Chapter XIII. Knowledge, Error, and Probable Opinion

by Bertrand Russell

　　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 doubt thatsome of our beliefs are erroneous; thus we are led to inquire whatcertainty we can ever have that such and such a belief is not erroneous.In other words, can we ever know anything at all, or do we merelysometimes by good luck believe what is true? Before we can attack thisquestion, we must, however, first decide what we mean by 'knowing', andthis 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 accord withthe way in which the word is commonly used. To take a very trivialinstance: If a man believes that the late Prime Minister's last name beganwith a B, he believes what is true, since the late Prime Minister was SirHenry Campbell Bannerman. But if he believes that Mr. Balfour was the latePrime Minister, he will still believe that the late Prime Minister's lastname began with a B, yet this belief, though true, would not be thought toconstitute knowledge. If a newspaper, by an intelligent anticipation,announces the result of a battle before any telegram giving the result hasbeen received, it may by good fortune announce what afterwards turns outto be the right result, and it may produce belief in some of its lessexperienced readers. But in spite of the truth of their belief, theycannot be said to have knowledge. Thus it is clear that a true belief isnot knowledge when it is deduced from a 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 mypremisses and my conclusion are true, the conclusion does not follow fromthe premisses.

　　But are we to say that nothing is knowledge except what is validly deducedfrom true premisses? Obviously we cannot say this. Such a definition is atonce too wide and too narrow. In the first place, it is too wide, becauseit is not enough that our premisses should be true, they must alsobe known. The man who believes that Mr. Balfour was the late PrimeMinister may proceed to draw valid deductions from the true premiss thatthe late Prime Minister's name began with a B, but he cannot be said to knowthe conclusions reached by these deductions. Thus we shall have to amendour definition by saying that knowledge is what is validly deduced from knownpremisses. This, however, is a circular definition: it assumes that wealready know what is meant by 'known premisses'. It can, therefore, atbest define one sort of knowledge, the sort we call derivative, as opposedto intuitive knowledge. We may say: 'Derivative knowledge is whatis validly deduced from premisses known intuitively'. In this statementthere is no formal defect, but it leaves the definition of intuitiveknowledge still to seek.

　　Leaving on one side, for the moment, the question of intuitive knowledge,let us consider the above suggested definition of derivative knowledge.The chief objection to it is that it unduly limits knowledge. Itconstantly happens that people entertain a true belief, which has grown upin them because of some piece of intuitive knowledge from which it iscapable of being validly inferred, but from which it has not, as a matterof 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 in believingthat the King is dead, since this is the sort of announcement which wouldnot be made if it were false. And we are quite amply justified inbelieving that the newspaper asserts that the King is dead. But here theintuitive knowledge upon which our belief is based is knowledge of theexistence of sense-data derived from looking at the print which gives thenews. This knowledge scarcely rises into consciousness, except in a personwho cannot read easily. A child may be aware of the shapes of the letters,and pass gradually and painfully to a realization of their meaning. Butanybody accustomed to reading passes at once to what the letters mean, andis not aware, except on reflection, that he has derived this knowledgefrom the sense-data called seeing the printed letters. Thus although avalid inference from the-letters to their meaning is possible, and couldbe performed by the reader, it is not in fact performed, since he does notin fact perform 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 isa 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. These waysmay 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 parallel tothe psychological inference. This renders our definition of derivativeknowledge less precise than we could wish, since the word 'discoverable'is vague: it does not tell us how much reflection may be needed in orderto make the discovery. But in fact 'knowledge' is not a preciseconception: it merges into 'probable opinion', as we shall see more fullyin the course of the present chapter. A very precise definition,therefore, should not be sought, since any such definition must be more orless misleading.

　　The chief difficulty in regard to knowledge, however, does not arise overderivative knowledge, but over intuitive knowledge. So long as we aredealing with derivative knowledge, we have the test of intuitive knowledgeto fall back upon. But in regard to intuitive beliefs, it is by no meanseasy to discover any criterion by which to distinguish some as true andothers as erroneous. In this question it is scarcely possible to reach anyvery precise result: all our knowledge of truths is infected with somedegree of doubt, and a theory which ignored this fact would be plainlywrong. Something may be done, however, to mitigate the difficulties of thequestion.

　　Our theory of truth, to begin with, supplies the possibility ofdistinguishing certain truths as self-evident in a sense whichensures infallibility. When a belief is true, we said, there is acorresponding fact, in which the several objects of the belief form asingle complex. The belief is said to constitute knowledge of thisfact, provided it fulfils those further somewhat vague conditions which wehave been considering in the present chapter. But in regard to any fact,besides the 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 canat that hour know the fact that the sun is setting: this is knowledge ofthe fact by way of knowledge of truths; but you can also, if theweather is fine, look to the west and actually see the setting sun: youthen know the same fact by the way of knowledge of things.

　　Thus in regard to any complex fact, there are, theoretically, two ways inwhich it may be known: (1) by means of a judgement, in which its severalparts are judged to be related as they are in fact related; (2) by meansof acquaintance with the complex fact itself, which may (in a largesense) be called perception, though it is by no means confined to objectsof the senses. Now it will be observed that the second way of knowing acomplex fact, the way of acquaintance, is only possible when there reallyis such a fact, while the first way, like all judgement, is liable toerror. The second way gives us the complex whole, and is therefore onlypossible when its parts do actually have that relation which makes themcombine to form such a complex. The first way, on the contrary, gives usthe parts and the relation severally, and demands only the reality of theparts and the relation: the relation may not relate those parts in thatway, 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 to thetruth. When Othello believes that Desdemona loves Cassio, thecorresponding fact, if his belief were true, would be 'Desdemona's lovefor Cassio'. This would be a fact with which no one could haveacquaintance except Desdemona; hence in the sense of self-evidence that weare considering, the truth that Desdemona loves Cassio (if it were atruth) could only be self-evident to Desdemona. All mental facts, and allfacts concerning sense-data, have this same privacy: there is only oneperson to whom they can be self-evident in our present sense, since thereis only one person who can be acquainted with the mental things or thesense-data concerned. Thus no fact about any particular existing thing canbe self-evident to more than one person. On the other hand, facts aboutuniversals do not have this privacy. Many minds may be acquainted with thesame universals; hence a relation between universals may be known byacquaintance to many different people. In all cases where we know byacquaintance a complex fact consisting of certain terms in a certainrelation, we say that the truth that these terms are so related has thefirst or absolute kind of self-evidence, and in these cases the judgementthat the terms are so related must be true. Thus this sort ofself-evidence is an absolute guarantee of truth.

　　But although this sort of self-evidence is an absolute guarantee of truth,it does not enable us to be absolutely certain, in the case of anygiven judgement, that the judgement in question is true. Suppose we firstperceive the sun shining, which is a complex fact, and thence proceed tomake the judgement 'the sun is shining'. In passing from the perception tothe judgement, it is necessary to analyse the given complex fact: we haveto separate out 'the sun' and 'shining' as constituents of the fact. Inthis process it is possible to commit an error; hence even where a facthas the first or absolute kind of self-evidence, a judgement believed tocorrespond to the fact is not absolutely infallible, because it may notreally correspond to the fact. But if it does correspond (in the senseexplained in the preceding chapter), then it must be true.

　　The second sort of self-evidence will be that which belongs to judgementsin the first instance, and is not derived from direct perception of a factas a single complex whole. This second kind of self-evidence will havedegrees, from the very highest degree down to a bare inclination in favourof the belief. Take, for example, the case of a horse trotting away fromus along a hard road. At first our certainty that we hear the hoofs iscomplete; gradually, if we listen intently, there comes a moment when wethink perhaps it was imagination or the blind upstairs or our ownheartbeats; at last we become doubtful whether there was any noise at all;then we think we no longer hear anything, and at last we knowwe no longer hear anything. In this process, there is a continualgradation of self-evidence, from the highest degree to the least, not inthe sense-data themselves, but in the judgements based on them.

　　Or again: Suppose we are comparing two shades of colour, one blue and onegreen. We can be quite sure they are different shades of colour; but ifthe green colour is gradually altered to be more and more like the blue,becoming first a blue-green, then a greeny-blue, then blue, there willcome a moment when we are doubtful whether we can see any difference, andthen a moment when we know that we cannot see any difference. The samething happens in tuning a musical instrument, or in any other case wherethere is a continuous gradation. Thus self-evidence of this sort is amatter of degree; and it seems plain that the higher degrees are more tobe 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: it isnecessary 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; henceerrors of reasoning are not improbable where the difficulty is great.

　　From what has been said it is evident that, both as regards intuitiveknowledge and as regards derivative knowledge, if we assume that intuitiveknowledge is trustworthy in proportion to the degree of its self-evidence,there will be a gradation in trustworthiness, from the existence ofnoteworthy sense-data and the simpler truths of logic and arithmetic,which may be taken as quite certain, down to judgements which seem onlyjust more probable than their opposites. What we firmly believe, if it istrue, is called knowledge, provided it is either intuitive orinferred (logically or psychologically) from intuitive knowledge fromwhich it follows logically. What we firmly believe, if it is not true, iscalled error. What we firmly believe, if it is neither knowledgenor error, and also what we believe hesitatingly, because it is, or isderived from, something which has not the highest degree of self-evidence,may be called probable opinion. Thus the greater part of what wouldcommonly pass as knowledge is more or less probable opinion.

　　In regard to probable opinion, we can derive great assistance from coherence,which we rejected as the definition of truth, but may often use asa criterion. A body of individually probable opinions, if they aremutually coherent, become more probable than any one of them would beindividually. It is in this way that many scientific hypotheses acquiretheir probability. They fit into a coherent system of probable opinions,and thus become more probable than they would be in isolation. The samething applies to general philosophical hypotheses. Often in a single casesuch hypotheses may seem highly doubtful, while yet, when we consider theorder and coherence which they introduce into a mass of probable opinion,they become pretty nearly certain. This applies, in particular, to suchmatters as the distinction between dreams and waking life. If our dreams,night after night, were as coherent one with another as our days, weshould hardly know whether to believe the dreams or the waking life. As itis, the test of coherence condemns the dreams and confirms the wakinglife. But this test, though it increases probability where it issuccessful, never gives absolute certainty, unless there is certaintyalready at some point in the coherent system. Thus the mere organizationof probable opinion will never, by itself, transform it into indubitableknowledge.