THE PROBLEMS OF PHILOSOPHY

By Bertrand Russell

PREFACE

In the following pages I have confined myself in the main to thoseproblems of philosophy in regard to which I thought it possible to saysomething positive and constructive, since merely negative criticismseemed out of place. For this reason, theory of knowledge occupies alarger space than metaphysics in the present volume, and some topicsmuch discussed by philosophers are treated very briefly, if at all. 

I have derived valuable assistance from unpublished writings of G. E. Moore and J. M. Keynes: from the former, as regards the relationsof sense-data to physical objects, and from the latter as regardsprobability and induction. I have also profited greatly by thecriticisms and suggestions of Professor Gilbert Murray. 

1912

CHAPTER I. APPEARANCE AND REALITY

Is there any knowledge in the world which is so certain that noreasonable man could doubt it? This question, which at first sight mightnot seem difficult, is really one of the most difficult that canbe asked. When we have realized the obstacles in the way of astraightforward and confident answer, we shall be well launched on thestudy of philosophy--for philosophy is merely the attempt to answersuch ultimate questions, not carelessly and dogmatically, as we do inordinary life and even in the sciences, but critically, after exploringall that makes such questions puzzling, and after realizing all thevagueness and confusion that underlie our ordinary ideas. 

In daily life, we assume as certain many things which, on a closerscrutiny, are found to be so full of apparent contradictions that only agreat amount of thought enables us to know what it is that we really maybelieve. In the search for certainty, it is natural to begin with ourpresent experiences, and in some sense, no doubt, knowledge is to bederived from them. But any statement as to what it is that our immediateexperiences make us know is very likely to be wrong. It seems to me thatI am now sitting in a chair, at a table of a certain shape, on which Isee sheets of paper with writing or print. By turning my head I see outof the window buildings and clouds and the sun. I believe that the sunis about ninety-three million miles from the earth; that it is a hotglobe many times bigger than the earth; that, owing to the earth'srotation, it rises every morning, and will continue to do so for anindefinite time in the future. I believe that, if any other normalperson comes into my room, he will see the same chairs and tables andbooks and papers as I see, and that the table which I see is the same asthe table which I feel pressing against my arm. All this seems to beso evident as to be hardly worth stating, except in answer to a man whodoubts whether I know anything. Yet all this may be reasonably doubted, and all of it requires much careful discussion before we can be surethat we have stated it in a form that is wholly true. 

To make our difficulties plain, let us concentrate attention on thetable. To the eye it is oblong, brown and shiny, to the touch it issmooth and cool and hard; when I tap it, it gives out a wooden sound. Any one else who sees and feels and hears the table will agree with thisdescription, so that it might seem as if no difficulty would arise;but as soon as we try to be more precise our troubles begin. AlthoughI believe that the table is 'really' of the same colour all over, theparts that reflect the light look much brighter than the other parts, and some parts look white because of reflected light. I know that, ifI move, the parts that reflect the light will be different, so that theapparent distribution of colours on the table will change. It followsthat if several people are looking at the table at the same moment, notwo of them will see exactly the same distribution of colours, becauseno two can see it from exactly the same point of view, and any change inthe point of view makes some change in the way the light is reflected. 

For most practical purposes these differences are unimportant, but tothe painter they are all-important: the painter has to unlearn the habitof thinking that things seem to have the colour which common sense saysthey 'really' have, and to learn the habit of seeing things as theyappear. Here we have already the beginning of one of the distinctionsthat cause most trouble in philosophy--the distinction between'appearance' and 'reality', between what things seem to be and what theyare. The painter wants to know what things seem to be, the practical manand the philosopher want to know what they are; but the philosopher'swish to know this is stronger than the practical man's, and is moretroubled by knowledge as to the difficulties of answering the question. 

To return to the table. It is evident from what we have found, thatthere is no colour which pre-eminently appears to be _the_ colour of thetable, or even of any one particular part of the table--it appears tobe of different colours from different points of view, and there isno reason for regarding some of these as more really its colour thanothers. And we know that even from a given point of view the colour willseem different by artificial light, or to a colour-blind man, or to aman wearing blue spectacles, while in the dark there will be no colourat all, though to touch and hearing the table will be unchanged. Thiscolour is not something which is inherent in the table, but somethingdepending upon the table and the spectator and the way the light fallson the table. When, in ordinary life, we speak of _the_ colour of thetable, we only mean the sort of colour which it will seem to have to anormal spectator from an ordinary point of view under usual conditionsof light. But the other colours which appear under other conditionshave just as good a right to be considered real; and therefore, to avoidfavouritism, we are compelled to deny that, in itself, the table has anyone particular colour. 

The same thing applies to the texture. With the naked eye one can seethe grain, but otherwise the table looks smooth and even. If we lookedat it through a microscope, we should see roughnesses and hills andvalleys, and all sorts of differences that are imperceptible to thenaked eye. Which of these is the 'real' table? We are naturally temptedto say that what we see through the microscope is more real, but that inturn would be changed by a still more powerful microscope. If, then, wecannot trust what we see with the naked eye, why should we trust what wesee through a microscope? Thus, again, the confidence in our senses withwhich we began deserts us. 

The shape of the table is no better. We are all in the habit of judgingas to the 'real' shapes of things, and we do this so unreflectingly thatwe come to think we actually see the real shapes. But, in fact, as weall have to learn if we try to draw, a given thing looks differentin shape from every different point of view. If our table is 'really'rectangular, it will look, from almost all points of view, as if it hadtwo acute angles and two obtuse angles. If opposite sides are parallel, they will look as if they converged to a point away from the spectator;if they are of equal length, they will look as if the nearer side werelonger. All these things are not commonly noticed in looking at a table, because experience has taught us to construct the 'real' shape from theapparent shape, and the 'real' shape is what interests us as practicalmen. But the 'real' shape is not what we see; it is something inferredfrom what we see. And what we see is constantly changing in shape as wemove about the room; so that here again the senses seem not to give usthe truth about the table itself, but only about the appearance of thetable. 

Similar difficulties arise when we consider the sense of touch. It istrue that the table always gives us a sensation of hardness, and we feelthat it resists pressure. But the sensation we obtain depends upon howhard we press the table and also upon what part of the body we presswith; thus the various sensations due to various pressures or variousparts of the body cannot be supposed to reveal _directly_ any definiteproperty of the table, but at most to be _signs_ of some property whichperhaps _causes_ all the sensations, but is not actually apparent in anyof them. And the same applies still more obviously to the sounds whichcan be elicited by rapping the table. 

Thus it becomes evident that the real table, if there is one, is not thesame as what we immediately experience by sight or touch or hearing. Thereal table, if there is one, is not _immediately_ known to us at all, but must be an inference from what is immediately known. Hence, two verydifficult questions at once arise; namely, (1) Is there a real table atall? (2) If so, what sort of object can it be?

It will help us in considering these questions to have a few simpleterms of which the meaning is definite and clear. Let us give the nameof 'sense-data' to the things that are immediately known in sensation:such things as colours, sounds, smells, hardnesses, roughnesses, andso on. We shall give the name 'sensation' to the experience of beingimmediately aware of these things. Thus, whenever we see a colour, we have a sensation _of_ the colour, but the colour itself is asense-datum, not a sensation. The colour is that _of_ which we areimmediately aware, and the awareness itself is the sensation. It isplain that if we are to know anything about the table, it must beby means of the sense-data--brown colour, oblong shape, smoothness, etc. --which we associate with the table; but, for the reasons which havebeen given, we cannot say that the table is the sense-data, or eventhat the sense-data are directly properties of the table. Thus a problemarises as to the relation of the sense-data to the real table, supposingthere is such a thing. 

The real table, if it exists, we will call a 'physical object'. Thuswe have to consider the relation of sense-data to physical objects. The collection of all physical objects is called 'matter'. Thus our twoquestions may be re-stated as follows: (1) Is there any such thing asmatter? (2) If so, what is its nature?

The philosopher who first brought prominently forward the reasonsfor regarding the immediate objects of our senses as not existingindependently of us was Bishop Berkeley (1685-1753). His _ThreeDialogues between Hylas and Philonous, in Opposition to Sceptics andAtheists_, undertake to prove that there is no such thing as matter atall, and that the world consists of nothing but minds and their ideas. Hylas has hitherto believed in matter, but he is no match for Philonous, who mercilessly drives him into contradictions and paradoxes, and makeshis own denial of matter seem, in the end, as if it were almost commonsense. The arguments employed are of very different value: some areimportant and sound, others are confused or quibbling. But Berkeleyretains the merit of having shown that the existence of matter iscapable of being denied without absurdity, and that if there are anythings that exist independently of us they cannot be the immediateobjects of our sensations. 

There are two different questions involved when we ask whether matterexists, and it is important to keep them clear. We commonly mean by'matter' something which is opposed to 'mind', something which we thinkof as occupying space and as radically incapable of any sort of thoughtor consciousness. It is chiefly in this sense that Berkeley deniesmatter; that is to say, he does not deny that the sense-data which wecommonly take as signs of the existence of the table are really signsof the existence of _something_ independent of us, but he does denythat this something is non-mental, that it is neither mind nor ideasentertained by some mind. He admits that there must be something whichcontinues to exist when we go out of the room or shut our eyes, and thatwhat we call seeing the table does really give us reason for believingin something which persists even when we are not seeing it. But hethinks that this something cannot be radically different in nature fromwhat we see, and cannot be independent of seeing altogether, though itmust be independent of _our_ seeing. He is thus led to regard the 'real'table as an idea in the mind of God. Such an idea has the requiredpermanence and independence of ourselves, without being--as matter wouldotherwise be--something quite unknowable, in the sense that we can onlyinfer it, and can never be directly and immediately aware of it. 

Other philosophers since Berkeley have also held that, although thetable does not depend for its existence upon being seen by me, it doesdepend upon being seen (or otherwise apprehended in sensation) by_some_ mind--not necessarily the mind of God, but more often the wholecollective mind of the universe. This they hold, as Berkeley does, chiefly because they think there can be nothing real--or at any ratenothing known to be real except minds and their thoughts and feelings. We might state the argument by which they support their view in somesuch way as this: 'Whatever can be thought of is an idea in the mind ofthe person thinking of it; therefore nothing can be thought of exceptideas in minds; therefore anything else is inconceivable, and what isinconceivable cannot exist. '

Such an argument, in my opinion, is fallacious; and of course those whoadvance it do not put it so shortly or so crudely. But whether valid ornot, the argument has been very widely advanced in one form or another;and very many philosophers, perhaps a majority, have held that there isnothing real except minds and their ideas. Such philosophers are called'idealists'. When they come to explaining matter, they either say, likeBerkeley, that matter is really nothing but a collection of ideas, or they say, like Leibniz (1646-1716), that what appears as matter isreally a collection of more or less rudimentary minds. 

But these philosophers, though they deny matter as opposed to mind, nevertheless, in another sense, admit matter. It will be remembered thatwe asked two questions; namely, (1) Is there a real table at all? (2) Ifso, what sort of object can it be? Now both Berkeley and Leibniz admitthat there is a real table, but Berkeley says it is certain ideas in themind of God, and Leibniz says it is a colony of souls. Thus both of themanswer our first question in the affirmative, and only diverge from theviews of ordinary mortals in their answer to our second question. Infact, almost all philosophers seem to be agreed that there is a realtable: they almost all agree that, however much our sense-data--colour, shape, smoothness, etc. --may depend upon us, yet their occurrence isa sign of something existing independently of us, something differing, perhaps, completely from our sense-data, and yet to be regarded ascausing those sense-data whenever we are in a suitable relation to thereal table. 

Now obviously this point in which the philosophers are agreed--the viewthat there _is_ a real table, whatever its nature may be--is vitallyimportant, and it will be worth while to consider what reasons there arefor accepting this view before we go on to the further question asto the nature of the real table. Our next chapter, therefore, will beconcerned with the reasons for supposing that there is a real table atall. 

Before we go farther it will be well to consider for a moment what itis that we have discovered so far. It has appeared that, if we take anycommon object of the sort that is supposed to be known by the senses, what the senses _immediately_ tell us is not the truth about the objectas it is apart from us, but only the truth about certain sense-datawhich, so far as we can see, depend upon the relations between us andthe object. Thus what we directly see and feel is merely 'appearance', which we believe to be a sign of some 'reality' behind. But if thereality is not what appears, have we any means of knowing whether thereis any reality at all? And if so, have we any means of finding out whatit is like?

Such questions are bewildering, and it is difficult to know that eventhe strangest hypotheses may not be true. Thus our familiar table, which has roused but the slightest thoughts in us hitherto, has become aproblem full of surprising possibilities. The one thing we know about itis that it is not what it seems. Beyond this modest result, so far, wehave the most complete liberty of conjecture. Leibniz tells us it is acommunity of souls: Berkeley tells us it is an idea in the mind of God;sober science, scarcely less wonderful, tells us it is a vast collectionof electric charges in violent motion. 

Among these surprising possibilities, doubt suggests that perhaps thereis no table at all. Philosophy, if it cannot _answer_ so many questionsas we could wish, has at least the power of _asking_ questions whichincrease the interest of the world, and show the strangeness and wonderlying just below the surface even in the commonest things of daily life. 

CHAPTER II. THE EXISTENCE OF MATTER

In this chapter we have to ask ourselves whether, in any sense at all, there is such a thing as matter. Is there a table which has a certainintrinsic nature, and continues to exist when I am not looking, or isthe table merely a product of my imagination, a dream-table in a veryprolonged dream? This question is of the greatest importance. For ifwe cannot be sure of the independent existence of objects, we cannotbe sure of the independent existence of other people's bodies, andtherefore still less of other people's minds, since we have no groundsfor believing in their minds except such as are derived from observingtheir bodies. Thus if we cannot be sure of the independent existence ofobjects, we shall be left alone in a desert--it may be that the wholeouter world is nothing but a dream, and that we alone exist. This is anuncomfortable possibility; but although it cannot be strictly proved tobe false, there is not the slightest reason to suppose that it is true. In this chapter we have to see why this is the case. 

Before we embark upon doubtful matters, let us try to find some moreor less fixed point from which to start. Although we are doubting thephysical existence of the table, we are not doubting the existenceof the sense-data which made us think there was a table; we are notdoubting that, while we look, a certain colour and shape appear to us, and while we press, a certain sensation of hardness is experienced byus. All this, which is psychological, we are not calling in question. In fact, whatever else may be doubtful, some at least of our immediateexperiences seem absolutely certain. 

Descartes (1596-1650), the founder of modern philosophy, invented amethod which may still be used with profit--the method of systematicdoubt. He determined that he would believe nothing which he did not seequite clearly and distinctly to be true. Whatever he could bring himselfto doubt, he would doubt, until he saw reason for not doubting it. By applying this method he gradually became convinced that the onlyexistence of which he could be _quite_ certain was his own. He imagineda deceitful demon, who presented unreal things to his senses in aperpetual phantasmagoria; it might be very improbable that such a demonexisted, but still it was possible, and therefore doubt concerningthings perceived by the senses was possible. 

But doubt concerning his own existence was not possible, for if he didnot exist, no demon could deceive him. If he doubted, he must exist; ifhe had any experiences whatever, he must exist. Thus his own existencewas an absolute certainty to him. 'I think, therefore I am, ' he said(_Cogito, ergo sum_); and on the basis of this certainty he set to workto build up again the world of knowledge which his doubt had laid inruins. By inventing the method of doubt, and by showing that subjectivethings are the most certain, Descartes performed a great service tophilosophy, and one which makes him still useful to all students of thesubject. 

But some care is needed in using Descartes' argument. 'I think, therefore I am' says rather more than is strictly certain. It might seemas though we were quite sure of being the same person to-day as we wereyesterday, and this is no doubt true in some sense. But the real Self isas hard to arrive at as the real table, and does not seem to have thatabsolute, convincing certainty that belongs to particular experiences. When I look at my table and see a certain brown colour, what is quitecertain at once is not '_I_ am seeing a brown colour', but rather, 'a brown colour is being seen'. This of course involves something (orsomebody) which (or who) sees the brown colour; but it does not ofitself involve that more or less permanent person whom we call 'I'. Sofar as immediate certainty goes, it might be that the something whichsees the brown colour is quite momentary, and not the same as thesomething which has some different experience the next moment. 

Thus it is our particular thoughts and feelings that have primitivecertainty. And this applies to dreams and hallucinations as well as tonormal perceptions: when we dream or see a ghost, we certainly do havethe sensations we think we have, but for various reasons it is held thatno physical object corresponds to these sensations. Thus the certaintyof our knowledge of our own experiences does not have to be limited inany way to allow for exceptional cases. Here, therefore, we have, forwhat it is worth, a solid basis from which to begin our pursuit ofknowledge. 

The problem we have to consider is this: Granted that we are certain ofour own sense-data, have we any reason for regarding them as signs ofthe existence of something else, which we can call the physical object?When we have enumerated all the sense-data which we should naturallyregard as connected with the table, have we said all there is to sayabout the table, or is there still something else--something not asense-datum, something which persists when we go out of the room? Commonsense unhesitatingly answers that there is. What can be bought and soldand pushed about and have a cloth laid on it, and so on, cannot bea _mere_ collection of sense-data. If the cloth completely hides thetable, we shall derive no sense-data from the table, and therefore, ifthe table were merely sense-data, it would have ceased to exist, andthe cloth would be suspended in empty air, resting, by a miracle, inthe place where the table formerly was. This seems plainly absurd; butwhoever wishes to become a philosopher must learn not to be frightenedby absurdities. 

One great reason why it is felt that we must secure a physical objectin addition to the sense-data, is that we want the same object fordifferent people. When ten people are sitting round a dinner-table, it seems preposterous to maintain that they are not seeing the sametablecloth, the same knives and forks and spoons and glasses. But thesense-data are private to each separate person; what is immediatelypresent to the sight of one is not immediately present to the sight ofanother: they all see things from slightly different points of view, andtherefore see them slightly differently. Thus, if there are to be publicneutral objects, which can be in some sense known to many differentpeople, there must be something over and above the private andparticular sense-data which appear to various people. What reason, then, have we for believing that there are such public neutral objects?

The first answer that naturally occurs to one is that, althoughdifferent people may see the table slightly differently, still they allsee more or less similar things when they look at the table, andthe variations in what they see follow the laws of perspective andreflection of light, so that it is easy to arrive at a permanent objectunderlying all the different people's sense-data. I bought my table fromthe former occupant of my room; I could not buy _his_ sense-data, which died when he went away, but I could and did buy the confidentexpectation of more or less similar sense-data. Thus it is the fact thatdifferent people have similar sense-data, and that one person in a givenplace at different times has similar sense-data, which makes us supposethat over and above the sense-data there is a permanent public objectwhich underlies or causes the sense-data of various people at varioustimes. 

Now in so far as the above considerations depend upon supposing thatthere are other people besides ourselves, they beg the very question atissue. Other people are represented to me by certain sense-data, such asthe sight of them or the sound of their voices, and if I had noreason to believe that there were physical objects independent of mysense-data, I should have no reason to believe that other people existexcept as part of my dream. Thus, when we are trying to show that theremust be objects independent of our own sense-data, we cannot appeal tothe testimony of other people, since this testimony itself consists ofsense-data, and does not reveal other people's experiences unless ourown sense-data are signs of things existing independently of us. We musttherefore, if possible, find, in our own purely private experiences, characteristics which show, or tend to show, that there are in the worldthings other than ourselves and our private experiences. 

In one sense it must be admitted that we can never prove the existenceof things other than ourselves and our experiences. No logical absurdityresults from the hypothesis that the world consists of myself and mythoughts and feelings and sensations, and that everything else is merefancy. In dreams a very complicated world may seem to be present, andyet on waking we find it was a delusion; that is to say, we find thatthe sense-data in the dream do not appear to have corresponded with suchphysical objects as we should naturally infer from our sense-data. (Itis true that, when the physical world is assumed, it is possible tofind physical causes for the sense-data in dreams: a door banging, forinstance, may cause us to dream of a naval engagement. But although, inthis case, there is a physical cause for the sense-data, there is not aphysical object corresponding to the sense-data in the way in which anactual naval battle would correspond. ) There is no logical impossibilityin the supposition that the whole of life is a dream, in which weourselves create all the objects that come before us. But although thisis not logically impossible, there is no reason whatever to suppose thatit is true; and it is, in fact, a less simple hypothesis, viewed as ameans of accounting for the facts of our own life, than the common-sensehypothesis that there really are objects independent of us, whose actionon us causes our sensations. 

The way in which simplicity comes in from supposing that there reallyare physical objects is easily seen. If the cat appears at one moment inone part of the room, and at another in another part, it is naturalto suppose that it has moved from the one to the other, passing overa series of intermediate positions. But if it is merely a set ofsense-data, it cannot have ever been in any place where I did not seeit; thus we shall have to suppose that it did not exist at all while Iwas not looking, but suddenly sprang into being in a new place. Ifthe cat exists whether I see it or not, we can understand from our ownexperience how it gets hungry between one meal and the next; but ifit does not exist when I am not seeing it, it seems odd that appetiteshould grow during non-existence as fast as during existence. And if thecat consists only of sense-data, it cannot be hungry, since no hungerbut my own can be a sense-datum to me. Thus the behaviour of thesense-data which represent the cat to me, though it seems quite naturalwhen regarded as an expression of hunger, becomes utterly inexplicablewhen regarded as mere movements and changes of patches of colour, whichare as incapable of hunger as a triangle is of playing football. 

But the difficulty in the case of the cat is nothing compared to thedifficulty in the case of human beings. When human beings speak--thatis, when we hear certain noises which we associate with ideas, andsimultaneously see certain motions of lips and expressions of face--itis very difficult to suppose that what we hear is not the expressionof a thought, as we know it would be if we emitted the same sounds. Ofcourse similar things happen in dreams, where we are mistaken as to theexistence of other people. But dreams are more or less suggested by whatwe call waking life, and are capable of being more or less accounted foron scientific principles if we assume that there really is a physicalworld. Thus every principle of simplicity urges us to adopt the naturalview, that there really are objects other than ourselves and oursense-data which have an existence not dependent upon our perceivingthem. 

Of course it is not by argument that we originally come by our belief inan independent external world. We find this belief ready in ourselves assoon as we begin to reflect: it is what may be called an _instinctive_belief. We should never have been led to question this belief but forthe fact that, at any rate in the case of sight, it seems as if thesense-datum itself were instinctively believed to be the independentobject, whereas argument shows that the object cannot be identicalwith the sense-datum. This discovery, however--which is not at allparadoxical in the case of taste and smell and sound, and only slightlyso in the case of touch--leaves undiminished our instinctive belief thatthere _are_ objects _corresponding_ to our sense-data. Since this beliefdoes not lead to any difficulties, but on the contrary tends to simplifyand systematize our account of our experiences, there seems no goodreason for rejecting it. We may therefore admit--though with a slightdoubt derived from dreams--that the external world does really exist, and is not wholly dependent for its existence upon our continuing toperceive it. 

The argument which has led us to this conclusion is doubtless lessstrong than we could wish, but it is typical of many philosophicalarguments, and it is therefore worth while to consider briefly itsgeneral character and validity. All knowledge, we find, must be builtup upon our instinctive beliefs, and if these are rejected, nothingis left. But among our instinctive beliefs some are much stronger thanothers, while many have, by habit and association, become entangled withother beliefs, not really instinctive, but falsely supposed to be partof what is believed instinctively. 

Philosophy should show us the hierarchy of our instinctive beliefs, beginning with those we hold most strongly, and presenting each as muchisolated and as free from irrelevant additions as possible. It shouldtake care to show that, in the form in which they are finally set forth, our instinctive beliefs do not clash, but form a harmonious system. There can never be any reason for rejecting one instinctive beliefexcept that it clashes with others; thus, if they are found toharmonize, the whole system becomes worthy of acceptance. 

It is of course _possible_ that all or any of our beliefs may bemistaken, and therefore all ought to be held with at least some slightelement of doubt. But we cannot have _reason_ to reject a belief excepton the ground of some other belief. Hence, by organizing our instinctivebeliefs and their consequences, by considering which among them is mostpossible, if necessary, to modify or abandon, we can arrive, on thebasis of accepting as our sole data what we instinctively believe, at anorderly systematic organization of our knowledge, in which, though the_possibility_ of error remains, its likelihood is diminished by theinterrelation of the parts and by the critical scrutiny which haspreceded acquiescence. 

This function, at least, philosophy can perform. Most philosophers, rightly or wrongly, believe that philosophy can do much more thanthis--that it can give us knowledge, not otherwise attainable, concerning the universe as a whole, and concerning the nature ofultimate reality. Whether this be the case or not, the more modestfunction we have spoken of can certainly be performed by philosophy, andcertainly suffices, for those who have once begun to doubt the adequacyof common sense, to justify the arduous and difficult labours thatphilosophical problems involve. 

CHAPTER III. THE NATURE OF MATTER

In the preceding chapter we agreed, though without being able tofind demonstrative reasons, that it is rational to believe that oursense-data--for example, those which we regard as associated with mytable--are really signs of the existence of something independent of usand our perceptions. That is to say, over and above the sensations ofcolour, hardness, noise, and so on, which make up the appearance ofthe table to me, I assume that there is something else, of which thesethings are appearances. The colour ceases to exist if I shut my eyes, the sensation of hardness ceases to exist if I remove my arm fromcontact with the table, the sound ceases to exist if I cease to rap thetable with my knuckles. But I do not believe that when all these thingscease the table ceases. On the contrary, I believe that it is becausethe table exists continuously that all these sense-data will reappearwhen I open my eyes, replace my arm, and begin again to rap with myknuckles. The question we have to consider in this chapter is: Whatis the nature of this real table, which persists independently of myperception of it?

To this question physical science gives an answer, somewhat incompleteit is true, and in part still very hypothetical, but yet deserving ofrespect so far as it goes. Physical science, more or less unconsciously, has drifted into the view that all natural phenomena ought to be reducedto motions. Light and heat and sound are all due to wave-motions, whichtravel from the body emitting them to the person who sees light or feelsheat or hears sound. That which has the wave-motion is either aether or'gross matter', but in either case is what the philosopher would callmatter. The only properties which science assigns to it are position inspace, and the power of motion according to the laws of motion. Sciencedoes not deny that it _may_ have other properties; but if so, such otherproperties are not useful to the man of science, and in no way assisthim in explaining the phenomena. 

It is sometimes said that 'light _is_ a form of wave-motion', but thisis misleading, for the light which we immediately see, which we knowdirectly by means of our senses, is _not_ a form of wave-motion, butsomething quite different--something which we all know if we are notblind, though we cannot describe it so as to convey our knowledge to aman who is blind. A wave-motion, on the contrary, could quite well bedescribed to a blind man, since he can acquire a knowledge of space bythe sense of touch; and he can experience a wave-motion by a sea voyagealmost as well as we can. But this, which a blind man can understand, isnot what we mean by _light_: we mean by _light_ just that which a blindman can never understand, and which we can never describe to him. 

Now this something, which all of us who are not blind know, is not, according to science, really to be found in the outer world: it issomething caused by the action of certain waves upon the eyes and nervesand brain of the person who sees the light. When it is said that light_is_ waves, what is really meant is that waves are the physical cause ofour sensations of light. But light itself, the thing which seeing peopleexperience and blind people do not, is not supposed by science to formany part of the world that is independent of us and our senses. And verysimilar remarks would apply to other kinds of sensations. 

It is not only colours and sounds and so on that are absent from thescientific world of matter, but also _space_ as we get it through sightor touch. It is essential to science that its matter should be in _a_space, but the space in which it is cannot be exactly the space we seeor feel. To begin with, space as we see it is not the same as space aswe get it by the sense of touch; it is only by experience in infancythat we learn how to touch things we see, or how to get a sight ofthings which we feel touching us. But the space of science is neutral asbetween touch and sight; thus it cannot be either the space of touch orthe space of sight. 

Again, different people see the same object as of different shapes, according to their point of view. A circular coin, for example, thoughwe should always _judge_ it to be circular, will _look_ oval unless weare straight in front of it. When we judge that it _is_ circular, we arejudging that it has a real shape which is not its apparent shape, butbelongs to it intrinsically apart from its appearance. But this realshape, which is what concerns science, must be in a real space, notthe same as anybody's _apparent_ space. The real space is public, theapparent space is private to the percipient. In different people's_private_ spaces the same object seems to have different shapes; thusthe real space, in which it has its real shape, must be different fromthe private spaces. The space of science, therefore, though _connected_with the spaces we see and feel, is not identical with them, and themanner of its connexion requires investigation. 

We agreed provisionally that physical objects cannot be quite likeour sense-data, but may be regarded as _causing_ our sensations. These physical objects are in the space of science, which we may call'physical' space. It is important to notice that, if our sensationsare to be caused by physical objects, there must be a physical spacecontaining these objects and our sense-organs and nerves and brain. Weget a sensation of touch from an object when we are in contact with it;that is to say, when some part of our body occupies a place in physicalspace quite close to the space occupied by the object. We see an object(roughly speaking) when no opaque body is between the object and oureyes in physical space. Similarly, we only hear or smell or taste anobject when we are sufficiently near to it, or when it touches thetongue, or has some suitable position in physical space relatively toour body. We cannot begin to state what different sensations we shallderive from a given object under different circumstances unless weregard the object and our body as both in one physical space, for it ismainly the relative positions of the object and our body that determinewhat sensations we shall derive from the object. 

Now our sense-data are situated in our private spaces, either the spaceof sight or the space of touch or such vaguer spaces as other sensesmay give us. If, as science and common sense assume, there is one publicall-embracing physical space in which physical objects are, the relativepositions of physical objects in physical space must more or lesscorrespond to the relative positions of sense-data in our privatespaces. There is no difficulty in supposing this to be the case. If wesee on a road one house nearer to us than another, our other senses willbear out the view that it is nearer; for example, it will be reachedsooner if we walk along the road. Other people will agree that the housewhich looks nearer to us is nearer; the ordnance map will take thesame view; and thus everything points to a spatial relation between thehouses corresponding to the relation between the sense-data which we seewhen we look at the houses. Thus we may assume that there is a physicalspace in which physical objects have spatial relations corresponding tothose which the corresponding sense-data have in our private spaces. Itis this physical space which is dealt with in geometry and assumed inphysics and astronomy. 

Assuming that there is physical space, and that it does thus correspondto private spaces, what can we know about it? We can know _only_ what isrequired in order to secure the correspondence. That is to say, we canknow nothing of what it is like in itself, but we can know the sortof arrangement of physical objects which results from their spatialrelations. We can know, for example, that the earth and moon and sunare in one straight line during an eclipse, though we cannot know whata physical straight line is in itself, as we know the look of a straightline in our visual space. Thus we come to know much more about the_relations_ of distances in physical space than about the distancesthemselves; we may know that one distance is greater than another, orthat it is along the same straight line as the other, but we cannot havethat immediate acquaintance with physical distances that we have withdistances in our private spaces, or with colours or sounds or othersense-data. We can know all those things about physical space which aman born blind might know through other people about the space of sight;but the kind of things which a man born blind could never know about thespace of sight we also cannot know about physical space. We can know theproperties of the relations required to preserve the correspondence withsense-data, but we cannot know the nature of the terms between which therelations hold. 

With regard to time, our _feeling_ of duration or of the lapse of timeis notoriously an unsafe guide as to the time that has elapsed by theclock. Times when we are bored or suffering pain pass slowly, times whenwe are agreeably occupied pass quickly, and times when we are sleepingpass almost as if they did not exist. Thus, in so far as time isconstituted by duration, there is the same necessity for distinguishinga public and a private time as there was in the case of space. But in sofar as time consists in an _order_ of before and after, there is no needto make such a distinction; the time-order which events seem to have is, so far as we can see, the same as the time-order which they do have. Atany rate no reason can be given for supposing that the two orders arenot the same. The same is usually true of space: if a regiment of menare marching along a road, the shape of the regiment will look differentfrom different points of view, but the men will appear arranged in thesame order from all points of view. Hence we regard the order as truealso in physical space, whereas the shape is only supposed to correspondto the physical space so far as is required for the preservation of theorder. 

In saying that the time-order which events seem to have is the same asthe time-order which they really have, it is necessary to guard againsta possible misunderstanding. It must not be supposed that the variousstates of different physical objects have the same time-order as thesense-data which constitute the perceptions of those objects. Consideredas physical objects, the thunder and lightning are simultaneous; that isto say, the lightning is simultaneous with the disturbance of the air inthe place where the disturbance begins, namely, where the lightningis. But the sense-datum which we call hearing the thunder does not takeplace until the disturbance of the air has travelled as far as to wherewe are. Similarly, it takes about eight minutes for the sun's lightto reach us; thus, when we see the sun we are seeing the sun of eightminutes ago. So far as our sense-data afford evidence as to the physicalsun they afford evidence as to the physical sun of eight minutes ago; ifthe physical sun had ceased to exist within the last eight minutes, thatwould make no difference to the sense-data which we call 'seeingthe sun'. This affords a fresh illustration of the necessity ofdistinguishing between sense-data and physical objects. 

What we have found as regards space is much the same as what we findin relation to the correspondence of the sense-data with theirphysical counterparts. If one object looks blue and another red, we mayreasonably presume that there is some corresponding difference betweenthe physical objects; if two objects both look blue, we may presume acorresponding similarity. But we cannot hope to be acquainted directlywith the quality in the physical object which makes it look blue or red. Science tells us that this quality is a certain sort of wave-motion, andthis sounds familiar, because we think of wave-motions in the space wesee. But the wave-motions must really be in physical space, with whichwe have no direct acquaintance; thus the real wave-motions have not thatfamiliarity which we might have supposed them to have. And what holdsfor colours is closely similar to what holds for other sense-data. Thuswe find that, although the _relations_ of physical objects have allsorts of knowable properties, derived from their correspondence with therelations of sense-data, the physical objects themselves remain unknownin their intrinsic nature, so far at least as can be discovered by meansof the senses. The question remains whether there is any other method ofdiscovering the intrinsic nature of physical objects. 

The most natural, though not ultimately the most defensible, hypothesisto adopt in the first instance, at any rate as regards visualsense-data, would be that, though physical objects cannot, for thereasons we have been considering, be _exactly_ like sense-data, yet theymay be more or less like. According to this view, physical objects will, for example, really have colours, and we might, by good luck, see anobject as of the colour it really is. The colour which an object seemsto have at any given moment will in general be very similar, thoughnot quite the same, from many different points of view; we might thussuppose the 'real' colour to be a sort of medium colour, intermediatebetween the various shades which appear from the different points ofview. 

Such a theory is perhaps not capable of being definitely refuted, butit can be shown to be groundless. To begin with, it is plain that thecolour we see depends only upon the nature of the light-waves thatstrike the eye, and is therefore modified by the medium interveningbetween us and the object, as well as by the manner in which light isreflected from the object in the direction of the eye. The interveningair alters colours unless it is perfectly clear, and any strongreflection will alter them completely. Thus the colour we see is aresult of the ray as it reaches the eye, and not simply a property ofthe object from which the ray comes. Hence, also, provided certain wavesreach the eye, we shall see a certain colour, whether the object fromwhich the waves start has any colour or not. Thus it is quite gratuitousto suppose that physical objects have colours, and therefore there is nojustification for making such a supposition. Exactly similar argumentswill apply to other sense-data. 

It remains to ask whether there are any general philosophical argumentsenabling us to say that, if matter is real, it must be of such and sucha nature. As explained above, very many philosophers, perhaps most, haveheld that whatever is real must be in some sense mental, or at any ratethat whatever we can know anything about must be in some sense mental. Such philosophers are called 'idealists'. Idealists tell us that whatappears as matter is really something mental; namely, either (as Leibnizheld) more or less rudimentary minds, or (as Berkeley contended) ideasin the minds which, as we should commonly say, 'perceive' the matter. Thus idealists deny the existence of matter as something intrinsicallydifferent from mind, though they do not deny that our sense-data aresigns of something which exists independently of our private sensations. In the following chapter we shall consider briefly the reasons--in myopinion fallacious--which idealists advance in favour of their theory. 

CHAPTER IV. IDEALISM

The word 'idealism' is used by different philosophers in somewhatdifferent senses. We shall understand by it the doctrine that whateverexists, or at any rate whatever can be known to exist, must be insome sense mental. This doctrine, which is very widely held amongphilosophers, has several forms, and is advocated on several differentgrounds. The doctrine is so widely held, and so interesting in itself, that even the briefest survey of philosophy must give some account ofit. 

Those who are unaccustomed to philosophical speculation may be inclinedto dismiss such a doctrine as obviously absurd. There is no doubt thatcommon sense regards tables and chairs and the sun and moon and materialobjects generally as something radically different from minds and thecontents of minds, and as having an existence which might continue ifminds ceased. We think of matter as having existed long before therewere any minds, and it is hard to think of it as a mere product ofmental activity. But whether true or false, idealism is not to bedismissed as obviously absurd. 

We have seen that, even if physical objects do have an independentexistence, they must differ very widely from sense-data, and can onlyhave a _correspondence_ with sense-data, in the same sort of way inwhich a catalogue has a correspondence with the things catalogued. Hencecommon sense leaves us completely in the dark as to the true intrinsicnature of physical objects, and if there were good reason to regard themas mental, we could not legitimately reject this opinion merely becauseit strikes us as strange. The truth about physical objects _must_ bestrange. It may be unattainable, but if any philosopher believes thathe has attained it, the fact that what he offers as the truth is strangeought not to be made a ground of objection to his opinion. 

The grounds on which idealism is advocated are generally grounds derivedfrom the theory of knowledge, that is to say, from a discussion of theconditions which things must satisfy in order that we may be able toknow them. The first serious attempt to establish idealism on suchgrounds was that of Bishop Berkeley. He proved first, by arguments whichwere largely valid, that our sense-data cannot be supposed to have anexistence independent of us, but must be, in part at least, 'in' themind, in the sense that their existence would not continue if there wereno seeing or hearing or touching or smelling or tasting. So far, hiscontention was almost certainly valid, even if some of his argumentswere not so. But he went on to argue that sense-data were the onlythings of whose existence our perceptions could assure us; and thatto be known is to be 'in' a mind, and therefore to be mental. Hence heconcluded that nothing can ever be known except what is in some mind, and that whatever is known without being in my mind must be in someother mind. 

In order to understand his argument, it is necessary to understand hisuse of the word 'idea'. He gives the name 'idea' to anything whichis _immediately_ known, as, for example, sense-data are known. Thus aparticular colour which we see is an idea; so is a voice which we hear, and so on. But the term is not wholly confined to sense-data. There willalso be things remembered or imagined, for with such things also we haveimmediate acquaintance at the moment of remembering or imagining. Allsuch immediate data he calls 'ideas'. 

He then proceeds to consider common objects, such as a tree, forinstance. He shows that all we know immediately when we 'perceive' thetree consists of ideas in his sense of the word, and he argues thatthere is not the slightest ground for supposing that there is anythingreal about the tree except what is perceived. Its being, he says, consists in being perceived: in the Latin of the schoolmen its '_esse_'is '_percipi_'. He fully admits that the tree must continue to existeven when we shut our eyes or when no human being is near it. But thiscontinued existence, he says, is due to the fact that God continues toperceive it; the 'real' tree, which corresponds to what we called thephysical object, consists of ideas in the mind of God, ideas more orless like those we have when we see the tree, but differing in the factthat they are permanent in God's mind so long as the tree continuesto exist. All our perceptions, according to him, consist in apartial participation in God's perceptions, and it is because of thisparticipation that different people see more or less the same tree. Thusapart from minds and their ideas there is nothing in the world, nor isit possible that anything else should ever be known, since whatever isknown is necessarily an idea. 

There are in this argument a good many fallacies which have beenimportant in the history of philosophy, and which it will be as well tobring to light. In the first place, there is a confusion engendered bythe use of the word 'idea'. We think of an idea as essentially somethingin somebody's mind, and thus when we are told that a tree consistsentirely of ideas, it is natural to suppose that, if so, the treemust be entirely in minds. But the notion of being 'in' the mind isambiguous. We speak of bearing a person in mind, not meaning that theperson is in our minds, but that a thought of him is in our minds. Whena man says that some business he had to arrange went clean out of hismind, he does not mean to imply that the business itself was ever in hismind, but only that a thought of the business was formerly in his mind, but afterwards ceased to be in his mind. And so when Berkeley says thatthe tree must be in our minds if we can know it, all that he really hasa right to say is that a thought of the tree must be in our minds. Toargue that the tree itself must be in our minds is like arguing that aperson whom we bear in mind is himself in our minds. This confusionmay seem too gross to have been really committed by any competentphilosopher, but various attendant circumstances rendered it possible. In order to see how it was possible, we must go more deeply into thequestion as to the nature of ideas. 

Before taking up the general question of the nature of ideas, we mustdisentangle two entirely separate questions which arise concerningsense-data and physical objects. We saw that, for various reasons ofdetail, Berkeley was right in treating the sense-data which constituteour perception of the tree as more or less subjective, in the sense thatthey depend upon us as much as upon the tree, and would not exist if thetree were not being perceived. But this is an entirely different pointfrom the one by which Berkeley seeks to prove that whatever can beimmediately known must be in a mind. For this purpose arguments ofdetail as to the dependence of sense-data upon us are useless. It isnecessary to prove, generally, that by being known, things are shown tobe mental. This is what Berkeley believes himself to have done. Itis this question, and not our previous question as to the differencebetween sense-data and the physical object, that must now concern us. 

Taking the word 'idea' in Berkeley's sense, there are two quite distinctthings to be considered whenever an idea is before the mind. There ison the one hand the thing of which we are aware--say the colour of mytable--and on the other hand the actual awareness itself, the mental actof apprehending the thing. The mental act is undoubtedly mental, but isthere any reason to suppose that the thing apprehended is in any sensemental? Our previous arguments concerning the colour did not prove it tobe mental; they only proved that its existence depends upon the relationof our sense organs to the physical object--in our case, the table. Thatis to say, they proved that a certain colour will exist, in a certainlight, if a normal eye is placed at a certain point relatively tothe table. They did not prove that the colour is in the mind of thepercipient. 

Berkeley's view, that obviously the colour must be in the mind, seemsto depend for its plausibility upon confusing the thing apprehendedwith the act of apprehension. Either of these might be called an 'idea';probably either would have been called an idea by Berkeley. The actis undoubtedly in the mind; hence, when we are thinking of the act, we readily assent to the view that ideas must be in the mind. Then, forgetting that this was only true when ideas were taken as acts ofapprehension, we transfer the proposition that 'ideas are in the mind'to ideas in the other sense, i. E. To the things apprehended by our actsof apprehension. Thus, by an unconscious equivocation, we arrive at theconclusion that whatever we can apprehend must be in our minds. Thisseems to be the true analysis of Berkeley's argument, and the ultimatefallacy upon which it rests. 

This question of the distinction between act and object in ourapprehending of things is vitally important, since our whole power ofacquiring knowledge is bound up with it. The faculty of being acquaintedwith things other than itself is the main characteristic of a mind. Acquaintance with objects essentially consists in a relation between themind and something other than the mind; it is this that constitutes themind's power of knowing things. If we say that the things known must bein the mind, we are either unduly limiting the mind's power of knowing, or we are uttering a mere tautology. We are uttering a mere tautology ifwe mean by '_in_ the mind' the same as by '_before_ the mind', i. E. Ifwe mean merely being apprehended by the mind. But if we mean this, weshall have to admit that what, _in this sense_, is in the mind, may nevertheless be not mental. Thus when we realize the nature ofknowledge, Berkeley's argument is seen to be wrong in substance as wellas in form, and his grounds for supposing that 'ideas'--i. E. The objectsapprehended--must be mental, are found to have no validity whatever. Hence his grounds in favour of idealism may be dismissed. It remains tosee whether there are any other grounds. 

It is often said, as though it were a self-evident truism, that wecannot know that anything exists which we do not know. It is inferredthat whatever can in any way be relevant to our experience must be atleast capable of being known by us; whence it follows that if matterwere essentially something with which we could not become acquainted, matter would be something which we could not know to exist, and whichcould have for us no importance whatever. It is generally also implied, for reasons which remain obscure, that what can have no importance forus cannot be real, and that therefore matter, if it is not composed ofminds or of mental ideas, is impossible and a mere chimaera. 

To go into this argument fully at our present stage would be impossible, since it raises points requiring a considerable preliminary discussion;but certain reasons for rejecting the argument may be noticed atonce. To begin at the end: there is no reason why what cannot have any_practical_ importance for us should not be real. It is true that, if _theoretical_ importance is included, everything real is of _some_importance to us, since, as persons desirous of knowing the truth aboutthe universe, we have some interest in everything that the universecontains. But if this sort of interest is included, it is not the casethat matter has no importance for us, provided it exists even if wecannot know that it exists. We can, obviously, suspect that it mayexist, and wonder whether it does; hence it is connected with our desirefor knowledge, and has the importance of either satisfying or thwartingthis desire. 

Again, it is by no means a truism, and is in fact false, that we cannotknow that anything exists which we do not know. The word 'know' is hereused in two different senses. (1) In its first use it is applicable tothe sort of knowledge which is opposed to error, the sense in whichwhat we know is _true_, the sense which applies to our beliefs andconvictions, i. E. To what are called _judgements_. In this sense of theword we know _that_ something is the case. This sort of knowledge maybe described as knowledge of _truths_. (2) In the second use of the word'know' above, the word applies to our knowledge of _things_, which wemay call _acquaintance_. This is the sense in which we know sense-data. (The distinction involved is roughly that between _savoir_ and_connaître_ in French, or between _wissen_ and _kennen_ in German. )

Thus the statement which seemed like a truism becomes, when re-stated, the following: 'We can never truly judge that something with which weare not acquainted exists. ' This is by no means a truism, but on thecontrary a palpable falsehood. I have not the honour to be acquaintedwith the Emperor of China, but I truly judge that he exists. It maybe said, of course, that I judge this because of other people'sacquaintance with him. This, however, would be an irrelevant retort, since, if the principle were true, I could not know that any one elseis acquainted with him. But further: there is no reason why I should notknow of the existence of something with which nobody is acquainted. Thispoint is important, and demands elucidation. 

If I am acquainted with a thing which exists, my acquaintance givesme the knowledge that it exists. But it is not true that, conversely, whenever I can know that a thing of a certain sort exists, I or some oneelse must be acquainted with the thing. What happens, in cases where Ihave true judgement without acquaintance, is that the thing is known tome by _description_, and that, in virtue of some general principle, theexistence of a thing answering to this description can be inferredfrom the existence of something with which I am acquainted. In orderto understand this point fully, it will be well first to deal withthe difference between knowledge by acquaintance and knowledge bydescription, and then to consider what knowledge of general principles, if any, has the same kind of certainty as our knowledge of the existenceof our own experiences. These subjects will be dealt with in thefollowing chapters. 

CHAPTER V. KNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY DESCRIPTION

In the preceding chapter we saw that there are two sorts of knowledge:knowledge of things, and knowledge of truths. In this chapter we shallbe concerned exclusively with knowledge of things, of which in turn weshall have to distinguish two kinds. Knowledge of things, when it isof the kind we call knowledge by _acquaintance_, is essentially simplerthan any knowledge of truths, and logically independent of knowledgeof truths, though it would be rash to assume that human beings ever, in fact, have acquaintance with things without at the same time knowingsome truth about them. Knowledge of things by _description_, on thecontrary, always involves, as we shall find in the course of the presentchapter, some knowledge of truths as its source and ground. But first ofall we must make clear what we mean by 'acquaintance' and what we meanby 'description'. 

We shall say that we have _acquaintance_ with anything of which we aredirectly aware, without the intermediary of any process of inferenceor any knowledge of truths. Thus in the presence of my table I amacquainted with the sense-data that make up the appearance of mytable--its colour, shape, hardness, smoothness, etc. ; all these arethings of which I am immediately conscious when I am seeing and touchingmy table. The particular shade of colour that I am seeing may have manythings said about it--I may say that it is brown, that it is ratherdark, and so on. But such statements, though they make me know truthsabout the colour, do not make me know the colour itself any betterthan I did before so far as concerns knowledge of the colour itself, asopposed to knowledge of truths about it, I know the colour perfectly andcompletely when I see it, and no further knowledge of it itself is eventheoretically possible. Thus the sense-data which make up theappearance of my table are things with which I have acquaintance, thingsimmediately known to me just as they are. 

My knowledge of the table as a physical object, on the contrary, is notdirect knowledge. Such as it is, it is obtained through acquaintancewith the sense-data that make up the appearance of the table. We haveseen that it is possible, without absurdity, to doubt whether there isa table at all, whereas it is not possible to doubt the sense-data. Myknowledge of the table is of the kind which we shall call 'knowledgeby description'. The table is 'the physical object which causessuch-and-such sense-data'. This describes the table by means of thesense-data. In order to know anything at all about the table, we mustknow truths connecting it with things with which we have acquaintance:we must know that 'such-and-such sense-data are caused by a physicalobject'. There is no state of mind in which we are directly aware of thetable; all our knowledge of the table is really knowledge of truths, andthe actual thing which is the table is not, strictly speaking, knownto us at all. We know a description, and we know that there is just oneobject to which this description applies, though the object itself isnot directly known to us. In such a case, we say that our knowledge ofthe object is knowledge by description. 

All our knowledge, both knowledge of things and knowledge of truths, rests upon acquaintance as its foundation. It is therefore important toconsider what kinds of things there are with which we have acquaintance. 

Sense-data, as we have already seen, are among the things with whichwe are acquainted; in fact, they supply the most obvious and strikingexample of knowledge by acquaintance. But if they were the sole example, our knowledge would be very much more restricted than it is. We shouldonly know what is now present to our senses: we could not know anythingabout the past--not even that there was a past--nor could we know anytruths about our sense-data, for all knowledge of truths, as we shallshow, demands acquaintance with things which are of an essentiallydifferent character from sense-data, the things which are sometimescalled 'abstract ideas', but which we shall call 'universals'. We havetherefore to consider acquaintance with other things besides sense-dataif we are to obtain any tolerably adequate analysis of our knowledge. 

The first extension beyond sense-data to be considered is acquaintanceby _memory_. It is obvious that we often remember what we have seen orheard or had otherwise present to our senses, and that in such cases weare still immediately aware of what we remember, in spite of the factthat it appears as past and not as present. This immediate knowledge bymemory is the source of all our knowledge concerning the past: withoutit, there could be no knowledge of the past by inference, since weshould never know that there was anything past to be inferred. 

The next extension to be considered is acquaintance by _introspection_. We are not only aware of things, but we are often aware of being awareof them. When I see the sun, I am often aware of my seeing the sun; thus'my seeing the sun' is an object with which I have acquaintance. WhenI desire food, I may be aware of my desire for food; thus 'my desiringfood' is an object with which I am acquainted. Similarly we may beaware of our feeling pleasure or pain, and generally of the events whichhappen in our minds. This kind of acquaintance, which may be calledself-consciousness, is the source of all our knowledge of mental things. It is obvious that it is only what goes on in our own minds that can bethus known immediately. What goes on in the minds of others is knownto us through our perception of their bodies, that is, through thesense-data in us which are associated with their bodies. But for ouracquaintance with the contents of our own minds, we should be unable toimagine the minds of others, and therefore we could never arrive atthe knowledge that they have minds. It seems natural to suppose thatself-consciousness is one of the things that distinguish men fromanimals: animals, we may suppose, though they have acquaintance withsense-data, never become aware of this acquaintance. I do not meanthat they _doubt_ whether they exist, but that they have never becomeconscious of the fact that they have sensations and feelings, northerefore of the fact that they, the subjects of their sensations andfeelings, exist. 

We have spoken of acquaintance with the contents of our minds as_self_-consciousness, but it is not, of course, consciousness of our_self_: it is consciousness of particular thoughts and feelings. Thequestion whether we are also acquainted with our bare selves, as opposedto particular thoughts and feelings, is a very difficult one, upon whichit would be rash to speak positively. When we try to look into ourselveswe always seem to come upon some particular thought or feeling, and notupon the 'I' which has the thought or feeling. Nevertheless there aresome reasons for thinking that we are acquainted with the 'I', thoughthe acquaintance is hard to disentangle from other things. To make clearwhat sort of reason there is, let us consider for a moment what ouracquaintance with particular thoughts really involves. 

When I am acquainted with 'my seeing the sun', it seems plain that I amacquainted with two different things in relation to each other. On theone hand there is the sense-datum which represents the sun to me, on theother hand there is that which sees this sense-datum. All acquaintance, such as my acquaintance with the sense-datum which represents the sun, seems obviously a relation between the person acquainted and the objectwith which the person is acquainted. When a case of acquaintance is onewith which I can be acquainted (as I am acquainted with my acquaintancewith the sense-datum representing the sun), it is plain that the personacquainted is myself. Thus, when I am acquainted with myseeing the sun, the whole fact with which I am acquainted is'Self-acquainted-with-sense-datum'. 

Further, we know the truth 'I am acquainted with this sense-datum'. Itis hard to see how we could know this truth, or even understand what ismeant by it, unless we were acquainted with something which we call 'I'. It does not seem necessary to suppose that we are acquainted with a moreor less permanent person, the same to-day as yesterday, but it does seemas though we must be acquainted with that thing, whatever its nature, which sees the sun and has acquaintance with sense-data. Thus, in somesense it would seem we must be acquainted with our Selves as opposedto our particular experiences. But the question is difficult, andcomplicated arguments can be adduced on either side. Hence, althoughacquaintance with ourselves seems _probably_ to occur, it is not wise toassert that it undoubtedly does occur. 

We may therefore sum up as follows what has been said concerningacquaintance with things that exist. We have acquaintance in sensationwith the data of the outer senses, and in introspection with the data ofwhat may be called the inner sense--thoughts, feelings, desires, etc. ;we have acquaintance in memory with things which have been data eitherof the outer senses or of the inner sense. Further, it is probable, though not certain, that we have acquaintance with Self, as that whichis aware of things or has desires towards things. 

In addition to our acquaintance with particular existing things, we alsohave acquaintance with what we shall call _universals_, that is to say, general ideas, such as _whiteness_, _diversity_, _brotherhood_, and soon. Every complete sentence must contain at least one word which standsfor a universal, since all verbs have a meaning which is universal. Weshall return to universals later on, in Chapter IX; for the present, itis only necessary to guard against the supposition that whatever we canbe acquainted with must be something particular and existent. Awarenessof universals is called _conceiving_, and a universal of which we areaware is called a _concept_. 

It will be seen that among the objects with which we are acquaintedare not included physical objects (as opposed to sense-data), nor otherpeople's minds. These things are known to us by what I call 'knowledgeby description', which we must now consider. 

By a 'description' I mean any phrase of the form 'a so-and-so' or'the so-and-so'. A phrase of the form 'a so-and-so' I shall call an'ambiguous' description; a phrase of the form 'the so-and-so' (in thesingular) I shall call a 'definite' description. Thus 'a man' is anambiguous description, and 'the man with the iron mask' is a definitedescription. There are various problems connected with ambiguousdescriptions, but I pass them by, since they do not directly concernthe matter we are discussing, which is the nature of our knowledgeconcerning objects in cases where we know that there is an objectanswering to a definite description, though we are not acquainted withany such object. This is a matter which is concerned exclusively withdefinite descriptions. I shall therefore, in the sequel, speak simply of'descriptions' when I mean 'definite descriptions'. Thus a descriptionwill mean any phrase of the form 'the so-and-so' in the singular. 

We shall say that an object is 'known by description' when we know thatit is 'the so-and-so', i. E. When we know that there is one object, andno more, having a certain property; and it will generally be impliedthat we do not have knowledge of the same object by acquaintance. Weknow that the man with the iron mask existed, and many propositionsare known about him; but we do not know who he was. We know that thecandidate who gets the most votes will be elected, and in this case weare very likely also acquainted (in the only sense in which one canbe acquainted with some one else) with the man who is, in fact, thecandidate who will get most votes; but we do not know which of thecandidates he is, i. E. We do not know any proposition of the form 'A isthe candidate who will get most votes' where A is one of the candidatesby name. We shall say that we have 'merely descriptive knowledge' of theso-and-so when, although we know that the so-and-so exists, and althoughwe may possibly be acquainted with the object which is, in fact, theso-and-so, yet we do not know any proposition '_a_ is the so-and-so', where _a_ is something with which we are acquainted. 

When we say 'the so-and-so exists', we mean that there is just oneobject which is the so-and-so. The proposition '_a_ is the so-and-so'means that _a_ has the property so-and-so, and nothing else has. 'Mr. A. Is the Unionist candidate for this constituency' means 'Mr. A. Isa Unionist candidate for this constituency, and no one else is'. 'TheUnionist candidate for this constituency exists' means 'some one is aUnionist candidate for this constituency, and no one else is'. Thus, when we are acquainted with an object which is the so-and-so, we knowthat the so-and-so exists; but we may know that the so-and-so existswhen we are not acquainted with any object which we know to be theso-and-so, and even when we are not acquainted with any object which, infact, is the so-and-so. 

Common words, even proper names, are usually really descriptions. Thatis to say, the thought in the mind of a person using a proper namecorrectly can generally only be expressed explicitly if we replace theproper name by a description. Moreover, the description required toexpress the thought will vary for different people, or for the sameperson at different times. The only thing constant (so long as the nameis rightly used) is the object to which the name applies. But so long asthis remains constant, the particular description involved usually makesno difference to the truth or falsehood of the proposition in which thename appears. 

Let us take some illustrations. Suppose some statement made aboutBismarck. Assuming that there is such a thing as direct acquaintancewith oneself, Bismarck himself might have used his name directly todesignate the particular person with whom he was acquainted. In thiscase, if he made a judgement about himself, he himself might be aconstituent of the judgement. Here the proper name has the direct usewhich it always wishes to have, as simply standing for a certain object, and not for a description of the object. But if a person who knewBismarck made a judgement about him, the case is different. What thisperson was acquainted with were certain sense-data which he connected(rightly, we will suppose) with Bismarck's body. His body, as a physicalobject, and still more his mind, were only known as the body and themind connected with these sense-data. That is, they were known bydescription. It is, of course, very much a matter af chance whichcharacteristics of a man's appearance will come into a friend's mindwhen he thinks of him; thus the description actually in the friend'smind is accidental. The essential point is that he knows that thevarious descriptions all apply to the same entity, in spite of not beingacquainted with the entity in question. 

When we, who did not know Bismarck, make a judgement about him, thedescription in our minds will probably be some more or less vague massof historical knowledge--far more, in most cases, than is required toidentify him. But, for the sake of illustration, let us assume that wethink of him as 'the first Chancellor of the German Empire'. Here allthe words are abstract except 'German'. The word 'German' will, again, have different meanings for different people. To some it will recalltravels in Germany, to some the look of Germany on the map, and so on. But if we are to obtain a description which we know to be applicable, we shall be compelled, at some point, to bring in a reference to aparticular with which we are acquainted. Such reference is involved inany mention of past, present, and future (as opposed to definite dates), or of here and there, or of what others have told us. Thus it would seemthat, in some way or other, a description known to be applicable to aparticular must involve some reference to a particular with which weare acquainted, if our knowledge about the thing described is not to bemerely what follows _logically_ from the description. For example, 'themost long-lived of men' is a description involving only universals, which must apply to some man, but we can make no judgements concerningthis man which involve knowledge about him beyond what the descriptiongives. If, however, we say, 'The first Chancellor of the German Empirewas an astute diplomatist', we can only be assured of the truth of ourjudgement in virtue of something with which we are acquainted--usually atestimony heard or read. Apart from the information we convey to others, apart from the fact about the actual Bismarck, which gives importanceto our judgement, the thought we really have contains the one or moreparticulars involved, and otherwise consists wholly of concepts. 

All names of places--London, England, Europe, the Earth, the SolarSystem--similarly involve, when used, descriptions which start from someone or more particulars with which we are acquainted. I suspect thateven the Universe, as considered by metaphysics, involves such aconnexion with particulars. In logic, on the contrary, where we areconcerned not merely with what does exist, but with whatever might orcould exist or be, no reference to actual particulars is involved. 

It would seem that, when we make a statement about something only knownby description, we often _intend_ to make our statement, not in the forminvolving the description, but about the actual thing described. Thatis to say, when we say anything about Bismarck, we should like, if wecould, to make the judgement which Bismarck alone can make, namely, the judgement of which he himself is a constituent. In this we arenecessarily defeated, since the actual Bismarck is unknown to us. Butwe know that there is an object B, called Bismarck, and that B was anastute diplomatist. We can thus _describe_ the proposition we shouldlike to affirm, namely, 'B was an astute diplomatist', where B is theobject which was Bismarck. If we are describing Bismarck as 'the firstChancellor of the German Empire', the proposition we should like toaffirm may be described as 'the proposition asserting, concerning theactual object which was the first Chancellor of the German Empire, thatthis object was an astute diplomatist'. What enables us to communicatein spite of the varying descriptions we employ is that we know there isa true proposition concerning the actual Bismarck, and that however wemay vary the description (so long as the description is correct) theproposition described is still the same. This proposition, which isdescribed and is known to be true, is what interests us; but we are notacquainted with the proposition itself, and do not know it, though weknow it is true. 

It will be seen that there are various stages in the removal fromacquaintance with particulars: there is Bismarck to people who knew him;Bismarck to those who only know of him through history; the man withthe iron mask; the longest-lived of men. These are progressively furtherremoved from acquaintance with particulars; the first comes as near toacquaintance as is possible in regard to another person; in the second, we shall still be said to know 'who Bismarck was'; in the third, we donot know who was the man with the iron mask, though we can know manypropositions about him which are not logically deducible from the factthat he wore an iron mask; in the fourth, finally, we know nothingbeyond what is logically deducible from the definition of the man. Thereis a similar hierarchy in the region of universals. Many universals, like many particulars, are only known to us by description. But here, as in the case of particulars, knowledge concerning what is known bydescription is ultimately reducible to knowledge concerning what isknown by acquaintance. 

The fundamental principle in the analysis of propositions containingdescriptions is this: _Every proposition which we can understand must becomposed wholly of constituents with which we are acquainted_. 

We shall not at this stage attempt to answer all the objections whichmay be urged against this fundamental principle. For the present, weshall merely point out that, in some way or other, it must be possibleto meet these objections, for it is scarcely conceivable that we canmake a judgement or entertain a supposition without knowing what it isthat we are judging or supposing about. We must attach _some_ meaningto the words we use, if we are to speak significantly and not utter merenoise; and the meaning we attach to our words must be something withwhich we are acquainted. Thus when, for example, we make a statementabout Julius Caesar, it is plain that Julius Caesar himself is notbefore our minds, since we are not acquainted with him. We have in mindsome description of Julius Caesar: 'the man who was assassinated on theIdes of March', 'the founder of the Roman Empire', or, perhaps, merely'the man whose name was _Julius Caesar_'. (In this last description, _Julius Caesar_ is a noise or shape with which we are acquainted. )Thus our statement does not mean quite what it seems to mean, but meanssomething involving, instead of Julius Caesar, some description of himwhich is composed wholly of particulars and universals with which we areacquainted. 

The chief importance of knowledge by description is that it enables usto pass beyond the limits of our private experience. In spite of thefact that we can only know truths which are wholly composed of termswhich we have experienced in acquaintance, we can yet have knowledge bydescription of things which we have never experienced. In view of thevery narrow range of our immediate experience, this result is vital, anduntil it is understood, much of our knowledge must remain mysterious andtherefore doubtful. 

CHAPTER VI. ON INDUCTION

In almost all our previous discussions we have been concerned inthe attempt to get clear as to our data in the way of knowledge ofexistence. What things are there in the universe whose existence isknown to us owing to our being acquainted with them? So far, our answerhas been that we are acquainted with our sense-data, and, probably, with ourselves. These we know to exist. And past sense-data whichare remembered are known to have existed in the past. This knowledgesupplies our data. 

But if we are to be able to draw inferences from these data--if we areto know of the existence of matter, of other people, of the past beforeour individual memory begins, or of the future, we must know generalprinciples of some kind by means of which such inferences can be drawn. It must be known to us that the existence of some one sort of thing, A, is a sign of the existence of some other sort of thing, B, either atthe same time as A or at some earlier or later time, as, for example, thunder is a sign of the earlier existence of lightning. If this werenot known to us, we could never extend our knowledge beyond thesphere of our private experience; and this sphere, as we have seen, isexceedingly limited. The question we have now to consider is whethersuch an extension is possible, and if so, how it is effected. 

Let us take as an illustration a matter about which none of us, in fact, feel the slightest doubt. We are all convinced that the sun will riseto-morrow. Why? Is this belief a mere blind outcome of past experience, or can it be justified as a reasonable belief? It is not easy to finda test by which to judge whether a belief of this kind is reasonable ornot, but we can at least ascertain what sort of general beliefs wouldsuffice, if true, to justify the judgement that the sun will riseto-morrow, and the many other similar judgements upon which our actionsare based. 

It is obvious that if we are asked why we believe that the sun will riseto-morrow, we shall naturally answer 'Because it always has risen everyday'. We have a firm belief that it will rise in the future, because ithas risen in the past. If we are challenged as to why we believe thatit will continue to rise as heretofore, we may appeal to the laws ofmotion: the earth, we shall say, is a freely rotating body, and suchbodies do not cease to rotate unless something interferes from outside, and there is nothing outside to interfere with the earth between now andto-morrow. Of course it might be doubted whether we are quite certainthat there is nothing outside to interfere, but this is not theinteresting doubt. The interesting doubt is as to whether the lawsof motion will remain in operation until to-morrow. If this doubt israised, we find ourselves in the same position as when the doubt aboutthe sunrise was first raised. 

The _only_ reason for believing that the laws of motion will remain inoperation is that they have operated hitherto, so far as our knowledgeof the past enables us to judge. It is true that we have a greater bodyof evidence from the past in favour of the laws of motion than we havein favour of the sunrise, because the sunrise is merely a particularcase of fulfilment of the laws of motion, and there are countless otherparticular cases. But the real question is: Do _any_ number of casesof a law being fulfilled in the past afford evidence that it will befulfilled in the future? If not, it becomes plain that we have no groundwhatever for expecting the sun to rise to-morrow, or for expecting thebread we shall eat at our next meal not to poison us, or for any of theother scarcely conscious expectations that control our daily lives. Itis to be observed that all such expectations are only _probable_; thuswe have not to seek for a proof that they _must_ be fulfilled, butonly for some reason in favour of the view that they are _likely_ to befulfilled. 

Now in dealing with this question we must, to begin with, make animportant distinction, without which we should soon become involvedin hopeless confusions. Experience has shown us that, hitherto, thefrequent repetition of some uniform succession or coexistence has been a_cause_ of our expecting the same succession or coexistence on the nextoccasion. Food that has a certain appearance generally has a certaintaste, and it is a severe shock to our expectations when the familiarappearance is found to be associated with an unusual taste. Things whichwe see become associated, by habit, with certain tactile sensationswhich we expect if we touch them; one of the horrors of a ghost (inmany ghost-stories) is that it fails to give us any sensations of touch. Uneducated people who go abroad for the first time are so surprised asto be incredulous when they find their native language not understood. 

And this kind of association is not confined to men; in animals also itis very strong. A horse which has been often driven along a certainroad resists the attempt to drive him in a different direction. Domesticanimals expect food when they see the person who usually feeds them. Weknow that all these rather crude expectations of uniformity are liableto be misleading. The man who has fed the chicken every day throughoutits life at last wrings its neck instead, showing that more refinedviews as to the uniformity of nature would have been useful to thechicken. 

But in spite of the misleadingness of such expectations, theynevertheless exist. The mere fact that something has happened a certainnumber of times causes animals and men to expect that it will happenagain. Thus our instincts certainly cause us to believe that the sunwill rise to-morrow, but we may be in no better a position than thechicken which unexpectedly has its neck wrung. We have therefore todistinguish the fact that past uniformities _cause_ expectations as tothe future, from the question whether there is any reasonable ground forgiving weight to such expectations after the question of their validityhas been raised. 

The problem we have to discuss is whether there is any reason forbelieving in what is called 'the uniformity of nature'. The belief inthe uniformity of nature is the belief that everything that has happenedor will happen is an instance of some general law to which there are noexceptions. The crude expectations which we have been considering areall subject to exceptions, and therefore liable to disappoint those whoentertain them. But science habitually assumes, at least as a workinghypothesis, that general rules which have exceptions can be replaced bygeneral rules which have no exceptions. 'Unsupported bodies in air fall'is a general rule to which balloons and aeroplanes are exceptions. Butthe laws of motion and the law of gravitation, which account for thefact that most bodies fall, also account for the fact that balloons andaeroplanes can rise; thus the laws of motion and the law of gravitationare not subject to these exceptions. 

The belief that the sun will rise to-morrow might be falsified if theearth came suddenly into contact with a large body which destroyed itsrotation; but the laws of motion and the law of gravitation would notbe infringed by such an event. The business of science is to finduniformities, such as the laws of motion and the law of gravitation, to which, so far as our experience extends, there are no exceptions. In this search science has been remarkably successful, and it may beconceded that such uniformities have held hitherto. This brings us backto the question: Have we any reason, assuming that they have always heldin the past, to suppose that they will hold in the future?

It has been argued that we have reason to know that the future willresemble the past, because what was the future has constantly become thepast, and has always been found to resemble the past, so that we reallyhave experience of the future, namely of times which were formerlyfuture, which we may call past futures. But such an argument really begsthe very question at issue. We have experience of past futures, but notof future futures, and the question is: Will future futures resemblepast futures? This question is not to be answered by an argument whichstarts from past futures alone. We have therefore still to seek for someprinciple which shall enable us to know that the future will follow thesame laws as the past. 

The reference to the future in this question is not essential. The samequestion arises when we apply the laws that work in our experience topast things of which we have no experience--as, for example, in geology, or in theories as to the origin of the Solar System. The question wereally have to ask is: 'When two things have been found to be oftenassociated, and no instance is known of the one occurring without theother, does the occurrence of one of the two, in a fresh instance, giveany good ground for expecting the other?' On our answer to this questionmust depend the validity of the whole of our expectations as to thefuture, the whole of the results obtained by induction, and in factpractically all the beliefs upon which our daily life is based. 

It must be conceded, to begin with, that the fact that two things havebeen found often together and never apart does not, by itself, sufficeto _prove_ demonstratively that they will be found together in the nextcase we examine. The most we can hope is that the oftener things arefound together, the more probable it becomes that they will be foundtogether another time, and that, if they have been found together oftenenough, the probability will amount _almost_ to certainty. It cannever quite reach certainty, because we know that in spite of frequentrepetitions there sometimes is a failure at the last, as in the caseof the chicken whose neck is wrung. Thus probability is all we ought toseek. 

It might be urged, as against the view we are advocating, that weknow all natural phenomena to be subject to the reign of law, and thatsometimes, on the basis of observation, we can see that only one lawcan possibly fit the facts of the case. Now to this view there are twoanswers. The first is that, even if _some_ law which has no exceptionsapplies to our case, we can never, in practice, be sure that we havediscovered that law and not one to which there are exceptions. Thesecond is that the reign of law would seem to be itself only probable, and that our belief that it will hold in the future, or in unexaminedcases in the past, is itself based upon the very principle we areexamining. 

The principle we are examining may be called the _principle ofinduction_, and its two parts may be stated as follows:

(a) When a thing of a certain sort A has been found to be associatedwith a thing of a certain other sort B, and has never been founddissociated from a thing of the sort B, the greater the number of casesin which A and B have been associated, the greater is the probabilitythat they will be associated in a fresh case in which one of them isknown to be present;

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

As just stated, the principle applies only to the verification of ourexpectation in a single fresh instance. But we want also to know thatthere is a probability in favour of the general law that things of thesort A are _always_ associated with things of the sort B, provided asufficient number of cases of association are known, and no cases offailure of association are known. The probability of the general law isobviously less than the probability of the particular case, since if thegeneral law is true, the particular case must also be true, whereasthe particular case may be true without the general law being true. Nevertheless the probability of the general law is increased byrepetitions, just as the probability of the particular case is. We maytherefore repeat the two parts of our principle as regards the generallaw, thus:

(a) The greater the number of cases in which a thing of the sort A hasbeen found associated with a thing of the sort B, the more probable itis (if no cases of failure of association are known) that A is alwaysassociated with B;

b) Under the same circumstances, a sufficient number of cases of theassociation of A with B will make it nearly certain that A is alwaysassociated with B, and will make this general law approach certaintywithout limit. 

It should be noted that probability is always relative to certain data. In our case, the data are merely the known cases of coexistence of A andB. There may be other data, which _might_ be taken into account, whichwould gravely alter the probability. For example, a man who had seen agreat many white swans might argue, by our principle, that on thedata it was _probable_ that all swans were white, and this might be aperfectly sound argument. The argument is not disproved ny the fact thatsome swans are black, because a thing may very well happen in spite ofthe fact that some data render it improbable. In the case of the swans, a man might know that colour is a very variable characteristic in manyspecies of animals, and that, therefore, an induction as to colour ispeculiarly liable to error. But this knowledge would be a fresh datum, by no means proving that the probability relatively to our previous datahad been wrongly estimated. The fact, therefore, that things often failto fulfil our expectations is no evidence that our expectations will not_probably_ be fulfilled in a given case or a given class of cases. Thusour inductive principle is at any rate not capable of being _disproved_by an appeal to experience. 

The inductive principle, however, is equally incapable of being _proved_by an appeal to experience. Experience might conceivably confirmthe inductive principle as regards the cases that have been alreadyexamined; but as regards unexamined cases, it is the inductive principlealone that can justify any inference from what has been examined to whathas not been examined. All arguments which, on the basis of experience, argue as to the future or the unexperienced parts of the past orpresent, assume the inductive principle; hence we can never useexperience to prove the inductive principle without begging thequestion. Thus we must either accept the inductive principle on theground of its intrinsic evidence, or forgo all justification of ourexpectations about the future. If the principle is unsound, we have noreason to expect the sun to rise to-morrow, to expect bread to be morenourishing than a stone, or to expect that if we throw ourselves offthe roof we shall fall. When we see what looks like our best friendapproaching us, we shall have no reason to suppose that his body is notinhabited by the mind of our worst enemy or of some total stranger. Allour conduct is based upon associations which have worked in the past, and which we therefore regard as likely to work in the future; and thislikelihood is dependent for its validity upon the inductive principle. 

The general principles of science, such as the belief in the reignof law, and the belief that every event must have a cause, are ascompletely dependent upon the inductive principle as are the beliefs ofdaily life All such general principles are believed because mankind havefound innumerable instances of their truth and no instances of theirfalsehood. But this affords no evidence for their truth in the future, unless the inductive principle is assumed. 

Thus all knowledge which, on a basis of experience tells us somethingabout what is not experienced, is based upon a belief which experiencecan neither confirm nor confute, yet which, at least in its moreconcrete applications, appears to be as firmly rooted in us as manyof the facts of experience. The existence and justification of suchbeliefs--for the inductive principle, as we shall see, is not the onlyexample--raises some of the most difficult and most debated problems ofphilosophy. We will, in the next chapter, consider briefly what may besaid to account for such knowledge, and what is its scope and its degreeof certainty. 

CHAPTER VII. ON OUR KNOWLEDGE OF GENERAL PRINCIPLES

We saw in the preceding chapter that the principle of induction, whilenecessary to the validity of all arguments based on experience, is itself not capable of being proved by experience, and yet isunhesitatingly believed by every one, at least in all its concreteapplications. In these characteristics the principle of induction doesnot stand alone. There are a number of other principles which cannot beproved or disproved by experience, but are used in arguments which startfrom what is experienced. 

Some of these principles have even greater evidence than the principleof induction, and the knowledge of them has the same degree of certaintyas the knowledge of the existence of sense-data. They constitute themeans of drawing inferences from what is given in sensation; and if whatwe infer is to be true, it is just as necessary that our principlesof inference should be true as it is that our data should be true. Theprinciples of inference are apt to be overlooked because of theirvery obviousness--the assumption involved is assented to without ourrealizing that it is an assumption. But it is very important to realizethe use of principles of inference, if a correct theory of knowledgeis to be obtained; for our knowledge of them raises interesting anddifficult questions. 

In all our knowledge of general principles, what actually happensis that first of all we realize some particular application of theprinciple, and then we realize that the particularity is irrelevant, andthat there is a generality which may equally truly be affirmed. This isof course familiar in such matters as teaching arithmetic: 'two andtwo are four' is first learnt in the case of some particular pair ofcouples, and then in some other particular case, and so on, until atlast it becomes possible to see that it is true of any pair of couples. The same thing happens with logical principles. Suppose two men arediscussing what day of the month it is. One of them says, 'At least youwill admit that _if_ yesterday was the 15th to-day must be the 16th. ''Yes', says the other, 'I admit that. ' 'And you know', the firstcontinues, 'that yesterday was the 15th, because you dined with Jones, and your diary will tell you that was on the 15th. ' 'Yes', says thesecond; 'therefore to-day _is_ the 16th. '

Now such an argument is not hard to follow; and if it is granted thatits premisses are true in fact, no one will deny that the conclusionmust also be true. But it depends for its truth upon an instance of ageneral logical principle. The logical principle is as follows: 'Supposeit known that _if_ this is true, then that is true. Suppose it alsoknown that this _is_ true, then it follows that that is true. ' When itis the case that if this is true, that is true, we shall say that this'implies' that, and that that 'follows from' this. Thus our principlestates that if this implies that, and this is true, then that is true. In other words, 'anything implied by a true proposition is true', or'whatever follows from a true proposition is true'. 

This principle is really involved--at least, concrete instances of itare involved--in all demonstrations. Whenever one thing which we believeis used to prove something else, which we consequently believe, thisprinciple is relevant. If any one asks: 'Why should I accept the resultsof valid arguments based on true premisses?' we can only answer byappealing to our principle. In fact, the truth of the principle isimpossible to doubt, and its obviousness is so great that at first sightit seems almost trivial. Such principles, however, are not trivial tothe philosopher, for they show that we may have indubitable knowledgewhich is in no way derived from objects of sense. 

The above principle is merely one of a certain number of self-evidentlogical principles. Some at least of these principles must be grantedbefore any argument or proof becomes possible. When some of them havebeen granted, others can be proved, though these others, so long as theyare simple, are just as obvious as the principles taken for granted. Forno very good reason, three of these principles have been singled out bytradition under the name of 'Laws of Thought'. 

They are as follows:

(1) _The law of identity_: 'Whatever is, is. '

(2) _The law of contradiction_: 'Nothing can both be and not be. '

(3) _The law of excluded middle_: 'Everything must either be or not be. '

These three laws are samples of self-evident logical principles, butare not really more fundamental or more self-evident than various othersimilar principles: for instance, the one we considered just now, whichstates that what follows from a true premiss is true. The name 'laws ofthought' is also misleading, for what is important is not the fact thatwe think in accordance with these laws, but the fact that things behavein accordance with them; in other words, the fact that when we think inaccordance with them we think _truly_. But this is a large question, towhich we must return at a later stage. 

In addition to the logical principles which enable us to prove froma given premiss that something is _certainly_ true, there are otherlogical principles which enable us to prove, from a given premiss, that there is a greater or less probability that something is true. Anexample of such principles--perhaps the most important example is theinductive principle, which we considered in the preceding chapter. 

One of the great historic controversies in philosophy is the controversybetween the two schools called respectively 'empiricists' and'rationalists'. The empiricists--who are best represented by theBritish philosophers, Locke, Berkeley, and Hume--maintained that allour knowledge is derived from experience; the rationalists--who arerepresented by the Continental philosophers of the seventeenth century, especially Descartes and Leibniz--maintained that, in addition to whatwe know by experience, there are certain 'innate ideas' and 'innateprinciples', which we know independently of experience. It has nowbecome possible to decide with some confidence as to the truth orfalsehood of these opposing schools. It must be admitted, for thereasons already stated, that logical principles are known to us, andcannot be themselves proved by experience, since all proof presupposesthem. In this, therefore, which was the most important point of thecontroversy, the rationalists were in the right. 

On the other hand, even that part of our knowledge which is _logically_independent of experience (in the sense that experience cannot proveit) is yet elicited and caused by experience. It is on occasion ofparticular experiences that we become aware of the general laws whichtheir connexions exemplify. It would certainly be absurd to suppose thatthere are innate principles in the sense that babies are born with aknowledge of everything which men know and which cannot be deduced fromwhat is experienced. For this reason, the word 'innate' would not now beemployed to describe our knowledge of logical principles. The phrase'_a priori_' is less objectionable, and is more usual in modern writers. Thus, while admitting that all knowledge is elicited and caused byexperience, we shall nevertheless hold that some knowledge is _apriori_, in the sense that the experience which makes us think of itdoes not suffice to prove it, but merely so directs our attention thatwe see its truth without requiring any proof from experience. 

There is another point of great importance, in which the empiricistswere in the right as against the rationalists. Nothing can be known to_exist_ except by the help of experience. That is to say, if we wish toprove that something of which we have no direct experience exists, wemust have among our premisses the existence of one or more things ofwhich we have direct experience. Our belief that the Emperor of Chinaexists, for example, rests upon testimony, and testimony consists, in the last analysis, of sense-data seen or heard in reading or beingspoken to. Rationalists believed that, from general consideration asto what must be, they could deduce the existence of this or that in theactual world. In this belief they seem to have been mistaken. All theknowledge that we can acquire _a priori_ concerning existence seemsto be hypothetical: it tells us that if one thing exists, another mustexist, or, more generally, that if one proposition is true, another mustbe true. This is exemplified by the principles we have already dealtwith, such as '_if_ this is true, and this implies that, then that istrue', or '_if_ this and that have been repeatedly found connected, theywill probably be connected in the next instance in which one of them isfound'. Thus the scope and power of _a priori_ principles is strictlylimited. All knowledge that something exists must be in part dependenton experience. When anything is known immediately, its existence isknown by experience alone; when anything is proved to exist, withoutbeing known immediately, both experience and _a priori_ principles mustbe required in the proof. Knowledge is called _empirical_ when it restswholly or partly upon experience. Thus all knowledge which assertsexistence is empirical, and the only _a priori_ knowledge concerningexistence is hypothetical, giving connexions among things that exist ormay exist, but not giving actual existence. 

_A priori_ knowledge is not all of the logical kind we have beenhitherto considering. Perhaps the most important example of non-logical_a priori_ knowledge is knowledge as to ethical value. I am not speakingof judgements as to what is useful or as to what is virtuous, for suchjudgements do require empirical premisses; I am speaking of judgementsas to the intrinsic desirability of things. If something is useful, itmust be useful because it secures some end; the end must, if we havegone far enough, be valuable on its own account, and not merely becauseit is useful for some further end. Thus all judgements as to what isuseful depend upon judgements as to what has value on its own account. 

We judge, for example, that happiness is more desirable than misery, knowledge than ignorance, goodwill than hatred, and so on. Suchjudgements must, in part at least, be immediate and _a priori_. Like ourprevious _a priori_ judgements, they may be elicited by experience, andindeed they must be; for it seems not possible to judge whether anythingis intrinsically valuable unless we have experienced something ofthe same kind. But it is fairly obvious that they cannot be proved byexperience; for the fact that a thing exists or does not exist cannotprove either that it is good that it should exist or that it is bad. Thepursuit of this subject belongs to ethics, where the impossibility ofdeducing what ought to be from what is has to be established. In thepresent connexion, it is only important to realize that knowledge as towhat is intrinsically of value is _a priori_ in the same sense inwhich logic is _a priori_, namely in the sense that the truth of suchknowledge can be neither proved nor disproved by experience. 

All pure mathematics is _a priori_, like logic. This was strenuouslydenied by the empirical philosophers, who maintained that experience wasas much the source of our knowledge of arithmetic as of our knowledge ofgeography. They maintained that by the repeated experience of seeing twothings and two other things, and finding that altogether they made fourthings, we were led by induction to the conclusion that two thingsand two other things would _always_ make four things altogether. If, however, this were the source of our knowledge that two and two arefour, we should proceed differently, in persuading ourselves of itstruth, from the way in which we do actually proceed. In fact, a certainnumber of instances are needed to make us think of two abstractly, rather than of two coins or two books or two people, or two of any otherspecified kind. But as soon as we are able to divest our thoughts ofirrelevant particularity, we become able to see the general principlethat two and two are four; any one instance is seen to be _typical_, andthe examination of other instances becomes unnecessary. (1)

(1) Cf. A. N. Whitehead, _Introduction to Mathematics_ (Home UniversityLibrary). 

The same thing is exemplified in geometry. If we want to prove someproperty of _all_ triangles, we draw some one triangle and reason aboutit; but we can avoid making use of any property which it does not sharewith all other triangles, and thus, from our particular case, we obtaina general result. We do not, in fact, feel our certainty that two andtwo are four increased by fresh instances, because, as soon as we haveseen the truth of this proposition, our certainty becomes so great asto be incapable of growing greater. Moreover, we feel some quality ofnecessity about the proposition 'two and two are four', which isabsent from even the best attested empirical generalizations. Suchgeneralizations always remain mere facts: we feel that there might be aworld in which they were false, though in the actual world they happento be true. In any possible world, on the contrary, we feel that twoand two would be four: this is not a mere fact, but a necessity to whicheverything actual and possible must conform. 

The case may be made clearer by considering a genuinely-empiricalgeneralization, such as 'All men are mortal. ' It is plain that webelieve this proposition, in the first place, because there is no knowninstance of men living beyond a certain age, and in the second placebecause there seem to be physiological grounds for thinking that anorganism such as a man's body must sooner or later wear out. Neglectingthe second ground, and considering merely our experience of men'smortality, it is plain that we should not be content with one quiteclearly understood instance of a man dying, whereas, in the case of 'twoand two are four', one instance does suffice, when carefully considered, to persuade us that the same must happen in any other instance. Alsowe can be forced to admit, on reflection, that there may be some doubt, however slight, as to whether _all_ men are mortal. This may be madeplain by the attempt to imagine two different worlds, in one of whichthere are men who are not mortal, while in the other two and two makefive. When Swift invites us to consider the race of Struldbugs who neverdie, we are able to acquiesce in imagination. But a world where twoand two make five seems quite on a different level. We feel that such aworld, if there were one, would upset the whole fabric of our knowledgeand reduce us to utter doubt. 

The fact is that, in simple mathematical judgements such as 'two and twoare four', and also in many judgements of logic, we can know the generalproposition without inferring it from instances, although some instanceis usually necessary to make clear to us what the general propositionmeans. This is why there is real utility in the process of _deduction_, which goes from the general to the general, or from the general to theparticular, as well as in the process of _induction_, which goes fromthe particular to the particular, or from the particular to the general. It is an old debate among philosophers whether deduction ever gives_new_ knowledge. We can now see that in certain cases, at least, it doesdo so. If we already know that two and two always make four, and weknow that Brown and Jones are two, and so are Robinson and Smith, we candeduce that Brown and Jones and Robinson and Smith are four. This isnew knowledge, not contained in our premisses, because the generalproposition, 'two and two are four', never told us there were suchpeople as Brown and Jones and Robinson and Smith, and the particularpremisses do not tell us that there were four of them, whereas theparticular proposition deduced does tell us both these things. 

But the newness of the knowledge is much less certain if we take thestock instance of deduction that is always given in books on logic, namely, 'All men are mortal; Socrates is a man, therefore Socrates ismortal. ' In this case, what we really know beyond reasonable doubt isthat certain men, A, B, C, were mortal, since, in fact, they have died. If Socrates is one of these men, it is foolish to go the roundabout waythrough 'all men are mortal' to arrive at the conclusion that _probably_Socrates is mortal. If Socrates is not one of the men on whom ourinduction is based, we shall still do better to argue straight from ourA, B, C, to Socrates, than to go round by the general proposition, 'allmen are mortal'. For the probability that Socrates is mortal is greater, on our data, than the probability that all men are mortal. (This isobvious, because if all men are mortal, so is Socrates; but if Socratesis mortal, it does not follow that all men are mortal. ) Hence we shallreach the conclusion that Socrates is mortal with a greater approach tocertainty if we make our argument purely inductive than if we go by wayof 'all men are mortal' and then use deduction. 

This illustrates the difference between general propositions known _apriori_ such as 'two and two are four', and empirical generalizationssuch as 'all men are mortal'. In regard to the former, deduction is theright mode of argument, whereas in regard to the latter, induction isalways theoretically preferable, and warrants a greater confidence inthe truth of our conclusion, because all empirical generalizations aremore uncertain than the instances of them. 

We have now seen that there are propositions known _a priori_, and thatamong them are the propositions of logic and pure mathematics, as wellas the fundamental propositions of ethics. The question which mustnext occupy us is this: How is it possible that there should be suchknowledge? And more particularly, how can there be knowledge of generalpropositions in cases where we have not examined all the instances, andindeed never can examine them all, because their number is infinite?These questions, which were first brought prominently forward bythe German philosopher Kant (1724-1804), are very difficult, andhistorically very important. 

CHAPTER VIII. HOW _A PRIORI_ KNOWLEDGE IS POSSIBLE

Immanuel Kant is generally regarded as the greatest of the modernphilosophers. Though he lived through the Seven Years War and theFrench Revolution, he never interrupted his teaching of philosophy atKönigsberg in East Prussia. His most distinctive contribution was theinvention of what he called the 'critical' philosophy, which, assumingas a datum that there is knowledge of various kinds, inquired how suchknowledge comes to be possible, and deduced, from the answer to thisinquiry, many metaphysical results as to the nature of the world. Whether these results were valid may well be doubted. But Kantundoubtedly deserves credit for two things: first, for having perceivedthat we have _a priori_ knowledge which is not purely 'analytic', i. E. Such that the opposite would be self-contradictory, and secondly, for having made evident the philosophical importance of the theory ofknowledge. 

Before the time of Kant, it was generally held that whatever knowledgewas _a priori_ must be 'analytic'. What this word means will be bestillustrated by examples. If I say, 'A bald man is a man', 'A planefigure is a figure', 'A bad poet is a poet', I make a purely analyticjudgement: the subject spoken about is given as having at least twoproperties, of which one is singled out to be asserted of it. Suchpropositions as the above are trivial, and would never be enunciatedin real life except by an orator preparing the way for a piece ofsophistry. They are called 'analytic' because the predicate is obtainedby merely analysing the subject. Before the time of Kant it was thoughtthat all judgements of which we could be certain _a priori_ were of thiskind: that in all of them there was a predicate which was only partof the subject of which it was asserted. If this were so, we should beinvolved in a definite contradiction if we attempted to deny anythingthat could be known _a priori_. 'A bald man is not bald' would assertand deny baldness of the same man, and would therefore contradictitself. Thus according to the philosophers before Kant, the law ofcontradiction, which asserts that nothing can at the same time have andnot have a certain property, sufficed to establish the truth of all _apriori_ knowledge. 

Hume (1711-76), who preceded Kant, accepting the usual view as to whatmakes knowledge _a priori_, discovered that, in many cases which hadpreviously been supposed analytic, and notably in the case of cause andeffect, the connexion was really synthetic. Before Hume, rationalists atleast had supposed that the effect could be logically deduced from thecause, if only we had sufficient knowledge. Hume argued--correctly, aswould now be generally admitted--that this could not be done. Hence heinferred the far more doubtful proposition that nothing could be known_a priori_ about the connexion of cause and effect. Kant, who had beeneducated in the rationalist tradition, was much perturbed by Hume'sscepticism, and endeavoured to find an answer to it. He perceived thatnot only the connexion of cause and effect, but all the propositionsof arithmetic and geometry, are 'synthetic', i. E. Not analytic: inall these propositions, no analysis of the subject will reveal thepredicate. His stock instance was the proposition 7 + 5 = 12. He pointedout, quite truly, that 7 and 5 have to be put together to give 12: theidea of 12 is not contained in them, nor even in the idea of adding themtogether. Thus he was led to the conclusion that all pure mathematics, though _a priori_, is synthetic; and this conclusion raised a newproblem of which he endeavoured to find the solution. 

The question which Kant put at the beginning of his philosophy, namely'How is pure mathematics possible?' is an interesting and difficult one, to which every philosophy which is not purely sceptical must findsome answer. The answer of the pure empiricists, that our mathematicalknowledge is derived by induction from particular instances, we havealready seen to be inadequate, for two reasons: first, that the validityof the inductive principle itself cannot be proved by induction;secondly, that the general propositions of mathematics, such as 'twoand two always make four', can obviously be known with certainty byconsideration of a single instance, and gain nothing by enumeration ofother cases in which they have been found to be true. Thus our knowledgeof the general propositions of mathematics (and the same applies tologic) must be accounted for otherwise than our (merely probable)knowledge of empirical generalizations such as 'all men are mortal'. 

The problem arises through the fact that such knowledge is general, whereas all experience is particular. It seems strange that we shouldapparently be able to know some truths in advance about particularthings of which we have as yet no experience; but it cannot easily bedoubted that logic and arithmetic will apply to such things. We do notknow who will be the inhabitants of London a hundred years hence; butwe know that any two of them and any other two of them will make four ofthem. This apparent power of anticipating facts about things of whichwe have no experience is certainly surprising. Kant's solution of theproblem, though not valid in my opinion, is interesting. It is, however, very difficult, and is differently understood by different philosophers. We can, therefore, only give the merest outline of it, and even thatwill be thought misleading by many exponents of Kant's system. 

What Kant maintained was that in all our experience there are twoelements to be distinguished, the one due to the object (i. E. To what wehave called the 'physical object'), the other due to our own nature. Wesaw, in discussing matter and sense-data, that the physical object isdifferent from the associated sense-data, and that the sense-data are tobe regarded as resulting from an interaction between the physicalobject and ourselves. So far, we are in agreement with Kant. But whatis distinctive of Kant is the way in which he apportions the shares ofourselves and the physical object respectively. He considers that thecrude material given in sensation--the colour, hardness, etc. --is dueto the object, and that what we supply is the arrangement in spaceand time, and all the relations between sense-data which result fromcomparison or from considering one as the cause of the other or in anyother way. His chief reason in favour of this view is that we seemto have _a priori_ knowledge as to space and time and causality andcomparison, but not as to the actual crude material of sensation. We canbe sure, he says, that anything we shall ever experience must show thecharacteristics affirmed of it in our _a priori_ knowledge, becausethese characteristics are due to our own nature, and thereforenothing can ever come into our experience without acquiring thesecharacteristics. 

The physical object, which he calls the 'thing in itself', (1) he regardsas essentially unknowable; what can be known is the object as we have itin experience, which he calls the 'phenomenon'. The phenomenon, beinga joint product of us and the thing in itself, is sure to have thosecharacteristics which are due to us, and is therefore sure to conformto our _a priori_ knowledge. Hence this knowledge, though true of allactual and possible experience, must not be supposed to apply outsideexperience. Thus in spite of the existence of _a priori_ knowledge, wecannot know anything about the thing in itself or about what is notan actual or possible object of experience. In this way he tries toreconcile and harmonize the contentions of the rationalists with thearguments of the empiricists. 

(1) Kant's 'thing in itself' is identical in _definition_ withthe physical object, namely, it is the cause of sensations. In theproperties deduced from the definition it is not identical, since Kantheld (in spite of some inconsistency as regards cause) that we can knowthat none of the categories are applicable to the 'thing in itself'. 

Apart from minor grounds on which Kant's philosophy may be criticized, there is one main objection which seems fatal to any attempt to dealwith the problem of _a priori_ knowledge by his method. The thing tobe accounted for is our certainty that the facts must always conform tologic and arithmetic. To say that logic and arithmetic are contributedby us does not account for this. Our nature is as much a fact of theexisting world as anything, and there can be no certainty that it willremain constant. It might happen, if Kant is right, that to-morrowour nature would so change as to make two and two become five. Thispossibility seems never to have occurred to him, yet it is one whichutterly destroys the certainty and universality which he is anxiousto vindicate for arithmetical propositions. It is true that thispossibility, formally, is inconsistent with the Kantian view that timeitself is a form imposed by the subject upon phenomena, so that ourreal Self is not in time and has no to-morrow. But he will still haveto suppose that the time-order of phenomena is determined bycharacteristics of what is behind phenomena, and this suffices for thesubstance of our argument. 

Reflection, moreover, seems to make it clear that, if there is any truthin our arithmetical beliefs, they must apply to things equally whetherwe think of them or not. Two physical objects and two other physicalobjects must make four physical objects, even if physical objects cannotbe experienced. To assert this is certainly within the scope of whatwe mean when we state that two and two are four. Its truth is just asindubitable as the truth of the assertion that two phenomena and twoother phenomena make four phenomena. Thus Kant's solution unduly limitsthe scope of _a priori_ propositions, in addition to failing in theattempt at explaining their certainty. 

Apart from the special doctrines advocated by Kant, it is very commonamong philosophers to regard what is _a priori_ as in some sense mental, as concerned rather with the way we must think than with any fact ofthe outer world. We noted in the preceding chapter the three principlescommonly called 'laws of thought'. The view which led to their being sonamed is a natural one, but there are strong reasons for thinkingthat it is erroneous. Let us take as an illustration the law ofcontradiction. This is commonly stated in the form 'Nothing can both beand not be', which is intended to express the fact that nothing can atonce have and not have a given quality. Thus, for example, if a treeis a beech it cannot also be not a beech; if my table is rectangular itcannot also be not rectangular, and so on. 

Now what makes it natural to call this principle a law of _thought_is that it is by thought rather than by outward observation that wepersuade ourselves of its necessary truth. When we have seen that a treeis a beech, we do not need to look again in order to ascertain whetherit is also not a beech; thought alone makes us know that this isimpossible. But the conclusion that the law of contradiction is a lawof _thought_ is nevertheless erroneous. What we believe, when we believethe law of contradiction, is not that the mind is so made that it mustbelieve the law of contradiction. _This_ belief is a subsequent resultof psychological reflection, which presupposes the belief in the law ofcontradiction. The belief in the law of contradiction is a belief aboutthings, not only about thoughts. It is not, e. G. , the belief that if we_think_ a certain tree is a beech, we cannot at the same time _think_that it is not a beech; it is the belief that if the tree _is_ abeech, it cannot at the same time _be_ not a beech. Thus the law ofcontradiction is about things, and not merely about thoughts; andalthough belief in the law of contradiction is a thought, the law ofcontradiction itself is not a thought, but a fact concerning the thingsin the world. If this, which we believe when we believe the law ofcontradiction, were not true of the things in the world, the factthat we were compelled to _think_ it true would not save the law ofcontradiction from being false; and this shows that the law is not a lawof _thought_. 

A similar argument applies to any other _a priori_ judgement. When wejudge that two and two are four, we are not making a judgement about ourthoughts, but about all actual or possible couples. The fact that ourminds are so constituted as to believe that two and two are four, thoughit is true, is emphatically not what we assert when we assert that twoand two are four. And no fact about the constitution of our minds couldmake it _true_ that two and two are four. Thus our _a priori_ knowledge, if it is not erroneous, is not merely knowledge about the constitutionof our minds, but is applicable to whatever the world may contain, bothwhat is mental and what is non-mental. 

The fact seems to be that all our _a priori_ knowledge is concerned withentities which do not, properly speaking, _exist_, either in the mentalor in the physical world. These entities are such as can be named byparts of speech which are not substantives; they are such entities asqualities and relations. Suppose, for instance, that I am in my room. Iexist, and my room exists; but does 'in' exist? Yet obviously the word'in' has a meaning; it denotes a relation which holds between me and myroom. This relation is something, although we cannot say that it exists_in the same sense_ in which I and my room exist. The relation 'in' issomething which we can think about and understand, for, if we could notunderstand it, we could not understand the sentence 'I am in my room'. Many philosophers, following Kant, have maintained that relations arethe work of the mind, that things in themselves have no relations, but that the mind brings them together in one act of thought and thusproduces the relations which it judges them to have. 

This view, however, seems open to objections similar to those which weurged before against Kant. It seems plain that it is not thought whichproduces the truth of the proposition 'I am in my room'. It may be truethat an earwig is in my room, even if neither I nor the earwig nor anyone else is aware of this truth; for this truth concerns only the earwigand the room, and does not depend upon anything else. Thus relations, aswe shall see more fully in the next chapter, must be placed in a worldwhich is neither mental nor physical. This world is of great importanceto philosophy, and in particular to the problems of _a priori_knowledge. In the next chapter we shall proceed to develop its natureand its bearing upon the questions with which we have been dealing. 

CHAPTER IX. THE WORLD OF UNIVERSALS

At the end of the preceding chapter we saw that such entities asrelations appear to have a being which is in some way different fromthat of physical objects, and also different from that of minds and fromthat of sense-data. In the present chapter we have to consider what isthe nature of this kind of being, and also what objects there are thathave this kind of being. We will begin with the latter question. 

The problem with which we are now concerned is a very old one, since itwas brought into philosophy by Plato. Plato's 'theory of ideas' is anattempt to solve this very problem, and in my opinion it is one of themost successful attempts hitherto made. The theory to be advocated inwhat follows is largely Plato's, with merely such modifications as timehas shown to be necessary. 

The way the problem arose for Plato was more or less as follows. Letus consider, say, such a notion as _justice_. If we ask ourselves whatjustice is, it is natural to proceed by considering this, that, and theother just act, with a view to discovering what they have in common. They must all, in some sense, partake of a common nature, which will befound in whatever is just and in nothing else. This common nature, invirtue of which they are all just, will be justice itself, the pureessence the admixture of which with facts of ordinary life produces themultiplicity of just acts. Similarly with any other word which may beapplicable to common facts, such as 'whiteness' for example. The wordwill be applicable to a number of particular things because they allparticipate in a common nature or essence. This pure essence is whatPlato calls an 'idea' or 'form'. (It must not be supposed that 'ideas', in his sense, exist in minds, though they may be apprehended by minds. )The 'idea' _justice_ is not identical with anything that is just: it issomething other than particular things, which particular things partakeof. Not being particular, it cannot itself exist in the world of sense. Moreover it is not fleeting or changeable like the things of sense: itis eternally itself, immutable and indestructible. 

Thus Plato is led to a supra-sensible world, more real than the commonworld of sense, the unchangeable world of ideas, which alone gives tothe world of sense whatever pale reflection of reality may belong to it. The truly real world, for Plato, is the world of ideas; for whateverwe may attempt to say about things in the world of sense, we can onlysucceed in saying that they participate in such and such ideas, which, therefore, constitute all their character. Hence it is easy to passon into a mysticism. We may hope, in a mystic illumination, to see theideas as we see objects of sense; and we may imagine that the ideasexist in heaven. These mystical developments are very natural, but thebasis of the theory is in logic, and it is as based in logic that wehave to consider it. 

The word 'idea' has acquired, in the course of time, many associationswhich are quite misleading when applied to Plato's 'ideas'. We shalltherefore use the word 'universal' instead of the word 'idea', todescribe what Plato meant. The essence of the sort of entity that Platomeant is that it is opposed to the particular things that are given insensation. We speak of whatever is given in sensation, or is of the samenature as things given in sensation, as a _particular_; by oppositionto this, a _universal_ will be anything which may be shared by manyparticulars, and has those characteristics which, as we saw, distinguishjustice and whiteness from just acts and white things. 

When we examine common words, we find that, broadly speaking, propernames stand for particulars, while other substantives, adjectives, prepositions, and verbs stand for universals. Pronouns stand forparticulars, but are ambiguous: it is only by the context or thecircumstances that we know what particulars they stand for. The word'now' stands for a particular, namely the present moment; but likepronouns, it stands for an ambiguous particular, because the present isalways changing. 

It will be seen that no sentence can be made up without at least oneword which denotes a universal. The nearest approach would be some suchstatement as 'I like this'. But even here the word 'like' denotesa universal, for I may like other things, and other people may likethings. Thus all truths involve universals, and all knowledge of truthsinvolves acquaintance with universals. 

Seeing that nearly all the words to be found in the dictionary standfor universals, it is strange that hardly anybody except students ofphilosophy ever realizes that there are such entities as universals. Wedo not naturally dwell upon those words in a sentence which do not standfor particulars; and if we are forced to dwell upon a word which standsfor a universal, we naturally think of it as standing for some one ofthe particulars that come under the universal. When, for example, wehear the sentence, 'Charles I's head was cut off', we may naturallyenough think of Charles I, of Charles I's head, and of the operationof cutting off _his_ head, which are all particulars; but we do notnaturally dwell upon what is meant by the word 'head' or the word'cut', which is a universal: We feel such words to be incomplete andinsubstantial; they seem to demand a context before anything can bedone with them. Hence we succeed in avoiding all notice of universals assuch, until the study of philosophy forces them upon our attention. 

Even among philosophers, we may say, broadly, that only those universalswhich are named by adjectives or substantives have been much or oftenrecognized, while those named by verbs and prepositions have beenusually overlooked. This omission has had a very great effect uponphilosophy; it is hardly too much to say that most metaphysics, sinceSpinoza, has been largely determined by it. The way this has occurredis, in outline, as follows: Speaking generally, adjectives and commonnouns express qualities or properties of single things, whereasprepositions and verbs tend to express relations between two or morethings. Thus the neglect of prepositions and verbs led to the beliefthat every proposition can be regarded as attributing a property to asingle thing, rather than as expressing a relation between two or morethings. Hence it was supposed that, ultimately, there can be no suchentities as relations between things. Hence either there can be onlyone thing in the universe, or, if there are many things, they cannotpossibly interact in any way, since any interaction would be a relation, and relations are impossible. 

The first of these views, advocated by Spinoza and held in our own dayby Bradley and many other philosophers, is called _monism_; the second, advocated by Leibniz but not very common nowadays, is called _monadism_, because each of the isolated things is called a _monad_. Both theseopposing philosophies, interesting as they are, result, in my opinion, from an undue attention to one sort of universals, namely the sortrepresented by adjectives and substantives rather than by verbs andprepositions. 

As a matter of fact, if any one were anxious to deny altogether thatthere are such things as universals, we should find that we cannotstrictly prove that there are such entities as _qualities_, i. E. Theuniversals represented by adjectives and substantives, whereas wecan prove that there must be _relations_, i. E. The sort of universalsgenerally represented by verbs and prepositions. Let us take inillustration the universal _whiteness_. If we believe that there is sucha universal, we shall say that things are white because they have thequality of whiteness. This view, however, was strenuously denied byBerkeley and Hume, who have been followed in this by later empiricists. The form which their denial took was to deny that there are such thingsas 'abstract ideas '. When we want to think of whiteness, they said, weform an image of some particular white thing, and reason concerning thisparticular, taking care not to deduce anything concerning it which wecannot see to be equally true of any other white thing. As an account ofour actual mental processes, this is no doubt largely true. In geometry, for example, when we wish to prove something about all triangles, wedraw a particular triangle and reason about it, taking care not to useany characteristic which it does not share with other triangles. Thebeginner, in order to avoid error, often finds it useful to draw severaltriangles, as unlike each other as possible, in order to make sure thathis reasoning is equally applicable to all of them. But a difficultyemerges as soon as we ask ourselves how we know that a thing is whiteor a triangle. If we wish to avoid the universals _whiteness_ and_triangularity_, we shall choose some particular patch of white or someparticular triangle, and say that anything is white or a triangle if ithas the right sort of resemblance to our chosen particular. But then theresemblance required will have to be a universal. Since there are manywhite things, the resemblance must hold between many pairs of particularwhite things; and this is the characteristic of a universal. It will beuseless to say that there is a different resemblance for each pair, forthen we shall have to say that these resemblances resemble each other, and thus at last we shall be forced to admit resemblance as a universal. The relation of resemblance, therefore, must be a true universal. Andhaving been forced to admit this universal, we find that it is no longerworth while to invent difficult and unplausible theories to avoid theadmission of such universals as whiteness and triangularity. 

Berkeley and Hume failed to perceive this refutation of their rejectionof 'abstract ideas', because, like their adversaries, they only thoughtof _qualities_, and altogether ignored _relations_ as universals. Wehave therefore here another respect in which the rationalists appear tohave been in the right as against the empiricists, although, owing tothe neglect or denial of relations, the deductions made by rationalistswere, if anything, more apt to be mistaken than those made byempiricists. 

Having now seen that there must be such entities as universals, the nextpoint to be proved is that their being is not merely mental. By this ismeant that whatever being belongs to them is independent of their beingthought of or in any way apprehended by minds. We have already touchedon this subject at the end of the preceding chapter, but we must nowconsider more fully what sort of being it is that belongs to universals. 

Consider such a proposition as 'Edinburgh is north of London'. Here wehave a relation between two places, and it seems plain that the relationsubsists independently of our knowledge of it. When we come to know thatEdinburgh is north of London, we come to know something which has todo only with Edinburgh and London: we do not cause the truth of theproposition by coming to know it, on the contrary we merely apprehend afact which was there before we knew it. The part of the earth's surfacewhere Edinburgh stands would be north of the part where London stands, even if there were no human being to know about north and south, andeven if there were no minds at all in the universe. This is, of course, denied by many philosophers, either for Berkeley's reasons or forKant's. But we have already considered these reasons, and decided thatthey are inadequate. We may therefore now assume it to be true thatnothing mental is presupposed in the fact that Edinburgh is north ofLondon. But this fact involves the relation 'north of', which is auniversal; and it would be impossible for the whole fact to involvenothing mental if the relation 'north of', which is a constituent partof the fact, did involve anything mental. Hence we must admit that therelation, like the terms it relates, is not dependent upon thought, butbelongs to the independent world which thought apprehends but does notcreate. 

This conclusion, however, is met by the difficulty that the relation'north of' does not seem to _exist_ in the same sense in which Edinburghand London exist. If we ask 'Where and when does this relation exist?'the answer must be 'Nowhere and nowhen'. There is no place or time wherewe can find the relation 'north of'. It does not exist in Edinburgh anymore than in London, for it relates the two and is neutral as betweenthem. Nor can we say that it exists at any particular time. Noweverything that can be apprehended by the senses or by introspectionexists at some particular time. Hence the relation 'north of' isradically different from such things. It is neither in space nor intime, neither material nor mental; yet it is something. 

It is largely the very peculiar kind of being that belongs to universalswhich has led many people to suppose that they are really mental. Wecan think _of_ a universal, and our thinking then exists in a perfectlyordinary sense, like any other mental act. Suppose, for example, thatwe are thinking of whiteness. Then _in one sense_ it may be said thatwhiteness is 'in our mind'. We have here the same ambiguity as we notedin discussing Berkeley in Chapter IV. In the strict sense, it is notwhiteness that is in our mind, but the act of thinking of whiteness. Theconnected ambiguity in the word 'idea', which we noted at the same time, also causes confusion here. In one sense of this word, namely the sensein which it denotes the _object_ of an act of thought, whiteness is an'idea'. Hence, if the ambiguity is not guarded against, we may come tothink that whiteness is an 'idea' in the other sense, i. E. An act ofthought; and thus we come to think that whiteness is mental. But in sothinking, we rob it of its essential quality of universality. One man'sact of thought is necessarily a different thing from another man's; oneman's act of thought at one time is necessarily a different thing fromthe same man's act of thought at another time. Hence, if whiteness werethe thought as opposed to its object, no two different men could thinkof it, and no one man could think of it twice. That which many differentthoughts of whiteness have in common is their _object_, and this objectis different from all of them. Thus universals are not thoughts, thoughwhen known they are the objects of thoughts. 

We shall find it convenient only to speak of things _existing_ when theyare in time, that is to say, when we can point to some time at whichthey exist (not excluding the possibility of their existing at alltimes). Thus thoughts and feelings, minds and physical objects exist. But universals do not exist in this sense; we shall say that they_subsist_ or _have being_, where 'being' is opposed to 'existence'as being timeless. The world of universals, therefore, may also bedescribed as the world of being. The world of being is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builderof metaphysical systems, and all who love perfection more than life. Theworld of existence is fleeting, vague, without sharp boundaries, without any clear plan or arrangement, but it contains all thoughts andfeelings, all the data of sense, and all physical objects, everythingthat can do either good or harm, everything that makes any difference tothe value of life and the world. According to our temperaments, we shallprefer the contemplation of the one or of the other. The one we do notprefer will probably seem to us a pale shadow of the one we prefer, andhardly worthy to be regarded as in any sense real. But the truth is thatboth have the same claim on our impartial attention, both are real, and both are important to the metaphysician. Indeed no sooner have wedistinguished the two worlds than it becomes necessary to consider theirrelations. 

But first of all we must examine our knowledge of universals. Thisconsideration will occupy us in the following chapter, where we shallfind that it solves the problem of _a priori_ knowledge, from which wewere first led to consider universals. 

CHAPTER X. ON OUR KNOWLEDGE OF UNIVERSALS

In regard to one man's knowledge at a given time, universals, likeparticulars, may be divided into those known by acquaintance, thoseknown only by description, and those not known either by acquaintance orby description. 

Let us consider first the knowledge of universals by acquaintance. It isobvious, to begin with, that we are acquainted with such universals aswhite, red, black, sweet, sour, loud, hard, etc. , i. E. With qualitieswhich are exemplified in sense-data. When we see a white patch, we areacquainted, in the first instance, with the particular patch; but byseeing many white patches, we easily learn to abstract the whitenesswhich they all have in common, and in learning to do this we arelearning to be acquainted with whiteness. A similar process will make usacquainted with any other universal of the same sort. Universals of thissort may be called 'sensible qualities'. They can be apprehended withless effort of abstraction than any others, and they seem less removedfrom particulars than other universals are. 

We come next to relations. The easiest relations to apprehend are thosewhich hold between the different parts of a single complex sense-datum. For example, I can see at a glance the whole of the page on which Iam writing; thus the whole page is included in one sense-datum. But Iperceive that some parts of the page are to the left of other parts, and some parts are above other parts. The process of abstraction in thiscase seems to proceed somewhat as follows: I see successively a numberof sense-data in which one part is to the left of another; I perceive, as in the case of different white patches, that all these sense-datahave something in common, and by abstraction I find that what they havein common is a certain relation between their parts, namely the relationwhich I call 'being to the left of'. In this way I become acquaintedwith the universal relation. 

In like manner I become aware of the relation of before and after intime. Suppose I hear a chime of bells: when the last bell of the chimesounds, I can retain the whole chime before my mind, and I can perceivethat the earlier bells came before the later ones. Also in memory Iperceive that what I am remembering came before the present time. Fromeither of these sources I can abstract the universal relation of beforeand after, just as I abstracted the universal relation 'being to theleft of'. Thus time-relations, like space-relations, are among thosewith which we are acquainted. 

Another relation with which we become acquainted in much the same way isresemblance. If I see simultaneously two shades of green, I can seethat they resemble each other; if I also see a shade of red: at the sametime, I can see that the two greens have more resemblance to each otherthan either has to the red. In this way I become acquainted with theuniversal _resemblance_ or _similarity_. 

Between universals, as between particulars, there are relations of whichwe may be immediately aware. We have just seen that we can perceivethat the resemblance between two shades of green is greater than theresemblance between a shade of red and a shade of green. Here we aredealing with a relation, namely 'greater than', between two relations. Our knowledge of such relations, though it requires more power ofabstraction than is required for perceiving the qualities of sense-data, appears to be equally immediate, and (at least in some cases) equallyindubitable. Thus there is immediate knowledge concerning universals aswell as concerning sense-data. 

Returning now to the problem of _a priori_ knowledge, which we leftunsolved when we began the consideration of universals, we findourselves in a position to deal with it in a much more satisfactorymanner than was possible before. Let us revert to the proposition 'twoand two are four'. It is fairly obvious, in view of what has been said, that this proposition states a relation between the universal 'two' andthe universal 'four'. This suggests a proposition which we shallnow endeavour to establish: namely, _All _a priori_ knowledge dealsexclusively with the relations of universals_. This proposition isof great importance, and goes a long way towards solving our previousdifficulties concerning _a priori_ knowledge. 

The only case in which it might seem, at first sight, as if ourproposition were untrue, is the case in which an _a priori_ propositionstates that _all_ of one class of particulars belong to some otherclass, or (what comes to the same thing) that _all_ particulars havingsome one property also have some other. In this case it might seemas though we were dealing with the particulars that have the propertyrather than with the property. The proposition 'two and two are four' isreally a case in point, for this may be stated in the form 'any twoand any other two are four', or 'any collection formed of two twos is acollection of four'. If we can show that such statements as this reallydeal only with universals, our proposition may be regarded as proved. 

One way of discovering what a proposition deals with is to ask ourselveswhat words we must understand--in other words, what objects we must beacquainted with--in order to see what the proposition means. As soon aswe see what the proposition means, even if we do not yet know whetherit is true or false, it is evident that we must have acquaintance withwhatever is really dealt with by the proposition. By applying this test, it appears that many propositions which might seem to be concerned withparticulars are really concerned only with universals. In the specialcase of 'two and two are four', even when we interpret it as meaning'any collection formed of two twos is a collection of four', it is plainthat we can understand the proposition, i. E. We can see what it is thatit asserts, as soon as we know what is meant by 'collection' and 'two'and 'four'. It is quite unnecessary to know all the couples in theworld: if it were necessary, obviously we could never understand theproposition, since the couples are infinitely numerous and thereforecannot all be known to us. Thus although our general statement _implies_statements about particular couples, _as soon as we know that there aresuch particular couples_, yet it does not itself assert or imply thatthere are such particular couples, and thus fails to make any statementwhatever about any actual particular couple. The statement made is about'couple', the universal, and not about this or that couple. 

Thus the statement 'two and two are four' deals exclusively withuniversals, and therefore may be known by anybody who is acquaintedwith the universals concerned and can perceive the relation between themwhich the statement asserts. It must be taken as a fact, discoveredby reflecting upon our knowledge, that we have the power of sometimesperceiving such relations between universals, and therefore of sometimesknowing general _a priori_ propositions such as those of arithmetic andlogic. The thing that seemed mysterious, when we formerly consideredsuch knowledge, was that it seemed to anticipate and control experience. This, however, we can now see to have been an error. _No_ factconcerning anything capable of being experienced can be knownindependently of experience. We know _a priori_ that two things and twoother things together make four things, but we do _not_ know _a priori_that if Brown and Jones are two, and Robinson and Smith are two, thenBrown and Jones and Robinson and Smith are four. The reason is that thisproposition cannot be understood at all unless we know that there aresuch people as Brown and Jones and Robinson and Smith, and this we canonly know by experience. Hence, although our general proposition is _apriori_, all its applications to actual particulars involve experienceand therefore contain an empirical element. In this way what seemedmysterious in our _a priori_ knowledge is seen to have been based uponan error. 

It will serve to make the point clearer if we contrast our genuine _apriori_ judgement with an empirical generalization, such as 'all men aremortals'. Here as before, we can _understand_ what the propositionmeans as soon as we understand the universals involved, namely _man_ and_mortal_. It is obviously unnecessary to have an individual acquaintancewith the whole human race in order to understand what our propositionmeans. Thus the difference between an _a priori_ general propositionand an empirical generalization does not come in the _meaning_ of theproposition; it comes in the nature of the _evidence_ for it. In theempirical case, the evidence consists in the particular instances. We believe that all men are mortal because we know that there areinnumerable instances of men dying, and no instances of their livingbeyond a certain age. We do not believe it because we see a connexionbetween the universal _man_ and the universal _mortal_. It is true thatif physiology can prove, assuming the general laws that govern livingbodies, that no living organism can last for ever, that gives aconnexion between _man_ and _mortality_ which would enable us to assertour proposition without appealing to the special evidence of _men_dying. But that only means that our generalization has been subsumedunder a wider generalization, for which the evidence is still of thesame kind, though more extensive. The progress of science is constantlyproducing such subsumptions, and therefore giving a constantly widerinductive basis for scientific generalizations. But although this givesa greater _degree_ of certainty, it does not give a different _kind_:the ultimate ground remains inductive, i. E. Derived from instances, andnot an _a priori_ connexion of universals such as we have in logic andarithmetic. 

Two opposite points are to be observed concerning _a priori_ generalpropositions. The first is that, if many particular instances are known, our general proposition may be arrived at in the first instance byinduction, and the connexion of universals may be only subsequentlyperceived. For example, it is known that if we draw perpendicularsto the sides of a triangle from the opposite angles, all threeperpendiculars meet in a point. It would be quite possible to be firstled to this proposition by actually drawing perpendiculars in manycases, and finding that they always met in a point; this experiencemight lead us to look for the general proof and find it. Such cases arecommon in the experience of every mathematician. 

The other point is more interesting, and of more philosophicalimportance. It is, that we may sometimes know a general proposition incases where we do not know a single instance of it. Take such a case asthe following: We know that any two numbers can be multiplied together, and will give a third called their _product_. We know that all pairsof integers the product of which is less than 100 have been actuallymultiplied together, and the value of the product recorded in themultiplication table. But we also know that the number of integers isinfinite, and that only a finite number of pairs of integers ever havebeen or ever will be thought of by human beings. Hence it follows thatthere are pairs of integers which never have been and never will bethought of by human beings, and that all of them deal with integers theproduct of which is over 100. Hence we arrive at the proposition:'All products of two integers, which never have been and never willbe thought of by any human being, are over 100. ' Here is a generalproposition of which the truth is undeniable, and yet, from the verynature of the case, we can never give an instance; because any twonumbers we may think of are excluded by the terms of the proposition. 

This possibility, of knowledge of general propositions of which noinstance can be given, is often denied, because it is not perceivedthat the knowledge of such propositions only requires a knowledge of therelations of universals, and does not require any knowledge of instancesof the universals in question. Yet the knowledge of such generalpropositions is quite vital to a great deal of what is generallyadmitted to be known. For example, we saw, in our early chapters, that knowledge of physical objects, as opposed to sense-data, is onlyobtained by an inference, and that they are not things with which we areacquainted. Hence we can never know any proposition of the form 'thisis a physical object', where 'this' is something immediately known. Itfollows that all our knowledge concerning physical objects is such thatno actual instance can be given. We can give instances of the associatedsense-data, but we cannot give instances of the actual physical objects. Hence our knowledge as to physical objects depends throughout upon thispossibility of general knowledge where no instance can be given. And thesame applies to our knowledge of other people's minds, or of any otherclass of things of which no instance is known to us by acquaintance. 

We may now take a survey of the sources of our knowledge, as they haveappeared in the course of our analysis. We have first to distinguishknowledge of things and knowledge of truths. In each there are twokinds, one immediate and one derivative. Our immediate knowledge ofthings, which we called _acquaintance_, consists of two sorts, accordingas the things known are particulars or universals. Among particulars, wehave acquaintance with sense-data and (probably) with ourselves. Amonguniversals, there seems to be no principle by which we can decide whichcan be known by acquaintance, but it is clear that among those thatcan be so known are sensible qualities, relations of space and time, similarity, and certain abstract logical universals. Our derivativeknowledge of things, which we call knowledge by _description_, alwaysinvolves both acquaintance with something and knowledge of truths. Ourimmediate knowledge of _truths_ may be called _intuitive_ knowledge, and the truths so known may be called _self-evident_ truths. Among suchtruths are included those which merely state what is given in sense, andalso certain abstract logical and arithmetical principles, and (thoughwith less certainty) some ethical propositions. Our _derivative_knowledge of truths consists of everything that we can deduce fromself-evident truths by the use of self-evident principles of deduction. 

If the above account is correct, all our knowledge of truths dependsupon our intuitive knowledge. It therefore becomes important to considerthe nature and scope of intuitive knowledge, in much the same way as, at an earlier stage, we considered the nature and scope of knowledge byacquaintance. But knowledge of truths raises a further problem, whichdoes not arise in regard to knowledge of things, namely the problem of_error_. Some of our beliefs turn out to be erroneous, and thereforeit becomes necessary to consider how, if at all, we can distinguishknowledge from error. This problem does not arise with regardto knowledge by acquaintance, for, whatever may be the object ofacquaintance, even in dreams and hallucinations, there is no errorinvolved so long as we do not go beyond the immediate object: error canonly arise when we regard the immediate object, i. E. The sense-datum, as the mark of some physical object. Thus the problems connectedwith knowledge of truths are more difficult than those connectedwith knowledge of things. As the first of the problems connectedwith knowledge of truths, let us examine the nature and scope of ourintuitive judgements. 

CHAPTER XI. ON INTUITIVE KNOWLEDGE

There is a common impression that everything that we believe ought to becapable of proof, or at least of being shown to be highly probable. Itis felt by many that a belief for which no reason can be given is anunreasonable belief. In the main, this view is just. Almost all ourcommon beliefs are either inferred, or capable of being inferred, fromother beliefs which may be regarded as giving the reason for them. As arule, the reason has been forgotten, or has even never been consciouslypresent to our minds. Few of us ever ask ourselves, for example, whatreason there is to suppose the food we are just going to eat will notturn out to be poison. Yet we feel, when challenged, that a perfectlygood reason could be found, even if we are not ready with it at themoment. And in this belief we are usually justified. 

But let us imagine some insistent Socrates, who, whatever reason wegive him, continues to demand a reason for the reason. We must sooneror later, and probably before very long, be driven to a point where wecannot find any further reason, and where it becomes almost certain thatno further reason is even theoretically discoverable. Starting with thecommon beliefs of daily life, we can be driven back from point to point, until we come to some general principle, or some instance of a generalprinciple, which seems luminously evident, and is not itself capableof being deduced from anything more evident. In most questions ofdaily life, such as whether our food is likely to be nourishing and notpoisonous, we shall be driven back to the inductive principle, which wediscussed in Chapter VI. But beyond that, there seems to be no furtherregress. The principle itself is constantly used in our reasoning, sometimes consciously, sometimes unconsciously; but there is noreasoning which, starting from some simpler self-evident principle, leads us to the principle of induction as its conclusion. And the sameholds for other logical principles. Their truth is evident to us, and weemploy them in constructing demonstrations; but they themselves, or atleast some of them, are incapable of demonstration. 

Self-evidence, however, is not confined to those among generalprinciples which are incapable of proof. When a certain number oflogical principles have been admitted, the rest can be deduced fromthem; but the propositions deduced are often just as self-evident asthose that were assumed without proof. All arithmetic, moreover, canbe deduced from the general principles of logic, yet the simplepropositions of arithmetic, such as 'two and two are four', are just asself-evident as the principles of logic. 

It would seem, also, though this is more disputable, that there are someself-evident ethical principles, such as 'we ought to pursue what isgood'. 

It should be observed that, in all cases of general principles, particular instances, dealing with familiar things, are more evidentthan the general principle. For example, the law of contradiction statesthat nothing can both have a certain property and not have it. This isevident as soon as it is understood, but it is not so evident as that aparticular rose which we see cannot be both red and not red. (It is ofcourse possible that parts of the rose may be red and parts not red, orthat the rose may be of a shade of pink which we hardly know whether tocall red or not; but in the former case it is plain that the rose as awhole is not red, while in the latter case the answer is theoreticallydefinite as soon as we have decided on a precise definition of 'red'. )It is usually through particular instances that we come to be able tosee the general principle. Only those who are practised in dealing withabstractions can readily grasp a general principle without the help ofinstances. 

In addition to general principles, the other kind of self-evident truthsare those immediately derived from sensation. We will call such truths'truths of perception', and the judgements expressing them we willcall 'judgements of perception'. But here a certain amount of careis required in getting at the precise nature of the truths that areself-evident. The actual sense-data are neither true nor false. Aparticular patch of colour which I see, for example, simply exists: itis not the sort of thing that is true or false. It is true that there issuch a patch, true that it has a certain shape and degree of brightness, true that it is surrounded by certain other colours. But the patchitself, like everything else in the world of sense, is of a radicallydifferent kind from the things that are true or false, and thereforecannot properly be said to be _true_. Thus whatever self-evident truthsmay be obtained from our senses must be different from the sense-datafrom which they are obtained. 

It would seem that there are two kinds of self-evident truths ofperception, though perhaps in the last analysis the two kinds maycoalesce. First, there is the kind which simply asserts the _existence_of the sense-datum, without in any way analysing it. We see a patchof red, and we judge 'there is such-and-such a patch of red', or morestrictly 'there is that'; this is one kind of intuitive judgement ofperception. The other kind arises when the object of sense is complex, and we subject it to some degree of analysis. If, for instance, we see a_round_ patch of red, we may judge 'that patch of red is round'. This isagain a judgement of perception, but it differs from our previous kind. In our present kind we have a single sense-datum which has both colourand shape: the colour is red and the shape is round. Our judgementanalyses the datum into colour and shape, and then recombines them bystating that the red colour is round in shape. Another example of thiskind of judgement is 'this is to the right of that', where 'this'and 'that' are seen simultaneously. In this kind of judgement thesense-datum contains constituents which have some relation to eachother, and the judgement asserts that these constituents have thisrelation. 

Another class of intuitive judgements, analogous to those of sense andyet quite distinct from them, are judgements of _memory_. There is somedanger of confusion as to the nature of memory, owing to the fact thatmemory of an object is apt to be accompanied by an image of the object, and yet the image cannot be what constitutes memory. This is easily seenby merely noticing that the image is in the present, whereas what isremembered is known to be in the past. Moreover, we are certainly ableto some extent to compare our image with the object remembered, sothat we often know, within somewhat wide limits, how far our image isaccurate; but this would be impossible, unless the object, as opposed tothe image, were in some way before the mind. Thus the essence of memoryis not constituted by the image, but by having immediately before themind an object which is recognized as past. But for the fact of memoryin this sense, we should not know that there ever was a past at all, nor should we be able to understand the word 'past', any more than a manborn blind can understand the word 'light'. Thus there must be intuitivejudgements of memory, and it is upon them, ultimately, that all ourknowledge of the past depends. 

The case of memory, however, raises a difficulty, for it is notoriouslyfallacious, and thus throws doubt on the trustworthiness of intuitivejudgements in general. This difficulty is no light one. But let usfirst narrow its scope as far as possible. Broadly speaking, memory istrustworthy in proportion to the vividness of the experience and to itsnearness in time. If the house next door was struck by lightning half aminute ago, my memory of what I saw and heard will be so reliable thatit would be preposterous to doubt whether there had been a flash atall. And the same applies to less vivid experiences, so long as they arerecent. I am absolutely certain that half a minute ago I was sitting inthe same chair in which I am sitting now. Going backward over the day, I find things of which I am quite certain, other things of which I amalmost certain, other things of which I can become certain by thoughtand by calling up attendant circumstances, and some things of which Iam by no means certain. I am quite certain that I ate my breakfast thismorning, but if I were as indifferent to my breakfast as a philosophershould be, I should be doubtful. As to the conversation at breakfast, I can recall some of it easily, some with an effort, some only with alarge element of doubt, and some not at all. Thus there is a continualgradation in the degree of self-evidence of what I remember, and acorresponding gradation in the trustworthiness of my memory. 

Thus the first answer to the difficulty of fallacious memory is to saythat memory has degrees of self-evidence, and that these correspondto the degrees of its trustworthiness, reaching a limit of perfectself-evidence and perfect trustworthiness in our memory of events whichare recent and vivid. 

It would seem, however, that there are cases of very firm belief in amemory which is wholly false. It is probable that, in these cases, whatis really remembered, in the sense of being immediately before the mind, is something other than what is falsely believed in, though somethinggenerally associated with it. George IV is said to have at last believedthat he was at the battle of Waterloo, because he had so often said thathe was. In this case, what was immediately remembered was his repeatedassertion; the belief in what he was asserting (if it existed) wouldbe produced by association with the remembered assertion, and wouldtherefore not be a genuine case of memory. It would seem that cases offallacious memory can probably all be dealt with in this way, i. E. Theycan be shown to be not cases of memory in the strict sense at all. 

One important point about self-evidence is made clear by the case ofmemory, and that is, that self-evidence has degrees: it is not a qualitywhich is simply present or absent, but a quality which may be more orless present, in gradations ranging from absolute certainty down to analmost imperceptible faintness. Truths of perception and some of theprinciples of logic have the very highest degree of self-evidence;truths of immediate memory have an almost equally high degree. Theinductive principle has less self-evidence than some of the otherprinciples of logic, such as 'what follows from a true premiss must betrue'. Memories have a diminishing self-evidence as they become remoterand fainter; the truths of logic and mathematics have (broadly speaking)less self-evidence as they become more complicated. Judgements ofintrinsic ethical or aesthetic value are apt to have some self-evidence, but not much. 

Degrees of self-evidence are important in the theory of knowledge, since, if propositions may (as seems likely) have some degree ofself-evidence without being true, it will not be necessary to abandonall connexion between self-evidence and truth, but merely to say that, where there is a conflict, the more self-evident proposition is to beretained and the less self-evident rejected. 

It seems, however, highly probable that two different notions arecombined in 'self-evidence' as above explained; that one of them, which corresponds to the highest degree of self-evidence, is really aninfallible guarantee of truth, while the other, which corresponds toall the other degrees, does not give an infallible guarantee, but only agreater or less presumption. This, however, is only a suggestion, whichwe cannot as yet develop further. After we have dealt with the natureof truth, we shall return to the subject of self-evidence, in connexionwith the distinction between knowledge and error. 

CHAPTER XII. TRUTH AND FALSEHOOD

Our knowledge of truths, unlike our knowledge of things, has anopposite, namely _error_. So far as things are concerned, we may knowthem or not know them, but there is no positive state of mind which canbe described as erroneous knowledge of things, so long, at any rate, as we confine ourselves to knowledge by acquaintance. Whatever we areacquainted with must be something; we may draw wrong inferences fromour acquaintance, but the acquaintance itself cannot be deceptive. Thusthere is no dualism as regards acquaintance. But as regards knowledge oftruths, there is a dualism. We may believe what is false as well aswhat is true. We know that on very many subjects different peoplehold different and incompatible opinions: hence some beliefs must beerroneous. Since erroneous beliefs are often held just as stronglyas true beliefs, it becomes a difficult question how they are to bedistinguished from true beliefs. How are we to know, in a given case, that our belief is not erroneous? This is a question of the verygreatest difficulty, to which no completely satisfactory answer ispossible. There is, however, a preliminary question which is rather lessdifficult, and that is: What do we _mean_ by truth and falsehood? It isthis preliminary question which is to be considered in this chapter. Inthis chapter we are not asking how we can know whether a belief is trueor false: we are asking what is meant by the question whether a beliefis true or false. It is to be hoped that a clear answer to this questionmay help us to obtain an answer to the question what beliefs aretrue, but for the present we ask only 'What is truth?' and 'What isfalsehood?' not 'What beliefs are true?' and 'What beliefs are false?'It is very important to keep these different questions entirelyseparate, since any confusion between them is sure to produce an answerwhich is not really applicable to either. 

There are three points to observe in the attempt to discover the natureof truth, three requisites which any theory must fulfil. 

(1) Our theory of truth must be such as to admit of its opposite, falsehood. A good many philosophers have failed adequately to satisfythis condition: they have constructed theories according to which allour thinking ought to have been true, and have then had the greatestdifficulty in finding a place for falsehood. In this respect our theoryof belief must differ from our theory of acquaintance, since in the caseof acquaintance it was not necessary to take account of any opposite. 

(2) It seems fairly evident that if there were no beliefs there couldbe no falsehood, and no truth either, in the sense in which truth iscorrelative to falsehood. If we imagine a world of mere matter, therewould be no room for falsehood in such a world, and although it wouldcontain what may be called 'facts', it would not contain any truths, inthe sense in which truths are things of the same kind as falsehoods. In fact, truth and falsehood are properties of beliefs and statements:hence a world of mere matter, since it would contain no beliefs orstatements, would also contain no truth or falsehood. 

(3) But, as against what we have just said, it is to be observed thatthe truth or falsehood of a belief always depends upon something whichlies outside the belief itself. If I believe that Charles I died on thescaffold, I believe truly, not because of any intrinsic quality of mybelief, which could be discovered by merely examining the belief, butbecause of an historical event which happened two and a half centuriesago. If I believe that Charles I died in his bed, I believe falsely: nodegree of vividness in my belief, or of care in arriving at it, preventsit from being false, again because of what happened long ago, and notbecause of any intrinsic property of my belief. Hence, although truthand falsehood are properties of beliefs, they are properties dependentupon the relations of the beliefs to other things, not upon any internalquality of the beliefs. 

The third of the above requisites leads us to adopt the view--which hason the whole been commonest among philosophers--that truth consists insome form of correspondence between belief and fact. It is, however, byno means an easy matter to discover a form of correspondence to whichthere are no irrefutable objections. By this partly--and partly by thefeeling that, if truth consists in a correspondence of thought withsomething outside thought, thought can never know when truth has beenattained--many philosophers have been led to try to find some definitionof truth which shall not consist in relation to something wholly outsidebelief. The most important attempt at a definition of this sort is thetheory that truth consists in _coherence_. It is said that the mark offalsehood is failure to cohere in the body of our beliefs, and that itis the essence of a truth to form part of the completely rounded systemwhich is The Truth. 

There is, however, a great difficulty in this view, or rather two greatdifficulties. The first is that there is no reason to suppose thatonly _one_ coherent body of beliefs is possible. It may be that, withsufficient imagination, a novelist might invent a past for the worldthat would perfectly fit on to what we know, and yet be quite differentfrom the real past. In more scientific matters, it is certain that thereare often two or more hypotheses which account for all the known factson some subject, and although, in such cases, men of science endeavourto find facts which will rule out all the hypotheses except one, thereis no reason why they should always succeed. 

In philosophy, again, it seems not uncommon for two rival hypothesesto be both able to account for all the facts. Thus, for example, it ispossible that life is one long dream, and that the outer world has onlythat degree of reality that the objects of dreams have; but althoughsuch a view does not seem inconsistent with known facts, there is noreason to prefer it to the common-sense view, according to which otherpeople and things do really exist. Thus coherence as the definitionof truth fails because there is no proof that there can be only onecoherent system. 

The other objection to this definition of truth is that it assumes themeaning of 'coherence' known, whereas, in fact, 'coherence' presupposesthe truth of the laws of logic. Two propositions are coherent when bothmay be true, and are incoherent when one at least must be false. Now inorder to know whether two propositions can both be true, we mustknow such truths as the law of contradiction. For example, the twopropositions, 'this tree is a beech' and 'this tree is not a beech', are not coherent, because of the law of contradiction. But if the law ofcontradiction itself were subjected to the test of coherence, we shouldfind that, if we choose to suppose it false, nothing will any longerbe incoherent with anything else. Thus the laws of logic supply theskeleton or framework within which the test of coherence applies, andthey themselves cannot be established by this test. 

For the above two reasons, coherence cannot be accepted as giving the_meaning_ of truth, though it is often a most important _test_ of truthafter a certain amount of truth has become known. 

Hence we are driven back to _correspondence with fact_ as constitutingthe nature of truth. It remains to define precisely what we mean by'fact', and what is the nature of the correspondence which must subsistbetween belief and fact, in order that belief may be true. 

In accordance with our three requisites, we have to seek a theory oftruth which (1) allows truth to have an opposite, namely falsehood, (2)makes truth a property of beliefs, but (3) makes it a property whollydependent upon the relation of the beliefs to outside things. 

The necessity of allowing for falsehood makes it impossible to regardbelief as a relation of the mind to a single object, which could be saidto be what is believed. If belief were so regarded, we should find that, like acquaintance, it would not admit of the opposition of truth andfalsehood, but would have to be always true. This may be made clearby examples. Othello believes falsely that Desdemona loves Cassio. Wecannot say that this belief consists in a relation to a single object, 'Desdemona's love for Cassio', for if there were such an object, thebelief would be true. There is in fact no such object, and thereforeOthello cannot have any relation to such an object. Hence his beliefcannot possibly consist in a relation to this object. 

It might be said that his belief is a relation to a different object, namely 'that Desdemona loves Cassio'; but it is almost as difficult tosuppose that there is such an object as this, when Desdemona does notlove Cassio, as it was to suppose that there is 'Desdemona's love forCassio'. Hence it will be better to seek for a theory of belief whichdoes not make it consist in a relation of the mind to a single object. 

It is common to think of relations as though they always held betweentwo terms, but in fact this is not always the case. Some relationsdemand three terms, some four, and so on. Take, for instance, therelation 'between'. So long as only two terms come in, the relation'between' is impossible: three terms are the smallest number that renderit possible. York is between London and Edinburgh; but if London andEdinburgh were the only places in the world, there could be nothingwhich was between one place and another. Similarly _jealousy_ requiresthree people: there can be no such relation that does not involve threeat least. Such a proposition as 'A wishes B to promote C's marriage withD' involves a relation of four terms; that is to say, A and B and C andD all come in, and the relation involved cannot be expressed otherwisethan in a form involving all four. Instances might be multipliedindefinitely, but enough has been said to show that there are relationswhich require more than two terms before they can occur. 

The relation involved in _judging_ or _believing_ must, if falsehood isto be duly allowed for, be taken to be a relation between several terms, not between two. When Othello believes that Desdemona loves Cassio, hemust not have before his mind a single object, 'Desdemona's love forCassio', or 'that Desdemona loves Cassio ', for that would require thatthere should be objective falsehoods, which subsist independently ofany minds; and this, though not logically refutable, is a theory to beavoided if possible. Thus it is easier to account for falsehood ifwe take judgement to be a relation in which the mind and the variousobjects concerned all occur severally; that is to say, Desdemona andloving and Cassio must all be terms in the relation which subsists whenOthello believes that Desdemona loves Cassio. This relation, therefore, is a relation of four terms, since Othello also is one of the terms ofthe relation. When we say that it is a relation of four terms, we do notmean that Othello has a certain relation to Desdemona, and has the samerelation to loving and also to Cassio. This may be true of some otherrelation than believing; but believing, plainly, is not a relation whichOthello has to _each_ of the three terms concerned, but to _all_ ofthem together: there is only one example of the relation of believinginvolved, but this one example knits together four terms. Thus theactual occurrence, at the moment when Othello is entertaining hisbelief, is that the relation called 'believing' is knitting togetherinto one complex whole the four terms Othello, Desdemona, loving, andCassio. What is called belief or judgement is nothing but this relationof believing or judging, which relates a mind to several things otherthan itself. An _act_ of belief or of judgement is the occurrencebetween certain terms at some particular time, of the relation ofbelieving or judging. 

We are now in a position to understand what it is that distinguishes atrue judgement from a false one. For this purpose we will adopt certaindefinitions. In every act of judgement there is a mind which judges, andthere are terms concerning which it judges. We will call the mind the_subject_ in the judgement, and the remaining terms the _objects_. Thus, when Othello judges that Desdemona loves Cassio, Othello is the subject, while the objects are Desdemona and loving and Cassio. The subject andthe objects together are called the _constituents_ of the judgement. It will be observed that the relation of judging has what is called a'sense' or 'direction'. We may say, metaphorically, that it puts itsobjects in a certain _order_, which we may indicate by means of theorder of the words in the sentence. (In an inflected language, the samething will be indicated by inflections, e. G. By the difference betweennominative and accusative. ) Othello's judgement that Cassio lovesDesdemona differs from his judgement that Desdemona loves Cassio, inspite of the fact that it consists of the same constituents, because therelation of judging places the constituents in a different order in thetwo cases. Similarly, if Cassio judges that Desdemona loves Othello, the constituents of the judgement are still the same, but their order isdifferent. This property of having a 'sense' or 'direction' is one whichthe relation of judging shares with all other relations. The 'sense'of relations is the ultimate source of order and series and a host ofmathematical concepts; but we need not concern ourselves further withthis aspect. 

We spoke of the relation called 'judging' or 'believing' as knittingtogether into one complex whole the subject and the objects. In thisrespect, judging is exactly like every other relation. Whenever arelation holds between two or more terms, it unites the terms into acomplex whole. If Othello loves Desdemona, there is such a complex wholeas 'Othello's love for Desdemona'. The terms united by the relation maybe themselves complex, or may be simple, but the whole which resultsfrom their being united must be complex. Wherever there is a relationwhich relates certain terms, there is a complex object formed of theunion of those terms; and conversely, wherever there is a complexobject, there is a relation which relates its constituents. When an actof believing occurs, there is a complex, in which 'believing' is theuniting relation, and subject and objects are arranged in a certainorder by the 'sense' of the relation of believing. Among the objects, as we saw in considering 'Othello believes that Desdemona loves Cassio', one must be a relation--in this instance, the relation 'loving'. Butthis relation, as it occurs in the act of believing, is not the relationwhich creates the unity of the complex whole consisting of the subjectand the objects. The relation 'loving', as it occurs in the act ofbelieving, is one of the objects--it is a brick in the structure, notthe cement. The cement is the relation 'believing'. When the belief is_true_, there is another complex unity, in which the relation which wasone of the objects of the belief relates the other objects. Thus, e. G. , if Othello believes _truly_ that Desdemona loves Cassio, then there isa complex unity, 'Desdemona's love for Cassio', which is composedexclusively of the _objects_ of the belief, in the same order as theyhad in the belief, with the relation which was one of the objectsoccurring now as the cement that binds together the other objects of thebelief. On the other hand, when a belief is _false_, there is no suchcomplex unity composed only of the objects of the belief. If Othellobelieves _falsely_ that Desdemona loves Cassio, then there is no suchcomplex unity as 'Desdemona's love for Cassio'. 

Thus a belief is _true_ when it _corresponds_ to a certain associatedcomplex, and _false_ when it does not. Assuming, for the sake ofdefiniteness, that the objects of the belief are two terms and arelation, the terms being put in a certain order by the 'sense' ofthe believing, then if the two terms in that order are united by therelation into a complex, the belief is true; if not, it is false. Thisconstitutes the definition of truth and falsehood that we were in searchof. Judging or believing is a certain complex unity of which a mind isa constituent; if the remaining constituents, taken in the order whichthey have in the belief, form a complex unity, then the belief is true;if not, it is false. 

Thus although truth and falsehood are properties of beliefs, yet theyare in a sense extrinsic properties, for the condition of the truth ofa belief is something not involving beliefs, or (in general) any mindat all, but only the _objects_ of the belief. A mind, which believes, believes truly when there is a _corresponding_ complex not involving themind, but only its objects. This correspondence ensures truth, and itsabsence entails falsehood. Hence we account simultaneously for the twofacts that beliefs (a) depend on minds for their _existence_, (b) do notdepend on minds for their _truth_. 

We may restate our theory as follows: If we take such a belief as'Othello believes that Desdemona loves Cassio', we will call Desdemonaand Cassio the _object-terms_, and loving the _object-relation_. Ifthere is a complex unity 'Desdemona's love for Cassio', consisting ofthe object-terms related by the object-relation in the same order asthey have in the belief, then this complex unity is called the _factcorresponding to the belief_. Thus a belief is true when there is acorresponding fact, and is false when there is no corresponding fact. 

It will be seen that minds do not _create_ truth or falsehood. Theycreate beliefs, but when once the beliefs are created, the mind cannotmake them true or false, except in the special case where they concernfuture things which are within the power of the person believing, suchas catching trains. What makes a belief true is a _fact_, and this factdoes not (except in exceptional cases) in any way involve the mind ofthe person who has the belief. 

Having now decided what we _mean_ by truth and falsehood, we have nextto consider what ways there are of knowing whether this or that beliefis true or false. This consideration will occupy the next chapter. 

CHAPTER XIII. KNOWLEDGE, ERROR, AND PROBABLE OPINION

The question as to what we mean by truth and falsehood, which weconsidered in the preceding chapter, is of much less interest than thequestion as to how we can know what is true and what is false. Thisquestion will occupy us in the present chapter. There can be no doubtthat _some_ of our beliefs are erroneous; thus we are led to inquirewhat certainty we can ever have that such and such a belief is noterroneous. In other words, can we ever _know_ anything at all, or do wemerely sometimes by good luck believe what is true? Before we can attackthis question, we must, however, first decide what we mean by 'knowing', and this question is not so easy as might be supposed. 

At first sight we might imagine that knowledge could be defined as 'truebelief'. When what we believe is true, it might be supposed that we hadachieved a knowledge of what we believe. But this would not accordwith the way in which the word is commonly used. To take a very trivialinstance: If a man believes that the late Prime Minister's last namebegan with a B, he believes what is true, since the late Prime Ministerwas Sir Henry Campbell Bannerman. But if he believes that Mr. Balfourwas the late Prime Minister, he will still believe that the late PrimeMinister's last name began with a B, yet this belief, though true, would not be thought to constitute knowledge. If a newspaper, by anintelligent anticipation, announces the result of a battle before anytelegram giving the result has been received, it may by good fortuneannounce what afterwards turns out to be the right result, and it mayproduce belief in some of its less experienced readers. But in spite ofthe truth of their belief, they cannot be said to have knowledge. Thusit is clear that a true belief is not knowledge when it is deduced froma false belief. 

In like manner, a true belief cannot be called knowledge when it isdeduced by a fallacious process of reasoning, even if the premisses fromwhich it is deduced are true. If I know that all Greeks are men and thatSocrates was a man, and I infer that Socrates was a Greek, I cannot besaid to _know_ that Socrates was a Greek, because, although my premissesand my conclusion are true, the conclusion does not follow from thepremisses. 

But are we to say that nothing is knowledge except what is validlydeduced from true premisses? Obviously we cannot say this. Such adefinition is at once too wide and too narrow. In the first place, it istoo wide, because it is not enough that our premisses should be _true_, they must also be _known_. The man who believes that Mr. Balfour was thelate Prime Minister may proceed to draw valid deductions from the truepremiss that the late Prime Minister's name began with a B, but hecannot be said to _know_ the conclusions reached by these deductions. Thus we shall have to amend our definition by saying that knowledgeis what is validly deduced from _known_ premisses. This, however, is acircular definition: it assumes that we already know what is meantby 'known premisses'. It can, therefore, at best define one sortof knowledge, the sort we call derivative, as opposed to intuitiveknowledge. We may say: '_Derivative_ knowledge is what is validlydeduced from premisses known intuitively'. In this statement there isno formal defect, but it leaves the definition of _intuitive_ knowledgestill to seek. 

Leaving on one side, for the moment, the question of intuitiveknowledge, let us consider the above suggested definition of derivativeknowledge. The chief objection to it is that it unduly limits knowledge. It constantly happens that people entertain a true belief, which hasgrown up in them because of some piece of intuitive knowledge from whichit is capable of being validly inferred, but from which it has not, as amatter of fact, been inferred by any logical process. 

Take, for example, the beliefs produced by reading. If the newspapersannounce the death of the King, we are fairly well justified inbelieving that the King is dead, since this is the sort of announcementwhich would not be made if it were false. And we are quite amplyjustified in believing that the newspaper asserts that the King isdead. But here the intuitive knowledge upon which our belief is basedis knowledge of the existence of sense-data derived from looking atthe print which gives the news. This knowledge scarcely rises intoconsciousness, except in a person who cannot read easily. A child may beaware of the shapes of the letters, and pass gradually and painfully toa realization of their meaning. But anybody accustomed to readingpasses at once to what the letters mean, and is not aware, except onreflection, that he has derived this knowledge from the sense-datacalled seeing the printed letters. Thus although a valid inference fromthe-letters to their meaning is possible, and _could_ be performedby the reader, it is not in fact performed, since he does not in factperform any operation which can be called logical inference. Yetit would be absurd to say that the reader does not _know_ that thenewspaper announces the King's death. 

We must, therefore, admit as derivative knowledge whatever is the resultof intuitive knowledge even if by mere association, provided there _is_a valid logical connexion, and the person in question could become awareof this connexion by reflection. There are in fact many ways, besideslogical inference, by which we pass from one belief to another: thepassage from the print to its meaning illustrates these ways. Theseways may be called 'psychological inference'. We shall, then, admit suchpsychological inference as a means of obtaining derivative knowledge, provided there is a discoverable logical inference which runs parallelto the psychological inference. This renders our definition ofderivative knowledge less precise than we could wish, since the word'discoverable' is vague: it does not tell us how much reflection may beneeded in order to make the discovery. But in fact 'knowledge' is not aprecise conception: it merges into 'probable opinion', as we shallsee more fully in the course of the present chapter. A very precisedefinition, therefore, should not be sought, since any such definitionmust be more or less misleading. 

The chief difficulty in regard to knowledge, however, does not ariseover derivative knowledge, but over intuitive knowledge. So long as weare dealing with derivative knowledge, we have the test of intuitiveknowledge to fall back upon. But in regard to intuitive beliefs, it isby no means easy to discover any criterion by which to distinguishsome as true and others as erroneous. In this question it is scarcelypossible to reach any very precise result: all our knowledge of truthsis infected with some degree of doubt, and a theory which ignored thisfact would be plainly wrong. Something may be done, however, to mitigatethe difficulties of the question. 

Our theory of truth, to begin with, supplies the possibility ofdistinguishing certain truths as _self-evident_ in a sense which ensuresinfallibility. When a belief is true, we said, there is a correspondingfact, in which the several objects of the belief form a single complex. The belief is said to constitute _knowledge_ of this fact, providedit fulfils those further somewhat vague conditions which we have beenconsidering in the present chapter. But in regard to any fact, besidesthe knowledge constituted by belief, we may also have the kind ofknowledge constituted by _perception_ (taking this word in its widestpossible sense). For example, if you know the hour of the sunset, you can at that hour know the fact that the sun is setting: this isknowledge of the fact by way of knowledge of _truths_; but you can also, if the weather is fine, look to the west and actually see the settingsun: you then know the same fact by the way of knowledge of _things_. 

Thus in regard to any complex fact, there are, theoretically, two waysin which it may be known: (1) by means of a judgement, in which itsseveral parts are judged to be related as they are in fact related; (2)by means of _acquaintance_ with the complex fact itself, which may (in alarge sense) be called perception, though it is by no means confined toobjects of the senses. Now it will be observed that the second way ofknowing a complex fact, the way of acquaintance, is only possible whenthere really is such a fact, while the first way, like all judgement, is liable to error. The second way gives us the complex whole, and istherefore only possible when its parts do actually have that relationwhich makes them combine to form such a complex. The first way, on thecontrary, gives us the parts and the relation severally, and demandsonly the reality of the parts and the relation: the relation may notrelate those parts in that way, and yet the judgement may occur. 

It will be remembered that at the end of Chapter XI we suggested thatthere might be two kinds of self-evidence, one giving an absoluteguarantee of truth, the other only a partial guarantee. These two kindscan now be distinguished. 

We may say that a truth is self-evident, in the first and most absolutesense, when we have acquaintance with the fact which corresponds tothe truth. When Othello believes that Desdemona loves Cassio, thecorresponding fact, if his belief were true, would be 'Desdemona'slove for Cassio'. This would be a fact with which no one could haveacquaintance except Desdemona; hence in the sense of self-evidence thatwe are considering, the truth that Desdemona loves Cassio (if it werea truth) could only be self-evident to Desdemona. All mental facts, andall facts concerning sense-data, have this same privacy: there is onlyone person to whom they can be self-evident in our present sense, sincethere is only one person who can be acquainted with the mental thingsor the sense-data concerned. Thus no fact about any particular existingthing can be self-evident to more than one person. On the other hand, facts about universals do not have this privacy. Many minds may beacquainted with the same universals; hence a relation between universalsmay be known by acquaintance to many different people. In all caseswhere we know by acquaintance a complex fact consisting of certain termsin a certain relation, we say that the truth that these terms are sorelated has the first or absolute kind of self-evidence, and in thesecases the judgement that the terms are so related _must_ be true. Thusthis sort of self-evidence is an absolute guarantee of truth. 

But although this sort of self-evidence is an absolute guarantee oftruth, it does not enable us to be _absolutely_ certain, in the case ofany given judgement, that the judgement in question is true. Supposewe first perceive the sun shining, which is a complex fact, and thenceproceed to make the judgement 'the sun is shining'. In passing fromthe perception to the judgement, it is necessary to analyse the givencomplex fact: we have to separate out 'the sun' and 'shining' asconstituents of the fact. In this process it is possible to commitan error; hence even where a _fact_ has the first or absolute kind ofself-evidence, a judgement believed to correspond to the fact is notabsolutely infallible, because it may not really correspond to thefact. But if it does correspond (in the sense explained in the precedingchapter), then it _must_ be true. 

The second sort of self-evidence will be that which belongs tojudgements in the first instance, and is not derived from directperception of a fact as a single complex whole. This second kind ofself-evidence will have degrees, from the very highest degree down to abare inclination in favour of the belief. Take, for example, the case ofa horse trotting away from us along a hard road. At first our certaintythat we hear the hoofs is complete; gradually, if we listen intently, there comes a moment when we think perhaps it was imagination or theblind upstairs or our own heartbeats; at last we become doubtful whetherthere was any noise at all; then we _think_ we no longer hear anything, and at last we _know_ we no longer hear anything. In this process, thereis a continual gradation of self-evidence, from the highest degree tothe least, not in the sense-data themselves, but in the judgements basedon them. 

Or again: Suppose we are comparing two shades of colour, one blue andone green. We can be quite sure they are different shades of colour; butif the green colour is gradually altered to be more and more like theblue, becoming first a blue-green, then a greeny-blue, then blue, there will come a moment when we are doubtful whether we can see anydifference, and then a moment when we know that we cannot see anydifference. The same thing happens in tuning a musical instrument, or inany other case where there is a continuous gradation. Thus self-evidenceof this sort is a matter of degree; and it seems plain that the higherdegrees are more to be trusted than the lower degrees. 

In derivative knowledge our ultimate premisses must have some degree ofself-evidence, and so must their connexion with the conclusions deducedfrom them. Take for example a piece of reasoning in geometry. It is notenough that the axioms from which we start should be self-evident: itis necessary also that, at each step in the reasoning, the connexion ofpremiss and conclusion should be self-evident. In difficult reasoning, this connexion has often only a very small degree of self-evidence;hence errors of reasoning are not improbable where the difficulty isgreat. 

From what has been said it is evident that, both as regards intuitiveknowledge and as regards derivative knowledge, if we assume thatintuitive knowledge is trustworthy in proportion to the degree of itsself-evidence, there will be a gradation in trustworthiness, from theexistence of noteworthy sense-data and the simpler truths of logic andarithmetic, which may be taken as quite certain, down to judgementswhich seem only just more probable than their opposites. What we firmlybelieve, if it is true, is called _knowledge_, provided it is eitherintuitive or inferred (logically or psychologically) from intuitiveknowledge from which it follows logically. What we firmly believe, if itis not true, is called _error_. What we firmly believe, if it is neitherknowledge nor error, and also what we believe hesitatingly, because itis, or is derived from, something which has not the highest degree ofself-evidence, may be called _probable opinion_. Thus the greaterpart of what would commonly pass as knowledge is more or less probableopinion. 

In regard to probable opinion, we can derive great assistance from_coherence_, which we rejected as the _definition_ of truth, but mayoften use as a _criterion_. A body of individually probable opinions, if they are mutually coherent, become more probable than any one of themwould be individually. It is in this way that many scientific hypothesesacquire their probability. They fit into a coherent system of probableopinions, and thus become more probable than they would be in isolation. The same thing applies to general philosophical hypotheses. Often in asingle case such hypotheses may seem highly doubtful, while yet, whenwe consider the order and coherence which they introduce into a mass ofprobable opinion, they become pretty nearly certain. This applies, inparticular, to such matters as the distinction between dreams andwaking life. If our dreams, night after night, were as coherent one withanother as our days, we should hardly know whether to believe the dreamsor the waking life. As it is, the test of coherence condemns thedreams and confirms the waking life. But this test, though it increasesprobability where it is successful, never gives absolute certainty, unless there is certainty already at some point in the coherent system. Thus the mere organization of probable opinion will never, by itself, transform it into indubitable knowledge. 

CHAPTER XIV. THE LIMITS OF PHILOSOPHICAL KNOWLEDGE

In all that we have said hitherto concerning philosophy, we havescarcely touched on many matters that occupy a great space in thewritings of most philosophers. Most philosophers--or, at any rate, verymany--profess to be able to prove, by _a priori_ metaphysical reasoning, such things as the fundamental dogmas of religion, the essentialrationality of the universe, the illusoriness of matter, the unrealityof all evil, and so on. There can be no doubt that the hope of findingreason to believe such theses as these has been the chief inspiration ofmany life-long students of philosophy. This hope, I believe, is vain. Itwould seem that knowledge concerning the universe as a whole is not tobe obtained by metaphysics, and that the proposed proofs that, in virtueof the laws of logic such and such things _must_ exist and such and suchothers cannot, are not capable of surviving a critical scrutiny. Inthis chapter we shall briefly consider the kind of way in which suchreasoning is attempted, with a view to discovering whether we can hopethat it may be valid. 

The great representative, in modern times, of the kind of view whichwe wish to examine, was Hegel (1770-1831). Hegel's philosophy is verydifficult, and commentators differ as to the true interpretation of it. According to the interpretation I shall adopt, which is that of many, ifnot most, of the commentators and has the merit of giving an interestingand important type of philosophy, his main thesis is that everythingshort of the Whole is obviously fragmentary, and obviously incapable ofexisting without the complement supplied by the rest of the world. Justas a comparative anatomist, from a single bone, sees what kind of animalthe whole must have been, so the metaphysician, according to Hegel, sees, from any one piece of reality, what the whole of reality mustbe--at least in its large outlines. Every apparently separate piece ofreality has, as it were, hooks which grapple it to the next piece;the next piece, in turn, has fresh hooks, and so on, until the wholeuniverse is reconstructed. This essential incompleteness appears, according to Hegel, equally in the world of thought and in the world ofthings. In the world of thought, if we take any idea which isabstract or incomplete, we find, on examination, that if we forgetits incompleteness, we become involved in contradictions; thesecontradictions turn the idea in question into its opposite, orantithesis; and in order to escape, we have to find a new, lessincomplete idea, which is the synthesis of our original idea and itsantithesis. This new idea, though less incomplete than the idea westarted with, will be found, nevertheless, to be still not whollycomplete, but to pass into its antithesis, with which it must becombined in a new synthesis. In this way Hegel advances until he reachesthe 'Absolute Idea', which, according to him, has no incompleteness, no opposite, and no need of further development. The Absolute Idea, therefore, is adequate to describe Absolute Reality; but all lower ideasonly describe reality as it appears to a partial view, not as it isto one who simultaneously surveys the Whole. Thus Hegel reaches theconclusion that Absolute Reality forms one single harmonious system, notin space or time, not in any degree evil, wholly rational, and whollyspiritual. Any appearance to the contrary, in the world we know, can beproved logically--so he believes--to be entirely due to our fragmentarypiecemeal view of the universe. If we saw the universe whole, as we maysuppose God sees it, space and time and matter and evil and all strivingand struggling would disappear, and we should see instead an eternalperfect unchanging spiritual unity. 

In this conception, there is undeniably something sublime, something towhich we could wish to yield assent. Nevertheless, when the argumentsin support of it are carefully examined, they appear to involve muchconfusion and many unwarrantable assumptions. The fundamental tenetupon which the system is built up is that what is incomplete must be notself-subsistent, but must need the support of other things before it canexist. It is held that whatever has relations to things outside itselfmust contain some reference to those outside things in its own nature, and could not, therefore, be what it is if those outside things did notexist. A man's nature, for example, is constituted by his memories andthe rest of his knowledge, by his loves and hatreds, and so on; thus, but for the objects which he knows or loves or hates, he could not bewhat he is. He is essentially and obviously a fragment: taken as thesum-total of reality he would be self-contradictory. 

This whole point of view, however, turns upon the notion of the 'nature'of a thing, which seems to mean 'all the truths about the thing'. It isof course the case that a truth which connects one thing with anotherthing could not subsist if the other thing did not subsist. But atruth about a thing is not part of the thing itself, although it must, according to the above usage, be part of the 'nature' of the thing. If we mean by a thing's 'nature' all the truths about the thing, thenplainly we cannot know a thing's 'nature' unless we know all the thing'srelations to all the other things in the universe. But if the word'nature' is used in this sense, we shall have to hold that the thingmay be known when its 'nature' is not known, or at any rate is not knowncompletely. There is a confusion, when this use of the word 'nature' isemployed, between knowledge of things and knowledge of truths. We mayhave knowledge of a thing by acquaintance even if we know very fewpropositions about it--theoretically we need not know any propositionsabout it. Thus, acquaintance with a thing does not involve knowledge ofits 'nature' in the above sense. And although acquaintance with a thingis involved in our knowing any one proposition about a thing, knowledgeof its 'nature', in the above sense, is not involved. Hence, (1)acquaintance with a thing does not logically involve a knowledge of itsrelations, and (2) a knowledge of some of its relations does not involvea knowledge of all of its relations nor a knowledge of its 'nature' inthe above sense. I may be acquainted, for example, with my toothache, and this knowledge may be as complete as knowledge by acquaintance evercan be, without knowing all that the dentist (who is not acquaintedwith it) can tell me about its cause, and without therefore knowing its'nature' in the above sense. Thus the fact that a thing has relationsdoes not prove that its relations are logically necessary. That is tosay, from the mere fact that it is the thing it is we cannot deducethat it must have the various relations which in fact it has. This only_seems_ to follow because we know it already. 

It follows that we cannot prove that the universe as a whole forms asingle harmonious system such as Hegel believes that it forms. And if wecannot prove this, we also cannot prove the unreality of space and timeand matter and evil, for this is deduced by Hegel from the fragmentaryand relational character of these things. Thus we are left to thepiecemeal investigation of the world, and are unable to know thecharacters of those parts of the universe that are remote from ourexperience. This result, disappointing as it is to those whose hopeshave been raised by the systems of philosophers, is in harmony withthe inductive and scientific temper of our age, and is borne out by thewhole examination of human knowledge which has occupied our previouschapters. 

Most of the great ambitious attempts of metaphysicians have proceeded bythe attempt to prove that such and such apparent features of the actualworld were self-contradictory, and therefore could not be real. Thewhole tendency of modern thought, however, is more and more in thedirection of showing that the supposed contradictions were illusory, andthat very little can be proved _a priori_ from considerations of what_must_ be. A good illustration of this is afforded by space andtime. Space and time appear to be infinite in extent, and infinitelydivisible. If we travel along a straight line in either direction, itis difficult to believe that we shall finally reach a last point, beyond which there is nothing, not even empty space. Similarly, if inimagination we travel backwards or forwards in time, it is difficult tobelieve that we shall reach a first or last time, with not even emptytime beyond it. Thus space and time appear to be infinite in extent. 

Again, if we take any two points on a line, it seems evident that theremust be other points between them however small the distance betweenthem may be: every distance can be halved, and the halves can be halvedagain, and so on _ad infinitum_. In time, similarly, however littletime may elapse between two moments, it seems evident that there will beother moments between them. Thus space and time appear to be infinitelydivisible. But as against these apparent facts--infinite extent andinfinite divisibility--philosophers have advanced arguments tending toshow that there could be no infinite collections of things, and thattherefore the number of points in space, or of instants in time, mustbe finite. Thus a contradiction emerged between the apparent nature ofspace and time and the supposed impossibility of infinite collections. 

Kant, who first emphasized this contradiction, deduced the impossibilityof space and time, which he declared to be merely subjective; and sincehis time very many philosophers have believed that space and time aremere appearance, not characteristic of the world as it really is. Now, however, owing to the labours of the mathematicians, notably GeorgCantor, it has appeared that the impossibility of infinite collectionswas a mistake. They are not in fact self-contradictory, but onlycontradictory of certain rather obstinate mental prejudices. Hence thereasons for regarding space and time as unreal have become inoperative, and one of the great sources of metaphysical constructions is dried up. 

The mathematicians, however, have not been content with showing thatspace as it is commonly supposed to be is possible; they have shown alsothat many other forms of space are equally possible, so far as logiccan show. Some of Euclid's axioms, which appear to common sense to benecessary, and were formerly supposed to be necessary by philosophers, are now known to derive their appearance of necessity from our merefamiliarity with actual space, and not from any _a priori_ logicalfoundation. By imagining worlds in which these axioms are false, themathematicians have used logic to loosen the prejudices of commonsense, and to show the possibility of spaces differing--some more, someless--from that in which we live. And some of these spaces differ solittle from Euclidean space, where distances such as we can measure areconcerned, that it is impossible to discover by observation whether ouractual space is strictly Euclidean or of one of these other kinds. Thus the position is completely reversed. Formerly it appeared thatexperience left only one kind of space to logic, and logic showed thisone kind to be impossible. Now, logic presents many kinds of space aspossible apart from experience, and experience only partially decidesbetween them. Thus, while our knowledge of what is has become lessthan it was formerly supposed to be, our knowledge of what may be isenormously increased. Instead of being shut in within narrow walls, ofwhich every nook and cranny could be explored, we find ourselves in anopen world of free possibilities, where much remains unknown becausethere is so much to know. 

What has happened in the case of space and time has happened, to someextent, in other directions as well. The attempt to prescribe to theuniverse by means of _a priori_ principles has broken down; logic, instead of being, as formerly, the bar to possibilities, has become thegreat liberator of the imagination, presenting innumerable alternativeswhich are closed to unreflective common sense, and leaving to experiencethe task of deciding, where decision is possible, between the manyworlds which logic offers for our choice. Thus knowledge as to whatexists becomes limited to what we can learn from experience--not towhat we can actually experience, for, as we have seen, there is muchknowledge by description concerning things of which we have no directexperience. But in all cases of knowledge by description, we need someconnexion of universals, enabling us, from such and such a datum, toinfer an object of a certain sort as implied by our datum. Thus inregard to physical objects, for example, the principle that sense-dataare signs of physical objects is itself a connexion of universals; andit is only in virtue of this principle that experience enables us toacquire knowledge concerning physical objects. The same applies tothe law of causality, or, to descend to what is less general, to suchprinciples as the law of gravitation. 

Principles such as the law of gravitation are proved, or rather arerendered highly probable, by a combination of experience with somewholly _a priori_ principle, such as the principle of induction. Thusour intuitive knowledge, which is the source of all our other knowledgeof truths, is of two sorts: pure empirical knowledge, which tells us ofthe existence and some of the properties of particular things withwhich we are acquainted, and pure _a priori_ knowledge, which gives usconnexions between universals, and enables us to draw inferences fromthe particular facts given in empirical knowledge. Our derivativeknowledge always depends upon some pure _a priori_ knowledge and usuallyalso depends upon some pure empirical knowledge. 

Philosophical knowledge, if what has been said above is true, does notdiffer essentially from scientific knowledge; there is no specialsource of wisdom which is open to philosophy but not to science, and theresults obtained by philosophy are not radically different from thoseobtained from science. The essential characteristic of philosophy, which makes it a study distinct from science, is criticism. It examinescritically the principles employed in science and in daily life; itsearches out any inconsistencies there may be in these principles, and it only accepts them when, as the result of a critical inquiry, noreason for rejecting them has appeared. If, as many philosophers havebelieved, the principles underlying the sciences were capable, whendisengaged from irrelevant detail, of giving us knowledge concerningthe universe as a whole, such knowledge would have the same claim on ourbelief as scientific knowledge has; but our inquiry has not revealed anysuch knowledge, and therefore, as regards the special doctrines of thebolder metaphysicians, has had a mainly negative result. But as regardswhat would be commonly accepted as knowledge, our result is in the mainpositive: we have seldom found reason to reject such knowledge as theresult of our criticism, and we have seen no reason to suppose manincapable of the kind of knowledge which he is generally believed topossess. 

When, however, we speak of philosophy as a _criticism_ of knowledge, itis necessary to impose a certain limitation. If we adopt the attitudeof the complete sceptic, placing ourselves wholly outside all knowledge, and asking, from this outside position, to be compelled to return withinthe circle of knowledge, we are demanding what is impossible, and ourscepticism can never be refuted. For all refutation must begin withsome piece of knowledge which the disputants share; from blank doubt, no argument can begin. Hence the criticism of knowledge which philosophyemploys must not be of this destructive kind, if any result is to beachieved. Against this absolute scepticism, no _logical_ argument can beadvanced. But it is not difficult to see that scepticism of this kindis unreasonable. Descartes' 'methodical doubt', with which modernphilosophy began, is not of this kind, but is rather the kind ofcriticism which we are asserting to be the essence of philosophy. His'methodical doubt' consisted in doubting whatever seemed doubtful; inpausing, with each apparent piece of knowledge, to ask himself whether, on reflection, he could feel certain that he really knew it. This is thekind of criticism which constitutes philosophy. Some knowledge, such asknowledge of the existence of our sense-data, appears quite indubitable, however calmly and thoroughly we reflect upon it. In regard to suchknowledge, philosophical criticism does not require that we shouldabstain from belief. But there are beliefs--such, for example, as thebelief that physical objects exactly resemble our sense-data--which areentertained until we begin to reflect, but are found to melt awaywhen subjected to a close inquiry. Such beliefs philosophy will bid usreject, unless some new line of argument is found to support them. But to reject the beliefs which do not appear open to any objections, however closely we examine them, is not reasonable, and is not whatphilosophy advocates. 

The criticism aimed at, in a word, is not that which, without reason, determines to reject, but that which considers each piece of apparentknowledge on its merits, and retains whatever still appears to beknowledge when this consideration is completed. That some risk of errorremains must be admitted, since human beings are fallible. Philosophymay claim justly that it diminishes the risk of error, and that in somecases it renders the risk so small as to be practically negligible. Todo more than this is not possible in a world where mistakes must occur;and more than this no prudent advocate of philosophy would claim to haveperformed. 

CHAPTER XV. THE VALUE OF PHILOSOPHY

Having now come to the end of our brief and very incomplete review ofthe problems of philosophy, it will be well to consider, in conclusion, what is the value of philosophy and why it ought to be studied. It isthe more necessary to consider this question, in view of the fact thatmany men, under the influence of science or of practical affairs, areinclined to doubt whether philosophy is anything better than innocentbut useless trifling, hair-splitting distinctions, and controversies onmatters concerning which knowledge is impossible. 

This view of philosophy appears to result, partly from a wrongconception of the ends of life, partly from a wrong conception of thekind of goods which philosophy strives to achieve. Physical science, through the medium of inventions, is useful to innumerable people whoare wholly ignorant of it; thus the study of physical science is tobe recommended, not only, or primarily, because of the effect on thestudent, but rather because of the effect on mankind in general. Thusutility does not belong to philosophy. If the study of philosophy hasany value at all for others than students of philosophy, it must be onlyindirectly, through its effects upon the lives of those who study it. It is in these effects, therefore, if anywhere, that the value ofphilosophy must be primarily sought. 

But further, if we are not to fail in our endeavour to determine thevalue of philosophy, we must first free our minds from the prejudicesof what are wrongly called 'practical' men. The 'practical' man, asthis word is often used, is one who recognizes only material needs, whorealizes that men must have food for the body, but is oblivious of thenecessity of providing food for the mind. If all men were well off, ifpoverty and disease had been reduced to their lowest possible point, there would still remain much to be done to produce a valuable society;and even in the existing world the goods of the mind are at least asimportant as the goods of the body. It is exclusively among the goods ofthe mind that the value of philosophy is to be found; and only those whoare not indifferent to these goods can be persuaded that the study ofphilosophy is not a waste of time. 

Philosophy, like all other studies, aims primarily at knowledge. Theknowledge it aims at is the kind of knowledge which gives unity andsystem to the body of the sciences, and the kind which results from acritical examination of the grounds of our convictions, prejudices, andbeliefs. But it cannot be maintained that philosophy has had any verygreat measure of success in its attempts to provide definite answers toits questions. If you ask a mathematician, a mineralogist, a historian, or any other man of learning, what definite body of truths has beenascertained by his science, his answer will last as long as you arewilling to listen. But if you put the same question to a philosopher, hewill, if he is candid, have to confess that his study has not achievedpositive results such as have been achieved by other sciences. It istrue that this is partly accounted for by the fact that, as soon asdefinite knowledge concerning any subject becomes possible, this subjectceases to be called philosophy, and becomes a separate science. Thewhole study of the heavens, which now belongs to astronomy, was onceincluded in philosophy; Newton's great work was called 'the mathematicalprinciples of natural philosophy'. Similarly, the study of the humanmind, which was a part of philosophy, has now been separated fromphilosophy and has become the science of psychology. Thus, to a greatextent, the uncertainty of philosophy is more apparent than real: thosequestions which are already capable of definite answers are placed inthe sciences, while those only to which, at present, no definite answercan be given, remain to form the residue which is called philosophy. 

This is, however, only a part of the truth concerning the uncertainty ofphilosophy. There are many questions--and among them those that are ofthe profoundest interest to our spiritual life--which, so far as wecan see, must remain insoluble to the human intellect unless its powersbecome of quite a different order from what they are now. Has theuniverse any unity of plan or purpose, or is it a fortuitous concourseof atoms? Is consciousness a permanent part of the universe, givinghope of indefinite growth in wisdom, or is it a transitory accident ona small planet on which life must ultimately become impossible? Are goodand evil of importance to the universe or only to man? Such questionsare asked by philosophy, and variously answered by various philosophers. But it would seem that, whether answers be otherwise discoverable ornot, the answers suggested by philosophy are none of them demonstrablytrue. Yet, however slight may be the hope of discovering an answer, itis part of the business of philosophy to continue the consideration ofsuch questions, to make us aware of their importance, to examine all theapproaches to them, and to keep alive that speculative interest in theuniverse which is apt to be killed by confining ourselves to definitelyascertainable knowledge. 

Many philosophers, it is true, have held that philosophy could establishthe truth of certain answers to such fundamental questions. They havesupposed that what is of most importance in religious beliefs could beproved by strict demonstration to be true. In order to judge of suchattempts, it is necessary to take a survey of human knowledge, and toform an opinion as to its methods and its limitations. On such a subjectit would be unwise to pronounce dogmatically; but if the investigationsof our previous chapters have not led us astray, we shall be compelledto renounce the hope of finding philosophical proofs of religiousbeliefs. We cannot, therefore, include as part of the value ofphilosophy any definite set of answers to such questions. Hence, oncemore, the value of philosophy must not depend upon any supposed body ofdefinitely ascertainable knowledge to be acquired by those who study it. 

The value of philosophy is, in fact, to be sought largely in its veryuncertainty. The man who has no tincture of philosophy goes throughlife imprisoned in the prejudices derived from common sense, from thehabitual beliefs of his age or his nation, and from convictions whichhave grown up in his mind without the co-operation or consent of hisdeliberate reason. To such a man the world tends to become definite, finite, obvious; common objects rouse no questions, and unfamiliarpossibilities are contemptuously rejected. As soon as we begin tophilosophize, on the contrary, we find, as we saw in our openingchapters, that even the most everyday things lead to problems to whichonly very incomplete answers can be given. Philosophy, though unable totell us with certainty what is the true answer to the doubts which itraises, is able to suggest many possibilities which enlarge our thoughtsand free them from the tyranny of custom. Thus, while diminishing ourfeeling of certainty as to what things are, it greatly increases ourknowledge as to what they may be; it removes the somewhat arrogantdogmatism of those who have never travelled into the region ofliberating doubt, and it keeps alive our sense of wonder by showingfamiliar things in an unfamiliar aspect. 

Apart from its utility in showing unsuspected possibilities, philosophyhas a value--perhaps its chief value--through the greatness of theobjects which it contemplates, and the freedom from narrow and personalaims resulting from this contemplation. The life of the instinctiveman is shut up within the circle of his private interests: family andfriends may be included, but the outer world is not regarded exceptas it may help or hinder what comes within the circle of instinctivewishes. In such a life there is something feverish and confined, incomparison with which the philosophic life is calm and free. The privateworld of instinctive interests is a small one, set in the midst of agreat and powerful world which must, sooner or later, lay our privateworld in ruins. Unless we can so enlarge our interests as to include thewhole outer world, we remain like a garrison in a beleagured fortress, knowing that the enemy prevents escape and that ultimate surrender isinevitable. In such a life there is no peace, but a constant strifebetween the insistence of desire and the powerlessness of will. In oneway or another, if our life is to be great and free, we must escape thisprison and this strife. 

One way of escape is by philosophic contemplation. Philosophiccontemplation does not, in its widest survey, divide the universe intotwo hostile camps--friends and foes, helpful and hostile, good andbad--it views the whole impartially. Philosophic contemplation, when itis unalloyed, does not aim at proving that the rest of the universe isakin to man. All acquisition of knowledge is an enlargement of the Self, but this enlargement is best attained when it is not directly sought. Itis obtained when the desire for knowledge is alone operative, by a studywhich does not wish in advance that its objects should have this or thatcharacter, but adapts the Self to the characters which it finds in itsobjects. This enlargement of Self is not obtained when, taking the Selfas it is, we try to show that the world is so similar to this Self thatknowledge of it is possible without any admission of what seems alien. The desire to prove this is a form of self-assertion and, like allself-assertion, it is an obstacle to the growth of Self which itdesires, and of which the Self knows that it is capable. Self-assertion, in philosophic speculation as elsewhere, views the world as a means toits own ends; thus it makes the world of less account than Self, and theSelf sets bounds to the greatness of its goods. In contemplation, onthe contrary, we start from the not-Self, and through its greatness theboundaries of Self are enlarged; through the infinity of the universethe mind which contemplates it achieves some share in infinity. 

For this reason greatness of soul is not fostered by those philosophieswhich assimilate the universe to Man. Knowledge is a form of unionof Self and not-Self; like all union, it is impaired by dominion, andtherefore by any attempt to force the universe into conformity withwhat we find in ourselves. There is a widespread philosophical tendencytowards the view which tells us that Man is the measure of all things, that truth is man-made, that space and time and the world of universalsare properties of the mind, and that, if there be anything not createdby the mind, it is unknowable and of no account for us. This view, ifour previous discussions were correct, is untrue; but in addition tobeing untrue, it has the effect of robbing philosophic contemplation ofall that gives it value, since it fetters contemplation to Self. Whatit calls knowledge is not a union with the not-Self, but a set ofprejudices, habits, and desires, making an impenetrable veil betweenus and the world beyond. The man who finds pleasure in such a theory ofknowledge is like the man who never leaves the domestic circle for fearhis word might not be law. 

The true philosophic contemplation, on the contrary, finds itssatisfaction in every enlargement of the not-Self, in everythingthat magnifies the objects contemplated, and thereby the subjectcontemplating. Everything, in contemplation, that is personal orprivate, everything that depends upon habit, self-interest, or desire, distorts the object, and hence impairs the union which the intellectseeks. By thus making a barrier between subject and object, suchpersonal and private things become a prison to the intellect. The freeintellect will see as God might see, without a _here_ and _now_, without hopes and fears, without the trammels of customary beliefsand traditional prejudices, calmly, dispassionately, in the sole andexclusive desire of knowledge--knowledge as impersonal, as purelycontemplative, as it is possible for man to attain. Hence also the freeintellect will value more the abstract and universal knowledge intowhich the accidents of private history do not enter, than the knowledgebrought by the senses, and dependent, as such knowledge must be, uponan exclusive and personal point of view and a body whose sense-organsdistort as much as they reveal. 

The mind which has become accustomed to the freedom and impartiality ofphilosophic contemplation will preserve something of the same freedomand impartiality in the world of action and emotion. It will viewits purposes and desires as parts of the whole, with the absence ofinsistence that results from seeing them as infinitesimal fragments ina world of which all the rest is unaffected by any one man's deeds. Theimpartiality which, in contemplation, is the unalloyed desire for truth, is the very same quality of mind which, in action, is justice, and inemotion is that universal love which can be given to all, and not onlyto those who are judged useful or admirable. Thus contemplation enlargesnot only the objects of our thoughts, but also the objects of ouractions and our affections: it makes us citizens of the universe, notonly of one walled city at war with all the rest. In this citizenshipof the universe consists man's true freedom, and his liberation from thethraldom of narrow hopes and fears. 

Thus, to sum up our discussion of the value of philosophy; Philosophyis to be studied, not for the sake of any definite answers to itsquestions, since no definite answers can, as a rule, be known to betrue, but rather for the sake of the questions themselves; becausethese questions enlarge our conception of what is possible, enrichour intellectual imagination and diminish the dogmatic assurance whichcloses the mind against speculation; but above all because, through thegreatness of the universe which philosophy contemplates, the mind alsois rendered great, and becomes capable of that union with the universewhich constitutes its highest good. 

BIBLIOGRAPHICAL NOTE

The student who wishes to acquire an elementary knowledge of philosophywill find it both easier and more profitable to read some of the worksof the great philosophers than to attempt to derive an all-round viewfrom handbooks. The following are specially recommended:

 Plato: _Republic_, especially Books VI and VII. Descartes: _Meditations_. Spinoza: _Ethics_. Leibniz: _The Monadology_. Berkeley: _Three Dialogues between Hylas and Philonous_. Hume: _Enquiry concerning Human Understanding_. Kant: _Prolegomena to any Future Metaphysic_.