as mental, we could not legitimately reject that view merely because it strikes us as strange. The truth about physical objects must be strange. It may be unattainable. But if a philosopher believes he has attained it, the strangeness of what he offers as the truth should not count as an objection to his view.

The arguments for idealism usually come from the theory of knowledge, that is, from a discussion of the conditions that things must satisfy for us to be able to know them. The first serious attempt to establish idealism on such grounds was made by Bishop Berkeley.

Berkeley first proved, by arguments that were largely valid, that our sense-data cannot be supposed to exist independently of us. They must be, at least partly, ‘in’ the mind, in the sense that they would not continue to exist if there were no seeing, hearing, touching, smelling, or tasting. So far, his claim was almost certainly valid, even if some of his arguments were not.

But he went on to argue that sense-data were the only things whose existence our perceptions could assure us of. He also argued that to be known is to be ‘in’ a mind, and therefore to be mental. From this he concluded that nothing can ever be known except what is in some mind, and that whatever is known without being in my mind must be in some other mind.

To understand his argument, we need to understand how he uses the word ‘idea’. He gives the name ‘idea’ to anything that is immediately known, in the way sense-data are known. So a particular colour we see is an idea, and so is a voice we hear, and so on.

But the term is not wholly confined to sense-data. It also covers things remembered or imagined, since we have immediate acquaintance with these too at the moment of remembering or imagining. All such immediate data he calls ‘ideas’.

He then turns to ordinary objects, such as a tree. He shows that everything we know immediately when we “perceive” the tree consists of ideas, in his sense of the word. He argues that there is not the slightest reason to suppose that anything about the tree is real except what is perceived. Its being, he says, consists in being perceived. In the Latin of the schoolmen, its esse is percipi.

He fully admits that the tree must go on existing when we shut our eyes or when no human being is nearby. But this continued existence, he says, is due to the fact that God continues to perceive it.

The “real” tree, which corresponds to what we have called the physical object, consists of ideas in the mind of God. These ideas are more or less like the ones we have when we see the tree. They differ in that they remain permanently in God’s mind for as long as the tree continues to exist.

According to Berkeley, all our perceptions consist in a partial sharing in God’s perceptions. Because of this sharing, different people see more or less the same tree. So apart from minds and their ideas there is nothing in the world. Nor could anything else ever be known, since whatever is known is necessarily an idea.

This argument contains a good many fallacies that have been important in the history of philosophy, and it will be useful to bring them to light. The first is a confusion produced by the word “idea.” We think of an idea as essentially something in somebody’s mind. So when we are told that a tree consists entirely of ideas, it is natural to suppose that the tree must then be entirely in minds.

But the notion of being “in” the mind is ambiguous. We speak of keeping a person in mind. We do not mean that the person is in our minds, only that a thought of him is. When someone says that a piece of business he had to arrange went clean out of his mind, he does not mean that the business itself was ever in his mind. He means only that a thought of it was once there and later ceased to be.

So when Berkeley says that the tree must be in our minds if we can know it, all he is really entitled to say is that a thought of the tree must be in our minds. To argue that the tree itself must be in our minds is like arguing that a person we keep in mind is himself inside our minds.

This confusion may seem too crude for any competent philosopher to have actually committed. But various surrounding circumstances made it possible. To see how, we must look more deeply into the nature of ideas.

Before taking up the general question of what ideas are, we must separate two entirely different questions about sense-data and physical objects. We saw that, for various detailed reasons, Berkeley was right to treat the sense-data that make up our perception of the tree as more or less subjective. They depend on us as much as on the tree, and they would not exist if the tree were not being perceived.

But this is an entirely different point from the one by which Berkeley tries to prove that whatever can be immediately known must be in a mind. For that purpose, detailed arguments about how sense-data depend on us are useless. What must be proved is the general claim that being known shows things to be mental.

Berkeley believes he has proved this. It is this question, not our earlier question about how sense-data differ from the physical object, that must now concern us.

If we take the word “idea” in Berkeley’s sense, there are two quite distinct things to consider whenever an idea is before the mind. On one side there is the thing we are aware of, say, the colour of my table. On the other side there is the awareness itself, the mental act of apprehending the thing.

The mental act is certainly mental. But is there any reason to suppose that the thing apprehended is in any sense mental? Our earlier arguments about the colour did not prove it to be mental. They proved only that its existence depends on the relation of our sense organs to the physical object, in this case the table.

That is, they proved that a certain colour will exist, in a certain light, if a normal eye is placed at a certain point in relation to the table. They did not prove that the colour is in the mind of the person perceiving it.

Berkeley’s view that the colour obviously must be in the mind seems to owe its plausibility to a confusion between the thing apprehended and the act of apprehending it. Either one could be called an “idea,” and Berkeley probably would have called either one an idea. The act is certainly in the mind. So when we are thinking of the act, we readily agree that ideas must be in the mind.

Then we forget that this was true only when ideas were taken as acts of apprehension. We carry the claim that “ideas are in the mind” over to ideas in the other sense: the things apprehended by our acts of apprehension. Through this unnoticed shift in meaning, we reach the conclusion that whatever we can apprehend must be in our minds. This seems to be the true analysis of Berkeley’s argument, and the basic fallacy on which it rests.

The distinction between act and object in our apprehension of things is vitally important, because our whole power of acquiring knowledge is bound up with it. The main characteristic of a mind is its capacity to be acquainted with things other than itself. Acquaintance with objects essentially consists in a relation between the mind and something other than the mind. This relation is what makes up the mind’s power of knowing things.

If we say that the things known must be in the mind, we are doing one of two things. Either we are unduly limiting the mind’s power of knowing, or we are stating a mere tautology. It is a mere tautology if by “in the mind” we mean the same as “before the mind,” that is, simply being apprehended by the mind. But if that is our meaning, we must admit that what is in the mind in this sense may nevertheless not be mental.

So once we understand the nature of knowledge, Berkeley’s argument turns out to be wrong in substance as well as in form. His reasons for supposing that “ideas,” meaning the objects apprehended, must be mental have no validity at all. His case for idealism may therefore be dismissed. It remains to see whether there are any other grounds for it.

It is often said, as if it were a self-evident truism, that we cannot know that anything exists which we do not know. From this it is inferred that whatever could in any way be relevant to our experience must at least be capable of being known by us.

It follows that if matter were essentially something we could never become acquainted with, it would be something we could not know to exist, and it could have no importance for us whatever. Usually it is also implied, for reasons that remain obscure, that what can have no importance for us cannot be real. Therefore matter, if it is not made of minds or mental ideas, is impossible, a mere chimera.

To examine this argument fully at our present stage is impossible, since it raises points that need considerable preliminary discussion. But some reasons for rejecting it can be noted at once.

To begin at the end: there is no reason why something with no practical importance for us should not be real. It is true that if theoretical importance is counted, everything real matters to us in some way. As people who want to know the truth about the universe, we have some interest in everything the universe contains.

But if this kind of interest is counted, then it is not true that matter has no importance for us, provided it exists, even if we cannot know that it exists. We can obviously suspect that it may exist and wonder whether it does. So it is connected with our desire for knowledge, and it matters to us by either satisfying or frustrating that desire.

Again, it is by no means a truism, and is in fact false, that we cannot know that anything exists which we do not know. The word “know” is being used here in two different senses.

1. In its first use, “know” applies to the kind of knowledge that is opposed to error. In this sense, what we know is true. It applies to our beliefs and convictions, that is, to what are called judgements. In this sense we know that something is the case. This kind of knowledge may be called knowledge of truths.
2. In its second use above, “know” applies to our knowledge of things, which we may call acquaintance. This is the sense in which we know sense-data.

The distinction is roughly the one between savoir and connaître in French, or between wissen and kennen in German.

So the statement that seemed like a truism becomes, when restated: “We can never truly judge that something we are not acquainted with exists.” This is by no means a truism. On the contrary, it is plainly false. I do not have the honour of being acquainted with the Emperor of China, but I truly judge that he exists.

Someone may reply that I judge this because other people are acquainted with him. But this reply is beside the point. If the principle were true, I could not know that anyone else is acquainted with him either. Further, there is no reason why I should not know of the existence of something that nobody is acquainted with. This point is important and needs explaining.

If I am acquainted with a thing that exists, my acquaintance gives me the knowledge that it exists. But the reverse does not hold. It is not true that whenever I can know that a thing of a certain sort exists, I or someone else must be acquainted with that thing.

When I have a true judgement without acquaintance, what happens is this. The thing is known to me by description. Then, by some general principle, the existence of a thing that fits this description can be inferred from the existence of something I am acquainted with.

To understand this point fully, we should first deal with the difference between knowledge by acquaintance and knowledge by description. Then we should ask what knowledge of general principles, if any, has the same kind of certainty as our knowledge that our own experiences exist. These subjects will be taken up in the following chapters.

CHAPTER V. KNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY DESCRIPTION

In the previous chapter we saw that there are two sorts of knowledge: knowledge of things and knowledge of truths. This chapter is concerned only with knowledge of things, which we must in turn divide into two kinds.

Knowledge of things, when it is the kind we call knowledge by acquaintance, is essentially simpler than any knowledge of truths. It is also logically independent of knowledge of truths. Still, it would be rash to assume that human beings ever actually have acquaintance with things without also knowing some truth about them.

Knowledge of things by description, by contrast, always involves some knowledge of truths as its source and basis, as we shall find in the course of this chapter. But first we must make clear what we mean by “acquaintance” and what we mean by “description.”

We shall say that we have acquaintance with anything we are directly aware of, without the help of any process of inference or any knowledge of truths. So when my table is in front of me, I am acquainted with the sense-data that make up its appearance: its colour, shape, hardness, smoothness, and so on. I am immediately conscious of all these when I am seeing and touching my table.

Many things may be said about the particular shade of colour I am seeing. I may say that it is brown, that it is rather dark, and so on. Such statements let me know truths about the colour. But they do not make me know the colour itself any better than I did before.

As far as knowledge of the colour itself goes, as opposed to knowledge of truths about it, I know the colour perfectly and completely when I see it. No further knowledge of the colour itself is even theoretically possible. So the sense-data that make up the appearance of my table are things I have acquaintance with: things immediately known to me just as they are.

My knowledge of the table as a physical object, by contrast, is not direct knowledge. Whatever knowledge I have of it comes through my acquaintance with the sense-data that make up the table’s appearance. We have seen that it is possible, without absurdity, to doubt whether there is a table at all. It is not possible to doubt the sense-data.

My knowledge of the table is the kind we shall call knowledge by description. The table is “the physical object that causes such-and-such sense-data.” This phrase describes the table by means of the sense-data.

To know anything at all about the table, we must know truths connecting it with things we are acquainted with. We must know that “such-and-such sense-data are caused by a physical object.” There is no state of mind in which we are directly aware of the table. All our knowledge of the table is really knowledge of truths, and the actual thing that is the table is not, strictly speaking, known to us at all.

What we know is a description. We also know that there is exactly one object to which this description applies, even though the object itself is not directly known to us. In such a case, we say that our knowledge of the object is knowledge by description.

All our knowledge, both knowledge of things and knowledge of truths, rests on acquaintance as its foundation. It is therefore important to consider what kinds of things we are acquainted with.

Sense-data, as we have already seen, are among the things we are acquainted with. In fact, they are the most obvious and striking example of knowledge by acquaintance. But if they were the only example, our knowledge would be far more limited than it is.

We would know only what is present to our senses right now. We could not know anything about the past, not even that there was a past. Nor could we know any truths about our sense-data. As we shall show, all knowledge of truths requires acquaintance with things of an essentially different character from sense-data. These are sometimes called “abstract ideas,” but we shall call them universals.

So if we want a reasonably adequate analysis of our knowledge, we must consider acquaintance with other things besides sense-data.

The first extension beyond sense-data is acquaintance through memory. We often remember what we have seen or heard, or what was otherwise present to our senses. In such cases we are still immediately aware of what we remember, even though it appears as past rather than present.

This immediate knowledge through memory is the source of all our knowledge of the past. Without it, there could be no knowledge of the past by inference, because we would never know that there was anything past to be inferred.

The next extension is acquaintance through introspection. We are not only aware of things; we are often aware of being aware of them. When I see the sun, I am often aware of my seeing the sun. So “my seeing the sun” is an object I am acquainted with.

Likewise, when I desire food, I may be aware of my desire for food, so “my desiring food” is an object I am acquainted with. In the same way, we may be aware of feeling pleasure or pain, and in general of the events that happen in our minds.

This kind of acquaintance, which may be called self-consciousness, is the source of all our knowledge of mental things. Clearly, only what goes on in our own minds can be known immediately in this way.

What goes on in other people’s minds is known to us through our perception of their bodies, that is, through the sense-data in us that are associated with their bodies. Without our acquaintance with the contents of our own minds, we could not imagine the minds of others. We could therefore never come to know that they have minds.

It seems natural to suppose that self-consciousness is one of the things that distinguish human beings from animals. Animals, we may suppose, are acquainted with sense-data but never become aware of this acquaintance.

I do not mean that they doubt whether they exist. I mean that they have never become conscious of the fact that they have sensations and feelings. Therefore they have never become conscious of the fact that they themselves, the subjects of those sensations and feelings, exist.

We have called acquaintance with the contents of our minds “self-consciousness.” But it is not, of course, consciousness of our self. It is consciousness of particular thoughts and feelings.

Whether we are also acquainted with our bare selves, as distinct from particular thoughts and feelings, is a very difficult question, and it would be rash to answer it confidently. When we try to look into ourselves, we always seem to come upon some particular thought or feeling, not upon the “I” that has the thought or feeling.

Still, there are some reasons for thinking that we are acquainted with the “I,” even though this acquaintance is hard to separate from other things. To make clear what kind of reason there is, let us consider for a moment what our acquaintance with particular thoughts really involves.

When I am acquainted with “my seeing the sun,” it seems plain that I am acquainted with two different things related to each other. On one side is the sense-datum that represents the sun to me. On the other is whatever it is that sees this sense-datum.

All acquaintance, such as my acquaintance with the sense-datum representing the sun, seems obviously to be a relation between the person who is acquainted and the object that person is acquainted with.

Sometimes a case of acquaintance is itself something I can be acquainted with, as I am acquainted with my acquaintance with the sense-datum representing the sun. In that case, the person who is acquainted is plainly myself. So when I am acquainted with my seeing the sun, the whole fact I am acquainted with is “Self-acquainted-with-sense-datum.”

Further, we know the truth “I am acquainted with this sense-datum.” It is hard to see how we could know this truth, or even understand what it means, unless we were acquainted with something we call “I.”

We need not suppose that we are acquainted with a more or less permanent person, the same today as yesterday. But it does seem that we must be acquainted with whatever it is, whatever its nature, that sees the sun and is acquainted with sense-data.

So in some sense, it seems, we must be acquainted with our Selves as distinct from our particular experiences. But the question is difficult, and complicated arguments can be made on either side. Although acquaintance with ourselves probably does occur, it is not wise to assert that it undoubtedly occurs.

We may therefore sum up what has been said about acquaintance with things that exist.

• In sensation, we are acquainted with the data of the outer senses.
• In introspection, we are acquainted with the data of what may be called the inner sense: thoughts, feelings, desires, and so on.
• In memory, we are acquainted with things that were once data of either the outer senses or the inner sense.

Further, it is probable, though not certain, that we are acquainted with the Self, as that which is aware of things or has desires toward them.

Besides our acquaintance with particular existing things, we are also acquainted with what we shall call universals. These are general ideas, such as whiteness, diversity, brotherhood, and so on.

Every complete sentence must contain at least one word that stands for a universal, because the meaning of every verb is universal. We shall return to universals later, in Chapter IX. For now, we need only guard against assuming that whatever we can be acquainted with must be something particular and existing.

Awareness of universals is called conceiving, and a universal we are aware of is called a concept.

Notice that the objects we are acquainted with do not include physical objects (as distinct from sense-data), nor other people’s minds. We know these things by what I call “knowledge by description,” which we must now consider.

By a “description” I mean any phrase of the form “a so-and-so” or “the so-and-so.” I shall call a phrase of the form “a so-and-so” an ambiguous description. I shall call a phrase of the form “the so-and-so” (in the singular) a definite description. So “a man” is an ambiguous description, and “the man with the iron mask” is a definite description.

There are various problems connected with ambiguous descriptions, but I shall pass them by, because they do not bear directly on our subject. Our subject is the nature of our knowledge of objects in cases where we know that some object answers to a definite description, yet we are not acquainted with any such object.

This question concerns definite descriptions only. From here on, therefore, I shall simply say “descriptions” when I mean “definite descriptions.” A description will mean any phrase of the form “the so-and-so” in the singular.

We shall say that an object is “known by description” when we know that it is “the so-and-so.” That is, we know that there is one object, and no more, that has a certain property. It will generally be implied that we do not also know the same object by acquaintance.

We know that the man with the iron mask existed, and many propositions about him are known. But we do not know who he was.

We know that the candidate who gets the most votes will be elected. In this case we may very well be acquainted with the man who will in fact get the most votes, in the only sense in which one can be acquainted with someone else. But we do not know which of the candidates he is.

That is, we do not know any proposition of the form “A is the candidate who will get the most votes,” where A is one of the candidates named. We shall say we have “merely descriptive knowledge” of the so-and-so when we know that the so-and-so exists, and we may even be acquainted with the object that is in fact the so-and-so, yet we do not know any proposition “a is the so-and-so,” where a is something we are acquainted with.

When we say “the so-and-so exists,” we mean that there is exactly one object that is the so-and-so. The proposition “a is the so-and-so” means that a has the property so-and-so and nothing else has it.

“Mr. A. is the Unionist candidate for this constituency” means “Mr. A. is a Unionist candidate for this constituency, and no one else is.” “The Unionist candidate for this constituency exists” means “someone is a Unionist candidate for this constituency, and no one else is.”

So when we are acquainted with an object that is the so-and-so, we know that the so-and-so exists. But we may know that the so-and-so exists when we are not acquainted with any object that we know to be the so-and-so. We may know it even when we are not acquainted with any object that in fact is the so-and-so.

Common words, even proper names, are usually descriptions in disguise. The thought in the mind of someone who uses a proper name correctly can generally be stated explicitly only if we replace the name with a description.

Moreover, the description needed to express the thought will differ from person to person, and even for the same person at different times. The only constant, as long as the name is used correctly, is the object the name applies to. And as long as that stays constant, the particular description involved usually makes no difference to whether the proposition containing the name is true or false.

Let us take some examples. Suppose someone makes a statement about Bismarck. If there is such a thing as direct acquaintance with oneself, Bismarck himself might have used his name directly to designate the particular person he was acquainted with.

In that case, if he made a judgement about himself, he himself might be a part of the judgement. Here the proper name has the direct use it always aims to have: it simply stands for a certain object, not for a description of that object.

The case is different when someone who knew Bismarck made a judgement about him. What this person was acquainted with were certain sense-data, which he connected (correctly, we will suppose) with Bismarck’s body.

Bismarck’s body, as a physical object, and still more his mind, were known to this person only as the body and the mind connected with those sense-data. In other words, they were known by description.

It is very much a matter of chance which features of a man’s appearance come to a friend’s mind when the friend thinks of him. So the description actually in the friend’s mind is accidental. The essential point is that he knows the various descriptions all apply to the same entity, even though he is not acquainted with that entity.

When we who did not know Bismarck make a judgment about him, the description in our minds will probably be a more or less vague mass of historical knowledge. In most cases, this is far more than is needed to identify him. For the sake of illustration, however, let us assume that we think of him as “the first Chancellor of the German Empire.”

In this description, every word is abstract except “German.” And the word “German” will itself mean different things to different people. To some it will call up memories of travels in Germany; to others, the shape of Germany on the map; and so on.

But if we are to obtain a description that we know applies to something, we will be forced at some point to bring in a reference to a particular with which we are acquainted. Any mention of past, present, and future (as opposed to definite dates) involves such a reference. So does any mention of here and there, or of what others have told us.

It seems, then, that a description known to apply to a particular must somehow involve a reference to a particular with which we are acquainted. Otherwise, our knowledge about the thing described would be limited to what follows logically from the description itself.

Take, for example, “the most long-lived of men.” This description involves only universals. It must apply to some man, but we can make no judgments about him that go beyond what the description already tells us.

If, however, we say, “The first Chancellor of the German Empire was an astute diplomat,” we can be sure our judgment is true only because of something with which we are acquainted. Usually this is testimony we have heard or read.

Set aside the information we pass on to others, and set aside the fact about the actual Bismarck that gives our judgment its importance. What remains is the thought we actually have. That thought contains the one or more particulars involved, and apart from them it consists entirely of concepts.

All names of places, such as London, England, Europe, the Earth, and the Solar System, work the same way. When we use them, they involve descriptions that start from one or more particulars with which we are acquainted. I suspect that even the Universe, as metaphysics considers it, involves such a connection with particulars.

Logic is different. It is concerned not merely with what does exist, but with whatever might or could exist or be. For that reason, it involves no reference to actual particulars.

When we make a statement about something known only by description, we often intend the statement to be about the actual thing described, not about the description. When we say anything about Bismarck, we would like, if we could, to make the judgment that only Bismarck can make: the judgment of which he himself is a constituent.

In this we are bound to fail, because the actual Bismarck is unknown to us. But we do know that there is an object B, called Bismarck, and that B was an astute diplomat. We can therefore describe the proposition we would like to affirm, namely, “B was an astute diplomat,” where B is the object that was Bismarck.

If we are describing Bismarck as “the first Chancellor of the German Empire,” then the proposition we would like to affirm can be described as follows: “the proposition asserting, about the actual object that was the first Chancellor of the German Empire, that this object was an astute diplomat.”

We use differing descriptions, yet we can still communicate. This is possible because we know there is a true proposition about the actual Bismarck. However we vary the description, as long as it is correct, the proposition described stays the same.

This proposition, which is described and known to be true, is what interests us. But we are not acquainted with the proposition itself, and we do not know it, even though we know that it is true.

There are, then, various stages of distance from acquaintance with particulars. There is Bismarck as known to people who knew him. There is Bismarck as known to those who know of him only through history. There is the man with the iron mask. And there is the longest-lived of men. Each of these is further removed from acquaintance with particulars than the one before.

The first comes as close to acquaintance as is possible with another person. In the second, we would still be said to know “who Bismarck was.”

In the third, we do not know who the man with the iron mask was. We can, however, know many propositions about him that cannot be logically deduced from the fact that he wore an iron mask. In the fourth, finally, we know nothing beyond what can be logically deduced from the definition of the man.

A similar hierarchy exists among universals. Many universals, like many particulars, are known to us only by description. But here too, as with particulars, knowledge about what is known by description can ultimately be reduced to knowledge about what is known by acquaintance.

The fundamental principle in analyzing propositions that contain descriptions is this: Every proposition we can understand must be made up entirely of constituents with which we are acquainted.

At this stage we will not try to answer all the objections that may be raised against this fundamental principle. For now, we will simply point out that these objections must somehow be answerable. It is hardly conceivable that we could make a judgment or entertain a supposition without knowing what we are judging or supposing about.

If we are to speak meaningfully and not just make noise, we must attach some meaning to the words we use. And the meaning we attach to our words must be something with which we are acquainted.

So when we make a statement about Julius Caesar, for example, it is plain that Julius Caesar himself is not before our minds, since we are not acquainted with him. What we have in mind is some description of him. It might be “the man who was assassinated on the Ides of March,” or “the founder of the Roman Empire.”

Or it might be merely “the man whose name was Julius Caesar.” In this last description, “Julius Caesar” is a sound or a written shape with which we are acquainted.

Our statement, then, does not mean quite what it seems to mean. Instead of involving Julius Caesar himself, it involves some description of him. That description is made up entirely of particulars and universals with which we are acquainted.

The chief importance of knowledge by description is that it lets us go beyond the limits of our private experience. We can know only truths composed entirely of terms we have experienced through acquaintance. Even so, we can have knowledge by description of things we have never experienced.

Since the range of our immediate experience is very narrow, this result is vital. Until it is understood, much of our knowledge must remain mysterious, and therefore doubtful.

CHAPTER VI. ON INDUCTION

In almost all our previous discussions, we have been trying to get clear about our data concerning knowledge of existence. What things in the universe do we know exist because we are acquainted with them?

So far, our answer has been that we are acquainted with our sense-data and, probably, with ourselves. These we know to exist. And past sense-data that we remember are known to have existed in the past. This knowledge supplies our data.

But suppose we want to draw inferences from these data. We might want to know that matter exists, that other people exist, that there was a past before our own memories begin, or that there will be a future. To do so, we must know general principles of some kind that allow such inferences to be drawn.

We must know that the existence of one sort of thing, A, is a sign of the existence of another sort of thing, B. B might exist at the same time as A, or earlier, or later. Thunder, for example, is a sign that lightning existed a moment before.

If we did not know this, we could never extend our knowledge beyond the sphere of our private experience. And that sphere, as we have seen, is extremely limited. The question we must now consider is whether such an extension is possible, and if so, how it is accomplished.

Let us take as an illustration something none of us actually doubts in the slightest. We are all convinced that the sun will rise tomorrow. Why? Is this belief merely a blind product of past experience, or can it be justified as a reasonable belief?

It is not easy to find a test for judging whether a belief of this kind is reasonable. But we can at least work out what sort of general beliefs would be enough, if true, to justify the judgment that the sun will rise tomorrow. The same beliefs would justify the many similar judgments on which our actions are based.

Obviously, if we are asked why we believe the sun will rise tomorrow, our natural answer will be, “Because it always has risen every day.” We firmly believe it will rise in the future because it has risen in the past.

If we are challenged about why we believe it will keep rising as before, we may appeal to the laws of motion. The earth, we will say, is a freely rotating body. Such bodies do not stop rotating unless something from outside interferes, and nothing outside will interfere with the earth between now and tomorrow.

Of course, one might doubt whether we are quite certain that nothing outside will interfere. But that is not the interesting doubt. The interesting doubt is whether the laws of motion will remain in operation until tomorrow. If this doubt is raised, we find ourselves in the same position we were in when the doubt about the sunrise was first raised.

The only reason for believing that the laws of motion will remain in operation is that they have operated up to now, as far as our knowledge of the past allows us to judge.

It is true that we have more evidence from the past in favor of the laws of motion than in favor of the sunrise. The sunrise is merely one particular case of the laws of motion being fulfilled, and there are countless other particular cases.

But the real question is this: Does any number of past cases of a law being fulfilled provide evidence that it will be fulfilled in the future?

If not, then plainly we have no ground at all for expecting the sun to rise tomorrow. Nor do we have any ground for expecting that the bread we eat at our next meal will not poison us, or for any of the other barely conscious expectations that govern our daily lives.

Note that all such expectations are only probable. So we do not need to look for a proof that they must be fulfilled. We need only look for some reason in favor of the view that they are likely to be fulfilled.

In dealing with this question, we must begin by making an important distinction. Without it, we would soon be caught up in hopeless confusion.

Experience has shown us that, up to now, the frequent repetition of some uniform sequence or coexistence has caused us to expect the same sequence or coexistence the next time.

Food with a certain appearance generally has a certain taste. It is a severe shock to our expectations when a familiar appearance turns out to go with an unusual taste.

Through habit, the things we see become associated with certain sensations of touch, which we expect to feel if we touch them. In many ghost stories, one of the horrors of a ghost is that it gives us no sensations of touch at all.

Uneducated people who go abroad for the first time are so surprised to find their native language not understood that they can hardly believe it.

This kind of association is not limited to human beings; it is very strong in animals too. A horse that has often been driven along a certain road resists being driven in a different direction. Domestic animals expect food when they see the person who usually feeds them.

We know that all these rather crude expectations of uniformity can mislead us. The man who has fed the chicken every day of its life finally wrings its neck instead. This shows that more refined views about the uniformity of nature would have been useful to the chicken.

But even though such expectations can mislead, they still exist. The mere fact that something has happened a certain number of times causes animals and humans to expect that it will happen again.

Our instincts, then, certainly cause us to believe that the sun will rise tomorrow. But we may be in no better position than the chicken that unexpectedly has its neck wrung.

We must therefore distinguish two things. One is the fact that past uniformities cause expectations about the future. The other is the question of whether there is any reasonable ground for giving weight to such expectations once their validity has been called into question.

The problem we must now discuss is whether there is any reason to believe in what is called “the uniformity of nature.” This is the belief that everything that has happened or will happen is an instance of some general law that has no exceptions.

The crude expectations we have been considering all have exceptions, so they can disappoint the people who hold them. Science, however, habitually assumes, at least as a working hypothesis, that general rules with exceptions can be replaced by general rules without exceptions.

Take the rule “Unsupported bodies in air fall.” Balloons and aeroplanes are exceptions to it. But the laws of motion and the law of gravitation, which explain why most bodies fall, also explain why balloons and aeroplanes can rise. So the laws of motion and the law of gravitation are not subject to these exceptions.

The belief that the sun will rise tomorrow could be proved false if the earth suddenly collided with a large body that destroyed its rotation. But such an event would not violate the laws of motion or the law of gravitation.

The business of science is to find uniformities like the laws of motion and the law of gravitation, to which, as far as our experience reaches, there are no exceptions. Science has been remarkably successful in this search, and we may grant that such uniformities have held so far.

This brings us back to the question: assuming that these uniformities have always held in the past, do we have any reason to suppose that they will hold in the future?

Some have argued that we do have reason to know the future will resemble the past. What was once the future has constantly become the past, and it has always been found to resemble the past. On this view, we actually have experience of the future, namely of times that were formerly future, which we may call “past futures.”

But this argument really assumes the very point in question. We have experience of past futures, but not of future futures. The question is whether future futures will resemble past futures, and an argument that starts from past futures alone cannot answer it. So we still need to find some principle that would let us know that the future will follow the same laws as the past.

The reference to the future is not essential to this question. The same question arises when we apply the laws that work in our experience to past things we have not experienced, as in geology, or in theories about the origin of the Solar System.

The question we really have to ask is this: “When two things have often been found together, and no instance is known of one occurring without the other, does the occurrence of one of them in a fresh instance give any good ground for expecting the other?”

Our answer to this question determines the validity of all our expectations about the future, of all the results obtained by induction, and indeed of practically all the beliefs on which our daily life is based.

We must grant, to begin with, that the fact that two things have often been found together and never apart does not, by itself, prove demonstratively that they will be found together in the next case we examine.

The most we can hope for is this: the more often things are found together, the more probable it becomes that they will be found together again. If they have been found together often enough, the probability will amount almost to certainty.

It can never quite reach certainty, because we know that despite frequent repetitions there is sometimes a failure in the end, as with the chicken whose neck is wrung. Probability is therefore all we should seek.

Someone might object to the view we are defending. They might say that we know all natural phenomena are subject to the reign of law, and that sometimes, on the basis of observation, we can see that only one law could possibly fit the facts of the case.

There are two answers to this. First, even if some exceptionless law applies to our case, we can never in practice be sure that we have discovered that law, rather than one that does have exceptions.

Second, the reign of law itself seems to be only probable. Our belief that it will hold in the future, or in unexamined cases in the past, is itself based on the very principle we are examining.

The principle we are examining may be called the principle of induction. Its two parts may be stated as follows:

(a) When a thing of a certain sort A has been found associated with a thing of a certain other sort B, and has never been found apart from a thing of sort B, then the greater the number of cases in which A and B have been associated, the greater the probability that they will be associated in a fresh case in which one of them is known to be present.

(b) Under the same circumstances, a sufficient number of cases of association will make the probability of a fresh association nearly a certainty, and will make it approach certainty without limit.

As just stated, the principle applies only to confirming our expectation in a single fresh instance. But we also want to know that there is a probability in favour of the general law that things of sort A are always associated with things of sort B, provided enough cases of association are known and no cases of failure are known.

The probability of the general law is obviously less than the probability of the particular case. If the general law is true, the particular case must also be true, but the particular case may be true without the general law being true.

Even so, repetitions increase the probability of the general law, just as they increase the probability of the particular case. We may therefore restate the two parts of our principle as they apply to the general law:

(a) The greater the number of cases in which a thing of sort A has been found associated with a thing of sort B, the more probable it is (if no cases of failure of association are known) that A is always associated with B.

(b) Under the same circumstances, a sufficient number of cases of the association of A with B will make it nearly certain that A is always associated with B, and will make this general law approach certainty without limit.

It should be noted that probability is always relative to certain data. In our case, the data are simply the known cases in which A and B occur together. There may be other data that could be taken into account and that would seriously alter the probability.

For example, a man who had seen a great many white swans might argue, using our principle, that on those data it was probable that all swans were white. This could be a perfectly sound argument.

The argument is not disproved by the fact that some swans are black, because something can very well happen even though certain data make it improbable.

In the case of the swans, a man might know that colour varies greatly in many animal species, so that an induction about colour is especially liable to error. But this knowledge would be a fresh datum. It would by no means prove that the probability relative to his previous data had been wrongly estimated.

So the fact that things often fail to fulfil our expectations is no evidence that our expectations will probably not be fulfilled in a given case or a given class of cases. Our inductive principle, at any rate, cannot be disproved by an appeal to experience.

The inductive principle, however, is equally impossible to prove by an appeal to experience. Experience might conceivably confirm it for the cases already examined. But for unexamined cases, only the inductive principle can justify any inference from what has been examined to what has not.

Every argument that uses experience to reach conclusions about the future, or about unexperienced parts of the past or present, assumes the inductive principle. So we can never use experience to prove the principle without assuming what we set out to prove.

We must therefore either accept the inductive principle because of its intrinsic evidence, or give up all justification for our expectations about the future.

If the principle is unsound, we have no reason to expect the sun to rise tomorrow, to expect bread to be more nourishing than a stone, or to expect that we will fall if we throw ourselves off the roof.

When we see what looks like our best friend approaching, we will have no reason to suppose that his body is not inhabited by the mind of our worst enemy or of some total stranger.

All our conduct rests on associations that have worked in the past and that we therefore regard as likely to work in the future. Whether this likelihood is valid depends on the inductive principle.

The general principles of science, such as the belief in the reign of law and the belief that every event must have a cause, depend on the inductive principle just as completely as the beliefs of daily life do.

All such general principles are believed because humanity has found countless instances of their truth and no instances of their falsehood. But this gives no evidence that they will be true in the future unless the inductive principle is assumed.

So all knowledge that uses experience as a basis to tell us something about what is not experienced rests on a belief that experience can neither confirm nor refute. Yet this belief, at least in its more concrete applications, seems as firmly rooted in us as many of the facts of experience.

The existence and justification of such beliefs raise some of the most difficult and most debated problems in philosophy, and the inductive principle, as we shall see, is not the only example. In the next chapter, we will briefly consider what may be said to account for such knowledge, and what its scope and degree of certainty are.

CHAPTER VII. ON OUR KNOWLEDGE OF GENERAL PRINCIPLES

We saw in the preceding chapter that the principle of induction is necessary for the validity of every argument based on experience, yet cannot itself be proved by experience. Even so, everyone believes it without hesitation, at least in all its concrete applications.

In these respects the principle of induction is not alone. There are a number of other principles that experience can neither prove nor disprove, but that are used in arguments starting from what we experience.

Some of these principles are even more evident than the principle of induction, and our knowledge of them is as certain as our knowledge that sense-data exist. They are the means by which we draw inferences from what is given in sensation.

If what we infer is to be true, our principles of inference must be true, just as our data must be true.

Principles of inference are easily overlooked precisely because they are so obvious. We accept the assumption without realizing that it is an assumption. Yet if we are to reach a correct theory of knowledge, it is very important to recognize how we use principles of inference, because our knowledge of them raises interesting and difficult questions.

In all our knowledge of general principles, what actually happens is this. We first realize some particular application of the principle. Then we realize that the particular details are irrelevant, and that a general statement can be made just as truly.

This is familiar in teaching arithmetic. “Two and two are four” is first learned in the case of some particular pair of couples, then in some other particular case, and so on, until finally we can see that it is true of any pair of couples.

The same thing happens with logical principles. Suppose two men are discussing what day of the month it is. One says, “At least you will admit that if yesterday was the 15th, today must be the 16th.”

“Yes,” says the other, “I admit that.”

“And you know,” the first continues, “that yesterday was the 15th, because you dined with Jones, and your diary will tell you that was on the 15th.”

“Yes,” says the second, “so today is the 16th.”

Such an argument is not hard to follow. If its premises are granted to be true in fact, no one will deny that the conclusion must also be true. But its truth depends on an instance of a general logical principle.

The logical principle is this: “Suppose it is known that if this is true, then that is true. Suppose it is also known that this is true. Then it follows that that is true.”

When it is the case that if this is true, that is true, we will say that this “implies” that, and that that “follows from” this. So our principle states that if this implies that, and this is true, then that is true. That is, “anything implied by a true proposition is true,” or “whatever follows from a true proposition is true.”

This principle is involved in every demonstration, or at least concrete instances of it are. Whenever we use one thing we believe to prove something else, which we then believe as a result, this principle is at work. Suppose someone asks, “Why should I accept the results of valid arguments based on true premises?” We can answer only by appealing to this principle.

In fact, the principle’s truth cannot be doubted. It is so obvious that at first glance it seems almost trivial. To the philosopher, however, such principles are not trivial. They show that we can have knowledge beyond all doubt that does not come in any way from objects of sense.

The principle just described is only one of a certain number of self-evident logical principles. At least some of these must be granted before any argument or proof is possible. Once some have been granted, others can be proved. Yet those others, as long as they are simple, are just as obvious as the ones taken for granted.

For no very good reason, tradition has singled out three of these principles under the name “Laws of Thought.” They are as follows:

1. The law of identity: “Whatever is, is.”
2. The law of contradiction: “Nothing can both be and not be.”
3. The law of excluded middle: “Everything must either be or not be.”

These three laws are samples of self-evident logical principles. But they are not really more fundamental or more self-evident than various other similar principles. One example is the principle we just considered, which states that whatever follows from a true premise is true.

The name “laws of thought” is also misleading. What matters is not that we think in accordance with these laws, but that things behave in accordance with them. That is, what matters is that when we think in accordance with them, we think truly. But this is a large question, and we must return to it later.

Some logical principles allow us to prove, from a given premise, that something is certainly true. Other logical principles allow us to prove, from a given premise, that something has a greater or lesser probability of being true. An example of these, perhaps the most important example, is the inductive principle, which we considered in the preceding chapter.

One of the great historic controversies in philosophy is between two schools, the “empiricists” and the “rationalists.” The empiricists, best represented by the British philosophers Locke, Berkeley, and Hume, held that all our knowledge comes from experience.

The rationalists, represented by the Continental philosophers of the seventeenth century, especially Descartes and Leibniz, held something more. In addition to what we know through experience, they said, there are certain “innate ideas” and “innate principles” that we know independently of experience.

It has now become possible to decide with some confidence which of these opposing schools is right. For the reasons already given, we must admit that logical principles are known to us. We must also admit that they cannot themselves be proved by experience, since all proof presupposes them. On this point, which was the most important in the controversy, the rationalists were right.

On the other hand, even the part of our knowledge that is logically independent of experience (in the sense that experience cannot prove it) is still drawn out and caused by experience. Particular experiences are the occasions on which we become aware of the general laws that their connections exemplify.

It would certainly be absurd to suppose that there are innate principles in the sense that babies are born knowing everything that people know which cannot be deduced from experience. For this reason, the word “innate” would no longer be used to describe our knowledge of logical principles. The phrase “a priori” is less objectionable and is more common among modern writers.

So while we admit that all knowledge is drawn out and caused by experience, we will still hold that some knowledge is a priori. By this we mean that the experience that leads us to think of it is not enough to prove it. That experience merely directs our attention so that we see its truth without needing any proof from experience.

There is another very important point on which the empiricists were right and the rationalists wrong. Nothing can be known to exist except with the help of experience. If we want to prove that something exists of which we have no direct experience, our premises must include the existence of one or more things of which we do have direct experience.

Our belief that the Emperor of China exists, for example, rests on testimony. And testimony consists, in the end, of sense-data seen or heard when we read or are spoken to. Rationalists believed that, from general considerations about what must be, they could deduce the existence of this or that in the actual world. In this belief they seem to have been mistaken.

All the knowledge about existence that we can acquire a priori seems to be hypothetical. It tells us that if one thing exists, another must exist. More generally, it tells us that if one proposition is true, another must be true.

The principles we have already dealt with illustrate this. One is “if this is true, and this implies that, then that is true.” Another is “if this and that have been repeatedly found connected, they will probably be connected in the next instance in which one of them is found.” The scope and power of a priori principles are therefore strictly limited.

All knowledge that something exists must depend partly on experience. When we know something immediately, we know its existence through experience alone. When we prove that something exists without knowing it immediately, the proof requires both experience and a priori principles.

Knowledge is called empirical when it rests wholly or partly on experience. So all knowledge that asserts existence is empirical. The only a priori knowledge about existence is hypothetical. It gives connections among things that exist or may exist, but it does not give actual existence.

Not all a priori knowledge is of the logical kind we have been considering so far. Perhaps the most important example of non-logical a priori knowledge is knowledge of ethical value. I am not speaking of judgments about what is useful or what is virtuous, since such judgments do require empirical premises. I am speaking of judgments about the intrinsic desirability of things.

If something is useful, it must be useful because it achieves some end. If we trace the chain far enough, that end must be valuable for its own sake, and not merely because it is useful for some further end. So all judgments about what is useful depend on judgments about what has value for its own sake.

We judge, for example, that happiness is more desirable than misery, knowledge more desirable than ignorance, goodwill more desirable than hatred, and so on. Such judgments must, at least in part, be immediate and a priori.

Like our earlier a priori judgments, they may be drawn out by experience, and indeed they must be. It seems impossible to judge whether anything is intrinsically valuable unless we have experienced something of the same kind. But it is fairly obvious that experience cannot prove them. The fact that a thing exists or does not exist cannot prove either that its existence is good or that it is bad.

Pursuing this subject belongs to ethics, which has the task of establishing that what ought to be cannot be deduced from what is. Here it is only important to see that knowledge of what is intrinsically valuable is a priori in the same sense that logic is a priori. That is, the truth of such knowledge can be neither proved nor disproved by experience.

All pure mathematics is a priori, like logic. The empirical philosophers strenuously denied this. They held that experience was as much the source of our knowledge of arithmetic as of our knowledge of geography.

On their view, we repeatedly saw two things and two other things and found that together they made four things. From these repeated experiences we were led by induction to conclude that two things and two other things would always make four things altogether.

If this were really the source of our knowledge that two and two are four, however, we would go about convincing ourselves of its truth differently from the way we actually do. In fact, we need a certain number of instances to make us think of two abstractly, rather than of two coins, two books, two people, or two of any other specific kind.

But as soon as we can strip our thoughts of irrelevant particulars, we are able to see the general principle that two and two are four. Any one instance is then seen to be typical, and examining other instances becomes unnecessary.

Geometry illustrates the same thing. If we want to prove some property of all triangles, we draw one triangle and reason about it. But we can avoid using any property that it does not share with all other triangles. In this way we obtain a general result from our particular case.

In fact, fresh instances do not make us feel any more certain that two and two are four. As soon as we have seen the truth of this proposition, our certainty becomes so great that it cannot grow any greater.

Moreover, we feel a certain quality of necessity about the proposition “two and two are four” that is missing from even the best-supported empirical generalizations. Such generalizations always remain mere facts. We feel that there might be a world in which they were false, though in the actual world they happen to be true.

In any possible world, by contrast, we feel that two and two would be four. This is not a mere fact but a necessity to which everything actual and possible must conform.

The case becomes clearer if we consider a genuinely empirical generalization, such as “All men are mortal.” Plainly, we believe this proposition for two reasons. First, there is no known instance of men living beyond a certain age. Second, there seem to be physiological grounds for thinking that an organism such as a human body must sooner or later wear out.

Set aside the second reason and consider only our experience of human mortality. It is plain that we would not be satisfied with one quite clearly understood instance of a man dying. In the case of “two and two are four,” by contrast, one instance, carefully considered, is enough to persuade us that the same must happen in any other instance.

Also, on reflection, we can be forced to admit that there may be some doubt, however slight, about whether all men are mortal. We can see this by trying to imagine two different worlds: one in which there are men who are not mortal, and another in which two and two make five.

When Swift invites us to consider the race of Struldbugs who never die, we can go along with it in imagination. But a world where two and two make five seems to be on quite a different level. We feel that such a world, if there were one, would overturn the whole structure of our knowledge and reduce us to complete doubt.

The fact is that in simple mathematical judgments such as “two and two are four,” and also in many judgments of logic, we can know the general proposition without inferring it from instances. Still, some instance is usually needed to make clear to us what the general proposition means.

This is why the process of deduction is genuinely useful, just as the process of induction is. Deduction goes from the general to the general, or from the general to the particular. Induction goes from the particular to the particular, or from the particular to the general.

Philosophers have long debated whether deduction ever gives new knowledge. We can now see that in certain cases, at least, it does. Suppose we already know that two and two always make four. Suppose we also know that Brown and Jones are two, and so are Robinson and Smith. Then we can deduce that Brown and Jones and Robinson and Smith are four.

This is new knowledge, not contained in our premises. The general proposition “two and two are four” never told us that there were such people as Brown, Jones, Robinson, and Smith. The particular premises do not tell us that there were four of them. The particular proposition we deduced tells us both of these things.

But the knowledge is much less clearly new if we take the standard example of deduction found in every logic textbook: “All men are mortal; Socrates is a man; therefore Socrates is mortal.” Here, what we really know beyond reasonable doubt is that certain men, A, B, and C, were mortal, because they have in fact died.

If Socrates is one of these men, it is foolish to take the roundabout route through “all men are mortal” to reach the conclusion that Socrates is probably mortal. If Socrates is not one of the men on whom our induction is based, we will still do better to argue directly from A, B, and C to Socrates than to detour through the general proposition “all men are mortal.”

On our evidence, the probability that Socrates is mortal is greater than the probability that all men are mortal. This is obvious: if all men are mortal, then so is Socrates, but if Socrates is mortal, it does not follow that all men are. So we come closer to certainty that Socrates is mortal by arguing purely inductively than by passing through “all men are mortal” and then using deduction.

This example shows the difference between general propositions known a priori, such as “two and two are four,” and empirical generalizations, such as “all men are mortal.” For the first kind, deduction is the right method of argument. For the second kind, induction is always preferable in theory and justifies greater confidence in our conclusion, because every empirical generalization is less certain than the particular instances of it.

We have now seen that some propositions are known a priori, including the propositions of logic and pure mathematics, as well as the fundamental propositions of ethics. The next question is: How can such knowledge exist at all?

More specifically, how can we know general propositions when we have not examined every instance, and never can, because the instances are infinite in number? These questions were first brought into prominence by the German philosopher Kant (1724–1804). They are very difficult, and historically very important.

CHAPTER VIII. HOW A PRIORI KNOWLEDGE IS POSSIBLE

Immanuel Kant is generally regarded as the greatest of the modern philosophers. Although he lived through the Seven Years’ War and the French Revolution, he never interrupted his teaching of philosophy at Königsberg in East Prussia.

His most distinctive contribution was the invention of what he called the “critical” philosophy. It took as a given that we have knowledge of various kinds and asked how such knowledge is possible. From the answer, Kant drew many metaphysical conclusions about the nature of the world. Whether those conclusions were valid may well be doubted.

But Kant certainly deserves credit for two things. First, he saw that we have a priori knowledge that is not purely “analytic,” meaning knowledge whose opposite would not be self-contradictory. Second, he made clear how philosophically important the theory of knowledge is.

Before Kant, it was generally held that all a priori knowledge must be “analytic.” Examples best show what this word means. If I say, “A bald man is a man,” “A plane figure is a figure,” or “A bad poet is a poet,” I make a purely analytic judgment.

In such a judgment, the subject is presented as having at least two properties, and one of them is singled out and asserted of it. Propositions like these are trivial. In real life, nobody would state them except perhaps a speaker preparing the ground for a misleading argument.

They are called “analytic” because the predicate is obtained simply by analyzing the subject. Before Kant, philosophers thought that every judgment we could be certain of a priori was of this kind: in each, the predicate was only part of the subject it was asserted of.

If that were so, then denying anything known a priori would involve us in a definite contradiction. “A bald man is not bald” would both assert and deny baldness of the same man, and so it would contradict itself.

According to the philosophers before Kant, then, the law of contradiction was enough to establish the truth of all a priori knowledge. That law states that nothing can at the same time have and not have a given property.

Hume (1711–76), who came before Kant, accepted the usual view of what makes knowledge a priori. But he discovered that in many cases previously thought to be analytic, and especially in the case of cause and effect, the connection was really synthetic.

Before Hume, the rationalists at least had supposed that, given enough knowledge, we could logically deduce the effect from the cause. Hume argued, correctly as most would now admit, that this cannot be done. From this he inferred a far more doubtful claim: that nothing at all can be known a priori about the connection between cause and effect.

Kant had been educated in the rationalist tradition, and Hume’s skepticism disturbed him greatly. He tried to find an answer to it. He saw that not only the connection of cause and effect, but all the propositions of arithmetic and geometry, are “synthetic,” that is, not analytic. In none of these propositions does analyzing the subject reveal the predicate.

His standard example was the proposition 7 + 5 = 12. He pointed out, quite rightly, that 7 and 5 have to be put together to give 12. The idea of 12 is not contained in them, nor even in the idea of adding them together.

This led him to conclude that all pure mathematics, though a priori, is synthetic. That conclusion raised a new problem, which he tried to solve.

The question Kant placed at the start of his philosophy was “How is pure mathematics possible?” It is an interesting and difficult question, and every philosophy that is not purely skeptical must find some answer to it.

We have already seen that the answer of the pure empiricists, that our mathematical knowledge comes by induction from particular instances, is inadequate. There are two reasons. First, the validity of the inductive principle itself cannot be proved by induction.

Second, the general propositions of mathematics, such as “two and two always make four,” can plainly be known with certainty by considering a single instance. They gain nothing from listing other cases in which they have proved true.

So our knowledge of the general propositions of mathematics, and the same applies to logic, must be explained differently from our merely probable knowledge of empirical generalizations such as “all men are mortal.”

The problem arises because such knowledge is general, while all experience is particular. It seems strange that we can apparently know some truths in advance about particular things we have not yet experienced. Yet it can hardly be doubted that logic and arithmetic will apply to such things.

We do not know who will live in London a hundred years from now. But we know that any two of them and any other two of them will make four of them. This apparent power to anticipate facts about things we have never experienced is certainly surprising.

Kant’s solution to this problem is interesting, although in my opinion it is not valid. It is also very difficult, and different philosophers understand it differently. So we can give only the barest outline of it, and many interpreters of Kant’s system will consider even that outline misleading.

Kant held that in all our experience we must distinguish two elements. One comes from the object, meaning what we have called the “physical object.” The other comes from our own nature.

In discussing matter and sense-data, we saw that the physical object is different from the sense-data associated with it, and that the sense-data should be regarded as the result of an interaction between the physical object and ourselves. Up to this point, we agree with Kant.

What is distinctive in Kant is how he divides the contributions of ourselves and of the physical object. He holds that the raw material given in sensation, such as color and hardness, comes from the object.

What we supply is the arrangement in space and time, together with all the relations between sense-data that arise from comparing them, from treating one as the cause of another, or in any other way.

His main reason for this view is that we seem to have a priori knowledge about space, time, causality, and comparison, but not about the raw material of sensation itself.

We can be sure, he says, that anything we ever experience must show the characteristics our a priori knowledge attributes to it. These characteristics come from our own nature, and so nothing can ever enter our experience without acquiring them.

Kant calls the physical object the “thing in itself,” and he regards it as essentially unknowable. What can be known is the object as we have it in experience, which he calls the “phenomenon.”

Kant’s “thing in itself” has the same definition as the physical object: it is the cause of sensations. But the properties he derives from this definition are not the same, because Kant held, despite some inconsistency regarding cause, that we can know that none of the categories apply to the “thing in itself.”

The phenomenon is a joint product of ourselves and the thing in itself. So it is certain to have the characteristics that come from us, and therefore certain to conform to our a priori knowledge.

It follows that this knowledge, though true of all actual and possible experience, must not be assumed to apply beyond experience. So even though a priori knowledge exists, we cannot know anything about the thing in itself, or about anything that is not an actual or possible object of experience.

In this way, Kant tries to reconcile the claims of the rationalists with the arguments of the empiricists.

Kant’s philosophy can be criticized on various minor grounds. But there is one main objection that seems fatal to any attempt to handle the problem of a priori knowledge by his method.

What needs explaining is our certainty that the facts must always conform to logic and arithmetic. Saying that we ourselves contribute logic and arithmetic does not explain this certainty.

Our nature is as much a fact about the existing world as anything else, and there can be no certainty that it will stay the same. If Kant is right, our nature might change tomorrow so that two and two would become five.

This possibility seems never to have occurred to him. Yet it completely destroys the certainty and universality that he is eager to secure for arithmetical propositions.

Formally, it is true, this possibility conflicts with Kant’s view that time itself is a form the subject imposes on phenomena, so that our real Self is not in time and has no tomorrow.

But Kant must still suppose that the time-order of phenomena is determined by characteristics of whatever lies behind phenomena. That is enough for the substance of our argument.

Reflection also seems to make clear that if our arithmetical beliefs are true at all, they must apply to things whether or not we think of them. Two physical objects and two other physical objects must make four physical objects, even if physical objects cannot be experienced.

Asserting this is certainly part of what we mean when we say that two and two are four. Its truth is just as beyond doubt as the claim that two phenomena and two other phenomena make four phenomena.

So Kant’s solution not only fails to explain the certainty of a priori propositions. It also wrongly narrows their scope.

Setting aside Kant’s particular doctrines, it is very common among philosophers to regard what is a priori as in some sense mental. On this view, it concerns the way we must think, rather than any fact about the outer world.

In the preceding chapter we noted the three principles commonly called “laws of thought.” The view that led to that name is a natural one, but there are strong reasons to think it mistaken. Take the law of contradiction as an illustration.

It is usually stated as “Nothing can both be and not be.” This is meant to express the fact that nothing can at the same time have and not have a given quality. For example, if a tree is a beech, it cannot also be not a beech. If my table is rectangular, it cannot also be not rectangular, and so on.

Calling this principle a law of thought seems natural because we become convinced of its necessary truth through thought, not through observing the outside world. Once we have seen that a tree is a beech, we do not need to look again to find out whether it is also not a beech. Thought alone tells us that this is impossible.

Even so, the conclusion that the law of contradiction is a law of thought is mistaken. When we believe the law of contradiction, we are not believing that the mind is so made that it must believe the law of contradiction. That second belief comes later, from psychological reflection, and that reflection already assumes belief in the law of contradiction.

The belief in the law of contradiction is a belief about things, not only about thoughts. For example, it is not the belief that if we think a certain tree is a beech, we cannot at the same time think that it is not a beech. It is the belief that if the tree is a beech, it cannot at the same time be not a beech.

So the law of contradiction is about things, and not merely about thoughts. Believing in the law is a thought, but the law itself is not a thought. It is a fact about the things in the world.

Suppose that what we believe, when we believe the law of contradiction, were not true of the things in the world. Then the fact that we were compelled to think it true would not save the law from being false. This shows that the law is not a law of thought.

A similar argument applies to any other a priori judgement. When we judge that two and two are four, we are not judging something about our thoughts. We are judging something about all actual or possible pairs of things.

It is true that our minds are so constituted that we believe two and two are four. But that fact is emphatically not what we assert when we say that two and two are four. And no fact about how our minds are constituted could make it true that two and two are four.

Our a priori knowledge, then, if it is not mistaken, is not merely knowledge about how our minds are constituted. It applies to whatever the world may contain, both what is mental and what is not.

The fact seems to be that all our a priori knowledge concerns entities that do not, strictly speaking, exist, either in the mental world or in the physical world. These entities can be named by parts of speech other than nouns. They are entities such as qualities and relations.

Suppose, for instance, that I am in my room. I exist, and my room exists, but does ‘in’ exist? Yet the word ‘in’ plainly has a meaning. It refers to a relation that holds between me and my room.

This relation is something, even though we cannot say that it exists in the same sense in which I and my room exist. The relation ‘in’ is something we can think about and understand. If we could not understand it, we could not understand the sentence ‘I am in my room’.

Many philosophers, following Kant, have held that relations are the work of the mind. On this view, things in themselves have no relations. Instead, the mind brings things together in a single act of thought, and in doing so it produces the relations it judges them to have.

This view, however, seems open to objections like those we raised earlier against Kant. It seems plain that thought does not produce the truth of the proposition ‘I am in my room’.

It may be true that an earwig is in my room even if neither I nor the earwig nor anyone else is aware of this truth. The truth concerns only the earwig and the room, and does not depend on anything else.

Relations, then, as we shall see more fully in the next chapter, must be placed in a world that is neither mental nor physical. This world is of great importance to philosophy, and especially to the problems of a priori knowledge. In the next chapter we shall go on to develop its nature and its bearing on the questions we have been discussing.

CHAPTER IX. THE WORLD OF UNIVERSALS

At the end of the previous chapter we saw that entities such as relations seem to have a kind of being that differs somehow from that of physical objects. It also differs from the being of minds and of sense-data.

In this chapter we have to consider two questions. What is the nature of this kind of being? And which objects have this kind of being? We will begin with the second question.

The problem we are now concerned with is a very old one, since Plato brought it into philosophy. Plato’s ‘theory of ideas’ is an attempt to solve exactly this problem, and in my opinion it is one of the most successful attempts made so far. The theory I shall argue for below is largely Plato’s, with only such changes as time has shown to be necessary.

The problem arose for Plato more or less as follows. Take a notion such as justice. If we ask ourselves what justice is, the natural way to proceed is to consider this, that, and the other just act, in order to discover what they have in common.

All just acts must, in some sense, share a common nature. This nature will be found in whatever is just and in nothing else. The common nature that makes them all just will be justice itself. It is the pure essence which, when mixed with the facts of ordinary life, produces the many different just acts.

The same holds for any other word that can be applied to common facts, such as ‘whiteness’. The word applies to a number of particular things because they all participate in a common nature or essence. This pure essence is what Plato calls an ‘idea’ or ‘form’.

It must not be supposed that ‘ideas’ in Plato’s sense exist in minds, though minds may grasp them. The ‘idea’ of justice is not identical with anything that is just. It is something other than particular things, something in which particular things share.

Because it is not particular, it cannot itself exist in the world of the senses. Nor is it fleeting or changeable like the things of sense. It is eternally itself, unchanging and indestructible.

So Plato is led to a world beyond the senses, more real than the ordinary world of sense. This is the unchanging world of ideas, and it alone gives the world of sense whatever pale reflection of reality that world may have.

For Plato, the truly real world is the world of ideas. Whatever we try to say about things in the world of sense, we can only succeed in saying that they participate in such and such ideas. Those ideas, therefore, make up their whole character.

From here it is easy to slip into mysticism. We may hope, in a moment of mystical illumination, to see the ideas the way we see objects of sense. And we may imagine that the ideas exist in heaven.

These mystical developments are very natural. But the basis of the theory lies in logic, and it is as a theory based in logic that we have to consider it.

Over time, the word ‘idea’ has picked up many associations that are quite misleading when applied to Plato’s ‘ideas’. We shall therefore use the word ‘universal’ instead of ‘idea’ to describe what Plato meant.

The essential feature of the kind of entity Plato meant is that it stands in contrast to the particular things given in sensation. We call anything given in sensation, or anything of the same nature as what is given in sensation, a particular.

In contrast, a universal will be anything that can be shared by many particulars. It has the features that, as we saw, distinguish justice and whiteness from just acts and white things.

When we examine ordinary words, we find that, broadly speaking, proper names stand for particulars. Other nouns, along with adjectives, prepositions, and verbs, stand for universals.

Pronouns stand for particulars, but they are ambiguous. Only the context or the circumstances tell us which particulars they stand for. The word ‘now’ stands for a particular, namely the present moment. But like pronouns, it stands for an ambiguous particular, because the present is always changing.

It follows that no sentence can be constructed without at least one word that refers to a universal. The closest we could come would be a statement such as ‘I like this’. But even here the word ‘like’ refers to a universal, since I may like other things, and other people may like things.

All truths, therefore, involve universals, and all knowledge of truths involves acquaintance with universals.

Nearly all the words found in the dictionary stand for universals. It is strange, then, that hardly anyone except students of philosophy ever realizes that there are such entities as universals.

We do not naturally dwell on the words in a sentence that do not stand for particulars. And if we are forced to dwell on a word that stands for a universal, we naturally think of it as standing for one of the particulars that fall under that universal.

Consider the sentence ‘Charles I’s head was cut off’. We may naturally think of Charles I, of Charles I’s head, and of the act of cutting off his head. These are all particulars.

But we do not naturally dwell on what is meant by the word ‘head’ or the word ‘cut’, which is a universal. We feel that such words are incomplete and insubstantial. They seem to need a context before anything can be done with them. So we manage to avoid noticing universals as such, until the study of philosophy forces them on our attention.

Even among philosophers, broadly speaking, only the universals named by adjectives or nouns have been widely or often recognized. Those named by verbs and prepositions have usually been overlooked.

This omission has had a very great effect on philosophy. It is hardly too much to say that most metaphysics since Spinoza has been largely shaped by it.

In outline, this is how it happened. Generally speaking, adjectives and common nouns express qualities or properties of single things. Prepositions and verbs, on the other hand, tend to express relations between two or more things.

Neglecting prepositions and verbs therefore led to the belief that every proposition can be treated as assigning a property to a single thing, rather than as expressing a relation between two or more things. From this it was assumed that, ultimately, there can be no such entities as relations between things.

Two conclusions then followed. Either there can be only one thing in the universe, or, if there are many things, they cannot possibly interact in any way. Any interaction would be a relation, and relations were held to be impossible.

The first view, put forward by Spinoza and held in our own day by Bradley and many other philosophers, is called monism. The second, put forward by Leibniz but not very common today, is called monadism, because each of the isolated things is called a monad.

Both of these opposing philosophies are interesting. In my opinion, however, both result from giving too much attention to one kind of universal: the kind represented by adjectives and nouns rather than by verbs and prepositions.

As a matter of fact, suppose someone wanted to deny altogether that there are such things as universals. We would find that we cannot strictly prove that there are qualities, the universals represented by adjectives and nouns. We can, however, prove that there must be relations, the sort of universals usually represented by verbs and prepositions.

Take the universal whiteness as an illustration. If we believe there is such a universal, we will say that things are white because they have the quality of whiteness. Berkeley and Hume vigorously denied this, and later empiricists have followed them. Their denial took the form of rejecting what they called “abstract ideas.”

When we want to think of whiteness, they said, we form an image of some particular white thing. We then reason about this particular, taking care not to infer anything about it that we cannot see to be equally true of every other white thing.

As a description of how our minds actually work, this is no doubt largely true. In geometry, for example, when we want to prove something about all triangles, we draw one particular triangle and reason about it. We take care not to use any feature that it does not share with other triangles.

A beginner, to avoid mistakes, often finds it useful to draw several triangles that are as unlike each other as possible. This makes sure that the reasoning applies equally to all of them.

But a difficulty appears as soon as we ask how we know that a thing is white, or is a triangle. If we want to avoid the universals whiteness and triangularity, we will choose some particular white patch or some particular triangle. We will then say that anything is white, or is a triangle, if it has the right kind of resemblance to the example we chose.

But then the required resemblance will itself have to be a universal. Since there are many white things, the resemblance must hold between many pairs of particular white things, and being shared by many particulars is exactly what marks a universal.

It is no use saying that each pair has its own separate resemblance. We would then have to say that these resemblances resemble each other, and in the end we would be forced to admit resemblance as a universal anyway. The relation of resemblance, therefore, must be a genuine universal.

Once we have been forced to admit this universal, it is no longer worth inventing difficult and implausible theories to avoid admitting universals such as whiteness and triangularity.

Berkeley and Hume did not see this refutation of their rejection of “abstract ideas.” Like their opponents, they thought only about qualities and completely ignored relations as universals.

Here, then, is another point on which the rationalists seem to have been right against the empiricists. Even so, because the rationalists neglected or denied relations, the conclusions they drew were, if anything, more likely to be mistaken than those of the empiricists.

We have now seen that there must be such entities as universals. The next thing to prove is that their being is not merely mental. This means that whatever being they have does not depend on their being thought of, or grasped by minds in any way.

We touched on this subject at the end of the previous chapter. Now we must consider more fully what kind of being belongs to universals.

Consider a proposition such as “Edinburgh is north of London.” Here we have a relation between two places, and it seems plain that the relation holds whether or not we know about it.

When we come to know that Edinburgh is north of London, we come to know something that concerns only Edinburgh and London. We do not make the proposition true by coming to know it. On the contrary, we merely grasp a fact that was already there before we knew it.

The part of the earth’s surface where Edinburgh stands would be north of the part where London stands even if no human being existed to know about north and south. It would be so even if there were no minds at all in the universe.

Many philosophers, of course, deny this, either for Berkeley’s reasons or for Kant’s. But we have already considered those reasons and decided that they are inadequate. We may therefore now assume that nothing mental is presupposed in the fact that Edinburgh is north of London.

This fact, however, involves the relation “north of,” which is a universal. The fact as a whole could not be free of anything mental if one of its component parts, the relation “north of,” did involve something mental.

So we must admit that the relation, like the places it relates, does not depend on thought. It belongs to the independent world that thought grasps but does not create.

This conclusion faces a difficulty, however. The relation “north of” does not seem to exist in the same sense in which Edinburgh and London exist. If we ask, “Where and when does this relation exist?” the answer must be “Nowhere and at no time.”

There is no place or time where we can find the relation “north of.” It does not exist in Edinburgh any more than in London, because it relates the two and is neutral between them. Nor can we say that it exists at any particular time.

Now, everything that can be grasped by the senses or by introspection exists at some particular time. The relation “north of” is therefore fundamentally different from such things. It is neither in space nor in time, neither material nor mental. Yet it is something.

The very unusual kind of being that belongs to universals is largely what has led many people to suppose that universals are really mental. We can think of a universal, and our thinking then exists in a perfectly ordinary sense, like any other mental act.

Suppose, for example, that we are thinking of whiteness. In one sense, it may then be said that whiteness is “in our mind.” This is the same ambiguity we noted when discussing Berkeley in Chapter IV. Strictly speaking, it is not whiteness that is in our mind, but the act of thinking of whiteness.

The related ambiguity in the word “idea,” which we noted at the same time, also causes confusion here. In one sense of the word, it means the object of an act of thought, and in that sense whiteness is an “idea.”

If we do not guard against this ambiguity, we may come to think that whiteness is an “idea” in the other sense, meaning an act of thought. That is how we come to think that whiteness is mental.

But thinking this way strips whiteness of its essential feature, which is universality. One person’s act of thought is necessarily a different thing from another person’s. And one person’s act of thought at one time is necessarily different from that same person’s act of thought at another time.

So if whiteness were the thought rather than its object, no two different people could think of it, and no one person could think of it twice.

What many different thoughts of whiteness have in common is their object, and this object is different from all of them. Universals, therefore, are not thoughts, although when they are known they are the objects of thoughts.

We will find it convenient to speak of things as existing only when they are in time. That is, a thing exists when we can point to some time at which it exists. This does not rule out the possibility that it exists at all times. In this sense, thoughts and feelings, minds and physical objects exist.

Universals, however, do not exist in this sense. We will say instead that they subsist, or have being, where “being” is contrasted with “existence” as being timeless. The world of universals, therefore, may also be described as the world of being.

The world of being is unchangeable, rigid, and exact. It delights the mathematician, the logician, the builder of metaphysical systems, and everyone who loves perfection more than life.

The world of existence is fleeting and vague, without sharp boundaries or any clear plan or arrangement. But it contains all thoughts and feelings, all the data of sense, and all physical objects. It contains everything that can do good or harm, and everything that makes any difference to the value of life and the world.

Depending on our temperaments, we will prefer to contemplate one world or the other. The one we do not prefer will probably seem to us a pale shadow of the one we do, hardly worth regarding as real in any sense.

But the truth is that both have an equal claim on our impartial attention. Both are real, and both are important to the metaphysician. In fact, as soon as we have distinguished the two worlds, we must consider how they are related to each other.

But first we must examine our knowledge of universals. That will be the subject of the following chapter. There we will find that it solves the problem of a priori knowledge, the problem that first led us to consider universals.

CHAPTER X. ON OUR KNOWLEDGE OF UNIVERSALS

Consider one person’s knowledge at a given time. Universals, like particulars, can be divided into three groups: those known by acquaintance, those known only by description, and those known neither by acquaintance nor by description.

Let us first consider knowledge of universals by acquaintance. To begin with, we are obviously acquainted with universals such as white, red, black, sweet, sour, loud, and hard. These are qualities that appear in sense-data.

When we see a white patch, we are acquainted in the first place with that particular patch. But by seeing many white patches, we easily learn to abstract the whiteness they all have in common. In learning to do this, we are becoming acquainted with whiteness.

A similar process makes us acquainted with any other universal of the same kind. Universals of this kind may be called “sensible qualities.” They can be grasped with less effort of abstraction than any others, and they seem less far removed from particulars than other universals are.

We come next to relations. The easiest relations to grasp are those that hold between the different parts of a single complex sense-datum.

For example, I can see at a glance the whole page on which I am writing, so the whole page is included in one sense-datum. But I perceive that some parts of the page are to the left of other parts, and some parts are above other parts.

In this case, the process of abstraction seems to go roughly as follows. I see, one after another, a number of sense-data in which one part is to the left of another. As with the different white patches, I perceive that all these sense-data have something in common.

By abstraction, I find that what they have in common is a certain relation between their parts, namely the relation I call “being to the left of.” In this way I become acquainted with the universal relation.

In the same way, I become aware of the relation of before and after in time. Suppose I hear a chime of bells. When the last bell of the chime sounds, I can keep the whole chime before my mind, and I can perceive that the earlier bells came before the later ones.

Also, in memory, I perceive that what I am remembering came before the present time. From either of these sources I can abstract the universal relation of before and after, just as I abstracted the universal relation “being to the left of.” So time-relations, like space-relations, are among those we are acquainted with.

Another relation we come to know in much the same way is resemblance. If I see two shades of green at the same time, I can see that they resemble each other.

If I also see a shade of red at the same time, I can see that the two greens resemble each other more than either resembles the red. In this way I become acquainted with the universal resemblance, or similarity.

Between universals, as between particulars, there are relations that we can be immediately aware of. We have just seen that we can perceive that the resemblance between two shades of green is greater than the resemblance between a shade of red and a shade of green.

Here we are dealing with a relation, namely “greater than,” between two relations. Knowing such relations requires more power of abstraction than perceiving the qualities of sense-data. Yet this knowledge seems just as immediate, and, at least in some cases, just as impossible to doubt. So there is immediate knowledge about universals as well as about sense-data.

Let us now return to the problem of a priori knowledge, which we left unsolved when we began considering universals. We are now in a position to deal with it far more satisfactorily than before.

Go back to the proposition “two and two are four.” Given what has been said, it is fairly obvious that this proposition states a relation between the universal “two” and the universal “four.”

This suggests a proposition that we will now try to establish: All a priori knowledge deals exclusively with the relations of universals. This proposition is of great importance, and it goes a long way toward solving our earlier difficulties about a priori knowledge.

The only case where our proposition might at first seem untrue is when an a priori proposition states that all members of one class of particulars belong to some other class. Equivalently, it states that all particulars with one property also have another property. In that case, it might seem that we are dealing with the particulars that have the property, rather than with the property itself.

The proposition “two and two are four” is actually a case of this kind. It can be stated as “any two and any other two are four,” or as “any collection formed of two twos is a collection of four.” If we can show that statements like this really deal only with universals, our proposition may be regarded as proved.

One way to discover what a proposition deals with is to ask which words we must understand in order to see what it means. Put differently, we ask which objects we must be acquainted with. Once we see what a proposition means, even before we know whether it is true or false, we must clearly be acquainted with whatever the proposition really deals with.

Applying this test shows that many propositions that seem to be about particulars are really about universals alone. Take “two and two are four,” even when we interpret it as “any collection formed of two twos is a collection of four.” We can plainly understand it, in the sense of seeing what it asserts, as soon as we know what is meant by “collection,” “two,” and “four.”

We do not need to know all the couples in the world. If we did, we obviously could never understand the proposition, since couples are infinitely numerous and cannot all be known to us. Our general statement does imply statements about particular couples, once we know that such couples exist. But the statement itself does not assert or imply that any such couples exist.

It therefore makes no statement at all about any actual particular couple. The statement is about “couple,” the universal, and not about this couple or that one.

The statement “two and two are four” therefore deals exclusively with universals. Anyone who is acquainted with the universals concerned, and who can perceive the relation between them that the statement asserts, can know it. When we reflect on our knowledge, we find that we sometimes have the power to perceive such relations between universals. We must accept this as a fact. It follows that we can sometimes know general a priori propositions, such as those of arithmetic and logic.

When we considered such knowledge earlier, what seemed mysterious was that it appeared to anticipate experience and control it in advance. We can now see that this impression was an error. No fact about anything that can be experienced can be known independently of experience.

We know a priori that two things and two other things together make four things. But we do not know a priori that if Brown and Jones are two, and Robinson and Smith are two, then Brown, Jones, Robinson, and Smith are four. We cannot understand this proposition at all unless we know that there are such people as Brown, Jones, Robinson, and Smith. We can know that only by experience.

So although our general proposition is a priori, all its applications to actual particulars involve experience and therefore contain an empirical element. What seemed mysterious about our a priori knowledge turns out to have rested on an error.

The point becomes clearer if we contrast a genuine a priori judgement with an empirical generalization, such as “all men are mortals.” Here, as before, we understand what the proposition means as soon as we understand the universals involved, namely man and mortal. We obviously do not need to be individually acquainted with the whole human race in order to understand it.

So the difference between an a priori general proposition and an empirical generalization does not lie in the meaning of the proposition. It lies in the kind of evidence we have for it. In the empirical case, the evidence consists of particular instances. We believe that all men are mortal because we know of innumerable instances of men dying, and of no instances of men living beyond a certain age.

We do not believe it because we see a connection between the universal man and the universal mortal. Admittedly, physiology might prove, by assuming the general laws that govern living bodies, that no living organism can last forever. That proof would connect man with mortality, and we could then assert our proposition without appealing to the specific evidence of men dying.

But that would only mean that our generalization had been brought under a wider generalization. The evidence for the wider generalization is still of the same kind, though there is more of it.

The progress of science constantly brings narrower generalizations under wider ones in this way. As a result, scientific generalizations rest on an ever wider inductive basis. This gives a greater degree of certainty, but not a different kind of certainty. The ultimate ground remains inductive, meaning derived from instances. It is not an a priori connection of universals like the connections we find in logic and arithmetic.

Two opposite points should be noted about a priori general propositions. The first is that, if many particular instances are known, we may first reach the general proposition by induction. We may perceive the connection of universals only later.

For example, it is known that if we draw a perpendicular from each angle of a triangle to the opposite side, all three perpendiculars meet at a single point. Someone might well reach this proposition first by actually drawing perpendiculars in many cases and finding that they always met at a point. That experience might then lead them to look for the general proof and find it. Every mathematician commonly meets with cases like this.

The second point is more interesting and has greater philosophical importance. We may sometimes know a general proposition even when we do not know a single instance of it. Consider the following case. We know that any two numbers can be multiplied together to give a third number, called their product.

We also know that every pair of integers whose product is less than 100 has actually been multiplied, and that the value of each product has been recorded in the multiplication table. But we know as well that the number of integers is infinite. Only a finite number of pairs of integers ever have been or ever will be thought of by human beings.

It follows that there are pairs of integers that never have been and never will be thought of by human beings. All of these pairs consist of integers whose product is over 100. We thus arrive at this proposition: “All products of two integers, which never have been and never will be thought of by any human being, are over 100.”

The truth of this general proposition is undeniable. Yet, by the very nature of the case, we can never give an instance of it. Any two numbers we might think of are excluded by the terms of the proposition itself.

People often deny that we can know general propositions of which no instance can be given. They deny it because they do not see that such knowledge requires only knowledge of the relations of universals. It does not require knowledge of any instances of those universals. Yet knowledge of such general propositions is essential to much of what is generally admitted to be known.

For example, we saw in our early chapters that we know physical objects, as opposed to sense-data, only by inference. Physical objects are not things we are acquainted with. So we can never know any proposition of the form “this is a physical object,” where “this” is something immediately known. It follows that, for everything we know about physical objects, no actual instance can be given.

We can give instances of the associated sense-data, but not of the actual physical objects. Our knowledge of physical objects therefore depends throughout on this possibility of general knowledge where no instance can be given. The same applies to our knowledge of other people’s minds, and to any other class of things of which we know no instance by acquaintance.

We can now survey the sources of our knowledge as they have appeared in the course of our analysis. First, we must distinguish knowledge of things from knowledge of truths. Each comes in two kinds, one immediate and one derivative.

Our immediate knowledge of things, which we called acquaintance, comes in two sorts, depending on whether the things known are particulars or universals. Among particulars, we are acquainted with sense-data and (probably) with ourselves. Among universals, there seems to be no principle for deciding which ones can be known by acquaintance. But those that clearly can be known this way include sensible qualities, relations of space and time, similarity, and certain abstract logical universals.

Our derivative knowledge of things, which we call knowledge by description, always involves both acquaintance with something and knowledge of truths.

Our immediate knowledge of truths may be called intuitive knowledge, and the truths known this way may be called self-evident truths. They include truths that merely state what is given in sense. They also include certain abstract logical and arithmetical principles, and, though with less certainty, some ethical propositions. Our derivative knowledge of truths consists of everything we can deduce from self-evident truths by using self-evident principles of deduction.

If this account is correct, all our knowledge of truths depends on our intuitive knowledge. It therefore becomes important to consider the nature and scope of intuitive knowledge, much as we earlier considered the nature and scope of knowledge by acquaintance.

But knowledge of truths raises a further problem that does not arise for knowledge of things: the problem of error. Some of our beliefs turn out to be mistaken. We must therefore consider how, if at all, we can distinguish knowledge from error.

This problem does not arise for knowledge by acquaintance. Whatever the object of acquaintance may be, even in dreams and hallucinations, no error is involved as long as we do not go beyond the immediate object. Error can arise only when we treat the immediate object, the sense-datum, as the sign of some physical object.

The problems connected with knowledge of truths are therefore more difficult than those connected with knowledge of things. As the first of these problems, let us examine the nature and scope of our intuitive judgements.

CHAPTER XI. ON INTUITIVE KNOWLEDGE

There is a common impression that everything we believe ought to be capable of proof, or at least of being shown to be highly probable. Many people feel that a belief for which no reason can be given is an unreasonable belief. In the main, this view is correct. Almost all our ordinary beliefs are either inferred from other beliefs or could be inferred from them. Those other beliefs can be regarded as giving the reason for them.

As a rule, we have forgotten the reason, or it was never consciously present to our minds at all. Few of us ever ask, for example, what reason there is to suppose that the food we are about to eat will not turn out to be poison. Yet when challenged, we feel that a perfectly good reason could be found, even if we cannot produce it at the moment. And in this belief we are usually justified.

But imagine some insistent Socrates who, whatever reason we give him, keeps demanding a reason for that reason. Sooner or later, and probably before very long, we will be driven to a point where we cannot find any further reason. At that point it becomes almost certain that no further reason could be discovered even in theory.

Starting from the ordinary beliefs of daily life, we can be pushed back step by step. Eventually we reach some general principle, or some instance of a general principle, that seems luminously evident and cannot itself be deduced from anything more evident. In most questions of daily life, such as whether our food is likely to be nourishing rather than poisonous, we will be driven back to the inductive principle, which we discussed in Chapter VI.

Beyond that principle, there seems to be no further step back. We constantly use the principle itself in our reasoning, sometimes consciously and sometimes unconsciously. But no reasoning that starts from some simpler self-evident principle leads to the principle of induction as its conclusion. The same holds for other logical principles. Their truth is evident to us, and we use them in constructing proofs. But they themselves, or at least some of them, cannot be proved.

Self-evidence, however, is not limited to the general principles that cannot be proved. Once a certain number of logical principles have been accepted, the rest can be deduced from them. Yet the deduced propositions are often just as self-evident as those assumed without proof.

Moreover, all of arithmetic can be deduced from the general principles of logic. Even so, the simple propositions of arithmetic, such as “two and two are four,” are just as self-evident as the principles of logic.

It also appears, though this is more open to dispute, that some ethical principles are self-evident, such as “we ought to pursue what is good.”

With every general principle, particular instances involving familiar things are more evident than the principle itself. The law of contradiction, for example, states that nothing can both have a certain property and not have it. This is evident as soon as it is understood. But it is not as evident as the fact that a particular rose we are looking at cannot be both red and not red.

Some cases may seem to be exceptions. Parts of the rose might be red and other parts not red. Or the rose might be a shade of pink that we hardly know whether to call red.

In the first case, the rose as a whole is plainly not red. In the second, the answer is theoretically definite once we settle on a precise definition of “red.”

We usually come to see a general principle through particular instances. Only people practiced in handling abstractions can easily grasp a general principle without the help of examples.

Besides general principles, the other kind of self-evident truth comes directly from sensation. We will call these “truths of perception,” and the judgements that express them “judgements of perception.” Some care is needed, however, to identify exactly which truths are self-evident here.

The sense-data themselves are neither true nor false. A particular patch of color that I see simply exists. It is not the sort of thing that can be true or false.

It is true that there is such a patch. It is true that the patch has a certain shape and brightness, and true that certain other colors surround it. But the patch itself, like everything else in the world of sense, is radically different in kind from the things that are true or false. So it cannot properly be called true. Whatever self-evident truths our senses provide must therefore be different from the sense-data they come from.

There seem to be two kinds of self-evident truths of perception, though in the final analysis the two may merge into one.

The first kind simply asserts that the sense-datum exists, without analyzing it at all. We see a patch of red, and we judge “there is such-and-such a patch of red,” or more strictly, “there is that.” This is one kind of intuitive judgement of perception.

The second kind arises when the object of sense is complex and we analyze it to some degree. If we see a round patch of red, for instance, we may judge “that patch of red is round.” This is also a judgement of perception, but it differs from the first kind.

Here we have a single sense-datum that has both color and shape: the color is red and the shape is round. Our judgement breaks the datum down into color and shape, then puts them back together by stating that the red color is round in shape.

Another example of this kind is “this is to the right of that,” where “this” and “that” are seen at the same moment. In judgements of this kind, the sense-datum contains parts that stand in some relation to one another, and the judgement asserts that they stand in that relation.

Judgements of memory form another class of intuitive judgements. They resemble judgements of sense, yet they are quite distinct from them.

The nature of memory is easily confused. Remembering an object tends to be accompanied by an image of it, and yet the image cannot be what constitutes the memory. This becomes clear once we notice that the image exists in the present, while what we remember is known to belong to the past.

Moreover, we can to some extent compare our image with the remembered object. We therefore often know, within fairly wide limits, how accurate the image is. This would be impossible unless the object itself, as distinct from the image, were somehow before the mind.

The essence of memory, then, is not the image. It is having an object immediately before the mind and recognizing that object as past.

Without memory in this sense, we would not know that there had ever been a past at all. We could no more understand the word “past” than someone born blind can understand the word “light.” There must therefore be intuitive judgements of memory, and all our knowledge of the past ultimately depends on them.

Memory raises a difficulty, however. It is notoriously unreliable, and so it casts doubt on whether intuitive judgements in general can be trusted. This is no small difficulty. But let us first narrow its scope as much as possible.

Broadly speaking, memory is trustworthy in proportion to how vivid the experience was and how recent it is. If the house next door was struck by lightning half a minute ago, my memory of what I saw and heard will be so reliable that it would be absurd to doubt whether there had been a flash at all.

The same holds for less vivid experiences, as long as they are recent. I am absolutely certain that half a minute ago I was sitting in the same chair I am sitting in now.

Going back over the day, I find some things I am quite certain of and others I am almost certain of. There are things I can become certain of by thinking and by recalling the surrounding circumstances. And there are some things I am not at all certain of.

I am quite certain that I ate breakfast this morning. But if I were as indifferent to my breakfast as a philosopher ought to be, I would be doubtful.

As for the conversation at breakfast, I can recall some of it easily and some only with effort. Some I recall with a large element of doubt, and some not at all. So there is a continuous gradation in how self-evident my memories are, and a matching gradation in how trustworthy my memory is.

The first answer to the problem of unreliable memory, then, is that memory has degrees of self-evidence. These degrees match its degrees of trustworthiness. They reach their limit, perfect self-evidence and perfect trustworthiness, in our memory of events that are recent and vivid.

There do seem to be cases, however, in which someone firmly believes a memory that is entirely false. In these cases, what is really remembered, in the sense of being immediately before the mind, is probably something other than what is falsely believed, though something usually connected with it.

George IV is said to have eventually believed that he had been at the battle of Waterloo, because he had said so many times. What he immediately remembered was his repeated assertion.

His belief in what he was asserting, if he really held it, would have been produced by association with the remembered assertion. It would therefore not be a genuine case of memory. Probably all cases of false memory can be handled this way: they can be shown not to be memory in the strict sense at all.

The case of memory makes one important point about self-evidence clear: self-evidence comes in degrees. It is not a quality that is simply present or absent. It can be more or less present, in gradations ranging from absolute certainty down to an almost imperceptible faintness.

Truths of perception and some principles of logic have the very highest degree of self-evidence. Truths of immediate memory have an almost equally high degree.

The inductive principle is less self-evident than some other principles of logic, such as “what follows from a true premise must be true.” Memories become less self-evident as they grow more distant and faint.

Broadly speaking, the truths of logic and mathematics become less self-evident as they grow more complicated. Judgements of intrinsic ethical or aesthetic value tend to have some self-evidence, but not much.

Degrees of self-evidence matter for the theory of knowledge. It seems likely that a proposition can have some degree of self-evidence without being true. If so, we need not abandon every connection between self-evidence and truth. We need only say that, where there is a conflict, we should keep the more self-evident proposition and reject the less self-evident one.

It seems highly probable, however, that “self-evidence,” as explained above, combines two different notions. One corresponds to the highest degree of self-evidence and is really an infallible guarantee of truth. The other corresponds to all the lower degrees. It gives no infallible guarantee, only a stronger or weaker presumption of truth.

This is only a suggestion, and we cannot develop it further yet. Once we have dealt with the nature of truth, we will return to self-evidence in connection with the distinction between knowledge and error.

CHAPTER XII. TRUTH AND FALSEHOOD

Our knowledge of truths, unlike our knowledge of things, has an opposite, namely error. With things, we may know them or not know them. But there is no positive state of mind that can be called mistaken knowledge of things, at least as long as we limit ourselves to knowledge by acquaintance.

Whatever we are acquainted with must be something. We may draw wrong inferences from our acquaintance, but the acquaintance itself cannot deceive us. So acquaintance involves no dualism of correct and mistaken.

Knowledge of truths, by contrast, does involve such a dualism. We may believe what is false as well as what is true. We know that on a great many subjects, different people hold different and incompatible opinions, so some beliefs must be mistaken.

Mistaken beliefs are often held just as firmly as true ones. This makes it hard to say how the two are to be told apart. How can we know, in any given case, that our belief is not mistaken? This question is extremely difficult, and no completely satisfactory answer to it is possible.

There is, however, a preliminary question that is somewhat less difficult: what do we mean by truth and falsehood? This chapter considers that preliminary question.

Here we are not asking how we can know whether a belief is true or false. We are asking what it means to ask whether a belief is true or false. A clear answer to this may, we hope, help us later to find out which beliefs are true.

For now, however, we ask only “What is truth?” and “What is falsehood?” We do not ask “Which beliefs are true?” and “Which beliefs are false?” It is very important to keep these questions entirely separate. Any confusion between them is sure to produce an answer that does not really apply to either.

In trying to discover the nature of truth, we must observe three points. Any theory must meet three requirements.

(1) Our theory of truth must allow for its opposite, falsehood. Many philosophers have failed to meet this condition adequately. They have built theories according to which all our thinking should have been true, and then had great difficulty finding a place for falsehood.

In this respect, our theory of belief must differ from our theory of acquaintance. With acquaintance, there was no opposite we needed to account for.

(2) It seems fairly evident that if there were no beliefs, there could be no falsehood. Nor could there be truth, in the sense in which truth is paired with falsehood.

Imagine a world of nothing but matter. Such a world would have no room for falsehood. It would contain what we might call “facts,” but it would not contain any truths, in the sense in which truths are things of the same kind as falsehoods.

Truth and falsehood are, in fact, properties of beliefs and statements. A world of mere matter would contain no beliefs or statements, and so it would also contain no truth or falsehood.

(3) Against what we have just said, however, the truth or falsehood of a belief always depends on something outside the belief itself.

If I believe that Charles I died on the scaffold, my belief is true. It is not true because of some inner quality that could be discovered just by examining the belief. It is true because of a historical event that happened two and a half centuries ago.

If I believe that Charles I died in his bed, my belief is false. No amount of vividness in the belief, or care in arriving at it, can keep it from being false. Again, this is because of what happened long ago, not because of any inner property of my belief.

So although truth and falsehood are properties of beliefs, they depend on how beliefs relate to other things, not on any internal quality of the beliefs themselves.

The third of these requirements leads us to adopt the view that truth consists in some form of correspondence between belief and fact. On the whole, this has been the most common view among philosophers. It is by no means easy, however, to find a form of correspondence that is free of objections that cannot be answered.

Partly for this reason, and partly from a further worry, many philosophers have tried to define truth without relating it to anything wholly outside belief. The worry is this: if truth consists in thought corresponding with something outside thought, then thought can never know when it has reached the truth.

The most important attempt at a definition of this kind is the theory that truth consists in coherence. On this view, the mark of falsehood is a failure to fit together with the rest of our beliefs. The essence of a truth is to form part of the completely rounded system which is The Truth.

There is, however, a great difficulty in this view, or rather two great difficulties. The first is that there is no reason to suppose that only one coherent body of beliefs is possible. A novelist with enough imagination might invent a past for the world that fits perfectly with everything we know, and yet is quite different from the real past.

In more scientific matters, it is certain that two or more hypotheses often account for all the known facts on some subject. In such cases, scientists try to find facts that will rule out every hypothesis but one. There is no reason, however, why they should always succeed.

In philosophy, too, it seems fairly common for two rival hypotheses both to account for all the facts. It is possible, for example, that life is one long dream, and that the outer world is only as real as the objects in dreams.

Such a view does not seem inconsistent with the known facts. Yet there is no reason to prefer it to the common-sense view, according to which other people and things really exist. Coherence therefore fails as a definition of truth, because there is no proof that only one coherent system can exist.

The second objection is that this definition assumes we already know what “coherence” means. In fact, coherence presupposes that the laws of logic are true. Two propositions are coherent when both may be true. They are incoherent when at least one of them must be false.

To know whether two propositions can both be true, we must already know truths such as the law of contradiction. For example, the propositions “this tree is a beech” and “this tree is not a beech” are not coherent. They fail to cohere because of the law of contradiction.

Now suppose we subjected the law of contradiction itself to the test of coherence. If we chose to suppose it false, nothing would be incoherent with anything else any longer. The laws of logic supply the skeleton or framework within which the test of coherence operates. They cannot themselves be established by that test.

For these two reasons, coherence cannot be accepted as giving the meaning of truth. It is, however, often a most important test of truth, once a certain amount of truth has become known.

We are therefore driven back to correspondence with fact as what makes up the nature of truth. It remains to define precisely what we mean by “fact,” and what kind of correspondence must hold between belief and fact for a belief to be true.

In keeping with our three requirements, we must look for a theory of truth that:

1. allows truth to have an opposite, namely falsehood;
2. makes truth a property of beliefs; but
3. makes it a property that depends wholly on the relation of beliefs to things outside them.

The need to allow for falsehood makes it impossible to treat belief as a relation of the mind to a single object, which could be called “what is believed.” If belief were understood this way, it would be like acquaintance. It would not allow for the opposition of truth and falsehood, and would have to be always true.

Examples make this clear. Othello falsely believes that Desdemona loves Cassio. We cannot say that this belief consists in a relation to a single object, “Desdemona’s love for Cassio.” If there were such an object, the belief would be true.

In fact there is no such object, so Othello cannot have any relation to it. His belief, therefore, cannot possibly consist in a relation to this object.

Someone might say that his belief is a relation to a different object, namely “that Desdemona loves Cassio.” But when Desdemona does not love Cassio, it is almost as hard to suppose that such an object exists as it was to suppose that “Desdemona’s love for Cassio” exists. It is better, then, to look for a theory of belief that does not make it a relation of the mind to a single object.

People commonly think of relations as always holding between two terms, but this is not always so. Some relations require three terms, some four, and so on. Take the relation “between.” With only two terms, this relation is impossible. Three terms is the smallest number that makes it possible.

York is between London and Edinburgh. But if London and Edinburgh were the only places in the world, nothing could be between one place and another. Similarly, jealousy requires three people. There can be no such relation that does not involve at least three.

A proposition such as “A wishes B to promote C’s marriage with D” involves a relation of four terms. A, B, C, and D all come into it, and the relation cannot be expressed in any form that leaves out any of the four.

Examples could be multiplied indefinitely. But enough has been said to show that some relations require more than two terms before they can occur.

If falsehood is to be properly allowed for, the relation involved in judging or believing must be taken as a relation between several terms, not two. When Othello believes that Desdemona loves Cassio, he must not have before his mind a single object, such as “Desdemona’s love for Cassio” or “that Desdemona loves Cassio.”

That would require objective falsehoods, existing independently of any minds. This theory cannot be refuted by logic, but it is one to avoid if possible.

It is easier to account for falsehood if we take judgement to be a relation in which the mind and each of the objects concerned appear separately. Desdemona, loving, and Cassio must all be terms in the relation that holds when Othello believes that Desdemona loves Cassio. Since Othello is also a term, this is a relation of four terms.

In calling it a relation of four terms, we do not mean that Othello has a certain relation to Desdemona, and the same relation to loving, and again to Cassio. That may be true of some other relation, but not of believing.

Believing is plainly not a relation Othello has to each of the three terms one at a time. It is a relation to all of them together. Only one instance of the relation of believing is involved, but this one instance knits together four terms.

So what actually happens, at the moment Othello holds his belief, is this: the relation called “believing” is knitting together the four terms Othello, Desdemona, loving, and Cassio into one complex whole.

What we call belief or judgement is nothing but this relation of believing or judging, which relates a mind to several things other than itself. An act of belief or judgement is the occurrence of this relation between certain terms at some particular time.

We can now understand what distinguishes a true judgement from a false one. For this purpose, we will adopt certain definitions. In every act of judgement there is a mind that judges, and there are terms about which it judges.

We will call the mind the subject of the judgement, and the remaining terms the objects. When Othello judges that Desdemona loves Cassio, Othello is the subject, and the objects are Desdemona, loving, and Cassio. The subject and objects together are called the constituents of the judgement.

Notice that the relation of judging has what is called a “sense” or “direction.” Speaking metaphorically, it puts its objects in a certain order. We can indicate that order by the order of words in a sentence. In an inflected language, the same thing is shown by inflections, such as the difference between nominative and accusative.

Othello’s judgement that Cassio loves Desdemona differs from his judgement that Desdemona loves Cassio, even though both have the same constituents. The difference is that the relation of judging places the constituents in a different order in each case.

Similarly, if Cassio judges that Desdemona loves Othello, the constituents are still the same, but their order is different.

The relation of judging shares this property of having a “sense” or “direction” with all other relations. The “sense” of relations is the ultimate source of order, of series, and of a host of mathematical concepts. We need not pursue this aspect further here.

We described the relation of “judging” or “believing” as knitting the subject and objects together into one complex whole. In this respect, judging is exactly like every other relation. Whenever a relation holds between two or more terms, it unites them into a complex whole.

If Othello loves Desdemona, there is such a complex whole as “Othello’s love for Desdemona.” The terms united by a relation may themselves be complex or simple, but the whole that results from their union must be complex.

Wherever a relation relates certain terms, there is a complex object formed by the union of those terms. Conversely, wherever there is a complex object, there is a relation that relates its constituents.

When an act of believing occurs, there is a complex in which “believing” is the uniting relation. The subject and objects are arranged in a certain order by the “sense” of that relation.

As we saw with “Othello believes that Desdemona loves Cassio,” one of the objects must itself be a relation. In this instance it is “loving.” But “loving,” as it occurs in the act of believing, is not the relation that creates the unity of the whole made up of subject and objects.

In the act of believing, the relation “loving” is one of the objects. It is a brick in the structure, not the cement. The cement is the relation “believing.”

When the belief is true, there is another complex unity. In it, the relation that was one of the objects of the belief now relates the other objects.

If Othello believes truly that Desdemona loves Cassio, then there is a complex unity, “Desdemona’s love for Cassio.” It is made up only of the objects of the belief, in the same order they had in the belief. The relation that was one of the objects now appears as the cement binding together the other objects.

When a belief is false, on the other hand, there is no such complex unity composed only of the objects of the belief. If Othello falsely believes that Desdemona loves Cassio, then there is no such complex unity as “Desdemona’s love for Cassio.”

A belief, then, is true when it corresponds to a certain associated complex, and false when it does not. To be definite, assume the objects of the belief are two terms and a relation, with the terms put in a certain order by the “sense” of the believing.

If the two terms, in that order, are united by the relation into a complex, the belief is true. If not, it is false.

This is the definition of truth and falsehood we were looking for. Judging or believing is a certain complex unity of which a mind is a constituent. If the remaining constituents, taken in the order they have in the belief, form a complex unity, then the belief is true. If not, it is false.

So although truth and falsehood are properties of beliefs, they are in a sense external properties. The condition for a belief’s truth does not involve beliefs, or, in general, any mind at all. It involves only the objects of the belief.

A mind that believes believes truly when there is a corresponding complex that involves not the mind but only its objects. This correspondence ensures truth, and its absence means falsehood.

This accounts at once for two facts about beliefs: (a) they depend on minds for their existence, and (b) they do not depend on minds for their truth.

We may restate our theory as follows. Take the belief “Othello believes that Desdemona loves Cassio.” We will call Desdemona and Cassio the object-terms, and loving the object-relation.

Suppose there is a complex unity, “Desdemona’s love for Cassio,” made up of the object-terms related by the object-relation in the same order they have in the belief. This complex unity is called the fact corresponding to the belief. A belief is true when there is a corresponding fact, and false when there is no corresponding fact.

It follows that minds do not create truth or falsehood. They create beliefs. But once a belief has been created, the mind cannot make it true or false, except in one special case: when the belief concerns future things that are within the believer’s power, such as catching a train.

What makes a belief true is a fact. Except in exceptional cases, this fact does not involve the mind of the person who holds the belief in any way.

Now that we have decided what we mean by truth and falsehood, we must next consider what ways there are of knowing whether a given belief is true or false. That question will occupy the next chapter.

CHAPTER XIII. KNOWLEDGE, ERROR, AND PROBABLE OPINION

In the preceding chapter we considered what we mean by truth and falsehood. That question is much less interesting than the question of how we can know what is true and what is false, which will occupy us in this chapter.

There is no doubt that some of our beliefs are mistaken. This leads us to ask what certainty we can ever have that any particular belief is not mistaken. Can we ever know anything at all, or do we merely believe what is true sometimes, by good luck?

Before we can tackle this question, however, we must first decide what we mean by “knowing.” This is not as easy as one might suppose.

At first sight, we might imagine that knowledge could be defined as “true belief.” When what we believe is true, we might suppose we have achieved knowledge of it. But this would not match the way the word is commonly used.

Take a very trivial example. Suppose a man believes that the last name of the late Prime Minister began with a B. He believes something true, since the late Prime Minister was Sir Henry Campbell Bannerman.

But suppose he believes this because he thinks Mr. Balfour was the late Prime Minister. He still believes that the late Prime Minister’s name began with a B. Yet this belief, though true, would not be thought to count as knowledge.

Or suppose a newspaper makes an intelligent guess and announces the result of a battle before any telegram reporting the result has arrived. By good fortune, it may announce what later turns out to be the right result, and some of its less experienced readers may believe it. Yet even though their belief is true, they cannot be said to have knowledge.

So it is clear that a true belief is not knowledge when it is deduced from a false belief.

In the same way, a true belief cannot be called knowledge when it is reached by faulty reasoning, even if the premises it starts from are true.

Suppose I know that all Greeks are men and that Socrates was a man, and I infer that Socrates was a Greek. I cannot be said to know that Socrates was a Greek. My premises and my conclusion are all true, but the conclusion does not follow from the premises.

Should we then say that nothing is knowledge except what is validly deduced from true premises? Obviously not. Such a definition is both too wide and too narrow.

First, it is too wide, because it is not enough for our premises to be true; they must also be known. The man who believes that Mr. Balfour was the late Prime Minister may go on to draw valid deductions from the true premise that the late Prime Minister’s name began with a B. But he cannot be said to know the conclusions he reaches this way.

So we must amend our definition: knowledge is what is validly deduced from known premises. This, however, is circular. It assumes we already know what is meant by “known premises.” At best, then, it can define only one kind of knowledge, the kind we call derivative, as opposed to intuitive knowledge.

We may say: “Derivative knowledge is what is validly deduced from premises known intuitively.” This statement has no formal flaw, but it still leaves intuitive knowledge undefined.

Setting intuitive knowledge aside for the moment, let us consider this proposed definition of derivative knowledge. The chief objection to it is that it limits knowledge too much.

It constantly happens that people hold a true belief that has grown up in them because of some piece of intuitive knowledge. The belief could be validly inferred from that intuitive knowledge. As a matter of fact, however, it was not inferred from it by any logical process.

Take, for example, the beliefs we get from reading. If the newspapers announce the death of the King, we are fairly well justified in believing that the King is dead, since this is the kind of announcement that would not be made if it were false. And we are fully justified in believing that the newspaper says the King is dead.

But here the intuitive knowledge on which our belief rests is knowledge of the existence of sense-data: the ones we get from looking at the printed news. This knowledge hardly reaches consciousness, except in someone who cannot read easily.

A child may be aware of the shapes of the letters and move gradually and painfully to grasping what they mean. But anyone used to reading goes straight to what the letters mean. Such a reader is not aware, except on reflection, that this knowledge came from the sense-data of seeing the printed letters.

So although a valid inference from the letters to their meaning is possible, and the reader could perform it, it is not in fact performed. The reader carries out no operation that could be called logical inference. Yet it would be absurd to say that the reader does not know that the newspaper announces the King’s death.

We must therefore count as derivative knowledge whatever results from intuitive knowledge, even by mere association, provided two conditions hold: there is a valid logical connection, and the person could become aware of that connection by reflection.

In fact, there are many ways besides logical inference by which we pass from one belief to another. The passage from the print to its meaning illustrates them. These ways may be called “psychological inference.”

We shall, then, accept psychological inference as a means of gaining derivative knowledge, provided there is a discoverable logical inference that runs parallel to the psychological one.

This makes our definition of derivative knowledge less precise than we could wish, since the word “discoverable” is vague. It does not tell us how much reflection may be needed to make the discovery.

But “knowledge” is not in fact a precise concept. It shades into “probable opinion,” as we shall see more fully later in this chapter. So we should not seek a very precise definition, since any such definition would be more or less misleading.

The chief difficulty about knowledge, however, arises not over derivative knowledge but over intuitive knowledge. As long as we are dealing with derivative knowledge, we can fall back on intuitive knowledge as a test. But with intuitive beliefs, it is far from easy to find any criterion for telling which are true and which are mistaken.

On this question we can hardly reach any very precise result. All our knowledge of truths is touched by some degree of doubt, and a theory that ignored this would plainly be wrong. Something can be done, however, to ease the difficulties of the question.

To begin with, our theory of truth makes it possible to single out certain truths as self-evident in a sense that guarantees they cannot be mistaken.

When a belief is true, we said, there is a corresponding fact in which the several objects of the belief form a single complex. The belief is said to be knowledge of this fact, provided it meets the further, somewhat vague conditions we have been considering in this chapter.

But with any fact, besides the knowledge that consists in belief, we may also have the kind of knowledge that consists in perception, taking this word in its widest possible sense.

For example, if you know the time of sunset, then at that time you can know the fact that the sun is setting. This is knowing the fact by way of knowledge of truths. But if the weather is fine, you can also look to the west and actually see the setting sun. You then know the same fact by way of knowledge of things.

So, in theory, there are two ways a complex fact may be known:

1. By a judgement, in which its several parts are judged to be related as they are in fact related.
2. By acquaintance with the complex fact itself. This may, in a broad sense, be called perception, though it is by no means confined to objects of the senses.

Notice that the second way, acquaintance, is possible only when there really is such a fact. The first way, like all judgement, is liable to error.

The second way gives us the complex whole. It is therefore possible only when the parts actually have the relation that makes them combine into such a complex.

The first way, by contrast, gives us the parts and the relation separately. It requires only that the parts and the relation be real. The relation may not in fact relate those parts in that way, and yet the judgement can still occur.

At the end of Chapter XI, we suggested that there might be two kinds of self-evidence: one giving an absolute guarantee of truth, the other only a partial guarantee. We can now tell these two kinds apart.

We may say that a truth is self-evident in the first and most absolute sense when we have acquaintance with the fact that corresponds to it.

When Othello believes that Desdemona loves Cassio, the corresponding fact, if his belief were true, would be “Desdemona’s love for Cassio.” No one but Desdemona could be acquainted with this fact. So in the sense of self-evidence we are now considering, the truth that Desdemona loves Cassio (if it were a truth) could be self-evident only to Desdemona.

All mental facts, and all facts about sense-data, share this privacy. There is only one person to whom they can be self-evident in our present sense, because only one person can be acquainted with the mental things or sense-data involved. So no fact about any particular existing thing can be self-evident to more than one person.

Facts about universals, on the other hand, do not have this privacy. Many minds may be acquainted with the same universals, so a relation between universals may be known by acquaintance to many different people.

Whenever we know by acquaintance a complex fact made up of certain terms in a certain relation, we say that the truth that these terms are so related has the first, or absolute, kind of self-evidence. In these cases, the judgement that the terms are so related must be true. This kind of self-evidence is therefore an absolute guarantee of truth.

But although this kind of self-evidence absolutely guarantees truth, it does not let us be absolutely certain, for any given judgement, that the judgement is true.

Suppose we first perceive the sun shining, which is a complex fact, and then go on to make the judgement “the sun is shining.” To pass from the perception to the judgement, we must analyse the complex fact we were given. We have to separate out “the sun” and “shining” as parts of the fact.

In this process it is possible to make a mistake. So even where a fact has the first, absolute kind of self-evidence, a judgement believed to correspond to that fact is not absolutely infallible, because it may not really correspond. But if it does correspond, in the sense explained in the preceding chapter, then it must be true.

The second kind of self-evidence belongs to judgements in the first place. It does not come from directly perceiving a fact as a single complex whole. This second kind has degrees, ranging from the very highest down to a mere inclination in favour of the belief.

Take, for example, a horse trotting away from us along a hard road. At first we are completely certain that we hear the hoofs. Gradually, if we listen closely, there comes a moment when we think perhaps it was our imagination, or the blind upstairs, or our own heartbeat.

At last we grow doubtful whether there was any noise at all. Then we think we no longer hear anything, and finally we know we no longer hear anything.

Throughout this process there is a continuous gradation of self-evidence, from the highest degree to the lowest. The gradation lies not in the sense-data themselves but in the judgements based on them.

Or consider another case. Suppose we are comparing two shades of colour, one blue and one green. We can be quite sure they are different shades. Now suppose the green is gradually changed to look more and more like the blue. It becomes first a blue-green, then a greenish blue, then blue.

At some point we will become doubtful whether we can see any difference. Then a moment comes when we know that we cannot see any difference. The same thing happens when tuning a musical instrument, or in any other case where there is a continuous gradation. So self-evidence of this second kind is a matter of degree. It seems plain that the higher degrees deserve more trust than the lower ones.

In derivative knowledge, our ultimate premisses must have some degree of self-evidence. So must their connection with the conclusions we deduce from them. Take a piece of reasoning in geometry. It is not enough that the axioms we start from are self-evident. At each step of the reasoning, the connection between premiss and conclusion must also be self-evident.

In difficult reasoning, this connection often has only a very small degree of self-evidence. That is why errors of reasoning are not unlikely where the difficulty is great.

From all this, a conclusion follows for both intuitive and derivative knowledge. Assume that intuitive knowledge is trustworthy in proportion to its degree of self-evidence. Then there will be a scale of trustworthiness. At the top are the existence of noteworthy sense-data and the simpler truths of logic and arithmetic, which may be taken as quite certain. At the bottom are judgements that seem only slightly more probable than their opposites.

We can now sort our beliefs. What we firmly believe, if it is true, is called knowledge, provided it is either intuitive or inferred (logically or psychologically) from intuitive knowledge from which it follows logically. What we firmly believe, if it is not true, is called error.

The rest may be called probable opinion. This includes whatever we firmly believe that is neither knowledge nor error. It also includes what we believe hesitantly, because it either lacks the highest degree of self-evidence or is derived from something that lacks it. So the greater part of what would commonly pass as knowledge is more or less probable opinion.

With probable opinion, coherence can help us a great deal. We rejected coherence as the definition of truth, but we may often use it as a test of truth. A body of opinions, each probable on its own, becomes more probable when the opinions fit together than any one of them would be individually.

This is how many scientific hypotheses gain their probability. They fit into a coherent system of probable opinions, and so become more probable than they would be in isolation. The same holds for general philosophical hypotheses. Taken in a single case, such a hypothesis may seem highly doubtful. Yet when we consider the order and coherence it brings to a mass of probable opinion, it can become nearly certain.

This applies in particular to the distinction between dreams and waking life. If our dreams, night after night, were as coherent with one another as our days are, we would hardly know whether to believe the dreams or the waking life. As things are, the test of coherence condemns the dreams and confirms the waking life.

But this test, although it increases probability where it succeeds, never gives absolute certainty unless there is already certainty at some point in the coherent system. Merely organizing probable opinion will never, by itself, turn it into knowledge beyond doubt.

CHAPTER XIV. THE LIMITS OF PHILOSOPHICAL KNOWLEDGE

So far in our discussion of philosophy, we have barely touched on many matters that take up a great deal of space in the writings of most philosophers. Most philosophers, or at any rate very many, claim to be able to prove certain things by a priori metaphysical reasoning. These include the fundamental doctrines of religion, the essential rationality of the universe, the illusory nature of matter, the unreality of all evil, and so on.

There can be no doubt that the hope of finding reasons to believe such theses has been the chief inspiration of many people who have studied philosophy all their lives. This hope, I believe, is vain. It seems that knowledge about the universe as a whole cannot be obtained through metaphysics.

Some proposed proofs claim that, because of the laws of logic, certain things must exist and certain others cannot. These proofs, it seems, cannot survive critical examination. In this chapter we will briefly consider how such reasoning is attempted, in order to find out whether we can hope it might be valid.

The great modern representative of the kind of view we want to examine was Hegel (1770–1831). Hegel’s philosophy is very difficult, and commentators disagree about how to interpret it. I shall adopt the interpretation held by many, if not most, commentators. It also has the merit of presenting an interesting and important type of philosophy.

On this interpretation, Hegel’s main thesis is that everything short of the Whole is obviously fragmentary. Each such thing is obviously incapable of existing without the completion supplied by the rest of the world. A comparative anatomist can look at a single bone and see what kind of animal the whole must have been. In the same way, according to Hegel, the metaphysician can look at any one piece of reality and see what the whole of reality must be, at least in its broad outlines.

Every apparently separate piece of reality has, so to speak, hooks that attach it to the next piece. The next piece in turn has new hooks, and so on, until the whole universe is reconstructed. According to Hegel, this essential incompleteness appears equally in the world of thought and in the world of things.

In the world of thought, take any idea that is abstract or incomplete. On examination, we find that if we forget its incompleteness, we become entangled in contradictions. These contradictions turn the idea into its opposite, or antithesis. To escape, we have to find a new, less incomplete idea, which is the synthesis of our original idea and its antithesis.

This new idea is less incomplete than the one we started with. Yet it too will turn out not to be wholly complete. It will pass into its own antithesis, with which it must be combined in a new synthesis. Hegel advances in this way until he reaches the ‘Absolute Idea’. According to him, this idea has no incompleteness, no opposite, and no need of further development.

The Absolute Idea is therefore adequate to describe Absolute Reality. All lower ideas describe reality only as it appears from a partial view, not as it is to someone who surveys the Whole all at once. Hegel thus concludes that Absolute Reality forms one single harmonious system. It is not in space or time, not evil to any degree, wholly rational, and wholly spiritual.

He believes that any appearance to the contrary in the world we know can be proved logically to be entirely due to our fragmentary, piecemeal view of the universe. If we saw the universe whole, as we may suppose God sees it, space and time and matter and evil and all striving and struggling would disappear. Instead, we would see an eternal, perfect, unchanging spiritual unity.

There is undeniably something sublime in this conception, something we might wish to agree with. Nevertheless, when the arguments supporting it are carefully examined, they seem to involve much confusion and many unjustified assumptions.

The basic principle on which the system is built is that what is incomplete cannot stand on its own. It must need the support of other things before it can exist. On this view, whatever has relations to things outside itself must contain some reference to those outside things in its own nature. It therefore could not be what it is if those outside things did not exist.

A man’s nature, for example, is made up of his memories and the rest of his knowledge, his loves and hatreds, and so on. So without the objects he knows or loves or hates, he could not be what he is. He is essentially and obviously a fragment. If he were taken as the whole of reality, he would be self-contradictory.

This whole point of view, however, depends on the notion of the ‘nature’ of a thing, which seems to mean ‘all the truths about the thing’. Of course, a truth connecting one thing with another could not hold if the other thing did not exist. But a truth about a thing is not part of the thing itself, even though, on this usage, it must be part of the thing’s ‘nature’.

If a thing’s ‘nature’ means all the truths about it, then clearly we cannot know a thing’s ‘nature’ unless we know all its relations to all the other things in the universe. But if the word is used in this sense, we will have to hold that a thing may be known when its ‘nature’ is not known, or at least not known completely.

When the word ‘nature’ is used this way, it confuses knowledge of things with knowledge of truths. We may know a thing by acquaintance even if we know very few propositions about it. In theory, we need not know any propositions about it at all. So acquaintance with a thing does not involve knowledge of its ‘nature’ in this sense.

And although knowing any one proposition about a thing involves acquaintance with the thing, it does not involve knowledge of its ‘nature’ in this sense. Two points follow. First, acquaintance with a thing does not logically involve knowledge of its relations. Second, knowledge of some of its relations does not involve knowledge of all its relations, nor knowledge of its ‘nature’ in this sense.

For example, I may be acquainted with my toothache. This knowledge may be as complete as knowledge by acquaintance can ever be. Yet I may not know everything the dentist, who is not acquainted with it, can tell me about its cause. So I do not know its ‘nature’ in this sense.

Thus the fact that a thing has relations does not prove that those relations are logically necessary. From the mere fact that a thing is the thing it is, we cannot deduce that it must have the various relations it actually has. It only seems to follow because we already know it has them.

It follows that we cannot prove that the universe as a whole forms a single harmonious system of the kind Hegel believes it forms. And if we cannot prove this, we also cannot prove the unreality of space, time, matter, and evil. Hegel deduces their unreality from the fragmentary and relational character of these things.

We are therefore left to investigate the world piece by piece, and we cannot know the character of those parts of the universe that lie far from our experience. This result will disappoint those whose hopes have been raised by the systems of philosophers. But it fits the inductive and scientific temper of our age, and it is supported by the whole examination of human knowledge in our previous chapters.

Most of the great, ambitious attempts of metaphysicians have tried to prove that certain apparent features of the actual world are self-contradictory, and therefore cannot be real. The whole tendency of modern thought, however, increasingly shows that these supposed contradictions were illusory. It also shows that very little can be proved a priori from considerations of what must be.

Space and time offer a good illustration. They appear to be infinite in extent and infinitely divisible. If we travel along a straight line in either direction, it is hard to believe we will finally reach a last point, beyond which there is nothing, not even empty space.

Similarly, if we travel backward or forward in time in imagination, it is hard to believe we will reach a first or last time, with not even empty time beyond it. So space and time appear to be infinite in extent.

Again, take any two points on a line. However small the distance between them, it seems evident that there must be other points between them. Every distance can be halved, the halves can be halved again, and so on ad infinitum. Similarly in time, however little time passes between two moments, it seems evident that there will be other moments between them. So space and time appear to be infinitely divisible.

But against these apparent facts, infinite extent and infinite divisibility, philosophers have offered arguments meant to show that there could be no infinite collections of things. If so, the number of points in space, or of instants in time, must be finite. A contradiction thus arose between the apparent nature of space and time and the supposed impossibility of infinite collections.

Kant, who first emphasized this contradiction, concluded that space and time are impossible, and declared them merely subjective. Since his time, very many philosophers have believed that space and time are mere appearance, and do not belong to the world as it really is.

Now, however, the work of mathematicians, especially Georg Cantor, has shown that the supposed impossibility of infinite collections was a mistake. Such collections are not in fact self-contradictory. They only contradict certain rather stubborn mental prejudices. So the reasons for regarding space and time as unreal no longer hold, and one of the great sources of metaphysical systems has dried up.

The mathematicians, however, have gone further than showing that space, as it is commonly imagined, is possible. They have also shown that many other forms of space are equally possible, as far as logic can tell.

Some of Euclid’s axioms seem necessary to common sense, and philosophers once assumed that they were necessary. We now know that this appearance of necessity comes merely from our familiarity with actual space, not from any a priori logical foundation.

By imagining worlds in which these axioms are false, mathematicians have used logic to loosen the prejudices of common sense. They have shown that there could be spaces that differ, some more and some less, from the space we live in.

Some of these spaces differ so little from Euclidean space, over distances of the size we can measure, that observation cannot settle the matter. We have no way of discovering whether our actual space is strictly Euclidean or one of these other kinds.

The situation has therefore been completely reversed. Formerly it seemed that experience left only one kind of space for logic to consider, and logic then showed that one kind to be impossible. Now logic presents many kinds of space as possible, independently of experience, and experience only partly decides between them.

Our knowledge of what is has turned out to be smaller than it was once thought to be. But our knowledge of what may be has grown enormously. Instead of being shut inside narrow walls, every nook and cranny of which could be explored, we find ourselves in an open world of free possibilities. Much remains unknown there because there is so much to know.

What happened with space and time has happened, to some extent, in other areas as well. The attempt to dictate to the universe by means of a priori principles has broken down. Logic was formerly a barrier to possibilities. It has now become the great liberator of the imagination.

Logic presents countless alternatives that unreflective common sense never considers. It leaves to experience the task of deciding, where a decision is possible, among the many worlds that logic offers for our choice.

As a result, knowledge about what exists is limited to what we can learn from experience. This is not the same as what we can actually experience. As we have seen, there is a great deal of knowledge by description about things we have never directly experienced.

But every case of knowledge by description requires some connection of universals. That connection is what allows us to infer, from a given datum, that an object of a certain kind exists, because the datum implies it.

Take physical objects as an example. The principle that sense-data are signs of physical objects is itself a connection of universals. Experience gives us knowledge of physical objects only by virtue of this principle. The same holds for the law of causality, or, to take something less general, for principles such as the law of gravitation.

Principles like the law of gravitation are proved, or rather made highly probable, by combining experience with some wholly a priori principle, such as the principle of induction.

Our intuitive knowledge, which is the source of all our other knowledge of truths, is therefore of two kinds. Pure empirical knowledge tells us that particular things we are acquainted with exist, and tells us some of their properties. Pure a priori knowledge gives us connections between universals. It lets us draw inferences from the particular facts that empirical knowledge supplies.

Our derivative knowledge always depends on some pure a priori knowledge, and it usually also depends on some pure empirical knowledge.

If what I have said is true, philosophical knowledge does not differ essentially from scientific knowledge. Philosophy has no special source of wisdom that is closed to science, and the results philosophy reaches are not radically different from the results of science.

The essential characteristic that makes philosophy a distinct study is criticism. Philosophy critically examines the principles used in science and in daily life. It searches out any inconsistencies in these principles. It accepts them only when a critical inquiry has turned up no reason to reject them.

Many philosophers have believed that the principles underlying the sciences, once freed from irrelevant detail, could give us knowledge about the universe as a whole. If that were so, such knowledge would have the same claim on our belief as scientific knowledge has.

Our inquiry, however, has revealed no such knowledge. So with respect to the special doctrines of the bolder metaphysicians, its result has been mainly negative.

With respect to what is commonly accepted as knowledge, though, our result is mainly positive. Our criticism has seldom given us reason to reject such knowledge. We have found no reason to think human beings incapable of the kind of knowledge they are generally believed to have.

When we call philosophy a criticism of knowledge, however, we must add a certain limitation. Suppose we take the attitude of the complete sceptic. We place ourselves wholly outside all knowledge, and from that outside position we demand to be forced back inside the circle of knowledge. We are then demanding the impossible, and our scepticism can never be refuted.

Every refutation must begin from some piece of knowledge that both sides of the dispute share. From blank doubt, no argument can begin. So if philosophy’s criticism of knowledge is to achieve any result, it must not be of this destructive kind.

No logical argument can be brought against this absolute scepticism. Still, it is not hard to see that scepticism of this kind is unreasonable.

Descartes’ “methodical doubt,” with which modern philosophy began, is not of this kind. It is rather the kind of criticism that we are claiming is the essence of philosophy.

His methodical doubt consisted in doubting whatever seemed doubtful. With each apparent piece of knowledge, he paused to ask himself whether, on reflection, he could feel certain that he really knew it. This is the kind of criticism that makes up philosophy.

Some knowledge, such as knowledge that our sense-data exist, seems entirely beyond doubt, however calmly and thoroughly we reflect on it. Philosophical criticism does not require us to withhold belief in such knowledge.

Other beliefs, however, are held only until we begin to reflect, and then melt away under close inquiry. One example is the belief that physical objects exactly resemble our sense-data. Philosophy will tell us to reject such beliefs unless some new line of argument is found to support them.

But it is not reasonable to reject beliefs that seem open to no objection, however closely we examine them. Philosophy does not recommend doing so.

In short, the criticism we aim at is not the kind that decides, without reason, to reject. It considers each piece of apparent knowledge on its merits, and it keeps whatever still appears to be knowledge once that consideration is complete.

We must admit that some risk of error remains, since human beings are fallible. Philosophy can fairly claim that it reduces the risk of error, and that in some cases it makes the risk so small that it can be ignored in practice.

More than this is not possible in a world where mistakes are bound to occur. No prudent defender of philosophy would claim to have done more.

CHAPTER XV. THE VALUE OF PHILOSOPHY

We have now reached the end of our brief and very incomplete review of the problems of philosophy. In conclusion, it will be useful to consider what the value of philosophy is and why it ought to be studied.

This question is all the more necessary because many people doubt the worth of philosophy. Influenced by science or by practical affairs, they wonder whether philosophy is anything more than harmless but useless trifling: hair-splitting distinctions, and disputes about matters on which knowledge is impossible.

This view of philosophy seems to come partly from a mistaken idea of the ends of life. It also comes partly from a mistaken idea of the kind of goods that philosophy tries to achieve.

Physical science, through the inventions it makes possible, is useful to countless people who know nothing about it. The study of physical science is therefore worth recommending not only, or even mainly, because of its effect on the student. It is worth recommending because of its effect on humanity in general.

This kind of usefulness does not belong to philosophy. If studying philosophy has any value for people other than its students, that value can only be indirect, through its effects on the lives of those who study it. It is in these effects, then, if anywhere, that we must look first for the value of philosophy.

Further, if we are to succeed in determining the value of philosophy, we must first free our minds from the prejudices of people wrongly called “practical.” The “practical” man, as the word is often used, recognizes only material needs. He understands that people must have food for the body, but he overlooks the need to provide food for the mind.

Suppose everyone were well off, and poverty and disease had been reduced as far as possible. Much would still remain to be done to create a valuable society. And even in the world as it is, the goods of the mind are at least as important as the goods of the body.

The value of philosophy lies entirely among the goods of the mind. Only people who are not indifferent to these goods can be persuaded that studying philosophy is not a waste of time.

Philosophy, like every other study, aims first of all at knowledge. The knowledge it seeks is the kind that gives unity and system to the sciences as a whole. It is also the kind that comes from critically examining the grounds of our convictions, prejudices, and beliefs.

But no one can claim that philosophy has been very successful in providing definite answers to its questions. Ask a mathematician, a mineralogist, a historian, or any other learned person what definite body of truths his science has established. His answer will go on as long as you are willing to listen.

Put the same question to a philosopher, and if he is honest, he will have to admit that his study has not achieved positive results like those achieved by other sciences.

This is partly explained by the fact that once definite knowledge about a subject becomes possible, the subject stops being called philosophy and becomes a separate science. The whole study of the heavens, which now belongs to astronomy, was once part of philosophy. Newton’s great work was called “the mathematical principles of natural philosophy.”

Similarly, the study of the human mind was once part of philosophy. It has now been separated from philosophy and has become the science of psychology.

To a large extent, then, the uncertainty of philosophy is more apparent than real. Questions that can already be answered definitely are placed in the sciences. Only those that cannot yet be given a definite answer remain behind, and this remainder is what we call philosophy.

That, however, is only part of the truth about the uncertainty of philosophy. Many questions, including those of deepest interest to our spiritual life, seem bound to remain unsolvable by the human intellect. They will stay that way unless its powers become quite different in kind from what they are now.

Does the universe have any unity of plan or purpose, or is it a chance assembly of atoms? Is consciousness a permanent part of the universe, offering hope of unlimited growth in wisdom? Or is it a passing accident on a small planet where life must eventually become impossible? Do good and evil matter to the universe, or only to human beings?

Philosophy asks such questions, and different philosophers answer them differently. But whether or not answers can be found in some other way, it seems that none of the answers philosophy suggests can be shown to be true.

Yet however slight the hope of finding an answer, part of philosophy’s work is to keep considering such questions. It should make us aware of their importance and examine every approach to them. It should also keep alive the speculative interest in the universe, which tends to die if we confine ourselves to knowledge that can be definitely established.

Many philosophers, it is true, have held that philosophy could establish the truth of certain answers to these fundamental questions. They have supposed that what matters most in religious beliefs could be proved true by strict demonstration.

To judge such attempts, we must survey human knowledge and form a view of its methods and its limits. It would be unwise to speak dogmatically on such a subject. But if the investigations of our previous chapters have not misled us, we shall have to give up the hope of finding philosophical proofs of religious beliefs.

We cannot, therefore, count any definite set of answers to such questions as part of philosophy’s value. Once again, the value of philosophy must not depend on any supposed body of definitely established knowledge that its students are to acquire.

The value of philosophy lies largely in its very uncertainty. A person with no trace of philosophy goes through life imprisoned in prejudices. These come from common sense, from the habitual beliefs of his age or his nation, and from convictions that have grown up in his mind without the cooperation or consent of his deliberate reason.

To such a person the world tends to seem definite, finite, and obvious. Common objects raise no questions, and unfamiliar possibilities are rejected with contempt. As soon as we begin to philosophize, by contrast, we find, as we saw in our opening chapters, that even the most everyday things lead to problems that can be answered only very incompletely.

Philosophy cannot tell us with certainty the true answer to the doubts it raises. But it can suggest many possibilities that enlarge our thoughts and free them from the tyranny of custom. So while it reduces our feeling of certainty about what things are, it greatly increases our knowledge of what they may be.

It removes the somewhat arrogant dogmatism of those who have never traveled into the region of liberating doubt. And it keeps alive our sense of wonder by showing familiar things in an unfamiliar light.

Apart from its usefulness in revealing unsuspected possibilities, philosophy has another value, perhaps its chief one. That value comes from the greatness of the objects it contemplates, and from the freedom from narrow and personal aims that this contemplation produces.

The life of the instinctive person is shut up within the circle of private interests. Family and friends may be included, but the outer world matters only insofar as it may help or hinder what lies within the circle of instinctive wishes. There is something feverish and confined in such a life. Compared with it, the philosophic life is calm and free.

The private world of instinctive interests is a small one. It sits in the middle of a great and powerful world that must, sooner or later, lay our private world in ruins. Unless we can enlarge our interests enough to include the whole outer world, we remain like a garrison in a besieged fortress. We know that the enemy prevents escape and that final surrender is inevitable.

Such a life has no peace. Instead there is constant conflict between the insistence of desire and the powerlessness of will. In one way or another, if our life is to be great and free, we must escape this prison and this conflict.

One way of escape is through philosophic contemplation. In its widest survey, philosophic contemplation does not divide the universe into two hostile camps: friends and foes, helpful and hostile, good and bad. It views the whole impartially. When it is pure, philosophic contemplation does not aim to prove that the rest of the universe is akin to human beings.

All acquisition of knowledge enlarges the Self, but this enlargement is best achieved when it is not directly sought. It comes when the desire for knowledge alone is at work. It comes through a study that does not wish in advance for its objects to have this or that character. Instead, such a study adapts the Self to the characters it finds in those objects.

This enlargement of the Self does not happen when we take the Self as it is and try to show that the world closely resembles it. On that approach, we could know the world without admitting anything that seems alien. The desire to prove this is a form of self-assertion. Like all self-assertion, it obstructs the very growth of Self that it desires, and that the Self knows it is capable of.

Self-assertion, in philosophic speculation as elsewhere, treats the world as a means to its own ends. It therefore makes the world less important than the Self, and the Self sets limits to the greatness of its goods. In contemplation, by contrast, we start from the not-Self. Through the greatness of the not-Self, the boundaries of the Self are enlarged. Through the infinity of the universe, the mind that contemplates it gains some share in infinity.

For this reason, greatness of soul is not fostered by philosophies that make the universe resemble Man. Knowledge is a form of union between Self and not-Self. Like every union, it is damaged by domination. So it is damaged by any attempt to force the universe to conform to what we find in ourselves.

There is a widespread philosophical tendency toward a view that tells us Man is the measure of all things. On this view, truth is man-made. Space, time, and the world of universals are properties of the mind. And if anything exists that the mind did not create, it is unknowable and of no importance to us.

If our previous discussions were correct, this view is untrue. But besides being untrue, it robs philosophic contemplation of everything that gives it value, because it chains contemplation to the Self. What it calls knowledge is not a union with the not-Self. It is a set of prejudices, habits, and desires that form an impenetrable veil between us and the world beyond.

A person who takes pleasure in such a theory of knowledge is like someone who never leaves the family circle for fear that his word might not be law outside it.

True philosophic contemplation, by contrast, finds its satisfaction in every enlargement of the not-Self. It welcomes everything that magnifies the objects contemplated, and so magnifies the subject who contemplates them. In contemplation, everything personal or private distorts the object. This includes everything that depends on habit, self-interest, or desire. Such distortion damages the union the intellect seeks. By building a barrier between subject and object, these personal and private things become a prison for the intellect.

The free intellect will see as God might see. It will see without a here and now, without hopes and fears, without the chains of customary beliefs and traditional prejudices. It will see calmly and dispassionately, moved solely by the desire for knowledge. That knowledge will be as impersonal and as purely contemplative as a human being can attain.

For the same reason, the free intellect will value abstract and universal knowledge above the knowledge brought by the senses, because the accidents of private history do not enter into it. Sense knowledge necessarily depends on an exclusive and personal point of view. It also depends on a body whose sense organs distort as much as they reveal.

The mind that has grown used to the freedom and impartiality of philosophic contemplation will keep something of the same freedom and impartiality in the world of action and emotion. It will view its own purposes and desires as parts of the whole. It will not insist on them, because it sees them as tiny fragments in a world where everything else is unaffected by any one person’s deeds.

The impartiality that, in contemplation, is the pure desire for truth is the very same quality of mind that, in action, is justice. In emotion, it is the universal love that can be given to everyone, not only to those judged useful or admirable.

So contemplation enlarges not only the objects of our thoughts but also the objects of our actions and our affections. It makes us citizens of the universe, not merely of one walled city at war with all the rest. Man’s true freedom consists in this citizenship of the universe. In it lies his liberation from the bondage of narrow hopes and fears.

To sum up our discussion of the value of philosophy: philosophy should not be studied for the sake of any definite answers to its questions, since as a rule no definite answers can be known to be true. It should be studied rather for the sake of the questions themselves.

These questions enlarge our idea of what is possible, enrich our intellectual imagination, and reduce the dogmatic confidence that closes the mind to speculation. But above all, philosophy is worth studying because, through the greatness of the universe it contemplates, the mind too is made great. It becomes capable of that union with the universe which is its highest good.

BIBLIOGRAPHICAL NOTE

A student who wants an elementary knowledge of philosophy will find it both easier and more rewarding to read some works of the great philosophers than to try to get a well-rounded view from handbooks. The following are especially recommended:

Plato: Republic, especially Books VI and VII.
Descartes: Meditations.
Spinoza: Ethics.
Leibniz: The Monadology.
Berkeley: Three Dialogues between Hylas and Philonous.
Hume: Enquiry concerning Human Understanding.
Kant: Prolegomena to any Future Metaphysic.

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