sign in sign up
<<
Home , Bertrand Russell

Skill Module On Induction: A Discussion of Hume and Russell’s View on

Introductory Note: This will only be entertaining if the discussion includes students who are on both sides of the fence on this issue. As this will be labeled under , I would like to encourage science majors to make this one of their skill modules.

The purpose of this skill module is many: to become acquainted with philosophical jargon, to be introduced to two prolific , to practice thinking abstractly, arguing, and criticizing abstract .

In this Skill module, portions of the enlightened ’s Enquiry Concerning Human Understanding and arguably the most influential ’s (no, influential and philosopher do not form an oxymoron) – – The Problems of will be discussed. Specifically, how reasonable using induction as a solid form of finding is looked at. Questioning empiricism and at least aware of its flaws (or perhaps what you believe are perceived flaws) can be quite insightful, especially to scientists - who use empiricism every they use the .

Task 1: Read both excerpts from David Hume and Bertrand Russell (found in that order below). If you don’t know a word, look it up. In order to competently complete Task 2, knowing all of the jargon in both articles will be necessary. Ignore Russell’s talk about sense-data at the very beginning – unless you want to read the first chapter of his book.

Task 2: A date will be to discuss/argue what was read for 1-2 hours, at an interesting location. This will give you an of what it is like to be a graduate student of philosophy at a bar. The group will be no larger than 6 people, including an UGTA moderator. Each student will contribute significantly to the discussion/debate.

Enquiry Concerning Human Understanding1 By David Hume

Section 4: Sceptical doubts about the operations of the understanding Part 1

All the objects of human reason or enquiry fall naturally into two kinds, namely relatio ns of ideas and matters of . The first kind include geome‐try, algebra, and arithmeti c, and indeed every that is either intui‐tively or demonstratively certain. That the square of the hypotenuse is equal to the squares of the other two sides expresses a re lation between those figures. That three five equals half of thirty expresses a relati on between those . of this kind can be discovered purely by thinki ng, with no need to attend to anything that actually exists anywhere in the uni‐verse. Th e that demonstrated would still be certain and self‐ evident even if there n ever were a circle or triangle in .

Matters of fact, which are the second objects of human reason, are not estab‐lished in th e same way; and we cannot have such strong grounds for think‐ing them true. The cont rary of every of fact is still possible, because it doesn’t imply a contradiction and is conceived by the as easily and clearly as if it conformed perfectly to relity. That the sun will not rise tomorrow is just as intelligible as ‐ and no more contradictory than ‐ the that the sun will rise tomorrow. It would therefore be a waste of time t o try to demonstrate [= ‘prove absolutely rigorously’] its falsehood. If it were demon‐str atively false, it would imply a contradiction and so could never be clearly conceived by the mind.

1 This document has been excerpted by Kevan Edwards, with permission, from a manuscript tra nslated and edited by Jonathan Bennett. Bennett’s translations of this and other early modern te xts can be found online at: http://www.earlymoderntexts.com. Bennett uses square [brackets] to enclose edito‐rial explanations and small ∙dots∙ to indicate material that has been added to the o riginal text, but can be read as though it were part of the original text. The present editor has als o used square brackets to indicate omissions of material from Bennett’s text ([...]). Bennett inden ts some passages that are not quotations in order to facili‐tate comprehension of the text. The pr esent editor has added a paragraph break and has put several important terms and passages in bold font. 1 So it may be worth our time and trouble to try to answer this: What sorts of grounds do we have for being sure of matters of fact ‐ propositions about what exists and what is th e case ‐ that are not attested by our present senses or the records of our memory? [...]

All reasonings about matters of fact seem to be based on the relation of cause and effect, which is the only relation that can take us beyond the of our memory and sen ses. If you ask someone why he some matter of fact which is not now present to him ‐ for instance that his friend is now in France ‐ he will give you a reason; and this r eason will be some other fact, such as that he has received a letter from his friend or that his friend had planned to go to France. Someone who finds a watch or other machine o n a desert island will conclude that there have been men on that island. All our reasonin gs concerning fact are like this. When we reason in this way, we suppose that the presen t fact is connected with the one that we infer from it. If there were to bind the t wo together, the inference of one from the other would be utterly shaky. [...]

So if we want to understand the basis of our confidence about matters of fact, we must f ind out how we come to know about cause and effect.

I venture to assert, as true without exception, that about causes is never acq uired through a priori reasoning, and always comes from our ex‐perience of finding tha t particular objects are constantly associated with one other. [When Hume is discussing cause and effect, his word ‘’ often covers events as well as things.] Present an obje ct to a man whose skill and are as great as you like; if the object is of a kind t hat is entirely new to him, no amount of studying of its perceptible qualities will enable him to discover any of its causes or effects. Adam, even if his reasoning abili‐ties were p erfect from the start, could not have inferred from the fluidity and transparency of wate r that it could drown him, or from the light and warmth of that it could burn him. T he qualities of an object that appear to the senses never reveal the causes that produced the object or the effects that it wll have; nor can our reason, unaided by , ever draw any conclu‐sion about real and matters of fact.

The proposition that causes and effects are discoverable not by reason but by ex‐perienc e will be freely granted (1) with regard to objects that we remember having once been al together unknown to us; for in those cases we remember the time when we were quite u nable to tell what would arise from those ob‐jects. Present two smooth pieces of marble to a man who has no knowledge 2 of ‐ he will not be able to work out that they will stick together in such a way th at it takes great force to separate them by pullng them directly away from one another, while it will be easy to slide them apart. (2) Events that are not much like the common c ourse of nature are also readily agreed to be known only by experience; and nobody thi nks that the explosion of gunpowder, or the attraction of a magnet, could ever be discov ered by ar‐guments a priori ‐ ∙that is, by simply thinking about the matter, without brin ging in anything known from experience∙. (3) Similarly, when an effect is to de pend on an intricate machinery or secret structure of parts we don’t hesitate to attribute all ur knowledge of it to experience. No‐one would assert that he can give the ultimate r eason why milk or bread is nour‐ishing for a man but not for a lion or a tiger.

[...]

If you are not yet convinced that absolutely all the laws of nature and opera‐tions of bod ies can be known only by experience, consider the following. If we are asked to say wha t the effects will be of some object, without consult‐ing past experience of it, how can th e mind go about doing this? It must in‐vent or imagine some event as being the object’s effect; and clearly this in‐vention must be entirely arbitrary. The mind can’t possibly fin d the effect in the supposed cause, however carefully we examine it, for the effect is tota lly different from the cause and therefore can never be discovered in it. in the se cond billiard ball is a distinct event from motion in the first, and nothing in the first ball’ s motion even hints at motion in the second. A stone raised into the air and left without any support immediately falls; but if we consider this situation a priori we shall find not hing that generates the idea of a downward rather than an upward o some other motion in the stone.

[...]

In short, every effect is a distinct event from its cause. So it can’t be discov‐ered in the ca use, and the first invention or conception of it a priori must be wholly arbitrary. Further more, even after it has been suggested, the linking of it with the cause must still appear as arbitrary, because plenty of other possible effects must seem just as consistent and na tural from reason’s point of view. So there isn’t the slightest hope of reaching any concl usions about causes and effects without the help of experience.

[...] 3 Part 2 (of Section 4)

But we haven’t yet found an acceptable answer to the question that I initially asked. Eac h solution raises new questions that are as hard to answer as the first one was, and that l ead us on to further enquiries. To the question, What is the nature of all our reasonings concerning matter of fact? the proper answer seems to be that they are based on the rela tion of cause and effect. When it is further asked, What is the foundation of all our reaso nings about cause and effect? we can answer in one word, experience. But if we persist with questions, and ask, What are inferences from experience based on? this raises a ne w question that may be harder still. [...]

In this section I shall settle for something easy, offering only a negative an‐swer to the q uestion I have raised ∙about what inferences from experience are based on∙. It is this: eve n after we have experience of the operations of cause and effect, the conclusions we dra w from that experience are not based on reasoning or on any process of the understan ding. I shall try to explain and defend this answer.

[...] All that past experience can tell us, directly and for sure, concerns the behaviour of t he particular objects we observed, at the particular time when we observed them. ∙My e xperience directly and certainly informs me that that fire consumed coal then; but it is si lent about the behaviour of the same fire a few minutes later, and about other fires at an y time∙. Why should this experience be extended to future times and to other objects, w hich for all we know may only seem similar? ‐ that is what I want to know. The bread th at I formerly ate nourished me; that is, a body with such and such sensible quali‐ties did at that time have such and such secret powers. [By ‘sensible qualities’ Hume means pro perties that can be directly experienced with the senses.] But does it follow that other br ead must also nourish me at other times, and that the same perceptible qualities must al ways be accompanied by the same secret powers? It does not seem to follow necessarily . Anyway, it must be admitted that in such a case as this the mind draws a conclusion; it takes a certain step, goes through a process of thought or inference, which needs to be e xplained. These two propositions are far from being the same:

I have found that such and such an object has always had such and such an effect .

I foresee that other objects which appear similar will have similar ef‐fects.

4 The second proposition is always inferred from the first; and if you wish I shall grant th at it is rightly inferred. But if you insist that the inference is made by a chain of reasonin g, I challenge you to produce the reasoning. The connection between these propositions is not intuitive [that is, the second does not self‐evidently and immediately follow from the first]. If the inference is to be conducted through reason alone, it must be with help f rom some in‐termediate step. But when I try to think what that intermediate step might be, I am defeated. Those who assert that it really exists and is the origin of all our conclu sions about matters of fact owe us an account of wha it is.

∙They haven’t given any account of this, which I take to be evidence that none can be gi ven∙. If many penetrating and able philosophers try and fail to discover a connecting pr oposition or intermediate step through whichthe understanding can perform this infere nce from past effects to future ones, my negative of thought about this will eventual ly be found entirely con‐vincing. But as the question is still new, the reader may not trus t his own abilities enough to conclude that because he can’t find a certain argument it d oesn’t exist. In that case I need to tackle a harder task than I have so far un‐dertaken ‐ na mely, going through all the branches of human knowledge one by one, trying to show t hat none can give us such an argument.

All reasonings fall into two kinds: (1) demonstrative reasoning, or that con‐cerning relat ions of ideas, and (2) factual reasoning, or that concerning mat‐ters of fact and existence. That no demonstrative arguments are involved in (2) seems evident; since there is no o utright contradiction in supposing that the course of nature will change so that an object that seems like nes we have experienced will have different or contrary effects from the irs. Can’t I clearly and distinctly conceive that snowy stuff falling from the clouds might taste salty or feel hot? Is there anything unintelligible about supposing that all the trees will flourish in December and lose their leaves in June? Now, if something is intelligible and can be distinctly conceived, it implies no con‐tradiction and can never be proved fa lse by any demonstrative argument or abstract a priori reasoning.

So if there are arguments to justify us in trusting past experience and making it the stan dard of our future judgment, these arguments must concern mat‐ters of fact and real exi stence, to put it in terms of the classification I have given. But reasoning about matters o f fact, if I have described it accurately, can’t provide us with the argument we are lookin g for. According to my ac‐count, all arguments about existence are based on the relati on of cause and 5 effect; our knowledge of that relation is derived entirely from experience; and in dra wing conclusions from experience we assume that the future will be like the past. So if we try to prove this assumption by [reasoning based on matters of fact], i.e. argume nts regarding existence, we shall ob‐viously be going in a circle, taking for granted th e very point that is in question.2

[...]

[...] All inferences from experience are based on the assumption that the fu‐ture will rese mble the past, and that similar powers will be combined with similar sensible qualities. As soon as the suspicion is planted that the course of nature may change, so that the pas t stops being a guide to the future, all experience becomes useless and can’t support any inference or conclusion. So no arguments from experience can support this resemblanc e of the past to the future, because all such arguments are based on the assumption of th at resemblance. However regular the course of things has been, that fact on its own does n’t prove that the future will also be regular.

It’s no use your claiming to have learned the nature of bodies from your past experience . Their secret nature, and consequently all their effects and influ‐ence, may change with out any change in their sensible qualities. This hap‐pens sometimes with regard to some objects: Why couldn’t it happen always with regard to all? What , what process of argument, secures you against this? You may say that I don’t behave as though I had do ubts about this; but that would reflect a misunderstanding of why I am raising these qu estions. When I am considering how to act, I am quite satisfied that the fu‐ture will be li ke the past; but as a philosopher with an enquiring ‐ I won’t say sceptical ‐ turn of mind, I want to know what this confidence is based on. Nothing I have read, no research I ha ve done, has yet been able to remove my difficulty. Can I do better than to put the diffic ulty before the public, even though I may not have much hope of being given a solution ? In this way we shall at least be aware of our ignorance, even if we don’t increase our k nowledge.

It would be inexcusably arrogant to conclude that because I haven’t discov‐ered a certai n argument it doesn’t really exist. Even if learned men down the

2 The present editor has made several minor omissions/modifications in this para‐graph that are not indicated with parentheses. 6 centuries have searched for something without finding it, perhaps it would still be rash to conclude with confidence that the must surpass human understanding. Even t hough we examine all the sources of our knowledge and conclude that they are unfit for a given subject, we may still suspect that the list of sources is not complete or our exami nation of them not accurate. With regard to our present subject, however, there are reas ons to think that my conclusion is certainly right and that I am not arrogant in thinking so.

[...]

Section 5: Sceptical solution of these doubts Part 1

Suppose that a highly intelligent and thoughtful person were suddenly brought into thi s world; he would immediately observe one event following another, but that is all he c ould discover. He would not be able by any rea‐soning to reach the idea of cause and eff ect, because (firstly) the particular powers by which all natural operations are performe d are never perceived through the senses, and (secondly) there is no reason to conclude that one event causes another merely because it precedes it. Their occurring together ma y be arbitrary and casual, with no causal connection between them. In short, until such a person had more experience he could never reason about any matter of fact, or be sure of anything beyond what was immediately pre‐sent to his memory and senses.

Now suppose that our person gains more experience, and lives long enough in the worl d to observe similar objects or events occurring together con‐stantly; now what conclusi on does he draw from this experience? He imme‐diately infers the existence of one objec t from the appearance of the other! Yet all his experience has not given him any idea or knowledge of the secret power by which one object produces another; nor can any proc ess of reason‐ing have led him to draw this inference. But he finds that he can’t help dra w‐ing it: and he will not be swayed from this even if he becomes convinced that there is no support for the inference. Something else is at work, compelling him to g o through with it.

It is custom or habit. When we are inclined to behave or think in some way, not because it can be justified by reasoning or some process of the under‐standing but just because we have behaved or thought like that so often in the past, we always say that this inclin ation is the effect of ‘custom’. In using 7 that word we don’t claim to give the basic reason for the inclination. All we are doing is to point out a fundamental feature of human nature which eve‐ryone agrees is there, an d which is well known by its effects. Perhaps that is as far as we can go. Perhaps, that is, we can’t discover the cause of this cause, and must rest content with it as the deepest w e can go in explaining our con‐clusions from experience. Our ability to go that far shoul d satisfy us; we oughtn’t to complain about the narrowness of our faculties because they won’t take us any further. We do at least have here a very intelligible propo‐sition and perhaps a true one: After the constant conjunction of two objects ‐ heat and flame, for in stance, or weight and solidity ‐ sheer habit makes us expect the one when we experience the other. Indeed, this hypothesis seems to be the only one that could explain why we d raw from a thousand instances an inference which we can’t raw from a single one that is exactly like each of the thou‐sand. Reason isn’t like that. The conclusions it draws from considering one circle are the same as it would form after surveying all the circles in the uni‐verse. But no man, having seen only one body move after being pushed by another, could infer that every other body will move after a similar collision. All inferences from experience, therefore, are effects of custom and not of reasoning.

[...]

What are we to conclude from all this? Something that is far removed from the common of philosophy, yet is very simple:

All beliefs about matters of fact or real existence are derived merely from someth ing that is present to the memory or senses, and a customary association of that with some other thing.

Or in other words: having found in many cases that two kinds of objects ‐ flame and hea t, snow and cold ‐ have always gone together, and being pre‐sented with a new instance of flame or snow, the mind’s habits lead it to ex‐pect heat or cold and to believe that he at or cold exists now and will be ex‐perienced if one comes closer. This is the inevi table result of placing the mind in such circumstances. That our should react in t hat way in those circumstances is as unavoidable as that we should feel when we r eceive bnefits, or hatred when we are deliberately harmed. These opera‐tions of the are a kind of natural instinct, which no reasoning or process of the thought and underst anding can either produce or prevent. Bertrand Russell: The Problems of Philosophy (1912) Graciously provided by (www.gutenberg.org) CHAPTER VI ON INDUCTION In all our previous discussions we have been concerned in the attempt to get clear as to our data in the way of knowledge of existence. What things are there in the whose existence is known to us owing to our being acquainted with them? So far, our answer has been that we are acquainted with our sense-data, and, probably, with ourselves. These we know to exist. And past sense-data which are remembered are known to have existed in the past. This knowledge supplies our data. But if we are to be able to draw inferences from these data--if we are to know of the existence of matter, of other people, of the past before our individual memory begins, or of the future, we must know general 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 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, for example, thunder is a sign of the earlier existence of lightning. If this were not known to us, we could never extend our knowledge beyond the sphere of our private experience; and this sphere, as we have seen, is exceedingly limited. The question we have now to consider is whether such 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 rise to-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 find a test by which to judge whether a belief of this kind is reasonable or not, but we can at least ascertain what sort of general beliefs would suffice, if true, to justify the judgement that the sun will rise to-morrow, and the many other similar judgements upon which our actions are based. It is obvious that if we are asked why we believe that the sun will rise to-morrow, we shall naturally answer 'Because it always has risen every day'. We have a firm belief that it will rise in the future, because it has risen in the past. If we are challenged as to why we believe that it will 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 not cease to rotate unless something interferes from outside, and there is nothing outside to interfere with the earth between now and to-morrow. Of course it might be doubted whether we are quite certain that there is nothing outside to interfere, but this is not the interesting doubt. The interesting doubt is as to whether the laws of motion will remain in operation until to-morrow. If this doubt is raised, we find ourselves in the same position as when the doubt about the sunrise was first raised. The _only_ reason for believing that the laws of motion will remain in operation is that they have operated hitherto, so far as our knowledge of the past enables us to judge. It is true that we have a greater body of evidence from the past in favour of the laws of motion than we have in favour of the sunrise, because the sunrise is merely a particular case of fulfilment of the laws of motion, and there are countless other particular cases. But question is: Do _any_ of cases of a law being fulfilled in the past afford evidence that it will be fulfilled in the future? If not, it becomes plain that we have no ground whatever for expecting the sun to rise to-morrow, or for expecting the bread we shall eat at our next meal not to poison us, or for any of the other scarcely conscious expectations that control our daily lives. It is to be observed that all such expectations are only _probable_; thus we have not to seek for a that they _must_ be fulfilled, but only for some reason in favour of the view that they are _likely_ to be fulfilled. Now in dealing with this question we must, to begin with, make an important distinction, without which we should soon become involved in hopeless confusions. Experience has shown us that, hitherto, the frequent repetition of some uniform succession or coexistence has been a _cause_ of our expecting the same succession or coexistence on the next occasion. Food that has a certain appearance generally has a certain taste, and it is a severe shock to our expectations when the familiar appearance is found to be associated with an unusual taste. Things which we see become associated, by habit, with certain tactile sensations which we expect if we touch them; one of the horrors of a ghost (in many 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 as to be incredulous when they find their native not understood. And this kind of association is not confined to men; in animals also it is very strong. A horse which has been often driven along a certain road resists the attempt to drive him in a different direction. Domestic animals expect food when they see the person who usually feeds them. We know that all these rather crude expectations of uniformity are liable to be misleading. The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken. But in spite of the misleadingness of such expectations, they nevertheless exist. The mere fact that something has happened a certain number of times causes animals and men to expect that it will happen again. Thus our instincts 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 unexpectedly has its neck wrung. We have therefore to distinguish the fact that past uniformities _cause_ expectations as to the future, from the question whether there is any reasonable ground for giving weight to such expectations after the question of their validity has been raised. The problem we have to discuss is whether there is any reason for believing in what is called 'the uniformity of nature'. The belief in the uniformity of nature is the belief that everything that has happened or will happen is an instance of some general law to which there are no exceptions. The crude expectations which we have been considering are all subject to exceptions, and therefore liable to disappoint those who entertain them. But science habitually assumes, at least as a , that general rules which have exceptions can be replaced by general rules which have no exceptions. 'Unsupported bodies in air fall' is a general rule to which balloons and aeroplanes are exceptions. But the laws of motion and the law of gravitation, which account for the fact that most bodies fall, also account for the fact that balloons and aeroplanes can rise; thus the laws of motion and the law of gravitation are not subject to these exceptions. The belief that the sun will rise to-morrow might be falsified if the earth came suddenly into contact with a large body which destroyed its rotation; but the laws of motion and the law of gravitation would not be infringed by such an event. The business of science is to find uniformities, 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 be conceded that such uniformities have held hitherto. This brings us back to the question: Have we any reason, assuming that they have always held in the past, to suppose that they will hold in the future? It has been argued that we have reason to know that the future will resemble the past, because what was the future has constantly become the past, and has always been found to resemble the past, so that we really have experience of the future, namely of times which were formerly future, which we may call past futures. But such an argument really begs the very question at issue. We have experience of past futures, but not of future futures, and the question is: Will future futures resemble past futures? This question is not to be answered by an argument which starts from past futures alone. We have therefore still to seek for some which shall enable us to know that the future will follow the same laws as the past. The reference to the future in this question is not essential. The same question arises when we apply the laws that work in our experience to past 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 we really have to ask is: 'When two things have been found to be often associated, and no instance is known of the one occurring without the other, does the occurrence of one of the two, in a fresh instance, give any good ground for expecting the other?' On our answer to this question must depend the validity of the whole of our expectations as to the future, the whole of the results obtained by induction, and in fact practically all the beliefs upon which our daily life is based. It must be conceded, to begin with, that the fact that two things have been found often together and never apart does not, by itself, suffice to _prove_ demonstratively that they will be found together in the next case we examine. The most we can hope is that the oftener things are found together, the more probable it becomes that they will be found together another time, and that, if they have been found together often enough, the probability will amount _almost_ to certainty. It can never quite reach certainty, because we know that in spite of frequent repetitions there sometimes is a failure at the last, as in the case of the chicken whose 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 all natural phenomena to be subject to the reign of law, and that sometimes, on the basis of , we can see that only one law can possibly fit the facts of the case. Now to this view there are two answers. The first is that, even if _some_ law which has no exceptions applies to our case, we can never, in practice, be sure that we have discovered that law and not one to which there are exceptions. The second 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 unexamined cases in the past, is itself based 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 with a thing of a certain other sort B, and has never been found dissociated from a thing of the sort B, the greater the number of cases in which A and B have been associated, the greater is the probability that they will be associated in a fresh case in which one of them is known to be present; (b) Under the same circumstances, a sufficient number of cases of association will make the probability of a fresh association nearly a certainty, and will make it approach certainty without limit. As just stated, the principle applies only to the verification of our expectation in a single fresh instance. But we want also to know that there is a probability in favour of the general law that things of the sort A are _always_ associated with things of the sort B, provided a sufficient number of cases of association are known, and no cases of failure of association are known. The probability of the general law is obviously less than the probability of the particular case, since if the general law is true, the particular case must also be true, whereas the particular case may be true without the general law being true. Nevertheless the probability of the general law is increased by repetitions, just as the probability of the particular case is. We may therefore repeat the two parts of our principle as regards the general law, thus: (a) The greater the number of cases in which a thing of the sort A has been 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 always associated with B; (b) Under the same circumstances, a sufficient number of cases of the association of A with B will make it nearly certain that A is always associated with B, and will make this general law approach certainty without 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 and B. There may be other data, which _might_ be taken into account, which would gravely alter the probability. For example, a man who had seen a great many white swans might argue, by our principle, that on the data it was _probable_ that all swans were white, and this might be a perfectly sound argument. The argument is not disproved ny the fact that some swans are black, because a thing may very well happen in spite of the 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 many species of animals, and that, therefore, an induction as to colour is peculiarly liable to error. But this knowledge would be a fresh datum, by no means proving that the probability relatively to our previous data had been wrongly estimated. The fact, therefore, that things often fail to fulfil our expectations is no evidence that our expectations will not _probably_ be fulfilled in a given case or a given of cases. Thus our 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 confirm the inductive principle as regards the cases that have been already examined; but as regards unexamined cases, it is the inductive principle alone that can justify any inference from what has been examined to what has not been examined. All arguments which, on the basis of experience, argue as to the future or the unexperienced parts of the past or present, assume the inductive principle; hence we can never use experience to prove the inductive principle without begging the question. Thus we must either accept the inductive principle on the ground of its intrinsic evidence, or forgo all justification of our expectations about the future. If the principle is unsound, we have no reason to expect the sun to rise to-morrow, to expect bread to be more nourishing than a stone, or to expect that if we throw ourselves off the roof we shall fall. When we see what looks like our best friend approaching us, we shall have no reason to suppose that his body is not inhabited by the mind of our worst enemy or of some total stranger. All our conduct is based upon associations which have worked in the past, and which we therefore regard as likely to work in the future; and this likelihood is dependent for its validity upon the inductive 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 completely dependent upon the inductive principle as are the beliefs of daily life All such general principles are believed because mankind have found innumerable instances of their truth and no instances of their falsehood. 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 something about what is not experienced, is based upon a belief which experience can neither confirm nor confute, yet which, at least in its more concrete applications, appears to be as firmly rooted in us as many of the facts of experience. The existence and justification of such beliefs--for the inductive principle, as we shall see, is not the only example--raises some of the most difficult and most debated problems of philosophy. We will, in the next chapter, consider briefly what may be said to account for such knowledge, and what is its scope and its degree of certainty.