Chapter XII. Truth and Falsehood

by Bertrand Russell

　　Our knowledge of truths, unlike our knowledge of things, has an opposite,namely error. So far as things are concerned, we may know them ornot know them, but there is no positive state of mind which can bedescribed as erroneous knowledge of things, so long, at any rate, as weconfine ourselves to knowledge by acquaintance. Whatever we are acquaintedwith must be something; we may draw wrong inferences from ouracquaintance, but the acquaintance itself cannot be deceptive. Thus thereis no dualism as regards acquaintance. But as regards knowledge of truths,there is a dualism. We may believe what is false as well as what is true.We know that on very many subjects different people hold different andincompatible opinions: hence some beliefs must be erroneous. Sinceerroneous beliefs are often held just as strongly as true beliefs, itbecomes a difficult question how they are to be distinguished from truebeliefs. How are we to know, in a given case, that our belief is noterroneous? This is a question of the very greatest difficulty, to which nocompletely satisfactory answer is possible. There is, however, apreliminary question which is rather less difficult, and that is: What dowe mean by truth and falsehood? It is this preliminary questionwhich is to be considered in this chapter. In this chapter we are notasking how we can know whether a belief is true or false: we are askingwhat is meant by the question whether a belief is true or false. It is tobe hoped that a clear answer to this question may help us to obtain ananswer to the question what beliefs are true, but for the present we askonly 'What is truth?' and 'What is falsehood?' not 'What beliefs aretrue?' and 'What beliefs are false?' It is very important to keep thesedifferent questions entirely separate, since any confusion between them issure to produce an answer which is not really applicable to either.

　　There are three points to observe in the attempt to discover the nature oftruth, 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 satisfy thiscondition: they have constructed theories according to which all ourthinking ought to have been true, and have then had the greatestdifficulty in finding a place for falsehood. In this respect our theory ofbelief must differ from our theory of acquaintance, since in the case ofacquaintance it was not necessary to take account of any opposite.

　　(2) It seems fairly evident that if there were no beliefs there could beno 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. Infact, truth and falsehood are properties of beliefs and statements: hencea world of mere matter, since it would contain no beliefs or statements,would also contain no truth or falsehood.

　　(3) But, as against what we have just said, it is to be observed that thetruth or falsehood of a belief always depends upon something which liesoutside 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 truth andfalsehood are properties of beliefs, they are properties dependent uponthe 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—whichhas on the whole been commonest among philosophers—that truthconsists in some form of correspondence between belief and fact. It is,however, by no means an easy matter to discover a form of correspondenceto which there are no irrefutable objections. By this partly—andpartly by the feeling that, if truth consists in a correspondence ofthought with something outside thought, thought can never know when truthhas been attained—many philosophers have been led to try to findsome definition of truth which shall not consist in relation to somethingwholly outside belief. The most important attempt at a definition of thissort is the theory that truth consists in coherence. It is saidthat the mark of falsehood is failure to cohere in the body of ourbeliefs, and that it is the essence of a truth to form part of thecompletely rounded system which 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 that only onecoherent body of beliefs is possible. It may be that, with sufficientimagination, a novelist might invent a past for the world that wouldperfectly fit on to what we know, and yet be quite different from the realpast. In more scientific matters, it is certain that there are often twoor more hypotheses which account for all the known facts on some subject,and although, in such cases, men of science endeavour to find facts whichwill rule out all the hypotheses except one, there is no reason why theyshould always succeed.

　　In philosophy, again, it seems not uncommon for two rival hypotheses to beboth able to account for all the facts. Thus, for example, it is possiblethat life is one long dream, and that the outer world has only that degreeof reality that the objects of dreams have; but although such a view doesnot seem inconsistent with known facts, there is no reason to prefer it tothe common-sense view, according to which other people and things doreally exist. Thus coherence as the definition of truth fails becausethere is no proof that there can be only one coherent 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 must know suchtruths as the law of contradiction. For example, the two propositions,'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 of contradictionitself were subjected to the test of coherence, we should find that, if wechoose to suppose it false, nothing will any longer be incoherent withanything else. Thus the laws of logic supply the skeleton or frameworkwithin which the test of coherence applies, and they themselves cannot beestablished by this test.

　　For the above two reasons, coherence cannot be accepted as giving the meaningof truth, though it is often a most important test of truth after acertain amount of truth has become known.

　　Hence we are driven back to correspondence with fact asconstituting the nature of truth. It remains to define precisely what wemean by 'fact', and what is the nature of the correspondence which mustsubsist between belief and fact, in order that belief may be true.

　　In accordance with our three requisites, we have to seek a theory of truthwhich (1) allows truth to have an opposite, namely falsehood, (2) makestruth a property of beliefs, but (3) makes it a property wholly dependentupon 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 clear byexamples. Othello believes falsely that Desdemona loves Cassio. We cannotsay 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 not loveCassio, as it was to suppose that there is 'Desdemona's love for Cassio'.Hence it will be better to seek for a theory of belief which does not makeit consist in a relation of the mind to a single object.

　　It is common to think of relations as though they always held between twoterms, but in fact this is not always the case. Some relations demandthree terms, some four, and so on. Take, for instance, the relation'between'. So long as only two terms come in, the relation 'between' isimpossible: three terms are the smallest number that render it possible.York is between London and Edinburgh; but if London and Edinburgh were theonly places in the world, there could be nothing which was between oneplace and another. Similarly jealousy requires three people: therecan be no such relation that does not involve three at least. Such aproposition as 'A wishes B to promote C's marriage with D' involves arelation of four terms; that is to say, A and B and C and D all come in,and the relation involved cannot be expressed otherwise than in a forminvolving all four. Instances might be multiplied indefinitely, but enoughhas been said to show that there are relations which require more than twoterms before they can occur.

　　The relation involved in judging or believing must, iffalsehood is to be duly allowed for, be taken to be a relation betweenseveral terms, not between two. When Othello believes that Desdemona lovesCassio, he must not have before his mind a single object, 'Desdemona'slove for Cassio', or 'that Desdemona loves Cassio ', for that wouldrequire that there should be objective falsehoods, which subsistindependently of any minds; and this, though not logically refutable, is atheory to be avoided if possible. Thus it is easier to account forfalsehood if we take judgement to be a relation in which the mind and thevarious objects concerned all occur severally; that is to say, Desdemonaand loving and Cassio must all be terms in the relation which subsistswhen Othello believes that Desdemona loves Cassio. This relation,therefore, is a relation of four terms, since Othello also is one of theterms of the relation. When we say that it is a relation of four terms, wedo not mean that Othello has a certain relation to Desdemona, and has thesame relation 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 allof them together: there is only one example of the relation of believinginvolved, but this one example knits together four terms. Thus the actualoccurrence, at the moment when Othello is entertaining his belief, is thatthe relation called 'believing' is knitting together into one complexwhole the four terms Othello, Desdemona, loving, and Cassio. What iscalled belief or judgement is nothing but this relation of believing orjudging, which relates a mind to several things other than itself. An actof belief or of judgement is the occurrence between certain terms at someparticular time, of the relation of believing 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 subjectin the judgement, and the remaining terms the objects. Thus, whenOthello judges that Desdemona loves Cassio, Othello is the subject, whilethe objects are Desdemona and loving and Cassio. The subject and theobjects together are called the constituents of the judgement. Itwill be observed that the relation of judging has what is called a 'sense'or 'direction'. We may say, metaphorically, that it puts its objects in acertain order, which we may indicate by means of the order of thewords in the sentence. (In an inflected language, the same thing will beindicated by inflections, e.g. by the difference between nominative andaccusative.) Othello's judgement that Cassio loves Desdemona differs fromhis judgement that Desdemona loves Cassio, in spite of the fact that itconsists of the same constituents, because the relation of judging placesthe constituents in a different order in the two cases. Similarly, ifCassio judges that Desdemona loves Othello, the constituents of thejudgement are still the same, but their order is different. This propertyof having a 'sense' or 'direction' is one which the relation of judgingshares with all other relations. The 'sense' of relations is the ultimatesource of order and series and a host of mathematical concepts; but weneed not concern ourselves further with this 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 a relationholds between two or more terms, it unites the terms into a complex whole.If Othello loves Desdemona, there is such a complex whole as 'Othello'slove for Desdemona'. The terms united by the relation may be themselvescomplex, or may be simple, but the whole which results from their beingunited must be complex. Wherever there is a relation which relates certainterms, there is a complex object formed of the union of those terms; andconversely, wherever there is a complex object, there is a relation whichrelates its constituents. When an act of believing occurs, there is acomplex, in which 'believing' is the uniting relation, and subject andobjects are arranged in a certain order by the 'sense' of the relation ofbelieving. Among the objects, as we saw in considering 'Othello believesthat Desdemona loves Cassio', one must be a relation—in thisinstance, the relation 'loving'. But this relation, as it occurs in theact of believing, is not the relation which creates the unity of thecomplex whole consisting of the subject and the objects. The relation'loving', as it occurs in the act of believing, is one of the objects—itis a brick in the structure, not the cement. The cement is the relation'believing'. When the belief is true, there is another complexunity, in which the relation which was one of the objects of the beliefrelates the other objects. Thus, e.g., if Othello believes trulythat Desdemona loves Cassio, then there is a complex unity, 'Desdemona'slove for Cassio', which is composed exclusively of the objects ofthe belief, in the same order as they had in the belief, with the relationwhich was one of the objects occurring now as the cement that bindstogether the other objects of the belief. On the other hand, when a beliefis false, there is no such complex unity composed only of theobjects of the belief. If Othello believes falsely that Desdemonaloves Cassio, then there is no such complex unity as 'Desdemona's love forCassio'.

　　Thus a belief is true when it corresponds to a certainassociated complex, and false when it does not. Assuming, for thesake of definiteness, that the objects of the belief are two terms and arelation, the terms being put in a certain order by the 'sense' of thebelieving, then if the two terms in that order are united by the relationinto a complex, the belief is true; if not, it is false. This constitutesthe definition of truth and falsehood that we were in search of. Judgingor believing is a certain complex unity of which a mind is a constituent;if the remaining constituents, taken in the order which they have in thebelief, form a complex unity, then the belief is true; if not, it isfalse.

　　Thus although truth and falsehood are properties of beliefs, yet they arein a sense extrinsic properties, for the condition of the truth of abelief is something not involving beliefs, or (in general) any mind atall, but only the objects of the belief. A mind, which believes,believes truly when there is a corresponding complex not involvingthe mind, 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) donot depend on minds for their truth.

　　We may restate our theory as follows: If we take such a belief as 'Othellobelieves that Desdemona loves Cassio', we will call Desdemona and Cassiothe object-terms, and loving the object-relation. If thereis a complex unity 'Desdemona's love for Cassio', consisting of theobject-terms related by the object-relation in the same order as they havein the belief, then this complex unity is called the fact correspondingto the belief. Thus a belief is true when there is a correspondingfact, 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, such ascatching trains. What makes a belief true is a fact, and this factdoes not (except in exceptional cases) in any way involve the mind of theperson who has the belief.

　　Having now decided what we mean by truth and falsehood, we havenext to consider what ways there are of knowing whether this or thatbelief is true or false. This consideration will occupy the next chapter.