BERTRAND RUSSELL

HUMAN

KNOWLEDGE

Its Scope and Limits

LONDON

GEORGE ALLEN AND UNWIN LTD

Ruskin House, Museum Street

1923.

First Published Reprinted . Reprinted . Reprinted .

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PREFACE

The following pages are addressed, not only or primarily to professional philosophers, but to that much larger public which is interested in philosophical questions without being willing or able to devote more than a limited amount of time to considering them. Descartes, Leibniz, Locke, Berkeley, and Hume wrote for a public of this sort, and I think it is unfortunate that during the last hundred and sixty years or so philosophy has come to be regarded as almost as technical as mathematics. Logic, it must be admitted, is technical in the same way as mathematics is, but logic, I maintain, is not part of philosophy. Philosophy proper deals with matters of interest to the general educated public, and loses much of its value if only a few pro- fessionals can understand what is said.

In this book I have sought to deal, as comprehensively as I am able, with a very large question: how comes it that human beings, whose contacts with the world are brief and personal and limited, are nevertheless able to know as much as they do know? Is the belief in our knowledge partly illusory? And, if not, what must we know otherwise than through the senses? Since I have dealt in earlier books with some parts of this problem, I am compelled to repeat, in a larger context, discussions of certain matters which I have considered elsewhere, but I have reduced such repetition to the minimum compatible with my purpose.

One of the difficulties of the subject with which I am concerned is that we must employ words which are common in ordinary speech, such as “belief”, “truth”, “knowledge”, and “percep- tion”. Since these words, in their every-day uses, are vague and unprecise, and since no precise words are ready to hand by which to replace them, it is inevitable that everything said in the earlier stages of our inquiry should be unsatisfactory from the point of view that we hope to arrive at in the end. Our increase of knowledge, assuming that we are successful, is like that of a traveller approaching a mountain through a haze: at first only certain large features are discernible, 'and even they have indistinct boundaries, but gradually more detail becomes visible and edges become sharper. So, in our discussions, it is

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human knowledge: its scope and limits

impossible first to clear up one problem and then proceed to another, for the intervening haze envelops all alike. At every stage, though one part of our problem may be in the focus of attention, all parts are more or less relevant. The different key words that we must use are all interconnected, and so long as some remain vague, others must, more or less, share this defect. It follows that what is said at first is liable to require emendation later VThe Prophet announced that if two texts of the Koran appeared inconsistent, the later text was to be taken as authorita- tive, and I should wish the reader to apply a similar principle in 'interpreting what is said in this book.

The book has been read in typescript by my friend and pupil Mr. C. K. Hill, and I am indebted to him for many valuable criticisms, suggestions, and emendations. Large parts of the typescript have also been read by Mr. Hiram J. McLendon, who has made a number of useful suggestions.

Part III, Chapter IV, on “Physics and Experience”, is a reprint, with few alterations, of a little book with the above title, published by the Cambridge University Press, to whom I owe thanks for permission to reprint it.

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CONTENTS

INTRODUCTION PAGE 9

PART I. THE WORLD OF SCIENCE

I Individual and Social Knowledge 17

II The Universe of Astronomy 23

III The World of Physics 29

IV Biological Evolution 43

V The Physiology of Sensation and Volition 51

VI The Science of Mind 57

PART II. LANGUAGE

I The Uses of Language 71

II Ostensive Definition 78

III Proper Names 87

IV Egocentric Particulars 100

V Suspended Reactions: Knowledge and Belief 109

VI Sentences 119

VII External Reference of Ideas and Beliefs 123

VIII Truth: Elementary Forms 127

IX Logical Words and Falsehood 136

X General Knowledge 146

XI Fact, Belief, Truth, and Knowledge 159

PART III. SCIENCE AND PERCEPTION INTRODUCTION 177

I Knowledge of Facts and Knowledge of Laws 180

II Solipsism 191

III Probable Inference in Common-sense Practice 198

IV Physics and Experience 21 1

V Time in Experience / 226

VI Space in Psychology 233

VII Mind and Matter 240

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HUMAN knowledge: its scope and limits

I	PART IV. SCIENTIFIC CONCEPTS Interpretation	tPAGE 251
II	Minimum Vocabularies	259
III	Structure	267
IV	Structure and Minimum Vocabularies	274
V	Time, Public and Private	284
VI	Space in Classical Physics	295
VII	Space-Time	305
VIII	The Principle of Individuation	310
IX	Causal Laws	326
X	Space-time and Causality	337
	PART V. PROBABILITY INTRODUCTION	353
I	Kinds of Probability	356
II	Mathematical Probability	362
III	The Finite-Frequency Theory	368
IV	The Mises-Reichenbach Theory	380
V	Keynes’s Theory of Probability	390
VI	Degrees of Credibility	398
VII	Probability and Induction	00 H
PART	VI. POSTULATES OF SCIENTIFIC INFERENCE
I	Kinds of Knowledge	439
II	The Role of Induction	45i
III	The Postulate of Natural Kinds	456
IV	Knowledge Transcending Experience	463
V	Causal Lines	47i
VI	Structure and Causal Laws	479
VII	Interaction	494
VIII	Analogy	501
IX	Summary of Postulates	506
X	The Limits of Empiricism	516

Index 528

8

INTRODUCTION

The central purpose of this book is to examine the relation between individual experience and the general body of scientific knowledge. It is taken for granted that scientific knowledge, in its broad outlines, is to be accepted. Scepticism, while logically impeccable, is psychologically impossible, and there is an element of frivolous insincerity in any philosophy which pretends to accept it. Moreover, if scepticism is to be theoretically defensible it must reject all inferences from what is experienced; a partial scepticism, such as the denial of physical events experienced by no one, or a solipsism which allows events in my future or in my unremembered past, has no logical justification, since it must admit principles of inference which lead to beliefs that it rejects.

Ever since Kant, or perhaps it would be more just to say ever since Berkeley, there has been what I regard as a mistaken tendency among philosophers to allow the description of the world to be influenced unduly by considerations derived from the nature of human knowledge. To scientific common sense (which I accept) it is plain that only an infinitesimal part of the universe is known, that there were countless ages during which there was no knowledge, and that there probably will be countless ages without knowledge in the future. Cosmically and causally, knowledge is an unimportant feature of the universe; a science which omitted to mention its occurrence might, from an im- personal point of view, suffer only from a very trivial imperfection. In describing the world, subjectivity is a vice. Kant spoke of "himself as having effected a “Copernican revolution”, but he would have been more accurate if he had spoken of a “Ptolemaic counter-revolution”, since he put Man back at the centre from which Copernicus had dethroned him.

But when we ask, not “what sort of world do we live in?” but “how do we come by our knowledge about the world?” subjectivity is in order. What each man knows is, in an important sense, dependent upon his own individual experience: he knows what he has seen and heard, what he has read and what he has been told, and also what, from these data, he has been able to infer. It is individual, not collective, experience that is here in

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HUMAN KNOWLEDGE: ITS SCOPE AND LIMITS

question, for an inference is required to pass from my data to the acceptance of testimony. If I believe that there is such a place as Semipalatinsk, I believe it because of things that have happened to me\ and unless certain substantial principles of inference are accepted, I shall have to admit that all these things might have happened to me without there being any such place.

The desire to escape from subjectivity in the description of the world (which I share) has led some modern philosophers astray — at least so it seems to me — in relation to theory of knowledge. Finding its problems distasteful, they have tried to deny that these problems exists That data are private. And indi- vidual is a thesis which has been familiar since the time of Protagoras. This thesis has been denied because it has been thought, as Protagoras thought, that, if admitted, it must lead to the conclusion that all knowledge is private and individual.

(For my part, while I admit the thesis, I deny the conclusion; how and why, the following pages are intended to show.

In virtue of certain events in my own life, I have a number of beliefs about events that I do not experience — the thoughts and feelings of other people, the physical objects that surround me, the historical and geological past of the earth, and the remote regions of the universe that are studied in astronomy. For my part, I accept these beliefs as valid, apart from errors of detail. By this acceptance I commit myself to the view that there are valid processes of inference from events to other events — more particularly, from events of which I am aware without inference to events of which I have no such awareness. To discover what these processes are is a matter of analysis of scientific and common-sense procedure, in so far as such procedure is generally accepted as scientifically valid.

Inference from a group of events to other events can only be justified if the world has certain characteristics which are not logically necessary. So far as deductive logic can show, any collection of events might be the whole universe; if, then, I am ever to be able to infer events, I must accept principles of inference which lie outside deductive logic. All inference from events to events demands some kind of interconnection between different occurrences. Such interconnection is traditionally asserted in the principle of causality or natural law. It is implied, as we shall find, in whatever limited validity may be assigned to

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INTRODUCTION

induction by simple enumeration. But the traditional ways of formulating the kind of interconnection that must be postulated are in many ways defective, some being too stringent and some not sufficiently sdt To discover the minimum principles required toj justify scientific inferences is one ofthe mam^purposes of this book j ' iris ’'^ifonimoilpace*' to say that the substantial inferences of science, as opposed to those of logic and mathematics, are only probable — that is to say, when the premisses are true and the inference correct, the conclusion is only likely to be true. It is therefore necessary to examine what is meant by “probability”. It will be found that there are two different concepts that may be meant. On the one hand, there is mathematical probability: if a class has n members, and m of them have a certain characteristic, the mathematical probability that an unspecified member of this class will have the characteristic in question is m/n. On the other hand, there is a wider and vaguer concept, which I call “degree of credibility”, which is the amount of credence that it is rational to assign to a more or less uncertain proposition. Both kinds of proba- bility are involved in stating the principles of scientific inference.

The course of our inquiry, in broad outline, will be as follows.

Part I, on the world of science, describes some of the main features of the universe which scientific investigation has made probable. This Part may be taken as setting the goal which inference must be able to reach, if our data and our principles of inference are to justify scientific practice.

Part II, on language, is still concerned with preliminaries. These are mainly of two sorts. On the one hand, it is important to make clear the meanings of certain fundamental terms, such as “fact” and “truth”. On the other hand, it is necessary to examine the relation of sensible experience to empirical concepts such as “red”, “hard”, “metre”, or “second”. In addition, we shall examine the relation of words having an essential reference to the speaker, such as “here” and “now”, to impersonal words, such as those assigning latitude, longitude, and date. This raises problems, of considerable importance and some difficulty, which are concerned with the relation of individual experience to the socially recognized body of general knowledge.

In Part III, on Science and Perception, we begin our main inquiry. We are concerned, here, to disentangle data from inferences in what ordinarily passes for empirical knowledge.

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HUMAN knowledge: its scope and limits

We are not yet concerned to justify inferences, or to investigate the principles according to which they are made, but we are concerned to show that inferences (as opposed to logical Xr ^ constructions) are necessary to science. We are concerned also to distinguish between two kinds of space and time, one sub- jective and appertaining to data, the other objective and inferred. Incidentally we shall contend that solipsism, except in an extreme form in which it has never been entertained, is an illogical half- way house between the fragmentary world of data and the complete world of science.

Part IV, on scientific concepts, is concerned to analyse the fundamental concepts of the inferred scientific world, more especially physical space, historical _time, and causal laws. The terms employed in mathematical physics are required to fulfil two kinds of conditions: on the one hand, they must satisfy certain formulae; on the other hand, they must be so interpreted as to yield results that can be confirmed or confuted by observa- tion. Through the latter condition they are linked to data, though somewhat loosely; through the former they become determinate as regards certain structural properties. But considerable latitude of interpretation remains. It is prudent to use this latitude in such a way as to minimize the part played by inference as opposed to construction; on this ground, for example, point- instants in space-time are constructed as groups of events or of qualities. Throughout this Part the two concepts of space-time structure and causal chains assume a gradually increasing importance.ftAs Part III was concerned to discover what can be counted as data, so Part IV is concerned to set forth, in a general wav, what, if science is to be justified, mimi-he afrle to infer from our 5atal

Since it is Admitted that scientific inferences, as a rule, only confer probability on their conclusions, Part V proceeds to the examination of Probability. This term is capable of various interpretations, and has been differently defined by different authors. These interpretations and definitions are examined, and so are the attempts to connect induction with probability. In this matter the conclusion reached is, in the main, that advocated by Keynes: that inductions do not make their conclusions probable unless certain conditions are fulfilled, and that experience alone can never prove that these conditions are fulfilled.

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INTRODUCTION

Part VI, on the postulates of scientific inference, endeavours to discover what are the” minimum assumptions, anterior^to experience, that are required to justify usTn inferring laws from a^collection oFdata; and further, to inqinre~~ih~ whaF sense, if any, we can be said to know that These lis's^^

The main logical function tTiaf' t^^assumptiohs Tiave to fulfil is that of conferring a high probability on the conclusions of inductions that satisfy certain conditions. For this purpose, since only probability is in question, we do not need to assume that such-and-such a connection of events occurs always, but only that it occurs frequently. For example, one of the assumptions that appear necessary is that of separable causal chains, such as are exhibited by light-rays or sound-waves. This assumption can be stated as follows : when an event having a complex space- time structure occurs, it frequently happens that it is one of a train of events having the same or a very similar structure. (A more exact statement will be found in Chapter VI of this Part.) This is part of a wider assumption of regularity, or natural law, which, however, requires to be stated in more specific forms than is usual, for in its usual form it turns out to be a tautology.

That scientific inference requires, for its validity, principles which experience cannot render even probable, is, I believe, an inescapable conclusion from the logic of probability. For empiricism, it is an awkward conclusion. But I think it can be rendered somewhat more palatable by the analysis of the concept of “knowledge” undertaken in Part II. “Knowledge”, in my opinion, is a much less precise concept than is generally thought, and has its roots more deeply embedded in unverbalized animal behaviour than most philosophers have been willing to admit. The logically basic assumptions to which our analysis leads us are psychologically the end of a long series of refinements which start from habits of expectation in animals, such as that what has a certain kind of smell will be good to eat. To ask, therefore, whether we “know” the postulates of scientific inference, is not so definite a question as it seems. The answer must be: in one sense, yes, in another sense, no; but in the sense in which “no” is the right answer we know nothing whatever, and “knowledge” in this sense is a delusive vision. The perplexities of philosophers are due, in a large measure, to their unwillingness to awaken from this blissful dream.

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PART I

THE WORLD OF SCIENCE

Chapter I

INDIVIDUAL AND SOCIAL KNOWLEDGE

Scientific knowledge aims at being wholly impersonal, and tries to state what has been discovered by the collective intellect of mankind. In this chapter I shall consider how far it succeeds in this aim, and what elements of individual knowledge have to be sacrificed in order to achieve the measure of success that is possible.

The community knows both more and less than the individual : it knows, in its collective capacity, all the contents of the Encyclopaedia and all the contributions to the Proceedings of learned bodies, but it does not know the warm and intimate things that make up the colour and texture of an individual life. When a man says “I can never convey the horror I felt on seeing Buchenwald” or “no words can express my joy at seeing the sea again after years in a prison camp”, he is saying something which is strictly and precisely true : he possesses, through his experience, knowledge not possessed by those whose experience has been different, and not completely capable of verbal expression. If he is a superb literary artist he may create in sensitive readers a state of mind not wholly unlike his own, but if he tries scientific methods the stream of his experience will be lost and dissipated in a dusty desert.

Language, our sole means of communicating scientific know- ledge, is essentially social in its origin and in its main functions. It is true that, if a mathematician were wrecked or a desert island with a note-book and a pencil, he would, in all likelihood, seek to make his solitude endurable by calculations using the language of mathematics; it is true also that a man may keep a diary which he intends to conceal from all eyes but his own. On a more every- day plane, most of us use words in solitary thinking. Nevertheless the chief purpose of language is communication, and to serve this purpose it must be public, not a private dialect invented by the speaker. It follows that what is most personal in each individual's experience tends to evaporate during the process of ' translation into language. What is more, the very publicity of language is in large part a delusion. A given form of words will usually be

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B

human knowledge: its scope and limits

interpreted by competent hearers in such a way as to be true for all of them or false for all of them, but in spite of this it will not have the same meaning for all of them. Differences which do not affect the truth or falsehood of a statement are usually of little practical importance, and are therefore ignored, with the result that we all believe our private world to be much more like the public world than it really is.

This is easily proved by considering the process of learning to understand language. There are two ways of getting to know what a word means : one is by a definition in terms of other words, which is called verbal definition ; the other is by frequently hearing the word when the object which it denotes is present, which is called ostensive definition. It is obvious that ostensive definition is alone possible in the beginning, since verbal definition pre- supposes a knowledge of the words used in the definiens. You can learn by a verbal definition that a pentagon is a plane figure with five sides, but a child does not learn in this way the meaning of every-day words such as “rain”, “sun”, “dinner”, or “bed”. These are taught by using the appropriate word emphatically while the child is noticing the object concerned. Consequently the meaning that the child comes to attach to the word is a product of his personal experience, and varies according to his circumstances and his sensorium. A child who frequently experiences a mild drizzle will attach a different idea to the word “rain” from that formed by a child who has only experienced tropical torrents. A short-sighted and a long-sighted child will connect different images with the word “bed”.

It is true that education tries to depersonalize language, and with a certain measure of success. “Rain” is no longer the familiar phenomenon, but “drops of water falling from clouds towards the earth”, and “water” is no longer what makes you wet, but H20. As for hydrogen and oxygen, they have verbal definitions which have to be learnt by heart ; whether you understand them does not matter. And so, as your instruction proceeds, the world of words becomes more and more separated from the world of the senses ; you acquire the art of using words correctly, as you might acquire the art of playing the fiddle; in the end you become such a virtuoso in the manipulation of phrases that you need hardly ever remember that words have meanings. You have then become completely a public character, and even your inmost thoughts are

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INDIVIDUAL AND SOCIAL KNOWLEDGE

suitable for the encyclopaedia. But you can no longer hope to be a poet, and if you try to be a lover you will find your depersonalized language not very successful in generating the desired emotions. You have sacrificed expression to communication, and what you can communicate turns out to be abstract and dry.

It is an important fact that the nearer we come to the complete abstractness of logic, the less is the unavoidable difference between different people in the meaning attached to a word. I see no reason why there should be any difference at all between two suitably educated persons in the idea conveyed to them by the word “3481”. The words “or” and “not” are capable of having exactly the same meaning for two different logicians. Pure mathematics, throughout, works with concepts which are capable of being completely public and impersonal. The reason is that they derive nothing from the senses, and that the senses are the source of privacy. The body is a sensitive recording instrument, constantly transmitting messages from the outside world; the messages reaching one body are never quite the same as those reaching another, though practical and social exigencies have taught us ways of disregarding the differences between the percepts of neighbouring persons. In constructing physics we have emphasized the spatio-temporal aspect of our perceptions, which is the aspect that is most abstract and most nearly akin to logic and mathematics. This we have done in the pursuit of publicity, in order to communicate what is communicable and to cover up the rest in a dark mantle of oblivion.

Space and time, however, as human beings know them, are not in reality so impersonal as science pretends. Theologians conceive God as viewing both space and time from without, impartially, and with a uniform awareness of the whole; science tries to imitate this impartiality with some apparent success, but the success is in part illusory. Human beings differ from the theologians* God in the fact that their space and time have a here and now. What is here and now is vivid, what is remote has a gradually increasing dimness. All our knowledge of events radiates from a space-time centre, which is the little region that we are occupying at the moment. “Here” is a vague term: in astronomical cosmology the Milky Way may count as “here”, in the study of the Milky Way “here” is the solar system, in the study of the solar system “here” is the earth, in geography it is

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human knowledge: its scope and limits

the town or district in which we live, in physiological studies of sensation it is the brain as opposed to the rest of the body. Larger “heres” always contain smaller ones as parts; all “heres” contain the brain of the speaker, or part of it. Similar considerations apply to “now”.

Science professes to eliminate “here” and “now”. When some event occurs on the earth's surface, we give its position in the space-time manifold by assigning latitude, longitude, and date. We have developed a technique which insures that all accurate observers with accurate instruments will arrive at the same estimate of latitude, longitude, and date. Consequently there is no longer anything personal in these estimates, in so far as we are content with numerical statements of which the meaning is not too closely investigated. Having arbitrarily decided that the longitude of Greenwich and the latitude of the equator are to be zero, other latitudes and longitudes follow. But what is “Greenwich”? This is hardly the sort of term that ought to occur in an impartial survey of the universe, and its definition is not mathematical. The best way to define “Greenwich” is to take a man to it and say: “Here is Greenwich.” If some one else has already determined the latitude and longitude of the place where you are, “Greenwich” can be defined by its latitude and longitude relative to that place; it is, for example, so many degrees east and so many degrees north of New York. But this does not get rid of “here”, which is now New York instead of Greenwich.

Moreover it is absurd to define either Greenwich or New York by its latitude and longitude. Greenwich is an actual place, inhabited by actual people, and containing buildings which ante- date its longitudinal pre-eminence. You can, of course, describe Greenwich, but there always might be another town with the same characteristics. If you want to be sure that your description applies to no other place, the only way is to mention its relation to some other place, for instance, by saying that it is so many miles down the Thames from London Bridge. But then you will have to define “London Bridge”. Sooner or later you are faced with the necessity of defining some place as “here”, and this is an egocentric definition, since the place in question is not “here” for everybody. There may be a way of escape from this con- clusion; at a later stage, we will resume the question. But there is no obvious or easy way of escape, and until one is found all

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INDIVIDUAL AND SOCIAL KNOWLEDGE

determinations of latitude and longitude are infected with the subjectivity of “here”. This means that, although different people assign the same latitude and longitude to a place, they do not, in ultimate analysis, attach the same meaning to the figures at which they arrive.

The common world in which we believe ourselves to live is a construction, partly scientific, partly pre-scientific. We perceive tables as circular or rectangular, in spite of the fact that a painter, to reproduce their appearance, has to paint ellipses or non- rectangular quadrilaterals. We see a person as of about the same size whether he is two feet from us or twelve. Until our attention is drawn to the facts, we are quite unconscious of the corrections that experience has led us to make in interpreting sensible appear- ances. There is a long journey from the child who draws two eyes in a profile to the physicist who talks of electrons and protons, but throughout this journey there is one constant purpose: to eliminate the subjectivity of sensation, and substitute a kind of knowledge which can be the same for all percipients. Gradually the difference between what is sensed and what is believed to be objective grows greater; the child’s profile with two eyes is still very like what is seen, but the electrons and protons have only a remote resemblance of logical structure. The electrons and protons, however, have the merit that they may be what actually exists where there are no sense-organs, whereas our immediate visual data, owing to their subjectivity, are almost certainly not what takes place in the physical objects that we are said to see.

The electrons and protons — assuming it scientifically correct to believe in them — do not depend for their existence upon being perceived; on the contrary, there is every reason to believe that they existed for countless ages before there were any percipients in the universe. But although perception is not needed for their existence, it is needed to give us a reason for believing in their existence. Hundreds of thousands of years ago, a vast and remote region emitted incredible numbers of photons, which wandered through the universe in all directions. At last a very few of them hit a photographic plate, in which they caused chemical changes which made parts of the plate look black instead of whjte when examined by an astronomer. This tiny effect upon a minute but highly educated organism is our only reason for believing in the existence of a nebula comparable in size with the Milky Way.

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human knowledge: its scope and limits

ijferThe order for knowledge is the inverse of the causal order. In the order" for knowledge, what comes first is the brief subjective experience of the astronomer looking at a pattern of black and white, and what comes last is the nebula, vast, remote, and belonging to the distant past.

In considering the reasons for believing in any empirical statement, we cannot escape from perception with all its personal limitations. How far the information which we obtain from this tainted source can be purified in the filter of scientific method, and emerge resplendently godlike in its impartiality, is a difficult question, with which we shall be much concerned. But there is one thing that is obvious from the start: only in so far as the initial perceptual datum is trustworthy can there be any reason for accepting the vast cosmic edifice of inference which is based upon it.

I am not suggesting that the initial perceptual datum must be accepted as indubitable ; that is by no means the case. There are well-known methods of strengthening or weakening the force of individual testimony; certain methods are used in the law courts, somewhat different ones are used in science. But all depend upon the principle that some weight is to be attached to every piece of testimony, for it is only in virtue of this principle that a number of concordant testimonies are held to give a high probability. Individual percepts are the basis of all our knowledge, and no method exists by which we can begin with data which are public to many observers.

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Chapter II

THE UNIVERSE OF ASTRONOMY

Jk stronomy is the oldest of the sciences, and the contempla-

L\ tion of the heavens, with their periodic regularities, gave A. Vmen their first conceptions of natural law. But in spite of its age, astronomy is as vigorous as at any former time, and as important in helping us to form a just estimate of man’s position in the universe.

When the Greeks began inventing astronomical hypotheses, the apparent motions of the sun and moon and planets among the fixed stars had already been observed for thousands of years by the Babylonians and Egyptians, who had also learned to predict lunar eclipses with certainty and solar eclipses with a considerable risk of error. The Greeks, like other ancient nations, believed the heavenly bodies to be gods, or at any rate each closely controlled by its own god or goddess. Some, it is true, questioned this opinion : Anaxagoras, in the time of Pericles, maintained that the sun was a red-hot stone and that the moon was made of earth. But for this opinion he was prosecuted and compelled to fly from Athens. It is very questionable whether either Plato or Aristotle was equally rationalistic. But it was not the most rationalistic among the Greeks who were the best astronomers; it was the Pythagoreans, to whom superstition suggested what happened to be good hypotheses.

The Pythagoreans, towards the end of the fifth century b.c., discovered that the earth is spherical; about a hundred years later, Eratosthenes estimated the earth’s diameter correctly within about fifty miles. Heraclides of Pontus, during the fourth century, maintained that the earth rotates once a day and that Venus and Mercury describe orbits about the sun. Aristarchus of Samos, in the third century, advocated the complete Copernican system, and worked out a theoretically correct method of estimating the distances of the sun and moon. As regards the sun this result, it is true, was wildly wrong, owing to inaccuracy in his data; but a hundred years later Posidonius made an estimate which was about half of the correct figure. This extraordinarily vigorous advance, however, did not continue, and much of it was for-

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human knowledge: its scope and limits

gotten in the general decay of intellectual energy during later antiquity.

The cosmos, as it appears, for instance, in Plotinus, was a cosy and human little abode in comparison with what it has since become. The supreme deity regulated the whole, but each star was a subordinate deity, similar to a human being but in every way nobler and wiser. Plotinus finds fault with the Gnostics for believing that, in the created universe, there is nothing more worthy of admiration than the human soul. The beauty of the heavens, to him, is not only visual, but also moral and intellectual. The sun and moon and planets are exalted spirits, actuated by such motives as appeal to the philosopher in his best moments. He rejects with indignation the morose view of the Gnostics (and later of the Manicheans) that the visible world was created by a wicked Demiurge and must be despised by every aspirant to true virtue. On the contrary, the bright beings that adorn the sky are wise and good, and such as to console the philosopher amid the welter of folly and disaster that was overtaking the Roman Empire.

The medieval Christian cosmos, though less austere than that of the Manicheans, was shorn of some elements of poetic fancy that paganism had preserved to the end. The change, however, was not very great, for angels and archangels more or less took the place of the polytheists’ celestial divinities. Both the scientific and the poetic elements of the medieval cosmos are set forth in Dante’s Paradiso ; the scientific elements are derived from Aristotle and Ptolemy. The earth is spherical, and at the centre of the universe ; Satan is at the centre of the earth, and hell is an inverted cone of which he forms the apex. At the antipodes of Jerusalem is the Mount of Purgatory, at whose summit is the earthly paradise, which is just in contact with the sphere of the moon.

The heavens consist of ten concentric spheres, that of the moon being the lowest. Everything below the moon is subject to cor- ruption and decay; everything from the moon upwards is in- destructible. Above the moon, the spheres in their order are those of Mercury, Venus, the Sun, Mars, Jupiter, Saturn and the fixed stars, beyond which is the Primum Mobile. Last of all, above the Primum Mobile, is the Empyrean, which has no motion, and in which there are no times or places. God, the Aristotelian Unmoved Mover, causes the rotation of the Primum Mobile, which, in turn,

24

THE UNIVERSE OF ASTRONOMY

communicates its motion to the sphere of the fixed stars, and so on downwards to the sphere of the moon. Nothing is said in Dante as to the sizes of the various spheres, but he is able to traverse them all in the space of twenty-four hours. Clearly the universe as he conceived it was somewhat minute by modern standards; it was also very recent, having been created a few thousand years ago. The spheres, which all had the earth at the centre, afforded the eternal abodes of the elect. The elect consisted of those baptized persons who had reached the required standard both in faith and works, together with the patriarchs and prophets who had foreseen the coming of Christ, and a very few pagans who, while on earth, had been miraculously enlightened.

It was against this picture of the universe that the pioneers of modern astronomy had to contend. It is interesting to contrast the commotion about Copernicus with the almost complete oblivion that befell Aristarchus. Cleanthes the Stoic had urged that Aristarchus should be prosecuted for impiety, but the Govern- ment was apathetic; perhaps if he had been persecuted, like Galileo, his theories might have won wider publicity. There were, however, other more important reasons for the difference between the posthumous fame of Aristarchus and that of Copernicus. In Greek times astronomy was an amusement of the idle rich — a very dignified amusement, it is true, but not an integrated part of the life of the community. By the sixteenth century, science had invented gunpowder and the mariner’s compass, the discovery of America had shown the limitations of ancient geognosis, Catholic orthodoxy had begun to seem an obstacle to material progress, and the fury of obscurantist theologians made the men of science appear as heroic champions of a new wisdom. The seventeenth century, with the telescope, the science of dynamics, and the law of gravitation, completed the triumph of the scientific outlook, not only as the key to pure knowledge, but as a powerful means of economic progress. From this time onwards, science was recognized as a matter of social and not merely individual interest.

The theory of the sun and planets as a finished system was practically completed by Newton. As against Aristotle and the medieval philosophers it appeared that the sun, not the earth, is the centre of the solar system; that the heavenly Bodies, left to themselves, would move in straight lines, not in circles; that in fact they move neither in straight lines nor in circles, but in

25

human knowledge: its scope and limits

ellipses ; and that no action from outside is necessary to preserve their motion. But as regards the origin of the system Newton had nothing scientific to say; he supposed that at the Creation the planets had been hurled by the hand of God in a tangential direction, and had then been left by Him to the operation of the law of gravitation. Before Newton, Descartes had attempted a theory of the origin of the solar system, but his theory proved untenable. Kant and Laplace invented the nebular hypothesis, according to which the sun was formed by the condensation of a primitive nebula, and threw off the planets successively as a result of increasingly rapid rotation. This theory also proved defective, and modern astronomers incline to the view that the planets were caused by the passage of another star through the near neighbourhood of the sun. The subject remains obscure, but no one doubts that, by some mechanism, the planets came out of the sun.

The most remarkable astronomical progress in recent times has been in relation to the stars and the nebulae. The nearest of the fixed stars, Alpha Centauri, is at a distance of about 25 X io12 miles, or 4-2 light-years. (Light travels 186,000 miles a second; a light-year is the distance it travels in a year.) The first deter- mination of the distance of a star was in 1835; since then, by various ingenious methods, greater and greater distances have been computed. It is believed that the most distant object that can be detected with the most powerful telescope now in existence is about 500 million light-years away.

Something is now known of the general structure of the universe. The sun is a star in the galaxy, which is an assembly of about 300,000 million stars, about 150,000 light-years across and between 25,000 and 40,000 light-years thick. The total mass of the galaxy is about 160,000 million times the mass of the sun; the mass of the sun is about 2 X io27 tons. The whole of this system is slowly rotating about its centre of gravity ; the sun takes about 225 million years to complete its orbit round the milky way.

In the space beyond the milky way, other systems of stars, of approximately the same size as the milky way, are scattered at fairly regular intervals throughout the space that our telescopes can explore. These systems are called extra-galactic nebulae ; it is thought that about 30 millions of them are visible, but the census is not yet complete. The average distance between two nebulae is

26

THE UNIVERSE OF ASTRONOMY

about 2 million light-years. (Most of these facts are taken from Hubble, The Realm of the Nebulae , 1936.)

One of the oddest facts about the nebulae is that the lines in their spectra, with very few exceptions, are shifted towards the red, and that the amount of the shift is proportional to the distance of the nebula. The only plausible explanation is that the nebulae are moving away from us, and that the most distant ones are receding most quickly. At a distance of 135 million light-years, this velocity amounts to 14,300 miles per second (Hubble, Plate VIII, p. 1 18). At a certain distance, the velocity would become equal to the velocity of light, and the nebulae would therefore be invisible however powerful our telescopes might be.

The general theory of relativity has an explanation to offer of this curious phenomenon. The theory maintains that the universe is of finite size — not that it has an edge, outside which there is something which is not part of the universe, but that it is a three- dimensional sphere, in which the straightest possible lines return in time to their starting-point, as on the surface of the earth. The theory goes on to predict that the universe must be either con- tracting or expanding; it then uses the observed facts about the nebulae to decide for expansion. According to Eddington, the universe doubles in size every 1,300 million years or so. (New Pathways in Science , p. 210.) If this is true, the universe was once quite small, but will in time become rather large.

This brings us to the question of the ages of the earth and the stars and the nebulae. On grounds that are largely geological, the age of the earth is estimated at about 3,000 million years. The age of the sun and the other stars is still a matter of controversy. If, in the interior of a star, matter can be annihilated by transforming an electron and a proton into radiation, the stars may be several million million years old; if not, only a few thousand million. (H. Spencer Jones, Worlds Without End , p. 231.) On the whole, the latter view seems to be prevailing.

There is even some reason to think that the universe had a beginning in time; Eddington used to maintain that it began in about 90,000 million B.c, This is certainly more than the 4,004 in which our great-grandfathers believed, but it is still a finite period, and raises all the old puzzles as to what was going on before that date.

The net result of this summary survey of the astronomical

27

HUMAN knowledge: its scope and limits

When the forces to which a body is subject are not constant, the principle does not allow us to take each separately for a finite time, but if the finite time is short the result of taking each separately will be approximately right, and the shorter the time the more nearly right it will be, approaching complete rightness as a limit.

It must be understood that this law is purely empirical ; there is no mathematical reason for its truth. It is to be believed in so far as there is evidence for it, and no further. In quantum mechanics it is not assumed, and there are phenomena which seem to show that it is not true in atomic occurrences. But in the physics of large-scale occurrences it remains true, and in classical physics it played a very important role.

From Newton to the end of the nineteenth century, the progress of physics involved no basically new principles. The first revo- lutionary novelty was Planck's introduction of the quantum constant h in the year 1900. But before considering quantum theory, which is chiefly important in connection with the structure and behaviour of atoms, a few words must be said about relativity, which involved a departure from Newtonian principles much slighter than that of quantum theory.

^Newton believed that, in addition to matter, there is absolute space and absolute time. That is to say, there is a three-dimensional manifold of points and a one-dimensional manifold of instants, and there is~^TRree-term relation involving matter* space, and timejliamely the relation of “occupying” a point at an instant. In this view Newton agreed with Democritus and the other atomists of antiquity, who believed in “atoms and the void". Other philosophers had maintained that empty space is nothing, and that there must be matter everywhere. This was Descartes' opinion, and also that of Leibniz, with whom Newton (using Dr. Clarke as his mouthpiece) had a controversy on the subject.

Whatever physicists might hold as a matter of philosophy, Newton’s view was implicit in the technique of dynamics, and there were, as he pointed out, empirical reasons for preferring it. If water in a bucket is rotated, it climbs up the sides, but if the bucket is rotated while the water is kept still, the surface of the water remains flat. We can therefore distinguish between rotation of the water and rotation of the bucket, which we ought not to be able to do if rotation were merely relative. Since Newton's time

3*

THE WORLD OF PHYSICS

other arguments of the same sort have accumulated. Foucault’s pendulum, the flattening of the earth at the poles, and the fact that bodies weigh less in low latitudes than in high ones, would enable us to infer that the earth rotates even if the sky were always covered with clouds; in fact, on Newtonian principles we can say that the rotation of the earth, not the revolution of the heavens, causes the succession of night and day and the rising and setting of the stars. But if space is purely relative, the difference between the statements “the earth rotates” and “the heavens revolve” is purely verbal : both must be ways of describing the same pheno- mena.

^Einstein showed how to avoid Newton’s conclusions, and make spatio-temporal position purely relative. But his theory of relativity did much more than this. In the special theory of relativity he showed that between two events there is a relation, which may be called “interval”, which can be divided in many different ways into what we should regard as a spatial distance and what we should regard as a lapse of time. All these different ways are equally legitimate ; there is not one way which is more “right” than the others. The choice between them is a matter of pure convention, like the choice between the metric system and the system of feet and inches !j

It follows from this that the fundamental manifold of physics cannot consist of persistent particles in motion, but must consist of a four-dimensional manifold of “events’*? There will be three co-ordinates to fix the position of the event in space, and one to fix its position in time, but a change of co-ordinates may alter the time-co-ordinate as well as the space co-ordinates, and not only, as before, by a constant amount, the same for all events — as, for example, when dating is altered from the Mohammedan era to the Christian.

The general theory of relativity — published in 1915, ten years after the special theory — was primarily a geometrical theory of gravitation. This part of the theory may be considered firmly established. But it has also more speculative features. It contains, in its equations, what is called the “cosmical constant”, which determines the size of the universe at any time. This part of the theory, as I mentioned before, is held to show that the universe is growing either continually larger or continually smaller.^ The shift towards the red in the spectra of distant nebulae is held to

33

c

human knowledge: its scope and limits

show that they are moving away from us with a velocity pro- portional to their distance from us. This leads to the conclusion that the universe is expanding, not contracting. It must be under- stood that, according to this theory, the universe is finite but unbounded, like the surface of a sphere, but in three dimensions. All this involves non-Euclidean geometry, and is apt to seem mysterious to those whose imagination is obstinately Euclidean.

Two kinds of departure from Euclidean space are involved in the general theory of relativity. On the one hand, there are what may be called the small-scale departures (where the solar system, e.g., is regarded as “small”), and on the other hand the large-scale departure of the universe as a whole. The small-scale departures occur in the neighbourhood of matter, and account for gravitation. They may be compared to hills and valleys on the surface of the earth. The large-scale departure may be compared with the fact that the earth is round and not flat. If you start from any point on the earth’s surface and travel as straight as you can, you will ultimately return to your starting-point. So, it is held, the straightest line possible in the universe will ultimately return into itself. The analogy with the surface of the earth fails in that the earth’s surface is two-dimensional and has regions outside it, whereas the spherical space of the universe is three-dimensional and has nothing outside it. The present circumference of the universe is between 6,000 and 60,000 million light-years, but the size of the universe is doubled about every 1,300 million years. All this, however, must still be regarded as open to doubt.

According to Professor E. A. Milne,1 there is a great deal more that is questionable in Einstein’s theory. Professor Milne holds that there is no need to regard space as non-Euclidean, and that the geometry we adopt can be decided entirely by motives of convenience. The difference between different geometries, accord- ing to him, is a difference in language, not in what is described. Where physicists disagree it is rash for an outsider to have an opinion, but I incline to think that Professor Milne is very likely to be in the right.

^.Quantum theory, in contrast to the theory of relativity, is mainly concerned with the smallest things about which knowledge is pdssiBTe, Tiamely atoms and their structure. During the nine-

1 Relativity Gravitation qnd World Structure . By E. A. Milne. Oxford,

*935-

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THE WORLD OF PHYSICS

teenth century the atomic constitution of matter became well established, and it was found that the different elements could be placed in a series starting with hydrogen and ending with uranium. The place of an element in this series is called its “atomic number”. Hydrogen has the atomic number i, and uranium 92. There are two gaps in the series at present, so that the number of known elements is 90, not 92; but the gaps may be filled any day, as a number of previously existing gaps have been. In general, but not always, the atomic number increases with the atomic weight. Before Rutherford, there was no plausible theory as to the structure of atoms, or as to the physical properties which caused them to fall into a series. The series was determined by their chemical properties alone, and of these properties no physical explanation existed.

The Rutherford-Bohr atom, as it is called after its two inventors, had a beautiful simplicity, now, alas, lost. But although it has become only a pictorial approximation to the truth, it can still be used when extreme accuracy is not required, and without it the modern quantum theory could never have arisen. It is therefore still necessary to say something about it.

Rutherford gave experimental reasons for regarding an atom as composed of a nucleus carrying positive electricity surrounded by very much lighter bodies, called “electrons”, which carried negative electricity, and revolved, like planets, in orbits about the nucleus. When the atom is not electrified, the number of planetary electrons is the atomic number of the element concerned ; at all times, the atomic number measures the net positive electricity carried by the nucleus. The hydrogen atom consists of a nucleus and one planetary electron; the nucleus of the hydrogen atom is called a “proton”. It was found that the nuclei of other elements could be regarded as composed of protons and electrons, the number of protons being greater than that of the electrons by the atomic number of the element. Thus helium, which is number 2, has a nucleus consisting of four protons and two electrons. The atomic weight is practically determined by the number of protons, since a proton has about 1,850 times the mass of an electron, so that the contribution of the electrons to the total mass is almost negligible.

It has been found that, in addition to electrons and protons, there are two other constituents of atoms, which are called “positrons” and “neutrons”. A positron is just like an electron,

35

HUMAN knowledge: its scope and limits

except that it carries positive instead of negative electricity; it has the same mass as an electron, and probably the same size, in so far as either can be said to have a size. The neutron has no electricity, but has approximately the same mass as a proton. It seems not unlikely that a proton consists of a positron and a neutron. If so, there are three ultimate kinds of constituents in the perfected Rutherford-Bohr atom: the neutron, which has mass but no electricity, the positron, carrying positive electricity, and the electron, carrying an equal amount of negative electricity.

But we must now return to theories which ante-date the discovery of neutrons and positrons.

Bohr added to the Rutherford picture a theory as to the possible orbits of electrons, which, for the first time, explained the lines in the spectrum of an element. This mathematical explanation was almost, but not quite, perfect in the cases of hydrogen and positively electrified helium; in other cases the mathematics was too difficult, but no reason appeared to suppose that the theory would give wrong results if the mathematics could be worked out. His theory made use of Planck’s quantum constant A, concerning which a few words must be said.

Planck, by studying radiation, proved that in a light or heat wave of frequency v the energy must be h.v or 2 h.v or 3 h.v or some other integral multiple of A . v , where A is “Planck’s con- stant”, of which the value in C.G.S. units is about 6-55 x 10“ 27, and the dimensions are those of action, i.e. energy x time. Before Planck, it had been supposed that the energy of a wave could vary continuously, but he showed conclusively that this could not be the case. The frequency of waves is the number that pass a given point in a second. In the case of light, the frequency determines the colour; violet light has the highest frequency, red light the lowest. There are other waves of just the same kind as light- waves, but not having the frequencies that cause visual sensations of colour. Higher frequencies than those of violet light are, in order, ultra-violet, X-rays and y-rays; lower frequencies, infra-red and those used in wireless telegraphy.

When an atom emits light, it does so because it has parted with an amount of energy equal to that in the light-wave. If it emits light of frequency v , it must, according to Planck’s theory, have parted with an amount, of energy measured by A . v or some integral multiple of h.v. Bohr supposed that this happened through

36

THE WORLD OF PHYSICS

a planetary electron jumping from a larger to a smaller orbit; consequently the change of orbit must be such as to involve a loss of energy h . v or some integral multiple of this amount. It followed that only certain orbits could be possible. In the hydrogen atom, there would be a smallest possible orbit, and the other possible ones would have 4, 9, 16, . . . times the radius of the minimum orbit. This theory, first propounded in 1913, was found to agree well with observation, and for a time won general acceptance. Gradually, however, it was found that there were facts which it could not explain, so that, though clearly a step on the way to the truth, it could no longer be accepted as it stood. The new and more radical quantum theory, which dates from 1925, is due in the main to two men, Heisenberg and Schrodinger.

In the modern theory there is no longer any attempt to make an imaginative picture of the atom. An atom only gives evidence of its existence when it emits energy, and therefore experimental evidence can only be of changes of energy. The new theory takes over from Bohr the doctrine that the energy in an atom must have one of a discrete series of values involving h; each of these is called an “energy lever’. But as to what gives the atom its energy the theory is prudently silent.

One of the oddest things about the theory is that it has abolished the distinction between waves and particles. Newton thought that light consisted of particles emitted by the source of the light; Huygens thought that it consisted of waves. The view of Huygens prevailed, and until recently was thought to be definitely estab- lished. But new experimental facts seemed to demand that light should consist of particles, which were called “photons”. Per contra, De Broglie suggested that matter consists of waves. In the end it was shown that everything in physics can be explained either on the particle hypothesis or on the wave hypothesis. There is therefore no physical difference between them, and either may be adopted in any problem as may suit our convenience. But whichever is adopted, it must be adhered to; we must not mix the two hypotheses in one calculation.

In quantum theory, individual atomic occurrences are not determined by the equations ; these suffice only to show that the possibilities form a discrete series, and that there' are rules determining how often each possibility will be realized in a large number of c*ses. There are reasons for believing that this absence

37

HUMAN knowledge: its scope and limits

of complete determinism is not due to any incompleteness in the theory, but is a genuine characteristic of small-scale occurrences. The regularity which is found in macroscopic phenomena is a statistical regularity. Phenomena involving large numbers of atoms remain deterministic, but what an individual atom may do in given circumstances is uncertain, not only because our knowledge is limited, but because there are no physical laws giving a determinate result.

There is another result of quantum theory, about which, in my opinion, too much fuss has been made, namely what is called Heisenberg’s uncertainty-principle. According to this there is a theoretical limit to the accuracy with which certain connected quantities can be simultaneously measured. In specifying the state of a physical system, there are certain pairs of connected quantities ; one such pair is position and momentum (or velocity, so long as the mass is constant), another is energy and time. It is of course a commonplace that no physical quantity can be measured with complete accuracy, but it had always been supposed that there was no theoretical limit to the increase of accuracy obtainable by improved technique. According to Heisenberg’s principle this is not the case. If we try to measure simultaneously two con- nected quantities of the above sort, any increase of accuracy in the measurement of one of them (beyond a certain point) involves a decrease in the accuracy of the measurement of the other. In fact, there will be errors in both measurements, and the product of these two errors can never be less than hjzTT. This means that, if one could be completely accurate, the error in the other would have to be infinite. Suppose, for instance, that you wish to deter- mine the position and velocity of a particle at a certain time: if you get the position very nearly right, there will be a large error in the velocity, and if you get the velocity very nearly right, there will be a large error as to the position. Similarly as regards energy and time: if you measure the energy very accurately, the time when the system has this energy will have a large margin of un- certainty, while if you fix the time very accurately the energy will become uncertain within wide limits. This is not a question of imperfection in our measuring apparatus, but is an essential principle of physics.

There are physical considerations which make this principle less surprising. It will be observed that h is a very small quantity,

38

THE WORLD OF PHYSICS

since it is of the order of io"27. Therefore wherever h is relevant we are concerned with matters involving very great minuteness. When an astronomer observes the sun, the sun preserves a lordly indifference to his proceedings. But when a physicist tries to find out what is happening to an atom, the apparatus by means of which he makes his observations is likely to have an effect upon the atom. Detailed considerations show that the sort of apparatus best suited for determining the position of an atom is likely to affect its velocity, while the sort of apparatus best suited for determining its velocity is likely to alter its position. Similar arguments apply to other pairs of related quantities. I do not think, therefore, that the uncertainty principle has the kind of philosophical importance that is sometimes attributed to it.

Quantum equations differ from those of classical physics in a very important respect, namely that they are not “linear”. This means that when you have discovered the effect of one cause alone, and then the effect of another cause alone, you cannot find the effect of both together by adding the two previous effects. This has very odd results. Suppose, for instance, that you have a screen with a small slit, and you bombard it with particles; some of these will get through the slit. Suppose now you close the first slit and make a second ; then some will get through the second slit. Now open both slits at once. You would think that the number getting through both slits would be the sum of the previous numbers, but this turns out not to be the case. The behaviour of the par- ticles at one slit seems to be affected by the existence of the other slit. The equations are such as to predict this result, but it remains surprising. In quantum mechanics there is less independence of causes than in classical physics, and this adds greatly to the difficulty of the calculations.

^Both relativity and quantum theory Jiave had the effect of replacing" the olef conception of “mass” by that of “energy”. “Mass” used to be defined as “quantity of matter”; “matter” was, on the one hand “substance” in the metaphysical sense, and on the other hand the technical form of the common-sense notion of “thing”. “Energy” was, in its early stages, a state of “matter”. It consisted of two parts, kinetic and potential. The kinetic energy of a particle is half the product of the' mass and the square of the velocity. The potential energy is measured by the work that would have to be done to bring the particle to its

39

HUMAN knowledge: its scope and limits

present position from some standard position. (This leaves a constant undetermined, but that is of no consequence.) If you carry a stone from the ground to the top of a tower, it acquires potential energy in the process; if you drop it from the top, the potential energy is gradually transformed into kinetic energy during the fall. In any self-contained system, the total energy is constant. There are various forms of energy, of which heat is one; there is a tendency for more and more of the energy in the universe to take the form of heat. The conservation of energy first became a well-grounded scientific generalization when Joule measured the mechanical equivalent of heat.

Relativity theory and experiment both showed that mass is not constant, as had been held, but is increased by rapid motion; if a particle could move as fast as light, its mass would become infinite. Since all motion is relative, the different estimates of mass formed by different observers, according to their motion relative to the particle in question, are all equally legitimate. So far as this theory is concerned, however, there is still one estimate of mass which may be considered fundamental, namely the estimate made by an observer who is at rest relatively to the body whose mass is to be measured. Since the increase of mass with velocity is only appreciable for velocities comparable with that of light, this case covers practically all observations except those of a and j8 particles ejected from radio-active bodies.

Quantum theory has made a greater inroad upon the concept of “mass”. It now appears that whenever energy is lost by radia- tion there is a corresponding loss of mass. The sun is held to be losing mass at the rate of four million tons a second. To take another instance: a helium atom, unelectrified, consists (in the language of Bohr’s theory) of four protons and four electrons, while a hydrogen atom consists of one proton and one electron. It might have been supposed that, assuming this to be the case, the mass of a helium atom would be four times that of a hydrogen atom. This, however, is not the case: taking the mass of the helium atom as 4, that of the hydrogen atom is not 1, but 1 -008. The reason is that energy is lost (by radiation) when four hydrogen atoms combine to form one helium atom — at least so we must suppose, for the process is not one which has ever been observed.

It is thought that the combination of four hydrogen atoms to

40

THE WORLD OF PHYSICS

form one atom of helium occurs in the interior of stars, and could be made to occur in terrestrial laboratories if we could produce temperatures comparable to those in the interior of stars. Almost all the loss of energy involved in building up elements other than hydrogen occurs in the transition to helium; in later stages the loss of energy is small. If helium, or any element other than hydrogen, could be artificially manufactured out of hydrogen, there would be in the process an enormous liberation of energy in the form of light and heat. This suggests the possibility of atomic bombs more destructive than the present ones, which are made by means of uranium. There would be a further advantage: the supply of uranium in the planet is very limited, and it is feared that it may be used up before the human race is exter- minated, but if the practically unlimited supply of hydrogen in the sea could be utilized there would be considerable reason to hope that homo sapiens might put an end to himself, to the great advantage of the other less ferocious animals.

But it is time to return to less cheerful topics.

The language of Bohr’s theory is still adequate for many pur- poses, but not for stating the fundamental principles of quantum physics. To state these principles, we must avoid all pictures of what goes on in an atom, and must abandon attempts to say what energy is. We must say simply: there is something quantitative, to which we give the name “energy”; this something is very unevenly distributed in space; there are small regions in which there is a great deal of it, which are called “atoms”, and are those in which, according to older conceptions, there was matter; these regions are perpetually absorbing or emitting energy in forms that have a periodic “frequency”. Quantum equations give rules determining the possible forms of energy emitted by a given atom, and the proportion of cases (out of a large number) in which each of the possibilities will be realized. Everything here is abstract and mathematical except the sensations of colour, heat, etc., produced by the radiant energy in the observing physicist.

Mathematical physics contains such an immense superstructure of theory that its basis in observation tends to be obscured. It is, however, an empirical study, and its empirical character appears most unequivocally where the physical constants are concerned. Eddington {New Pathways in Science , p. 230) gives the following list of the primitive constants of physics :

4i

HUMAN knowledge: its scope and limits

very different from the temperatures to which we are accustomed ; at these temperatures, molecules of a very high degree of com- plexity can come into existence.

What distinguishes living from dead matter? Primarily, its chemical constitution and cell structure. It is to be supposed that its other characteristics follow from these. The most notable of these others are assimilation and reproduction, which, in the lowest forms of life, are not very sharply distinguished from each other. The result of assimilation and reproduction is that, given a small amount of living matter in a suitable environment, the total amount will quickly increase. A pair of rabbits in Australia quickly become many tons of rabbit. A few measles bacilli in a child quickly become many millions. A few seeds dropped by birds on Krakatoa after volcanic devastation quickly became luxuriant vegetation. So far as animals are concerned, this property of living matter is not fully exhibited, since animals require food that is already organic; but plants can transform inorganic sub- stances into living matter. This is a purely chemical process, but it is one from which, presumably, most of the other peculiarities of living matter, considered as a whole, in some sense follow.

It is an essential feature of living matter that it is not chemically static, but is undergoing continual chemical change; it is, one may say, a natural chemical laboratory. Our blood undergoes one kind of change as it circulates round the body, and an opposite change when it comes in contact with air in the lungs. Food, from the moment of contact with the saliva, undergoes a series of elaborate processes, which end by giving it the chemical structure appropriate to some part of the body.

There is no reason, except the great complexity of the molecules that compose a living body, why such molecules should not be manufactured artificially; nor is there the slightest reason for supposing that, if they were manufactured, they would lack any- thing distinctive of living matter naturally generated. Aristotle thought that there was a vegetable soul in every plant or animal, and something similar has been widely believed by vitalists. But for this view there has come to be less and less plausibility as organic chemistry has progressed. The evidence, though not conclusive, tends to show that everything distinctive of living matter can be reduced to chemistry, and therefore ultimately to physics. The fundamental laws governing living matter are, in

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BIOLOGICAL EVOLUTION

all likelihood, the very same that govern the behaviour of the hydrogen atom, namely the laws of quantum mechanics.

One of the characteristics of living organisms that have seemed mysterious is the power of reproduction. Rabbits generate rabbits, robins generate robins, and worms generate worms. Development from an embryo does not occur in the simplest forms of life; unicellular organisms merely grow till they reach a certain size, and then split. Something of this survives in sexual reproduction: part of the female body becomes an ovum, part of the male body a sperm, but this part is so much less than half that it seems qualitatively, and not merely quantitatively, different from the process of splitting into two equal halves. It is not in the splitting, however, that the novelty consists, but in the combination of male and female elements to make a new organism, which, in the natural process of growth, becomes, in time, like its adult parents.

As a consequence of the Mendelian theory, the process of heredity has come to be more or less understood. It appears that in the ovum and in the sperm there are a certain fairly small number of “genes”, which carry the hereditary characteristics. The laws of heredity, like those of quantum theory, are discrete and statistical; in general, when grandparents differ in some character, we cannot tell which grandparent a given child will resemble, but we can tell the proportion, out of a large number, that will resemble this one or that as regards the character in question.

In general, the genes carry the parental character, but some- times there are sports, or “mutants”, which differ substantially from the parent. They occur naturally in a small proportion of cases, and they can be produced artificially by X-rays. It is these sports that give the best opportunity for evolution, i.e. for the development of new kinds of animals or plants by descent from old kinds.

The general idea of evolution is very old; it is already to be found in Anaximander (sixth century B.C.), who held that men are descended from fishes. But Aristotle and the Church banished such theories until the eighteenth century. Already Descartes, Kant, and Laplace had advocated a gradual origin for the solar system, in place of sudden creation followed by a complete absence of change. As soon as geologists had succeeded in determining the relative ages of different strata, it became evident from fossils

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HUMAN knowledge: its scope and limits

planets. Life, therefore, is almost certainly a very rare phenomenon. Even on the earth it is transitory : at first the earth was too hot, and in the end it will be too cold. Some highly conjectural dates are suggested in Spencer Jones’s Worlds Without End (p. 19). The age of the earth is probably less than 3,000 million years; the beginnings of life may be placed at about 1,700 million years ago. Mammals began about 60 million years ago ; anthropoid apes about 8 million, man about 1 million. It is probable that all forms of life on earth have evolved from unicellular organisms. How these were first formed we do not know, but their origin is no more mysterious than that of helium atoms. There is no reason to suppose living matter subject to any laws other than those to which inanimate matter is subject, and considerable reason to think that everything in the behaviour of living matter is theoreti- cally explicable in terms of physics and chemistry.

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Chapter V

THE PHYSIOLOGY OF SENSATION AND VOLITION

From the standpoint of orthodox psychology, there are two boundaries between the mental and physical, namely sen- sation and volition. (“Sensation” may be defined as the first mental effect of a physical cause^^^voTition^ as the last mental [cause of a physical effect .yf am not maintaining that these definitions will prove ultimately satisfactory, but only that they may be adopted as a guide in our preliminary survey. In the present chapter I shall not be concerned with either sensation or volition themselves, since they belong to psychology; I shall be concerned only with (the physiological antecedents and con- comitants of sensation, and (with the physiological concomitants and" consequents of volition. Before considering what science’has tcTsayT irwttttye worth while to look at the matter first from a common-sense point of view.

Suppose something is said to you, and in consequence you take some action; for example, you may be a soldier obeying the word of comman^Physics studies the sound waves that travel through the air until tney reach the ear ; physiology studies the consequent event in the ear and nerves and brain, up to the moment when you hear the sound ; psychology studies the sensation of hearing and the consequent volition; physiology then resumes the study of the process, and considers the outgoing chain of events from the brain to the muscles and the bodily movement expressing the volition; from that point^pnward, what happens is again part of the subject-matter of physics. The problem of the relation of mind and matter, which is part of the stock in trade of philosophy, comes to a head in the transition from events in the brain to the sensation, jpid from the volition to other events in the brain. It is thus a two-fold problem: (how does matter affect mind in sensation, ^and^iow does mind affect matter in volitional do not propose to consider this problem at this stage ; I mention it now only to show the relevance of certain parts of physiology to questions which philosophy must discuss.

The physiological processes which precede and accompany

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human knowledge: its scope and limits

sensation are admirably set forth in Adrian’s book The Basis of Sensation: The Action of the Sense Organs (London, 1928). As every one knows, there are two sorts of nerve fibres, those that carry messages into the brain, and those that carry messages out of it. The former alone are concerned in the physiology of sen- sation. Isolated nerves can be stimulated artificially by an electric current, and there is good reason to believe that the processes thus set up are essentially similar to those set up naturally in nerves that are still in place in a living body. When an isolated nerve is thus stimulated in an adequate manner, a disturbance is set up which travels along the nerve at a speed of about 220 miles an hour (100 metres a second). Each nerve consists of a bundle of nerve fibres running from the surface of the body to the brain or the spinal chord. The nerve fibres which carry mes- sages to the brain are called “afferent”, those which carry messages from the brain are called “efferent”. A nerve usually contains both afferent and efferent fibres, firoadly speaking, the afferent fibres start from sense-organs and the efferent fibres end in muscles.

The response of a nerve fibre to a stimulus is of what is called the “all-or-nothing” type, like the response of a gun to pressure on the trigger. A slight pressure on the trigger produces no result, but a pressure which is sufficiently great produces a specific result which is the same however great the pressure may be (within limits). Similarly when a nerve fibre is stimulated very slightly, or for a very brief period (less than • 00001 of a second), there is no result, but when the stimulus is sufficient a current travels along the nerve fibre for a very brief period (a few thousandths of a second), after which the nerve fibre is “tired” and will not transmit another current until it is rested. At first, for two or three thousandths of a second, the nerve fibre is completely refractory; then it recovers gradually. During the period of recovery a given stimulus produces a smaller response, and one which travels more slowly. Recovery is complete after about a tenth of a second. The result is that a constant stimulus does not produce a constant state of excitement in the nerve fibres, but a series of responses with quiescent periods between. The mes- sages that reach the brain are, as Adrian puts it, like a stream of bullets from a machine gun, not like a continuous stream of water.

It is supposed that in the brain, or the spinal column, there

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is a converse mechanism which reconverts the discrete impulses into a continuous process, but this, so far, is purely hypothetical.

Owing to the discontinuous nature of the response to a stimulus, the response will be exactly the same to a constant stimulus as to one which is intermittent with a frequency adapted to the period of recovery in the nerve. It would seem to follow that there can be no means of knowing whether the stimulus is constant or intermittent. But this is not altogether true. Suppose, for instance, that you are looking at a bright spot of light : if you could keep your eyes absolutely fixed, your sensations would be the same if the light flickered with appropriate rapidity as they would be if the light were steady. But in fact it is impossible to keep the eyes quite still, and therefore fresh unfatigued nerves are per- petually being brought into play.

A remarkable fact, which might seem to put a limit on the informative value of sensations, is, that the response of the nerve fibre ip the same to any stimulus of sufficient strength and dura- tion: there is just one message, and only one, that a given nerve fibre can transmit. But consider the analogy of a typewriter: if you press a given letter, only one result occurs, and yet the typewriter as a whole can transmit any information, however complicated.

The mechanism of the efferent nerve fibres appears to be just the same as that of the afferent nerve fibres ; the messages that travel from the brain to the muscles have the same jerky character as those that travel from the sense-organs to the brain.

But the most interesting question remains: what goes on in the brain between the arrival of a message by the afferent nerves and the departure of a message by the efferent nerves ? Suppose you read a telegram saying “all your property has been destroyed in an earthquake”, and you exclaim “heavens! I am ruined”. We feel, rightly or wrongly, that we know the psychological links, after a fashion, by introspection, but everybody is agreed that there must also be physiological links. The current brought into the vision centre by the optic nerve must pass thence to the speech centre, and then stimulate the muscles which produce your exclamation. How this happens is still obscure. But it seems clear that, from a physiological point of view, there is a unitary process from the physical stimulus to the muscular response. In man this process may be rendered exceedingly complex by the operation

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they are taught by different men. What physicists have to teach is fairly clear, but what have the psychologists to teach ?

There are those among psychologists who take a view which really denies to psychology the status of a separate science. Accord- ing to this school, psychology consists in the study of human and animal behaviour, and the only thing that distinguishes it from philosophy is its interest in the organism as a whole. The observations upon which the psychologist must rely, according to this view, are such as a man might make on animals other than himself; there is no science, say the adherents of this school, which has data that a man can only obtain by observation of him- self. While I admit the importance of what has been learnt by studying behaviour, I cannot accept this view. There are — and I am prepared to maintain this dogmatically — many kinds of events that I can observe when they happen to me, but not when they happen to any one else. I can observe my own pains and pleasures, my perceptions, my desires, my dreams. Analogy leads me to believe that other people have similar experiences, but this is an inference, not an observation. The dentist does not feel my toothache, though he may have admirable inductive grounds for believing that I do.

This suggests a possible definition of psychology, as the science of those occurrences which, by their very nature, can only be observed by one person. Such a definition, however, unless somewhat limited, will turn out to be too wide in one direction, while too narrow in another. When a number of people observe a public event, such as the bursting of a rocket or a broadcast by the Prime Minister, they do not all see or hear exactly the same thing: there are differences due to perspective, distance from the source of the sight or sound, defects in the sense-organs, and so on. Therefore if we were to speak with pedantic accuracy, we should have to say that everything that can be observed is private to one person. There is often, however, such a close similarity between the simultaneous percepts of different people that the minute differences can, for many purposes, be ignored; we then say that they are all perceiving the same occurrence, and we place this occurrence in a public world outside all the observers. Such occurrences are the data of physics, while those that have not this social and public character supply (so I suggest) the data of psychology.

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According to this view, a datum for physics is something abstracted from a system of correlated psychological data. When a crowd of people all observe a rocket bursting, they will ignore whatever there is reason to think peculiar and personal in their experience, and will not realize without an effort that there is any private element in what they see. But they can, if necessary, become aware of these elements. One part of the crowd sees the rocket on the right, one on the left, and so on. Thus when each person's perception is studied in its fullness, and not in the abstract form which is most convenient for conveying information about the outside world, the perception becomes a datum for psychology.

But although every physical datum is derived from a system of psychological data, the converse is not the case. Sensations resulting from a stimulus within the body will naturally not be felt by other people ; if I have a stomach-ache I am in no degree surprised to find that others are not similarly afflicted. There are afferent nerves from the muscles, which cause sensations when the muscles are used; these sensations, naturally, are only felt by the person concerned. It is only when the stimulus is outside the body of the percipient, and not always even then, that the sensa- tion is one of a system which together constitutes one datum for physics. If a fly is crawling on your hand, the visual sensations that it causes are public, but the tickling is private. Psychology is the science which deals with private data, and with the private aspects of data which common sense regards as public.

To this definition a fundamental objection is raised by a certain school of psychologists, who maintain that “introspection" is not a valid scientific method, and that nothing can be scientifically known except what is derived from public data. This view seems to me so absurd that if it were not widely held I should ignore it; but as it has become fashionable in various circles I shall state my reasons for rejecting it.

To begin with, we need a more precise definition of “public" and “private" data. “Public" data, for the purpose of those who reject introspection, are not only data which in fact are shared by other observers, but also those which might be so shared given suitable circumstances. Robinson Crusoe, on this view, is not being unscientifically introspective when he describes the crops he raised, although there is no other observer to confirm his

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narrative, for its later parts are confirmed by Man Friday, and its earlier parts might have been. But when he relates how he became persuaded that his misfortunes were a punishment for his previous sinful life, he is either saying something meaningless or telling what words he would have uttered if he had had any one to speak to — for what a man says is public, but what he thinks is private. To maintain that what he says expresses his thought is, according to this school, to say something not scientifically verifiable and therefore something which science should not say. To attempt — as Freud did — to make a science of dreams is a mistake; we cannot know what a man dreams, but only what he says he dreams. What he says he dreams is part of physics, since the saying consists of movements of lips and tongue and throat; but it is a wanton assumption to suppose that what he says in professing to relate his dream expresses an actual experience.

We shall have to define a “public” datum as one which can be observed by many people, provided they are suitably placed. They need not all observe it at once, provided there is reason to think that there has been no change meanwhile: two people cannot look down a microscope at the same time, but the enemies of introspection do not mean to exclude data obtained by means of microscopes. Or consider the fact that, if you press one eyeball upwards, everything looks double. What is meant by saying that things “look” double? This can only be interpreted by distinguish- ing between the visual perception and the physical fact, or else by a subterfuge. You may say: “When I say that Mr. A. is seeing double, I say nothing about his perceptions; what I say means: Tf Mr. A. is asked, he will say he is seeing double*.” Such an interpretation makes it meaningless to inquire whether Mr. A. is speaking the truth, and impossible to discover what it is that he thinks he is asserting.

Dreams are perhaps the most indubitable example of facts which can only be known by means of private data. When I remember a dream I can relate it, either truly or with embellish- ments; I can know which I am doing, but others seldom can. I knew a Chinese lady who, after a few lessons in psycho-analysis, began to have perfect text-book dreams; the analyst was de- lighted, but her friends were sceptical. Although no one except the lady could be sure of the truth, I maintain that the fact as to

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what she had dreamed was just as definitely such-and-such rather than so-and-so as in the case of a physical phenomenon.

We shall have to say: A “public” datum is one which generates similar sensations in all percipients throughout a certain space- time region, which must be considerably larger than the region occupied by one human body throughout (say) half a second — or rather, it is one which would generate such sensations if suitably placed percipients were present (this is to allow for Robinson Crusoe’s crops).

This distinction between public and private data is one which it is difficult to make precise. Roughly speaking, sight and hearing give public data, but not always. When a patient is suffering from jaundice everything looks yellow, but this yellowness is private. Many people are liable to a buzzing in the ears which is sub- jectively indistinguishable from the hum of telegraph wires in a wind. The privacy of such sensations is only known to the percipient through the negative testimony of other people. Touch gives public data in a sense, since different people can successively touch the same object. Smells can be so public as to become grounds of complaint to the sanitary authority. Tastes are public in a lesser degree, for, though two people cannot eat the same mouthful, they can eat contiguous portions of the same viand ; but the curate’s egg shows that this method is not quite reliable. It is, however, sufficiently reliable to establish a public distinction between good cooks and bad ones, though here introspection plays an essential part, for a good cook is one who causes pleasure to most consumers, and the pleasure of each is purely private.

I have kept this discussion on a common-sense level, but at a later stage I shall resume it, and try to probe more deeply into the whole question of private data as a basis for science. For the present I am content to say that the distinction between public and private data is one of degree, that it depends upon testimony which bears witness to the results of introspection, that physiology would lead to the expectation that sensations caused by a stimulus inside a human body would be private, and, finally, that many of the facts of which each one of us is most certain are known to us by means private to ourselves. Do you like the smell of rotten eggs ? Are you glad the war is over ? Have you a toothache ? These questions are not difficult for you to answer, but no one else can

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answer them except by inferences from your behaviour, including your testimony.

I conclude, therefore, that there is knowledge of private data, and that there is no reason why there should not be a science of them. This being granted, we can now inquire what psychology in fact has to say.

There is, to begin with, a matter of which the importance is often overlooked, and that is the correlation of physical occurrences with sensation. Physicists and astronomers base their assertions as to what goes on in the outer world upon the evidence of the senses, especially the sense of sight. But not a single one of the occurrences that we are told take place in the physical world is a sensation; how, then, can sensations confirm or confute a physical theory? Let us take an illustration belonging to the infancy of science. It was early discovered that an eclipse of the sun is due to the interposition of the moon, and it was found that eclipses could be predicted. Now what was directly verified when an eclipse occurred was a certain sequence of expected sensations. But the development of physics and physiology has gradually caused a vast gulf between the sensations of an astronomer watching an eclipse and the astronomical fact which he infers. Photons start from the sun, and when the moon is not in the way some of them reach an eye, where they set up the kind of complicated process that we considered in the last chapter; at last, when the process reaches the astronomer’s brain, the astronomer has a sensation.

The sensation can only be evidence of the astronomical fact if laws are known connecting the two, and the last stage in these laws must be one connecting stimulus and sensation, or connecting occurrences in the optic nerve or the brain with sensation. The sensation, it should be observed, is not at all like the astronomical fact, nor are the two necessarily connected. It would be possible to supply an artificial stimulus causing the astronomer to have an experience subjectively indistinguishable from what we call “seeing the sun”. And at best the resemblance between the sensation and the astronomical fact cannot be closer than that between a gramophone record and the music that it plays, or between a library catalogue and the books that it enumerates. It follows that, if physics is an empirical science, whose statements can be confirmed or confuted by observation, then physics must be supplemented by laws connecting stimulus and sensation.

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THE SCIENCE OF MIND

Now such laws belong to psychology. Therefore what is em- pirically verifiable is not pure physics in isolation, but physics plus a department of psychology. Psychology, accordingly, is an essential ingredient in every part of empirical science.

So far, however, we have not inquired whether there are any laws that connect one mental event with another. The laws of correlation so far considered have been such as connect a physical stimulus with a mental response; what we have now to consider is whether there are any causal laws which are entirely within one mind. If there are, psychology is to that extent an autonomous science. The association of ideas, as it appears for example in Hartley and Bentham, was a law of this kind, but the conditioned reflex and the law of habit, which have taken its place, are primarily physiological and only derivatively psychological, since association is thought to be caused by the creation of paths in the brain connecting one centre with another. We may still state the association of ideas in purely psychological terms, but when so stated it is not a law as to what always happens, but only as to what is apt to happen. It has not therefore the character that science hopes to find in a causal law, or at least used to hope for before the rise of quantum theory.

The same thing may be said of psycho-analysis, which aims at discovering purely mental causal laws. I do not know of any psycho-analytic law which professes to say what will always happen in such and such circumstances. When a man, for example, suffers from claustrophobia, psycho-analysis will discover this or that past experience which is held to explain his trouble; but many people will have had the same experience without the same result. The experience in question, accordingly, though it may well be part of the cause of the phobia, cannot be its whole cause. We cannot, this being the case, find in psycho- analysis any examples of purely psychical causal laws.

In the last chapter we suggested, as a probable hypothesis, the view that all bodily behaviour is theoretically explicable in physical terms, without taking any account of the mental concomitants of physiological occurrences. This hypothesis, it should be observed, in no way decides our present question. If A and B are two events in the brain, and if A causes B, then if a is a mental concomitant of A, and b of B, it will follow that a causes A, which is a purely mental causal law. In fact, causal

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laws are not of the simple form “A causes B”, but in their true form the principle remains the same.

Although, at present, it is difficult to give important examples of really precise mental causal laws, it seems pretty certain, on a common-sense basis, that there are such laws. If you tell a man that he is both a knave and a fool, he will be angry; if you inform your employer that he is universally regarded as a swindler and a bloodsucker, he will invite you to seek employment elsewhere. Advertising and political propaganda supply a mass of materials for the psychology of belief. The feeling one has in a novel or a play as to whether the behaviour of the characters is “right” is based upon unformulated knowledge of mental causality, and so is shrewdness in handling people. In such cases, the knowledge involved is pre-scientific, but it could not exist unless there were scientific laws which could be ascertained by sufficient study.

There are a certain number of genuine causal laws of the kind in question, though so far they are mostly concerned with matters that have no great intrinsic interest. Take, for example, after-images: you look fixedly at a bright red object, and then shut your eyes; you see first a gradually fading red image, and then a green image, of approximately the same shape. This is a law for which the evidence is purely introspective. Or again, take a well-known illusion :

In the figure the two horizontal lines are parallel, but they look as if they approached each other towards the right. This again is a law for which the evidence is purely introspective. In both cases there are physiological explanations, but they do not invalidate the purely psychological laws.

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I conclude that, while some psychological laws involve physiology, others do not. Psychology is a science distinct from physics and physiology, and in part independent of them. All the data of physics are also data of psychology, but not vice versa ; data belonging to both are made the basis of quite different inferences in the two sciences. Introspection is valid as a source of data, and is to a considerable extent amenable to scientific controls.

There is much in psychology that is genuinely scientific although it lacks quantitative precision. Take, for example, the analysis of our spatial perceptions, and the building up of the common-sense notion of space from its sensational foundations. Berkeley’s theory of vision, according to which everything looks flat, is disproved by the stereoscope. The process by which we learn in infancy to touch a place that we see can be studied by observation. So can volitional control: a baby a few months old can be watched learning with delight to move its toes at will, instead of having to look on passively while they wriggle in purely reflex movements. When, in later life, you acquire some skill, such as riding a bicycle, you find yourself passing through stages: at first you will certain movements of your own body, in the hope that they will cause the desired movements of the bicycle, but afterwards you will the movements of the bicycle directly, and the necessary movements of your body result auto- matically. Such experiences throw much light on the psychology of volition.

Much psychology is involved in connecting sensory stimuli with the beliefs to which they give rise. I am thinking of such elementary occurrences as thinking “there’s a cat” when certain coloured patches in motion pass across your field of vision. It is obvious that the same sensory stimulus could be caused other- wise than by a cat, and your belief would then be false. You may see a room reflected in a mirror, and think that it is “real”. By studying such occurrences we become aware that a very large part of what we think we perceive consists of habits caused by past experience. Our life is full of expectations of which, as a rule, we only become aware when they are disappointed. Suppose you see half of a horse that is just coming round a corner; you may be very little interested, but if the other half proved to be cow and not horse you would experience a shock

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of surprise which would be almost unendurable. Yet it must be admitted that such an occurrence is logically possible.

The connection of pleasure and pain and desire with habit- formation can be studied experimentally. Pavlov, whose work nowhere appeals to introspection, put a dog in front of two doors, on one of which he had drawn an ellipse and on the other a circle. If the dog chose the right door he got his dinner; if he chose the wrong one he got an electric shock. Thus stimulated, the dog’s progress in geometry was amazingly rapid. Pavlov gradually made the ellipse less and less eccentric, but the dog still distinguished correctly, until the ratio of minor to major axis was reduced to 8:9, when the poor beast had a nervous breakdown. The utility of this experiment in connection with schoolboys and criminals is obvious.

Or, again, take the question: why do we believe what we do? In former times, philosophers would have said it was because God had implanted in us a natural light by which we knew the truth. In the early nineteenth century they might have said it was because we had weighed the evidence and found a preponder- ance on one side. But if you ask a modern advertiser or political propagandist he will give you a more scientific and more depressing answer. A large proportion of our beliefs are based on habit, conceit, self-interest, or frequent iteration. The advertiser relies mainly on the last of these, but if he is clever he combines it skilfully with the other three. It is hoped that by studying the psychology of belief, those who control propaganda will in time be able to make anybody believe anything. Then the totalitarian State will become invincible.

In regard to human knowledge there are two questions that may be asked: first, what do we know? and second, how do we know it? The first of these questions is answered by science, which tries to be as impersonal and as dehumanized as possible. In the resulting survey of the universe it is natural to start with astronomy and physics, which deal with what is large and what is universal; life and mind, which are rare and have, apparently, little influence on the course of events, must occupy a minor position m this impartial survey. But in relation to our second question, namely, how do we come by our knowledge, psychology is the most important of the sciences. Not only is it necessary to study psychologically the processes by which we draw inferences,

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but it turns out that all the data upon which our inferences should be based are psychological in character, that is to say, they are experiences of single individuals. The apparent publicity of our world is in part delusive and in part inferential; all the raw material of our knowledge consists of mental events in the lives of separate people. In this region, therefore, psychology is supreme.

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PART II

LANGUAGE

Chapter I

THE USES OF LANGUAGE

Language, like other things of mysterious importance, such as breath, blood, sex, and lightning, has been viewed superstitiously ever since men were capable of recording their thoughts. Savages fear to disclose their true name to an enemy, lest he should work evil magic by means of it. Origen assures us that pagan sorcerers could achieve more by using the sacred name Jehovah than by means of the names Zeus, Osiris, or Brahma. Familiarity makes us blind to the linguistic emphasis in the Commandment: “Thou shalt not take the name of the Lord in vain.” The habit of viewing language superstitiously is not yet extinct. “In the beginning was the Word”, says our version of St. John’s Gospel, and in reading some logical positivists I am tempted to think that their view is represented by this mistranslated text.

Philosophers, being bookish and theoretical folk, have been interested in language chiefly as a means of making statements and conveying information, but this is only one of its purposes, and perhaps not the most primitive. What is the purpose of language to a sergeant-major? On the one hand there is the language of words of command, designed to cause identical simultaneous bodily movements in a number of hearers ; on the other hand there is bad language, designed to cause humility in those in whom the expected bodily movements have not been caused. In neither case are words used, except incidentally, to state facts or convey information.

Language can be used to express emotions, or to influence the behaviour of others. Each of these functions can be performed, though with less adequacy, by pre-linguistic methods. Animals emit shrieks of pain, and infants, before they can speak, can express rage, discomfort, desire, delight, and a whole gamut of feelings, by cries and gurgles of different kinds. A sheep dog emits imper- atives to his flock bv means hardly distinguishable from those that the shepherd employs towards him. Between such noises and speech no sharp line can be drawn. When the dentist hurts you, you may emit an involuntary groan; this does not count as

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speech. But if he says “let me know if I hurt you”, and you then make the very same sound, it has become speech, and moreover speech of the sort intended to convey information. This example illustrates the fact that, in the matter of language as in other respects, there is a continuous gradation from animal behaviour to that of the most precise man of science, and from pre-linguistic noises to the polished diction of the lexicographer.

A sound expressive of emotion I shall call an “interjetion”. Imperatives and interjections can already be distinguished in the noises emitted by animals. When a hen clucks at her brood of chickens, she is uttering imperatives, but when she squawks in terror she is expressing emotion. But as appears from your groan at the dentist s, an interjection may convey information, and the outside observer cannot tell whether or not it is intended to do so. Gregarious animals emit distinctive noises when they find food, and other members of the herd are attracted when they hear these noises, but we cannot know whether the noises merely express pleasure or are also intended to state “food here”.

Whenever an animal is so constructed that a certain kind of circumstance causes a certain kind of emotion, and a certain kind of emotion causes a certain kind of noise, the noise conveys to a suitable observer two pieces of information, first, that the animal has a certain kind of feeling, and second, that a certain kind of circumstance is present. The sound that the animal emits is public, and the circumstance may be public — e.g. the presence of a shoal of fish if the animal is a sea-gull. The animal’s cry may act directly on the other members of its species, and we shall then say that they “understand” its cry. But this is to suppose a “mental” intermediary between the hearing of the cry and the bodily reaction to the sound, and there is no real reason to suppose any such intermediary except when the response is delayed. Much of the importance of language is connected with delayed responses, but I will not yet deal with this topic.

Language has two primary purposes, expression and com- munication. In its most primitive forms it differs little from some other forms of behaviour. A man may express sorrow by sighing, or by saying “alas!” or “woe is me!” He may communicate by pointing or by saying “look”. Expression and communication are not necessarily separated; if you say “look” because you see a ghost, you may say it in a tone that expresses horror. This

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applies not only to elementary forms of language; in poetry, and especially in songs, emotion and information are conveyed by the same means. Music may be considered as a form of language in which emotion is divorced from information, while the telephone book gives information without emotion. But in ordinary speech both elements are usually present.

Communication does not consist only of giving information; commands and questions must be included. Sometimes the two are scarcely separable: if you are walking with a child, and you say “there’s a puddle there”, the command “don’t step in it” is implicit. Giving information may be due solely to the fact that the information interests you, or may be designed to influence behaviour. If you have just seen a street accident, you will wish to tell your friends about it because your mind is full of it ; but if you tell a child that six times seven is forty-two you do so merely in the hope of influencing his (verbal) behaviour.

Language has two interconnected merits: first, that it is social, and second that it supplies public expression for “thoughts” which would otherwise remain private. Without language, or some pre-linguistic analogue, our knowledge of the environment is confined to what our own senses have shown us, together with such inferences as our congenital constitution may prompt; but by the help of speech we are able to know what others can relate, and to relate what is no longer sensibly present but only remembered. When we see or hear something which a companion is not seeing or hearing, we can often make him aware of it by the one word “look” or “listen”, or even by gestures. But if half an hour ago we saw a fox, it is not possible to make another person aware of this fact without language. This depends upon the fact that the word “fox” applies equally to a fox seen or a fox remembered, so that our memories, which in themselves are private, are represented to others by uttered sounds, which are public. Without language, only that part of our life which consists of public sensations would be communicable, and that only to those so situated as to be able to share the sensations in question.

It will be seen that the utility of language depends upon the distinction between public and private experiences, which is important in considering the empirical basis of physics. This distinction, in turn, depends partly on physiology, partly on the persistence of sound-waves and light quanta, which makes

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possible the two forms of language, speech and writing. Thus language depends upon physics, and could not exist without the approximately separable causal chains which, as we shall see, make physical knowledge possible, and since the publicity of sensible objects is only approximate, language applying to them, considered socially, must have a certain lack of precision. I need hardly say that I am not asserting that the existence of language requires a knowledge of physics. What I am saying is that language would be impossible if the physical world did not in fact have certain characteristics, and that the theory of language is at certain points dependent upon a knowledge of the physical world. Language is a means of externalizing and publicizing our own experiences. A dog cannot relate his autobiography; however eloquently he may bark, he cannot tell you that his parents were honest though poor. A man can do this, and he does it by correlating “thoughts” with public sensations.

Language serves not only to express thoughts, but to make possible thoughts which could not exist without it. It is sometimes maintained that there can be no thought without language, but to this view I cannot assent : I hold that there can be thought, and even true and false belief, without language. But however that may be, it cannot be denied that all fairly elaborate thoughts require words. I can know, in a sense, that I have five fingers, without knowing the word “five”, but I cannot know that the population of London is about eight millions unless I have acquired the language of arithmetic, nor can I have any thought at all closely corresponding to what is asserted in the sentence : “the ratio of the circumference of a circle to the diameter is approxi- mately 3-14159”. Language, once evolved, acquires a kind of autonomy : we can know, especially in mathematics, that a sentence asserts something true, although what it asserts is too complex to be apprehended even by the best minds. Let us consider for a moment what happens psychologically in such cases.

In mathematics, we start from rather simple sentences which we believe ourselves capable of understanding, and proceed, by rules of inference which we also believe ourselves to understand, to build up more and more complicated symbolic statements, which, if our initial assumptions are true, must be true whatever they may mean. As a rule it is unnecessary to know what they “mean”, if their “meaning” is taken to be a thought which

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might occur in the mind of a superhuman mathematical genius. But there is another kind of “meaning”, which gives occasion for pragmatism and instrumentalism. According to those who adopt this view of “meaning”, what a complicated mathematical sentence does is to give a rule for practical procedure in certain kinds of cases. Take, for instance, the above statement about the ratio of the circumference of a circle to the diameter. Suppose you are a brewer, and you desire hoops of a given diameter for your beer barrels, then the sentence gives you a rule by which you can find out how much material you will need. This rule may consist of a fresh sentence for each decimal point, and there is therefore no need ever to grasp its significance as a whole. The autonomy of language enables you to forego this tedious process of interpretation except at crucial moments.

There are two other uses of language that are of great import- ance; it enables us to conduct our transactions with the outer world by means of symbols that have (l) a certain degree of permanence in time, (2) a considerable degree of discreteness in space. Each of these merits is more marked in writing than in speech, but is by no means wholly absent in speech. Suppose you have a friend called Mr. Jones. As a physical object his boundaries are somewhat vague, both because he is continually losing and acquiring electrons, and because an electron, being a distribution of energy, does not cease abruptly at a certain distance from its centre. The surface of Mr. Jones, therefore, has a certain ghostly impalpable quality, which you do not like to associate with your solid-seeming friend. It is not necessary to go into the niceties of theoretical physics in order to show that Mr. Jones is sadly indeterminate. When he is cutting his toe nails, there is a finite time, though a short one, during which it is doubtful whether the parings are still part of him or not. When he eats a mutton chop, at what moment does it become part of him? When he breathes out carbon dioxide, is the carbon part of him until it passes his nostrils ? Even if we answer in the affirmative, there is a finite time during which it is questionable whether certain molecules have or have not passed beyond his nostrils. In these and other ways, it is doubtful what is part of Mr. Jones and what is not. So much for spatial vagueness.

There is the same problem as regards time. To the question “what are you looking at ?” you may answer “Mr. Jones”, although

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at one time you see him full-face, at another in profile, and at another from behind, and although at one time he may be running a race and at another time dozing in an arm-chair. There is another question, namely “what are you thinking of?” to which you may also answer “Mr. Jones”, though what is actually in your mind may be very different on different occasions : it may be Mr. Jones as a baby, or Mr. Jones being cross because his break- fast is late, or Mr. Jones receiving the news that he is to be knighted. What you are experiencing is very different on these various occasions, but for many practical purposes it is convenient to regard them as all having a common object, which we suppose to be the meaning of the name “Mr. Jones”. This name, especially when printed, though it cannot wholly escape the indefiniteness and transience of all physical objects, has much less of both than Mr. Jones has. Two instances of the printed words “Mr. Jones” are much more alike than (for instance) the spectacle of Mr. Jones running and the memory of Mr. Jones as a baby. And each instance, if printed, changes much more slowly than Mr. Jones does: it does not eat or breathe or cut its toe nails. The name, accordingly, makes it much easier than it would otherwise be to think of Mr. Jones as a single quasi-permanent entity, which, though untrue, is convenient in daily life.

Language, as appears from the above discussion of Mr. Jones, though a useful and even indispensable tool, is a dangerous one, since it begins by suggesting a definiteness, discreteness, and quasi-permanence in objects which physics seems to show that they do not possess. The philosopher, therefore, is faced with the difficult task of using language to undo the false beliefs that it suggests. Some philosophers, who shrink from the problems and uncertainties and complications involved in such a task, prefer to treat language as autonomous, and try to forget that it is intended to have a relation to fact and to facilitate dealings with the environment. Up to a point, such a treatment has great advantages: logic and mathematics would not have prospered as they have done if logicians and mathematicians had continually remembered that symbols should mean something. “Art for art's sake” is a maxim which has a legitimate sphere in logic as in painting (though in neither case does it give the whole truth). It may be that singing began as an incident in courtship, and that its biological purpose was to promote sexual intercourse ;

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but this fact (if it be a fact) will not help a composer to produce good music. Language is useful when you wish to order a meal in a restaurant, but this fact, similarly, is of no importance to the pure mathematician.

The philosopher, however, must pursue truth even at the expense of beauty, and in studying language he must not let himself be seduced by the siren songs of mathematics. Language, in its beginnings, is pedestrian and practical, using rough and ready approximations which have at first no beauty and only a very limited degree of truth. Subsequent refinements have too often had aesthetic rather than scientific motives, but from the inquiry upon which we are about to embark aesthetic motives must, however reluctantly, be relentlessly banished.

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Chapter II

OSTENSIVE DEFINITION

41 stensive definition” may be defined as “any process

I 1 by which a person is taught to understand a word other- wise than by the use of other words”. Suppose that, knowing no French, you are shipwrecked on the coast of Normandy : you make your way into a farmhouse, you see bread on the table, and, being famished, you point at it with an inquiring gesture. If the farmer thereupon says “pain9\ you will conclude, at least provisionally, that this is the French for “bread”, and you will be confirmed in this view if the word is not repeated when you point at other kinds of eatables. You will then have learnt the meaning of the word by ostensive definition. It is clear that, if you know no French and your teacher knows no English, you must depend upon this process during your first lessons, since you have no linguistic means of com- munication.

The process of ostensive definition, however, is better exem- plified when the learner knows no language at all than when he already possesses a language of his own. An adult knows that there are words, and will naturally suppose that the French have a way of naming bread. His knowledge takes the form: “ 4 Pain 9 means ‘bread’ ”. It is true that, when you were ship- wrecked, it was by means of actual bread that you acquired this knowledge, but if you had been shipwrecked with a dictionary the actual bread would not have been necessary. There are two stages in the acquisition of a foreign language, the first that in which you only understand by translating, the second that in which you can “think” in the foreign language. In the first stage you know that “pain” means “bread”, in the second stage you know that it means bread. The infant, possessing as yet no language, has to begin with the second stage. His success does credit to the capacities of the infant mind.

Knowing a language has two aspects, passive and active: passive when you understand what you hear, active when you can speak yourself. Dogs to some degree achieve the former, and children usually achieve it some time before the latter.

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Knowing a language does not mean a capacity for explicit explana- tion of what its words signify; it means that hearing the words has appropriate effects, and using them has appropriate causes. I have sometimes, in the course of travel, watched a quarrel springing up between two men whose language I did not under- stand, and it was difficult not to feel their mounting excitement ridiculous. But probably the first was accusing the second of being the offspring of parents who were not married, and the second was retorting that the first’s wife was unfaithful. If I had understood, the effect of the insult and the cause of the retort would have been obvious. As this example illustrates, a person knows a language when hearing certain sounds has certain effects and uttering them has certain causes. The process by which, in the infant, the establishment of these causal laws is begun, is the process of ostensive definition.

Ostensive definition, in its earliest form, requires certain conditions. There must be a feature of the environment which is noticeable, distinctive, emotionally interesting, and (as a rule) frequently recurring, and the adult must frequently utter the name of this feature at a moment when the infant is attending to it. Of course there are risks of error. Suppose the child has milk in a bottle. You may each time say “milk” or each time say “bottle”. In the former case the child may think “milk” is the right word for a bottle of water; in the latter case, he may think “bottle” the right word for a glass of milk. To avoid such errors, you should in theory apply Mill’s inductive canons, remembering that induction is a bodily habit, and only by courtesy a logical process. Instead of saying merely “milk” or merely “bottle”, you should say “bottle of milk”; you should then, on appropriate occasions, say “glass of milk” and “bottle of water”. In time, by the use of Mill’s canons, the infant, if he survives, will learn to speak correctly. But I am not giving practical pedagogic advice; I am merely exemplifying a theory.

The passive part in ostensive definition is merely the familiar business of association or the conditioned reflex. If a certain stimulus A produces in a child a certain reaction R, and is fre- quently experienced in conjunction with the word B, it will happen in time that B will produce the reaction R, or some part of it. As soon as this has happened, the word B has acquired a “mean- ing” for the child: it “means” A. The meaning may not be quite

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what the adult intended: the adult may have intended “bottle” and the child may understand the word as meaning milk. But that does not prevent the child from possessing a word that has meaning; it only signifies that the child's language is not yet correct English.

When an experience causes violent emotion, repetition may be unnecessary. If a child, after learning to understand “milk”, is given milk so hot as to scald his mouth, and you say “hot”, he may ever after understand this word. But when an experience is uninteresting, many repetitions may be necessary.

The active part in the learning of language requires other capacities, which however, are of less philosophic interest. Dogs cannot learn human speech because they are anatomically in- capable of producing the right sounds. Parrots, though they can produce more or less the right sounds, seem incapable of acquiring the right associations, so that their words do not have meaning. Infants, in common with the young of the higher animals, have an impulse to imitate adults of their own species, and therefore try to make the sounds that they hear. They may, on occasion, repeat sounds like a parrot, and only subsequently discover the “meaning” of the sounds. In that case the sounds cannot count as words until they have acquired meaning for the child. For every child it is a discovery that there are words, i.e. sounds with meaning. Learning to utter words is a joy to the child, largely because it enables him to communicate his wishes more definitely than he had been able to do by crying and making gestures. It is owing to this pleasure that children go through the mental labour and muscular practice involved in learning to talk.

In general, though not universally, repetition is necessary for an ostensive definition, for ostensive definition consists in the creation of a habit, and habits, as a rule, are learned gradually. The exceptional cases are illustrated by the proverbs “once bit, twice shy” and “the burnt dblild dreads the fire”. Apart from such unusually emotional matters, the words that have ostensive definitions denote frequently recurring features of the environ- ment, such as the members of the family, foods, toys, pet animals, etc. This involves the process of recognition, or something of the kind. Although a child’s mother looks somewhat different on different occasions, he thinks of her (when he begins to think) as always the same person, and feels no difficulty in applying the

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same name to her various epiphanies. Language, from the start, or rather from the start of reflection on language, embodies the belief in more or less permanent persons and things. This is perhaps the chief reason for the difficulty of any philosophy which dispenses with the notion of substance. If you were to tell a child that his mother is a series of sensible impressions, connected by similarity and causal relations, but without material identity, and if by a miracle you could make him understand what you meant, he would consider you demented and be filled with indignation. The process called “recognition” is therefore one that demands investigation.

Recognition, as a physiological or psychological occurrence, may or may not be veridical. It fails in an every-day sense to be veridical when we mistake one of two twins for the other, but it may be metaphysically misleading even when it is correct from the standpoint of common sense. Whether there is anything identical, and if so what, between two different appearances of Mr. A, is a dark and difficult question, which I shall consider in connection with proper names. For the moment I wish to consider recognition as a process which actually occurs, without regard to its interpretation.

The first stage in the development of this process is repetition of a learnt reaction when the stimulus is repeated. It must be a learnt reaction, since recognition must grow out of a process involving something, in later reactions to a given stimulus, which was not present in the first reaction. Suppose, for instance, you give a child a glass of milk containing bitter medicine: the first time he drinks the doctored milk and makes a face, but the second time he refuses the milk. This is subjectively something like recognition, even if the second time he is mistaken in supposing that the milk contains medicine. It is clear that this process may be purely physiological, and that it involves only similarity, not identity, in stimulus and response. The learning of words by ostensive definition can be brought wholly within this primitive stage. The child’s world contains a number of similar stimuli to which he has learnt to respond by similar noises, namely those that are instances of the word “milk”; it contains also another set of similar stimuli to which he has learnt to respond by instances of the word “mother”. In this there is nothing involving any beliefs or emotions in the child.

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HUMAN knowledge: its scope and limits

It is only as a result of subsequent reflection that the child, now become a philosopher, concludes that there is one word, “mother”, and one person, Mother. I believe this first step in philosophy to be mistaken. The word “mother”, I should say, is not a single entity, but a class of similar noises; and Mother herself is also not a single entity, but a class of causally connected occurrences. These speculations, however, are irrelevant to the process of ostensive definition, which, as we have just seen, requires only the very first stage on the road towards what would usually count as recognition, namely similar learnt responses to similar stimuli.

This primitive form of recognition is relevant in the analysis of memory and in explaining the similarity of an idea to an impression (to borrow Hume’s phraseology). When I remember a past event, I cannot make it itself occur again, though I may be able to make a similar event occur. But how do I know that the new event is similar to the old one ? Subjectively, I can only know by comparing an idea with an impression: I have an idea of the past event and an impression of the present event, and I perceive that they are similar. But this is not sufficient, since it does not prove that my idea of the past event is similar to my impression of th t past event when it existed. This, in fact, cannot be proved, and is in some sense one of the premisses of knowledge. But although it cannot be strictly proved, it can be in various ways confirmed. You may describe Mr. A while he is present, and your description may be recorded on a dictaphone. You may later describe him from memory, and compare your new description with the dictaphone record. If they agree closely, your memory may be accepted as correct.

This illustration depends upon a fact which is fundamental in this subject, namely, that we apply the same words to ideas as to the impressions which are their prototypes. This explains the possibility of learning a word ostensively by means of a single sensible occurrence. I saw Disraeli once, and once only, and was told, at the moment, “that’s Dizzy”. I have since very frequently remembered the occurrence, with the name “Dizzy” as an essential part of the memory. This has made it possible for a habit to be formed by repetition of the idea (in Hume’s sense), although the impression has never been repeated. It is obvious that ideas differ from impressions in various ways, but their

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similarity to their prototypes is vouched for by the fact that they cause the same words. The two questions, “what are you looking at?” and “what are you thinking of?” may, on two different occasions, be answered identically.

Let us consider the different kinds of words that are commonly learnt by means of ostensive definitions. What I have in mind is a logical form of the grammatical doctrine of parts of speech.

We have already had occasion for a preliminary consideration of proper names. I shall say no more about them at present, as they will be the subject of a separate chapter.

Next come names of species: man, woman, cat, dog, etc. A species of this sort consists of a number of separate individuals, having some recognizable degree of likeness to each other. In biology before Darwin, “species” was a prominent concept. God had created a pair of each species, and different species could not interbreed, or, in the exceptional cases when they could, such as horse and ass, the offspring was sterile. There was an elaborate hierarchy of genera, families, orders, etc. This kind of classification, which was and is convenient in biology, was extended by the scholastics to other regions, and impeded logic by creating the notion that some ways of classifying are more correct than others. As regards ostensive definition, different experiences will produce different results. Most children learn the word “dog” ostensively; some learn in this way the kinds of dogs, collies, St. Bernards, spaniels, poodles, etc., while others, who have little to do with dogs, may first meet with these words in books. No child learns the word “quadruped” ostensively, still less the word “animal” in the sense in which it includes oysters and limpets. He probably learns “ant”, “bee”, and “beetle” ostensively, and perhaps “insect”, but if so he will mistakenly include spiders until corrected.

(^Names of substances not obviously collections of individuals, such as “milk”, “bread”, “wood”, are apt to be learnt ostensively when they denote things familiar in every-day life. The atomic theory is an attempt to identify this class of objects with the former, so that milk, for instance, is a collection of milky individuals (molecules), just as the human race is a collection of men, women, and children. J But to unscientific apprehension such names of substances are not to be assimilated to species composed of separate individuals.

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Next come qualities: red, blue, hard, soft, hot, cold, etc. Many of these are usually learnt ostensively, but the less common ones, such as vermilion, may be described by their similarities and differences.

Names of certain relations, such as “up”, “down”, “right”, “left”, “before”, “after”, are usually learnt ostensively. So are such words as “quick” and “slow”.

There are a number of words of the sort that I call “ego- centric”, which differ in meaning according to the speaker and his position in time and space. Among these the simple ones are learnt ostensively, for instance “I”, “you”, “here”, “now”. These words raise problems which we will consider in a later chapter.

All the words I have mentioned hitherto belong to the public world. A spectator can see when a certain feature of the public environment is attracting a child’s attention, and then mention the name of this feature. But how about private experiences, such as stomach-ache, pain, or memory? Certainly some words denoting private kinds of experience are learnt ostensively. This is because the child shows in behaviour what he is feeling : there is a correlation between e.g. pain and tears.

There are no definite limits to what can be learnt by ostensive definition. “Cross”, “crescent”, “swastika” can be learnt in this way, but not “chiliagon”. But the point where this method of learning becomes impossible depends upon the child’s experience and capacity.

The words so far mentioned are all capable of being used as complete sentences, and are in fact so used in their most primitive employment. “Mother”, “dog”, “cat”, “milk”, and so on, may be used alone to express either recognition or desire. “Hard”, “soft”, “hot”, “cold” would be more naturally used to express recognition than desire, and usually to express recognition accompanied by surprise. If the toast is uneatable because it is old you may say “hard”; if a ginger biscuit has lost its crispness by exposure to air you may say “soft”. If the bath scalds you, you say “hot”; if it freezes you, you say “cold”. “Quick” is frequently used by parents as an imperative; “slow” is used similarly on roads and railways where there is a curve. The words “up” and “down” are habitually used as complete sentences by lift-boys; “in” and “out” are similarly used at turnstiles.

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“Before” and “after” are used as complete sentences in advertise- ments of hair-restorers. And so on and so on. It is to be noted that not only substantives and adjectives, but adverbs and pre- positions, may on occasion be used as complete sentences.

I think the elementary uses of a word may be distinguished as indicative, imperative, and interrogative. When a child sees his mother coming, he may say “mother!”; this is the indicative use. When he wants her, he calls “mother!”; this is the imperative use. When she dresses up as a witch and he begins to pierce the disguise, he may say “mother?”; this is the interrogative use. The indicative use must come first in the acquisition of language, since the association of word and object signified can only be created by the simultaneous presence of both. But the imperative use very quickly follows. This is relevant in considering what we mean by “thinking of” an object. It is obvious that the child who has just learnt to call his mother has found verbal expression for a state in which he had often been previously, that this state was associated with his mother, and that it has now become associated with the word “mother”. Before language, his state was only partially communicable; an adult, hearing him cry, could know that he wanted something, but had to guess what it was. But the fact that the word “mother!” expresses his state shows that, even before the acquisition of language, his state had a relation to his mother, namely the relation called “thinking of”. This relation is not created by language, but antedates it. What language does is to make it communicable.

“Meaning” is a word which must be interpreted somewhat differently according as it is applied to the indicative or the imperative. In the indicative, a word A means a feature B of the environment if, (i) when B is emphatically present to attention, A is uttered, or there is an impulse to utter A, and (2) when A is heard it arouses what may be called the “idea” of B, which shows itself either in looking for B or in behaviour such as would be caused by the presence of B. Thus in the indicative a word “means” an object if the sensible presence of the object causes the utterance of the word, and the hearing of the word has effects analogous, in certain respects, to the sensible presence of the object.

The imperative use of a word must be distinguished according as it is heard or uttered. Broadly speaking, an imperative heard

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— e.g. the word of command in the army — is understood when it causes a certain kind of bodily movement, or an impulse towards such a movement. An imperative uttered expresses a desire, and therefore requires the existence of an “idea” of the intended effect. Thus while it “expresses” something in the speaker, it “means” the external effect which it commands. The distinction between what is “meant” and what is “expressed” is essential in this use of words.

We have been concerned, in this chapter, only with the most primitive uses of the most primitive words. We have not considered the use of words in narrative or in hypothesis or in fiction, nor have we examined logical words such as “not”, “or”, “all”, and “some”; we have not inquired how learners acquire the correct use of such words as “than” or “of”, which do not denote recognizable features of any sensible environment. What we have decided is that a word may become associated with some notable feature of the environment (in general, one that occurs frequently), and that, when it is so associated, it is also associated with something that may be called the “idea” or “thought” of this feature. When such an association exists, the word “means” this feature of the environment; its utterance can be caused by the feature in question, and the hearing of it can cause the “idea” of this feature. This is the simplest kind of “meaning”, out of which other kinds are developed.

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Chapter III PROPER NAMES

There is a traditional distinction between “proper” names and “class” names, which is explained as consisting in the fact that a proper name applies, essentially, to only one object, whereas a class name applies to all objects of a certain kind, however numerous they may be. Thus “Napoleon” is a proper name, while “man” is a class name. It will be observed that a proper name is meaningless unless there is an object of which it is the name, but a class name is not subject to any such limitation. “Men whose heads do grow beneath their shoulders” is a perfectly good class name, although there are no instances of it. Again, it may happen that there is only one instance of a class name, e.g. “satellite of the earth”. In such a case, the one member may have a proper name (“the moon”), but the proper name does not have the same meaning as the class name, and has different syntactical functions. E.g. we can say: “ ‘Satellite of the earth’ is a unit class”, but we cannot say “the moon is a unit class”, because it is not a class, or at any rate not a class of the same logical type as “satellite of the earth”, and if taken as a class (e.g. of molecules) it is many, not one.

Many difficult questions arise in connection with proper names Of these there are two that are especially important: first, what is the precise definition of proper names? second, is it possible to express all our empirical knowledge in a language containing no proper names? This second question, we shall find, takes us to the heart of some of the most ancient and stubborn of philo- sophical disputes.

In seeking a definition of “proper name”, we may approach the subject from the point of view of metaphysics, logic, physics, syntax, or theory of knowledge. I will say a few preliminary words about each of these.

A. Metaphysical — It is fairly obvious that proper names owe their existence in ordinary language to the concept of “substance” — originally in the elementary form of “persons” and “things”. A substance or entity is named, and then properties are assigned to it. So long as this metaphysic was accepted, there was no

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difficulty as to proper names, which were the designations of such substances as were sufficiently interesting. Sometimes, it is true, we should give a name to a collection of substances, such as France or the sun. But such names, strictly speaking, were not necessary. In any case, we could extend our definition to embrace collections of substances.

But most of us, nowadays, do not accept “substance” as a useful notion. Are we then to adopt, in philosophy, a language without proper names? Or are we to find a definition of “proper name” which does not depend on “substance”? Or are we to conclude that the conception of “substance” has been too hastily rejected? For the present, I merely raise these questions, without attempting to answer them. All that I want to make clear at the moment is that proper names, as ordinarily understood, are ghosts of substances.

B. Syntactical . — It i9 clear that a syntactical definition of “proper name” must be relative to a given language or set of languages. In the languages of daily life, and also in most of those employed in logic, there is a distinction between subject and predicate, between relation-words and term-words. A “name” will be, in such languages, “a word which can never occur in a sentence except as a subject or a term-word”. Or again: a proper name is a word which may occur in any form of sentence not containing variables, whereas other words can only occur in sentences of appropriate form. Sometimes it is said that some words are “syncategorimatic”, which apparently means that they have no significance by themselves, but contribute to the significance of sentences in which they occur. According to this way of speaking, proper names are not syncategorimatic, but whether this can be a definition is a somewhat doubtful question. In any case, it is difficult to get a clear definition of the term “syncategorimatic”.

The chief inadequacy of the above syntactical point of view is that it does not, in itself, help us to decide whether it is possible to construct languages with a different kind of syntax, in which the distinctions we have been considering would disappear.

C. Logical . — Pure logic has no occasion for names, since its propositions contain only variables. But the logician may wonder, in his unprofessional moments, what constants could be sub- stituted for his variables. The logician announces, as one of his principles, that, if “fx” is true for every value of “#”, then "/»”

PROPER NAMES

is true, where “a” is any constant. This principle does not mention a constant, because “any constant” is a variable ; but it is intended to justify those who want to apply logic. Every application of logic or mathematics consists in the substitution of constants for variables; it is therefore essential, if logic or mathematics is to be applied, to know what sort of constants can be substituted for what sort of variables. If any kind of hierarchy is admitted among variables, “proper names” will be “constants which are values of variables of lowest type”. There are, however, a number of difficulties in such a view. I shall not therefore pursue it further.

D. Physical . — There are here two points of view to be con- sidered. The first is that a proper name is a word designating any continuous portion of space-time which sufficiently interests us; the second is that, this being the function of proper names, they are unnecessary, since any portion of space-time can be described by its co-ordinates. Carnap {Logical Syntax , pp. 12-13) explains that latitude and longitude, or space- time co-ordinates, can be substituted for place-names. “The method of designation by proper names is the primitive one ; that of positional designation corresponds to a more advanced stage of science, and has con- siderable methodological advantages over the former.” In the language he employs, co-ordinates, he says, replace such words as “Napoleon” or “Vienna”. This point of view deserves full discussion, which I shall undertake shortly.

E. Epistemological . — We have here, first, a distinction not identical with that between proper names and other words, but having perhaps some connection with it. This is the distinction between words having a verbal definition and words having only an ostensive definition. As to the latter, two points are obvious: (1) not all words can have verbal definitions; (2) it is largely arbitrary which words are to have only ostensive definitions. E.g. if “Napoleon” is defined ostensively, “Joseph Bonaparte” may be defined verbally as “Napoleon's oldest brother”. However, this arbitrariness is limited by the fact that, in the language of a given person, ostensive definitions are only possible within the limits of his experience. Napoleon’s friends might (subject to limitations) define him ostensively, but we cannot, since we can never say truly “ that is Napoleon”. There is obviously here a problem connected with that of proper names; how closely, I shall not discuss at present.

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We have, it is clear, a number of problems to consider, and, as is apt to happen in philosophy, it is difficult to be clear as to what precisely the problems are. I think we shall do best if we begin with Carnap’s substitution of co-ordinates for proper names. The question we have to consider is whether such a language can express the whole of our empirical knowledge.

In Carnap’s system, a group of four numbers is substituted for a space-time point. He illustrates by the example “Blue xly x2 , #3, jc4, meaning “the position (xv x2f x3l x 4) is blue”, instead of “Blue (a)” meaning “the object a is blue”. But now consider such a sentence as “Napoleon was in Elba during part of 1814”. Carnap, I am sure, will agree that this sentence is true, and that its truth is empirical, not logical. But if we translate it into his language it will become a logical truth. “Napoleon” will be replaced by “all quartets of numbers enclosed within such-and- such boundaries”; so will “Elba”, and so will “1814”. We shall then be stating that these three classes of quartets have a common part. This, however, is a fact of logic. Clearly this is not what we meant. We give the name “Napoleon” to a certain region, not because we are concerned with topology, but because that region has certain characteristics which make it interesting. We may defend Carnap by supposing, adopting a schematic simplification, that “Napoleon” is to mean “all regions having a certain quality say N”, while “Elba” is to mean “all regions having the quality E”. Then “Napoleon spent some time in Elba” will become: “The regions having the quality N and those having the quality E overlap.” This is no longer a fact of logic. But it has interpreted the proper names of ordinary language as disguised predicates.

But our schematic simplification is too violent. There is no quality, or collection of qualities, present wherever Napoleon was and absent wherever he was not. As an infant, he did not wear a cocked hat, or command armies, or fold his arms, while all these things were also done, at times, by other people. How, then, are we to define the word “Napoleon”? Let us continue to do our best for Carnap. In the moment of baptism, the priest decides that the name “Napoleon” is to apply to a certain small region in his neighbourhood, which has a more or less human shape, and that it is to apply to other future regions connected with this one, not only by continuity, which is not sufficient to secure material identity, but by certain causal laws, those, namely, which

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lead us to regard a body on two occasions as that of the same person. We may say: Given a temporally brief region having the characteristics of a living human body, it is an empirical fact that there are earlier and later regions connected with this one by physical laws, and having more or less similar characteristics ; the total of such regions is what we call a “person”, and one such region was called “Napoleon”. That naming is retro-active appears from a plaque on a certain house in Ajaccio saying: “Ici Napoleon fut con9u.”

This may be accepted as an answer to the objection that, on Carnap’s view, “Napoleon was once in Elba” would be a pro- position of logic. It leaves, however, some very serious questions. We saw that “Napoleon” cannot be defined simply by qualities, unless we are to hold it impossible that there should be two exactly similar individuals. One of the uses of space-time, how- ever, is to differentiate similar individuals in different places. Carnap has his sentences “Blue (3)”, “Blue (4)”, etc., meaning “the place 3 is blue”, “the place 4 is blue”, etc. We can, it is supposed, distinguish blue in one place from blue in another. But how are the places distinguished? Carnap takes space-time for granted, and never discusses how space-time places are dif- ferentiated. In fact, in his system, space-time regions have the characteristics of substance. The homogeneity of space-time is assumed in physics, and yet it is also assumed that there are different regions, which can be distinguished. Unless we are to accept the objectionable metaphysics of substance, wc shall have to suppose the regions distinguished by differences of quality. We shall then find that the regions need no longer be regarded as substantial, but as bundles of qualities.

Carnap’s co-ordinates, which replace names, are, of course, not assigned quite arbitrarily. The origin and the axes are arbitrary, but when they are fixed, the rest proceeds on a plan. The year which we call “1814” is differently named by the Mohammedans, who date from the Hejira, and by the Jewish era, which dates from the Creation. But the year we call “1815” will have the next number, in any system, to that given to what we call “1814”. It is because co-ordinates are not arbitrary that they are not names. Co-ordinates describe a point by its relations to the origin and the axes. But we must be able to say “ this is the origin”. If we are to be able to say this, we must be able to name the origin,

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HUMAN knowledge: its scope and limits

or to describe it in some way, and at first sight it might be thought that any possible way would be found to involve names. Take, for instance, longitude. The origin of longitude is the meridian of Greenwich, but it might equally well be any other meridian. We cannot define “Greenwich” as “longitude o°, latitude 520”, because, if we do, there is no means of ascertaining where longi- tude o° is. When we say “longitude o° is the longitude of Green- wich”, what we say is satisfactory because we can go to Greenwich and say “this is Greenwich”. Similarly, if we live at (say) longi- tude 40° W., we can say “the longitude of this place is 40° W.”, and then we can define longitude o° by relation to this place. But unless we have a way of knowing some places otherwise than by latitude and longitude, latitude and longitude become unmeaning. When we ask “what are the latitude and longitude of New York?” we are not asking the same sort of question as we should be if we descended into New York by a parachute and asked “what is the name of this city?” We are asking: “How far is New York west of Greenwich and north of the equator?” This question supposes New York and Greenwich known and already named.

It would be possible to assign a finite number of co-ordinates at haphazard, and then they would all be names. When (as is always done) they are assigned on a principle, they are descrip- tions, defining points by their relations to the origin and the axes. But these descriptions fail for the origin and the axes themselves, since, as regards them, the numbers are assigned arbitrarily. To answer the question “where is the origin?” we must have some method of identifying a place without mentioning its co-ordinates. It is the existence of such methods that is presupposed by the use of proper names.

I conclude, for the moment, that we cannot wholly dispense with proper names by means of co-ordinates. We can perhaps reduce the number of proper names, but we cannot avoid them altogether. Without proper names we can express the whole of theoretical physics, but no part of history or geography; this, at least, is our provisional conclusion so far, but we shall find reason to modify it later.

Let us consider a little further the substitution of descriptions for names. Somebody must be the tallest man now living in the United States. Let us suppose he is Mr. A. We may then, in place of “Mr. A”, substitute “the tallest man now living in the

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United States”, and this substitution will not, as a rule, alter the truth or falsehood of any sentence in which it is made. But it will alter the statement. One may know things about Mr. A that one does not know about the tallest man in the United States, and vice versa. One may know that Mr. A lives in Iowa, but not that the tallest man in the United States lives in Iowa. One may know that the tallest man in the United States is over ten years old, but one may not know whether Mr. A is man or boy. Then there is the proposition “Mr. A is the tallest man in the United States.” Mr. A may not know this; there may be a Mr. B who runs him close. But Mr. A certainly knows that Mr. A is Mr. A. This illustrates once more that there are some things which cannot be expressed by means of descriptions substituted for names.

The names of persons have verbal definitions in terms of “this”. Suppose you are in Moscow and some one says “that’s Stalin”, then “Stalin” is defined as “the person whom you are now seeing” — or, more fully: “that series of occurrences, constituting a person, of which this is one”. Here “this” is undefined, but “Stalin” is defined. I think it will be found that every name applied to some portion of space-time can have a verbal definition in which the word “this”, or some equivalent, occurs. This, I should say, is what distinguishes the name of an historical character from that of an imaginary person, such as Hamlet. Let us take a person with whom we are not acquainted, say Socrates. We may define him as “the philosopher who drank the hemlock”, but such a definition does not assure us that Socrates existed, and if he did not exist, “Socrates” is not a name. What does assure us that Socrates existed ? A variety of sentences heard or read. Each of these is a sensible occurrence in our own experience. Suppose we find in the Encyclopaedia the statement “Socrates was an Athenian philosopher”. The sentence, while we see it, is a this , and our faith in the Encyclopaedia leads us to say “this is true”. We can define “Socrates” as “the person described in the Encyclopaedia under the name ‘Socrates’ ”. Here the name “Socrates” is experienced. We can of course define “Hamlet” in a similar way, but some of the propositions used in the definition will be false. E.g. if we say “Hamlet was a Prince of Denmark who was the hero of one of Shakespeare’s tragedies”, this is false. What is true is: “ ‘Hamlet’ is a word which Shakespeare pretends to be the name of a Prince of Denmark”. It would thus seem to

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follow that, apart from such words as “this” and “that”, every name is a description involving some this , and is only a name in virtue of the truth of some proposition. (The proposition may be only “this is a name”, which is false if this is “Hamlet”.)

We must consider the question of minimum vocabularies. I call a vocabulary a “minimum” one if it contains no word which is capable of a verbal definition in terms of the other words of the vocabulary.^ Two minimum vocabularies dealing with the same subject-matter may not be equal ; there may be different methods of definition, some of which lead to a shorter residuum of undefined terms than others do. The question of minimum vocabularies is sometimes very important. Peano reduced the vocabulary of arithmetic to three words. It was an achievement in classical physics when all units were defined in terms of the units of mass, length, and time. The question I wish to discuss is: What characteristics must belong to a minimum vocabulary by means of which we can define all the words used in expressing our empirical knowledge or beliefs, in so far as such words have any precise meaning? More narrowly, to revert to a former example, what sort of minimum vocabulary is needed for “Napoleon was in Elba during part of 1814” and kindred state- ments? Perhaps, when we have answered this, we shall be able to define “names”. I assume, in the following discussion, that such historical-geographical statements are not analytic, that is to say, though they are true as a matter of fact, it would not be logically impossible for them to be false.

Let us revert to the theory, which is suggested by what Carnap says, that “Napoleon” is to be defined as a certain region of space-time. We objected that, in that case, “Napoleon was for a time in Elba” is analytic. It may be retorted: yes, but to find out what is not analytic you must inquire why we give a name to the portion of space-time that was Napoleon. We do so because it had certain peculiar characteristics. It was a person, and when adult it wore a cocked hat. We shall then say: “This portion of space-time is a person, and in its later portions it wears a cocked hat; that portion of space- time is a small island; this and that have a common part”. We have here three statements, the first two empirical, the third analytic. This seems unobjectionable. It leaves us with the problem of assigning co-ordinates, and also with that of defining such terms as “person” and “island”. Such

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terms as “person” and “island” can obviously be defined in terms of qualities and relations; they are general terms, and not (one would say) such as lead to proper names. The assigning of co- ordinates requires the assigning of origin and axes. We may, for simplicity, ignore the axes and concentrate on the origin. Can the origin be defined ?

Suppose, for example, you are engaged in planetary theory, not merely in a theoretical spirit, but with a view to the testing of your calculations by observations. Your origin, in that case, will have to be defined by something observable. It is universally agreed that absolute physical space-time is not observable. The things we can observe are, broadly speaking, qualities and spatio- temporal relations. We can say “I shall take the centre of the sun as my origin”. The centre of the sun is not observable, but the sun (in a sense) is. It is an empirical fact that I frequently have an experience which I call “seeing the sun”, and that I can observe what seem to be other people having a similar experience. “The sun” is a term which can be defined by qualities: round, hot, bright, of such-and-such apparent size, etc. It happens that there is only one object in my experience having these qualities, and that this object persists. I can give it a proper name, “the sun”, and say “I shall take the sun as my origin”. But since I have defined the sun by its qualities, it does not form part of a minimum vocabulary. It seems to follow that, while the words for qualities and spatio-temporal relations may form part of my minimum vocabulary, no words for physical spatio-temporal regions can do so. This is, in fact, merely a way of stating that physical spatio-temporal position is relative, not absolute.

Assuming this correct so far, the question arises whether we need names for qualities and spatio-temporal relations. Take colours, for example. It may be said that they can be designated by wave-lengths. This leads to Carnap’s contention that there is nothing in physics which cannot be known to a blind man. So far as theoretical physics is concerned, this is obviously true. It is true also, up to a point, in the empirical field. We see that the sky is blue, but a race of blind men could devise experiments showing that transverse waves of certain wave-lengths proceed from it, and this is just what the ordinary physicist qud physicist, is concerned to assert. The physicist, however, does not trouble to assert, and the blind man cannot assert, the proposition : “When

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light of a certain frequency strikes a normal eye, it causes a sensation of blue.,, This statement is not a tautology; it was a discovery, made many thousands of years after words for “blue” had been in common use.

The question whether the word “blue” can be defined is not easy. We might say: “Blue” is the name of colour-sensations caused by light of such-and-such frequencies. Or we might say: “Blue” is the name of those shades of colour which, in the spectrum, come between violet and green. Either of these definitions might enable us to procure for ourselves a sensation of blue. But when we had done so, we should be in a position to say: “So that is blue .” This would be a discovery, only to be made by actually experiencing blue. And in this statement, I should say, “that” is in one sense a proper name, though of that peculiar sort that I call “egocentric”.

We do not usually give names to smells and tastes, but we could do so. Before going to America, I knew the proposition “the smell of a skunk is disagreeable”. Now I know the two proposi- tions: “ that is the smell of a skunk”, and “ that is disagreeable”. Instead of “that”, we might use a name, say “pfui”, and should do so if we often wished to speak of the smell without men- tioning skunks. But to any one who had not had the requisite experience, the name would be an abbreviated description, not a name.

I conclude that names are to be applied to what is experienced, and that what is experienced does not have, essentially and neces- sarily, any such spatio-temporal uniqueness as belongs to a space- time region in physics. A word must denote something that can be recognized , and space-time regions, apart from qualities, cannot be recognized, since they are all alike. They are in fact logical fictions, but I am ignoring this for the moment.

There are occurrences that I experience, and I believe there are others that I do not experience. The occurrences that I experience are all complex, and can be analysed into qualities with spatial and temporal relations. The most important of these relations are compresence, contiguity, and succession. The words that we use to designate qualities are not precise; they all have the sort of vagueness that belongs to such words as “bald” and “fat”. This is true even of the words that we are most anxious to make precise, such as “centimetre” and “second”. Words

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designating qualities must be defined ostensively, if we are to be able to express observations; as soon as we substitute a verbal definition, we cease to express what is observed. The word “blue,” for instance, will mean “a colour like that ”, where that is a blue patch. How like that it must be to be blue, we cannot state with any precision.

This is all very well, but how about such words as “this” and “that”, which keep on intruding themselves? We think of the word “this” as designating something which is unique, and can only occur once. If, however, “this” denotes a bundle of corn- present qualities, there is no logical reason why it should not recur. I accept this. That is to say, I hold that there is no class of empirically known objects such that, if x is a mem- ber of the class, the statement “ x precedes x ” is logically impossible.

We are accustomed to think that the relation “precedes” is asymmetrical and transitive.1 “Time” and “event” are both con- cepts invented with a view to securing these properties to the relation “precedes”. Most people have discarded “time” as some- thing distinct from temporal succession, but they have not dis- carded “event”. An “event” is supposed to occupy some con- tinuous portion of space- time, at the end of which it ceases, and cannot recur. It is clear that a quality, or a complex of qualities, may recur; therefore an “event”, if non-recurrence is logically necessary, is not a bundle of qualities. What, then, is it, and how is it known? It will have the traditional characteristics of sub- stance, in that it will be a subject of qualities, but not defined when all its qualities are assigned. And how do we know that there is any class of objects the members of which cannot recur? If we are to know this, it might seem that it must be a case of synthetic a priori knowledge, and that if we reject the synthetic a priori , we must reject the impossibility of recurrence. We shall, of course, admit that, if we take a sufficiently large bundle of qualities, there will be no empirical instance of recurrence. Non- recurrence of such bundles may be accepted as a law of physics, but not as something necessary.

The view that I am suggesting is that an “event” may be defined as a complete bundle of compresent qualities, i.e. a bundle

1 I.e. that if A precedes B, B does not precede A, and if A precedes B and B precedes C, then A precedes C.

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having the two properties (a) that all the qualities in the bundle are compresent, (6) that nothing outside the bundle is compresent with every member of the bundle. I assume that, as a matter of empirical fact, no event recurs; that is to say, if a and b are events, and a is earlier than by there is some qualitative difference between a and b . For preferring this theory to one which makes an event indefinable, there are all the reasons commonly alleged against substance. If two events were exactly alike, nothing could ever lead us to suppose that they were two. In taking a census, we could not count one apart from the other, for, if we did, that would be a difference between them. And from the standpoint of language, a word must denote something that can be recog- nized, and this requires some recognizable quality. This leads to the conclusion that words such as “Napoleon” can be defined, and are therefore theoretically unnecessary; and that the same thing would be true of words designating events, if we were tempted to invent such words.

I conclude that, if we reduce our empirical vocabulary to a minimum, thereby excluding all words that have verbal definitions, we shall still need words for qualities, compresence, succession, and observed spatial relations, i.e. spatial relations which can be discriminated within a single sensible complex. It is an empirical fact that, if we form a complex of all the qualities that are all compresent with each other, this complex is found, so far as our experience goes, not to precede itself, i.e. not to recur. In forming the time-series, we generalize this observed fact.

The nearest approach to proper names in such a language will be the words for qualities and complexes of compresent qualities. These words will have the syntactical characteristics of proper names, but not certain other characteristics that we expect, for example that of designating a region which is spatio-tem- porally continuous. Whether, in these circumstances, such words are to be called “names”, is a matter of taste, as to which I express no opinion. What are commonly called proper names — e.g. “Socrates” — can, if I am right, be defined in terms of qualities and spatio-temporal relations, and this definition is an actual analysis. Most subject-predicate propositions, such as “Socrates is snub-nosed”, assert that a certain quality, named by the predicate, is one of a bundle of qualities named by the subject — this bundle being a unity in virtue of compresence and causal

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relations. Proper names in the ordinary sense, if this is right, are misleading, and embody a false metaphysic.

Note. — The above discussion of proper names is not intended to be conclusive. The subject will be resumed in other contexts, especially in Part IV, Chapter VIII.

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Chapter IV

EGOCENTRIC PARTICULARS

I give the name “egocentric particulars” to words of which the meaning varies with the speaker and his position in time and space. The four fundamental words of this sort are “I”, “this”, “here”, and “now”. The word “now” denotes a different point of time on each successive occasion when I use it; the word “here” denotes a different region of space after each time when I move; the word “I” denotes a different person according to who it is that utters it. Nevertheless there is obviously some sense in which these words have a constant meaning, which is the reason for the use of the words. This raises a problem, but before con- sidering it let us consider what other words are egocentric, and especially what words are really egocentric although intended not to be so.

Among obviously egocentric words are “near” and “far”, “past”, “present”, and “future”, “was”, “is”, and “will be”, and generally all forms of verbs involving tense. “This” and “that” are obviously egocentric; in fact, “this” might be taken as the only egocentric word not having a nominal definition. We could say that “I” means “the person experiencing this”, “now” means “the time ol this”, and “here” means “the place of this”. The word “this” is, in a sense, a proper name, but it differs from true proper names in the fact that its meaning is continually changing. This does not mean that it is ambiguous, like (say) “John Jones”, which is at all times the proper name of many different men. Unlike “John Jones”, “this” is at each moment the name of only one object in one person’s speech. Given the speaker and the time, the meaning of “this” is unambiguous, but when the speaker and the time are unknown we cannot tell what object it denotes. For this reason, the word is more satisfactory in speech than in print. If you hear a man say “this is an age of progress”, you know what age he refers to ; but if you read the same statement in a book it may be what Adam said when he invented the spade or what was said by any later optimist. You can only decide what the statement means by finding out when it was written, and in

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this sense its meaning is not self-contained but requires elucidation by extraneous information.

One of the aims of both science and common sense is to replace the shifting subjectivity of egocentric particulars by neutral public terms. “I” is replaced by my name, “here” by latitude and longitude, and “now” by date. Suppose I am walking with a friend on a dark night, and we lose touch with each other: he calls out “where are you?” and I reply “here I am”. Science will not accept such language; it will substitute “At 11.32 p.m. on January 30, 1946, B.R. was at longitude 40 3' 29" W. and at latitude 530 16' 14" N”. This information is impersonal: it gives a prescription by which a qualified person who possesses a sextant and a chronometer, and has the patience to wait for a sunny day, can determine where I was, which he may proclaim in the words “here is where he was”. If the matter is of sufficient importance, say in a trial for murder, this elaborate procedure may be worth the trouble it involves. But its appearance of complete imper- sonality is in part deceptive. Four items are involved: my name, the date, latitude, and longitude. In regard to each of these there is an element of egocentricity which is concealed by the fact that, for most purposes, it has no practical importance.

From a practical point of view, the impersonality is complete. Two competent persons, given time and opportunity, will both accept or both reject a statement of the form: “At time ty A was at longitude B, latitude C.” Let us call this statement “P”. There is a procedure for determining date, latitude, and longitude, which, if correctly observed, leads different people to the same result, in the sense that, if both say truly “he was here five minutes ago”, they must be in each other’s presence. This is the essential merit of scientific terminology and scientific technique. But when we examine closely the meanings of our scientific terms we find that the subjectivity we sought to avoid has not been wholly banished.

Let us begin with my name. We substitute “B.R.” for “I” or “you” or “he”, as the case may be, because “B.R.” is a public appellation, appearing on my passport and my identity card. If a policeman says “who are you?” I might reply by saying “look I this is who I am”, but this information is not what the policeman wants, so I produce my identity card and he is satisfied. But essentially I have only substituted one sensible impression for

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)

another. In looking at the identity card the policeman acquires a certain visual impression, which enables him to say “the name of the accused is B.R.” Another policeman, looking at the same identity card, will utter what is called the “same” sentence, that is to say, he will emit a series of noises closely similar to those emitted by the first policeman. It is this similarity, mistakenly regarded as identity, which is the merit of the name. If the two policemen had had to describe my appearance, the first, delaying me at the end of an all-day walk in the rain, might say “he was a furious red-faced tramp”, while the other might say “he was a benign old gentleman in evening dress”. The name has the merit of being less variable, but it remains something known only through the sensible impressions of individuals, of which no two are exactly alike. We always come back to “this is his name”, where this is a present occurrence. Or rather, to be exact, “his name is a class of sensible occurrences all very similar to this”. We secure, by our procedure, a method of providing sets of closely similar occurrences, but we do not wholly escape from “this”.

There is involved here a principle of considerable scope and importance, which deserves a more detailed exposition, to which we must now devote ourselves.

Let us begin with a homely illustration. Suppose you are acquainted with a certain Mrs. A, and you know that her mother, whom you have never met, is called Mrs. B. What does the name “Mrs. B” mean for you? Not what it means for those who know her, still less what it means for her herself. It must mean some- thing definable in terms of your experience, as must every word that you can use understandingly. For every word that you can understand must either have a nominal definition in terms of words having ostensive definitions, or must itself have an osten- sive definition; and ostensive definitions, as appears from the process by which they are effected, are only possible in relation to events that have occurred to you. Now the name “Mrs. B” is something that you have experienced; therefore when you speak of Mrs. B you may be mentally defining her as “the lady whose name is ‘Mrs. B’ ”. Or, if one were to concede (what would not be strictly accurate) that you are acquainted with Mrs. A, you might define “Mrs. B” as “the mother of Mrs. A”. In this way, although Mrs. B is outside your experience, you can interpret

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sentences in which her name occurs in such a way that your lack of experience does not prevent you from knowing if the sentences are true.

We can now generalize the process involved in the above illus- tration. Suppose there is some object a which you know by experience, and suppose you know (no matter how) that there is just one object to which a has a known relation R, but there is no such object in your experience. (In the above case, a is a Mrs. A, and R is the relation of daughter to mother.) You can then give a name to the object to which a has the relation R; let the name be “6”. (In our illustration it was “Mrs. B”.) It then becomes easy to forget that b is unknown to you although you may know multitudes of true sentences about b. But in fact, to speak correctly, you do not know sentences about b ; you know sentences in which the name ub" is replaced by the phrase “the object to which a has the relation R”. You know also that there are sentences about the actual object b which are verbally iden- tical with those that you know about the object to which a has the relation R — sentences pronounced by other people in which occurs as a name — but although you can describe these sentences, and know (within common-sense limits) which are true and which false, you do not know the sentences themselves. You may know that Mrs. A’s mother is rich, but you do not know what Mrs. B knows when she says “I am rich”.

The result of this state of affairs is that our knowledge seems to extend much further beyond our experience than it actually does. We may perhaps distinguish, in such cases as we have been considering, between what we can assert and what we intend. If I say “Mrs. B is rich”, I intend something about Mrs. B her- self, but what I actually assert is that Mrs. A has a rich mother. Another person may know of Mrs. B, not as the mother of Mrs. A, but as the mother of another daughter Mrs. C. In that case, when he says “Mrs. B is rich”, he means “Mrs. C has a rich mother”, which is not what I meant. But we both intend to say something about Mrs. B herself, though in this neither of us is successful. This does not matter in practice, as the things we respectively say about Mrs. A’s mother or Mrs. C’s mother would be true of Mrs. B if only we could say them. But although it does not matter in practice, it matters greatly in theory of knowledge. For in fact everybody except myself is to me in the position of Mrs. B ;

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of our supposed subjective prison. In this process of escape the interpretation of egocentric particulars is a very essential step.

Before attempting a precise account of egocentric words, let us briefly survey the picture of the world to which subsequent discussions will lead us.

There is one public space, namely the space of physics, and this space is occupied by public physical objects. But public space and public objects are not sensible; they are arrived at by a mixture of inference and logical construction. Sensible spaces and sensible objects differ from one person to another, though they have certain affinities to each other and to their public counter-parts.

There is one public time,1 in which not only physical events, but mental events also, have their place. There are also private times, which are those given in memory and expectation.

My whole private space is “here” in physical space, and my whole private time is “now” in public time. But there are also private “heres” and “nows” in private spaces and times.

When your friend calls out in the dark “where are you?” and you answer “here I am”, the “here” is one in physical space, since you are concerned to give information which will help another to find you. But if, when alone, you are looking for a lost object, and on finding it you exclaim “here it is”, the “here” may be either in public space or in your private space. Of course ordinary speech does not distinguish between public and private space. Broadly, “here” is where my body is — my physical body if I mean “here” in physical space, and my percept of my body if I mean “here” in my private space. But “here” may be much more narrowly localized, for instance if you are pointing out a thorn in your finger. One might say (though this would not quite accord with usage) that “here” is the place of whatever sensible object is occupying my attention. This, though not quite the usual meaning of the word, is the concept which most needs discussing in connection with the word “here”.

“Now” has a similar two-fold meaning, one subjective and one objective. When I review my life in memory, some of the things

1 This is subject to limitations connected with relativity. But as lan- guage and theory of knowledge are concerned with inhabitants of the earth, these may be ignored, since no two people have a relative velocity comparable to that of light.

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I remember seem a long time ago, others more recent, but all are in the past as compared with present percepts. This “past- ness”, however, is subjective: what I am remembering, I re- member now , and my recollecting is a present fact. If my memory is veridical, there was a fact to which my recollection has a certain relation, partly causal, partly of similarity ; this fact was objectively in the past. I maintain that, in addition to the objective relation of before-and-after, by which events are ordered in a public time-series, there is a subjective relation of more-or-less-remote, which holds between memories that all exist at the same objective time. The private time-series generated by this relation differs not only from person to person, but from moment to moment in the life of any one person. There is also a future in the private time-series, which is that of expectation. Both private and public time have, at each moment in the life of a percipient, one peculiar point, which is, at that moment, called “now”.

It is to be observed that “here” and “now” depend upon perception; in a purely material universe there would be no “here” and “now”. Perception is not impartial, but proceeds from a centre; our perceptual world is (so to speak) a perspective view of the common world. What is near in time and space generally gives rise to a more vivid and distinct memory or percept than what is far. The public world of physics has no such centre of illumination.

In defining egocentric particulars, we may take “this” as fundamental, in a sense in which “this” is not distinguished from “that”. I shall attempt an ostensive definition of “this”, and thence a nominal definition of the other egocentric particulars.

^This” denotes whatever, at the moment when the word is used, occupies the centre of attention. With words which are not egocentric, what is constant is something about the object indicated, but “this” denotes a different object on each occasion of its use: what is constant is not the object denoted, but its relation to the particular use of the word. Whenever the word is used, the person using it is attending to something, and the word indicates this something. When a word is not egocentric, there is no need to distinguish between different occasions when it is used, but we must make this distinction with egocentric? words, since what they indicate is something having a given relation to the particular use of the word. ^

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We may define “I” as “the person attending to this”, “now” as “the time of attending to this”, and “here” as “the place of attending to this”. We could equally well take “here-now” as fundamental; then “this” would be defined as “what is here- now”, and “I” as “what experiences this”.

Can two persons experience the same “this”, and if so, in what circumstances? I do not think this question can be decided by logical considerations : a priori , either answer would be possible. But taking the question empirically, it has an answer. When the “this” concerned is what common sense takes to be a percept of a physical object, difference of perspective makes a difference in the percept unavoidable, if the same physical object is concerned in the two cases. Two people looking at one tree, or listening to the song of one bird, are having somewhat different percepts. But two people looking at different trees might, theoretically, have exactly similar percepts, though this would be improbable. Two people may see exactly the same shade of colour, and are likely to do so if each is looking at a continuous band of colours, e.g. those of the rainbow. Two people looking at a square table will not see exactly similar quadrilaterals, but the quadrilaterals they see will have certain geometrical properties in common.

It thus appears that two people are more likely to have the same “this” if it is somewhat abstract than if it is fully concrete. In fact, broadly speaking, every increase of abstractness diminishes the difference between one person’s world and another’s. When we come to logic and pure mathematics, there need be no difference whatever : two people can attach exactly the same meaning to the word “or” or the word “371 ,294”. This is one reason why physics, in its endeavour to eliminate the privacy of sense, has grown progressively more abstract. This is also the reason for the view, which has been widely held by philosophers, that all true know- ledge is intellectual rather than sensible, and that the intellect iberates while the senses keep us in a personal prison. In such views there is an element of truth, but no more, except where logic and pure mathematics are concerned; for in all empirical knowledge liberation from sense can be only partial. It can, however, be carried to the point where two men’s interpretations of a given sentence are nearly certain to be both true or both false. The securing of this result is one of the aims (more or less un- conscious) governing the development of scientific concepts.

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Chapter V

SUSPENDED REACTIONS: KNOWLEDGE AND BELIEF

WE have been concerned hitherto with what may be called the “exclamatory” use of language, when it is used to denote some interesting feature of a man's present experience. So long as this use alone is in question, a single word can function as a sentence in the indicative. When Xenophon's Ten Thousand exclaimed “Sea! Sea!” they were using the word in this way. But a single word may also be used in other ways. A man found dying of thirst in the desert may murmur “water!” and is then uttering a request or expressing a desire; he may see a mirage and say “water?”; or he may see a spring and assert “water”. Sentences are needed to distinguish between these various uses of words. They are needed also — and this is perhaps their main use — to express what may be called “suspended reactions”. Suppose you intend to take a railway journey to-morrow, and you look up your train to-day : you do not propose, at the moment, to take any further action on the know- ledge you have acquired, but when the time comes you will behave in the appropriate manner. Knowledge, in the sense in which it does not merely register present sensible impressions, consists essentially of preparations for such delayed reactions. Such preparations may in all cases be called “beliefs”, but they are only to be called “knowledge” when they prompt successful reactions, or at any rate show themselves related to the facts with which they are concerned in some way which distinguishes them from preparations that would be called “errors”.

It is important not to exaggerate the role of language. In my view, there is in pre-linguistic experience something that may be called “belief”, and that may be true or false; there are also, I should say, what may be called “ideas”. Language immensely increases the number and complexity of possible beliefs and ideas, but is not, I am convinced, necessary for the simplest beliefs and ideas. A cat will watch for a long time at a mousehole, with her tail swishing in savage expectation; in such a case, one should say (so I hold) that the smell of mouse stimulates the “idea” of

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the rest of what makes up an actual mouse. The objection to such language comes, it seems to me, from an unduly intellectualist conception of what is meant by the word “idea”. I should define an “idea” as a state of an organism appropriate (in some sense) to something not sensibly present. All desire involves ideas in this sense, and desire is certainly pre-linguistic. Belief also, in an important sense, exists in the cat watching the mousehole, belief which is “true” if there is a mouse down the hole and “false” if not.

The word “mouse”, by itself, will not express the different attitudes of the cat while waiting for her prey and when seizing it; to express these different attitudes further developments of language are necessary. Command, desire, and narrative all involve the use of words describing something not sensibly present, and to distinguish them from each other and from the indicative various linguistic devices are necessary.

Perhaps the necessity to assume “ideas” as existing ante- cedently to language may be made more evident by considering what it is that words express. The dying man in the desert who murmurs “water 1” is clearly expressing a state in which a dying animal might be. How this state should be analysed is a difficult question, but we all, in a sense, know the meaning of the word “thirst”, and we all know that what this word means does not depend for its existence upon there being a word to denote it. The word “thirst” denotes a desire for something to drink, and such a desire involves, in the sense already explained, the presence of the “idea” of drink. What would commonly be called a man's “mental” life is entirely made up of ideas and attitudes towards them. Imagination, memory, desire, thought, and belief all involve ideas, and ideas are connected with suspended reactions. Ideas, in fact, are parts of causes of actions, which become complete causes when a suitable stimulus is applied. They are like explosives waiting to be exploded. In fact, the similarity may be very close. Trained soldiers, hearing the word “fire!” (which already existed in them as an idea) proceed to cause explosions. The similarity of language to explosives lies in the fact that a very small additional stimulus can produce a tremendous effect. Consider the effects which flowed from Hitler’s pronouncing the word “war!”

It is to be observed that words, when learnt, can become substitutes for ideas. There is a condition called “thinking of”

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SUSPENDED REACTIONS: KNOWLEDGE AND BELIEF

this or that, say water when you are in the desert. A dog appears, from its behaviour, to be capable of being in this condition ; so does an infant that cannot yet speak. When this condition exists, it prompts behaviour having reference to water. When the word “water” is known, the condition may consist (mainly, not wholly) in the presence of this word, either overtly pronounced or merely imagined. The word, when understood, has the same causal efficacy as the idea. Familiar knowledge is apt to be purely verbal; few schoolboys go beyond the words in reciting “William the Conqueror 1066”. Words and ideas are, in fact, interchangeable; both have meaning, and both have the same kind of causal relations to what they mean. The difference is that, in the case of words, the relation to what is meant is in the nature of a social convention, and is learnt by hearing speech, whereas in the case of ideas the relation is “natural”, i.e. it does not depend upon the behaviour of other people, but upon intrinsic similarity and (one must suppose) upon physiological processes existing in all human beings, and to a lesser extent in the higher animals.

“Knowledge”, which is, in most forms, connected with sus- pended reactions, is not a precise conception. Many of the difficulties of philosophers have arisen from regarding it as precise. Let us consider various ways of “knowing” the same fact. Suppose that, at 4 p.m. yesterday, I heard the noise of an explosion. When I heard it, I “knew” the noise in a certain sense, though not in the sense in which the word is usually employed. This sense, in spite of being unusual, cannot be discarded, since it is essential in explaining what is meant by “empirical verification”. Immediately afterwards, I may say “that was loud!” or “what was that noise?” This is “immediate memory”, which differs only in degree from sensation, since the physiological disturbance caused by the noise has not yet wholly subsided. Immediately before the explosion, if I have seen the train fired which leads to a charge of explosive, I may be in a state of tense expectation; this is, in a sense, akin to immediate memory, but directed to the near future. Next comes true memory : I now remember the bang I heard yesterday. My state is now made up of ideas (or images) or words, together with belief and a context which dates the occurrence remembered. I can imagine a bang just like , the one that I remember, but when I do this, belief and dating are absent. (The word “belief” is one which I shall discuss later.) Imagined

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HUMAN knowledge: its scope and limits

events are not included in knowledge or error, because of the absence of belief.

Sensation, immediate expectation, immediate memory, and true memory all give knowledge which is, in some degree and with appropriate limitations, independent of extraneous evidence. But most of the knowledge of people with any degree of education is not of any of these kinds. We know what we have been told or have read in books or newspapers; here words come first, and it is often unnecessary to realize what the words mean. When I believe “William the Conqueror 1066”, what I am really believing (as a rule) is: “the words ‘William the Conqueror 1066* are true”. This has the advantage that the words can be made sensible whenever I choose; the Conqueror is dead, but his name comes to life whenever I pronounce it. It has also the advantage that the name is public and the same for all, whereas the image (if any) employed in thinking of William will differ from person to person, and is sure to be too concrete. If (e.g.) we think of him on horse- back, that will not suit “William was born at Falaise”, because he was not born on horseback.

Sentences heard in narrative are, of course, not necessarily understood in this purely verbal manner; indeed a purely verbal understanding is essentially incomplete. A child reading an exciting adventure story will “live through5’ the adventures of the hero, particularly if the hero is of about the same age as the reader. If the hero leaps a chasm, the child’s muscles will grow taut; if the hero sees a lion about to spring, the child will hold his breath. Whatever happens to the hero, the child’s physiological condition is a reproduction, on a smaller scale, of the physiological condition of the hero. In adult life, the same result can be produced by good writing. When Shakespeare’s Antony says “I am dying, Egypt, dying”, we experience something which we do not experience when we see in The Times a notice of the death of some person unknown to us. One difference between poetry and bald statement is that poetry seeks to take the reader behind the words to what they signify.

The process called “verification” does not absolutely necessitate (but often involves) an imaginative understanding of words, but only a comparison of words used in advance with words used when the fact concerned becomes sensible. You say “this litmus paper will turn red”; I, later, say “this litmus paper has turned

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red”. Thus I need only pass outside the purely verbal region when I use a sentence to express a present sensible fact.

“Knowledge” is a vague concept for two reasons. First, because the meaning of a word is always more or less vague except in logic and pure mathematics ; and second, because all that we count as knowledge is in a greater or less degree uncertain, and there is no way of deciding how much uncertainty makes a belief un- worthy to be called “knowledge”, any more than how much loss of hair makes a man bald.

“Knowledge” is sometimes defined as “true belief”, but this definition is too wide. If you look at a clock which you believe to be going, but which in fact has stopped, and you happen to look at it at a moment when it is right, you will acquire a true belief as to the time of day, but you cannot be correctly said to have knowledge. The correct definition of “knowledge” need not concern us at the moment ; what concerns us now is belief.

Let us take some simple sentence expressing something that is or may be a sensible fact, such as “a loud bang is (or has been, or will be) taking place”. We will suppose it a fact that such a bang occurs at a place P at time ty and that the belief to be con- sidered refers to this particular bang. That is to say we will amend our sentence to “a loud bang occurs at place P at time ty\ We will call this sentence S. What sort of thing is happening to me when I believe this sentence, or rather when I believe what it expresses ?

There are a number of possibilities. First, I may be at or near the place P at the time t , and may hear the bang. In that case, at time t I have direct sensible knowledge of it; ordinary language would hardly call this “belief”, but for our purposes it is better to include it in the scope of the word. Obviously this sort of knowledge does not require words. No more does the immediate memory that subsists while I am still shaken by the noise. But how about more remote memory? Here, also, we may have no words, but an auditory image accompanied by a feeling which could be (but need not be) expressed in the words “that occurred”. Immediate expectation also does not need words. When you watch a door about to be slammed by the wind, your body and mind are in a state of expectation of noise, and if no noise Resulted you would experience a shock of surprise. This immediate expectation is different from our ordinary expectations about

”3

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HUMAN knowledge: its scope and limits

events that are not imminent. I expect that I shall get up to- morrow morning, but my body is not in that unpleasant condition in which it will be to-morrow morning when I am expecting to get up in a moment. I doubt whether it is possible, without words, to expect any event not in the immediate future. This is one of the differences between expectation and memory.

Belief about something outside my own experience seems usually only possible through the help of language, or some rudimentary beginning of language. Sea-gulls and cannibals have a “food-cry”, which in the cannibals is meant to give information, but in the sea-gulls may be a spontaneous expression of emotion, like a groan when the dentist hurts you. A noise of this sort is a word to the hearer, but not to the utterer. An animars behaviour may be affected by signs which have no analogy with language, for instance when it is in search of water in an unknown region. If a thirsty animal runs persistently down into a valley, I should be inclined to say that it “believes” there is water there, and in such a case there would be non-verbal belief in something that is as yet outside the animal’s experience. However, I do not wish to become involved in a controversy as to the meaning of words, so I will not insist upon the view that such behaviour shows “belief”.

Among human beings, the usual way of acquiring beliefs as to what has not been, and is not just about to be, experienced is through verbal testimony. To revert to our sentence S, some person whom we believe to be truthful pronounces it in our presence, and we then believe what the sentence asserts. I want to inquire what is actually occurring in us while we are believing the sentence.

We must, of course, distinguish a belief as a habit from the same belief when it is active. This distinction is necessary in regard to all habits. An acquired habit consists in the fact that a certain stimulus, whenever it occurs, now produces a certain reaction which it did not produce in the animal in question until the animal had had certain experiences. We must suppose that, even in the absence of the stimulus concerned, there is some difference between an animal that has a certain habit and one that lacks it. A man who understands the word “fire” must differ in some way from a man who does not, even when he is not hearing the word. We suppose the difference to be in the brain, but its

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nature is hypothetical. However, it is not a habit as a permanent character of an organism that concerns us, but the active habit, which is only displayed when the appropriate stimulus is applied. In the case we are investigating, the stimulus is the sentence