Chapter VI. On Indcution

by Bertrand Russell

　　In almost all our previous discussions we have been concerned in theattempt to get clear as to our data in the way of knowledge of existence.What things are there in the universe whose existence is known to us owingto our being acquainted with them? So far, our answer has been that we areacquainted with our sense-data, and, probably, with ourselves. These weknow to exist. And past sense-data which are remembered are known to haveexisted in the past. This knowledge supplies our data.

　　But if we are to be able to draw inferences from these data—if weare to know of the existence of matter, of other people, of the pastbefore our individual memory begins, or of the future, we must knowgeneral principles of some kind by means of which such inferences can bedrawn. It must be known to us that the existence of some one sort ofthing, A, is a sign of the existence of some other sort of thing, B,either at the same time as A or at some earlier or later time, as, forexample, thunder is a sign of the earlier existence of lightning. If thiswere not 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 whether suchan 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, orcan it be justified as a reasonable belief? It is not easy to find a testby which to judge whether a belief of this kind is reasonable or not, butwe can at least ascertain what sort of general beliefs would suffice, iftrue, to justify the judgement that the sun will rise to-morrow, and themany other similar judgements upon which our actions are 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 that itwill continue to rise as heretofore, we may appeal to the laws of motion:the earth, we shall say, is a freely rotating body, and such bodies do notcease to rotate unless something interferes from outside, and there isnothing outside to interfere with the earth between now and to-morrow. Ofcourse it might be doubted whether we are quite certain that there isnothing outside to interfere, but this is not the interesting doubt. Theinteresting doubt is as to whether the laws of motion will remain inoperation until to-morrow. If this doubt is raised, we find ourselves inthe same position as when the doubt about the sunrise was first raised.

　　The only reason for believing that the laws of motion will remainin operation 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 body ofevidence from the past in favour of the laws of motion than we have infavour of the sunrise, because the sunrise is merely a particular case offulfilment of the laws of motion, and there are countless other particularcases. But the real question is: Do any number of cases of a lawbeing fulfilled in the past afford evidence that it will be fulfilled inthe future? If not, it becomes plain that we have no ground whatever forexpecting the sun to rise to-morrow, or for expecting the bread we shalleat at our next meal not to poison us, or for any of the other scarcelyconscious expectations that control our daily lives. It is to be observedthat all such expectations are only probable; thus we have not toseek for a proof that they must be fulfilled, but only for somereason in favour of the view that they are likely to be fulfilled.

　　Now in dealing with this question we must, to begin with, make animportant distinction, without which we should soon become involved inhopeless confusions. Experience has shown us that, hitherto, the frequentrepetition of some uniform succession or coexistence has been a causeof our expecting the same succession or coexistence on the next occasion.Food that has a certain appearance generally has a certain taste, and itis a severe shock to our expectations when the familiar appearance isfound to be associated with an unusual taste. Things which we see becomeassociated, by habit, with certain tactile sensations which we expect ifwe touch them; one of the horrors of a ghost (in many ghost-stories) isthat it fails to give us any sensations of touch. Uneducated people who goabroad for the first time are so surprised as to be incredulous when theyfind their native language not understood.

　　And this kind of association is not confined to men; in animals also it isvery strong. A horse which has been often driven along a certain roadresists 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 liable tobe misleading. The man who has fed the chicken every day throughout itslife at last wrings its neck instead, showing that more refined views asto the uniformity of nature would have been useful to the chicken.

　　But in spite of the misleadingness of such expectations, they neverthelessexist. The mere fact that something has happened a certain number of timescauses animals and men to expect that it will happen again. Thus ourinstincts certainly cause us to believe that the sun will rise to-morrow,but we may be in no better a position than the chicken which unexpectedlyhas its neck wrung. We have therefore to distinguish the fact that pastuniformities cause expectations as to the future, from the questionwhether there is any reasonable ground for giving weight to suchexpectations after the question of their validity has 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 in theuniformity of nature is the belief that everything that has happened orwill happen is an instance of some general law to which there are noexceptions. The crude expectations which we have been considering are allsubject 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. But thelaws of motion and the law of gravitation, which account for the fact thatmost bodies fall, also account for the fact that balloons and aeroplanescan rise; thus the laws of motion and the law of gravitation are notsubject 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 not beinfringed by such an event. The business of science is to finduniformities, such as the laws of motion and the law of gravitation, towhich, so far as our experience extends, there are no exceptions. In thissearch science has been remarkably successful, and it may be conceded thatsuch uniformities have held hitherto. This brings us back to the question:Have we any reason, assuming that they have always held in the past, tosuppose 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 formerly future,which we may call past futures. But such an argument really begs the veryquestion at issue. We have experience of past futures, but not of futurefutures, and the question is: Will future futures resemble past futures?This question is not to be answered by an argument which starts from pastfutures alone. We have therefore still to seek for some principle whichshall enable us to know that the future will follow the same laws as thepast.

　　The reference to the future in this question is not essential. The samequestion arises when we apply the laws that work in our experience to pastthings 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, suffice toprove demonstratively that they will be found together in the nextcase we examine. The most we can hope is that the oftener things are foundtogether, the more probable it becomes that they will be found togetheranother time, and that, if they have been found together often enough, theprobability will amount almost to certainty. It can never quitereach certainty, because we know that in spite of frequent repetitionsthere sometimes is a failure at the last, as in the case of the chickenwhose neck is wrung. Thus probability is all we ought to seek.

　　It might be urged, as against the view we are advocating, that we know allnatural phenomena to be subject to the reign of law, and that sometimes,on the basis of observation, we can see that only one law can possibly fitthe facts of the case. Now to this view there are two answers. The firstis that, even if some law which has no exceptions applies to ourcase, we can never, in practice, be sure that we have discovered that lawand not one to which there are exceptions. The second is that the reign oflaw would seem to be itself only probable, and that our belief that itwill hold in the future, or in unexamined cases in the past, is itselfbased upon the very principle we are examining.

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

　　(a) When a thing of a certain sort A has been found to be associated witha thing of a certain other sort B, and has never been found dissociatedfrom a thing of the sort B, the greater the number of cases in which A andB have been associated, the greater is the probability that they will beassociated in a fresh case in which one of them is known 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, whereas theparticular 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 it is(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. Inour case, the data are merely the known cases of coexistence of A and B.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 the data itwas 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 of thefact that some data render it improbable. In the case of the swans, a manmight know that colour is a very variable characteristic in many speciesof animals, and that, therefore, an induction as to colour is peculiarlyliable to error. But this knowledge would be a fresh datum, by no meansproving that the probability relatively to our previous data had beenwrongly estimated. The fact, therefore, that things often fail to fulfilour expectations is no evidence that our expectations will not probablybe fulfilled in a given case or a given class of cases. Thus our inductiveprinciple is at any rate not capable of being disproved by anappeal to experience.

　　The inductive principle, however, is equally incapable of being provedby an appeal to experience. Experience might conceivably confirm theinductive principle as regards the cases that have been already examined;but as regards unexamined cases, it is the inductive principle alone thatcan justify any inference from what has been examined to what has not beenexamined. All arguments which, on the basis of experience, argue as to thefuture or the unexperienced parts of the past or present, assume theinductive principle; hence we can never use experience to prove theinductive principle without begging the question. Thus we must eitheraccept the inductive principle on the ground of its intrinsic evidence, orforgo all justification of our expectations about the future. If theprinciple is unsound, we have no reason to expect the sun to riseto-morrow, to expect bread to be more nourishing than a stone, or toexpect that if we throw ourselves off the roof we shall fall. When we seewhat looks like our best friend approaching us, we shall have no reason tosuppose that his body is not inhabited by the mind of our worst enemy orof some total stranger. All our conduct is based upon associations whichhave worked in the past, and which we therefore regard as likely to workin the future; and this likelihood is dependent for its validity upon theinductive principle.

　　The general principles of science, such as the belief in the reign of law,and the belief that every event must have a cause, are as completelydependent upon the inductive principle as are the beliefs of daily lifeAll such general principles are believed because mankind have foundinnumerable instances of their truth and no instances of their falsehood.But this affords no evidence for their truth in the future, unless theinductive 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 experience canneither confirm nor confute, yet which, at least in its more concreteapplications, appears to be as firmly rooted in us as many of the facts ofexperience. The existence and justification of such beliefs—for theinductive principle, as we shall see, is not the only example—raisessome of the most difficult and most debated problems of philosophy. Wewill, in the next chapter, consider briefly what may be said to accountfor such knowledge, and what is its scope and its degree of certainty.