Our Knowledge of the External World

„…something different is required if philosophy is to become a science, and to aim at results independent of the tastes and temperament of the philosopher who advocates them.”

„The speculations of the past as to the reality or unreality of the world of physics were baffled, at the outset, by the absence of any satisfactory theory of the mathematical infinite. This difficulty has been removed by the work of Georg Cantor.”

„Since my purpose was to illustrate method, I have included much that is tentative and incomplete, for it is not by the study of finished structures alone that the manner of construction can be learnt.”

„there is more likelihood of error in a very subtle, abstract, and difficult argument than in so patent a fact as the interrelatedness of the things in the world.”

„The barbaric substratum of human nature, unsatisfied in action, finds an outlet in imagination.”

„it is time to remember that biology is neither the only science, nor yet the model to which all other sciences must adapt themselves. Evolutionism, as I shall try to show, is not a truly scientific philosophy, either in its method or in the problems which it considers. The true scientific philosophy is something more arduous and more aloof, appealing to less mundane hopes, and requiring a severer discipline for its successful practice.”

„What biology has rendered probable is that the diverse species arose by adaptation from a less differentiated ancestry. This fact is in itself exceedingly interesting, but it is not the kind of fact from which philosophical consequences follow. Philosophy is general, and takes an impartial interest in all that exists. The changes suffered by minute portions of matter on the earth's surface are very important to us as active sentient beings; but to us as philosophers they have no greater interest than other changes in portions of matter elsewhere. And if the changes on the earth's surface during the last few millions of years appear to our present ethical notions to be in the nature of a progress, that gives no ground for believing that progress is a general law of the universe. Except under the influence of desire, no one would admit for a moment so crude a generalisation from such a tiny selection of facts. What does result, not specially from biology, but from all the sciences which deal with what exists, is that we cannot understand the world unless we can understand change and continuity.”

„The predominant interest of evolutionism is in the question of human destiny, or at least of the destiny of Life. It is more interested in morality and happiness than in knowledge for its own sake.”

„Knowledge concerning the future—which is the kind of knowledge that must be sought if we are to know about human destiny—is possible within certain narrow limits.”

„Philosophers have too often, in the past, permitted themselves to pronounce on empirical questions, and found themselves, as a result, in disastrous conflict with well-attested facts. We must, therefore, renounce the hope that philosophy can promise satisfaction to our mundane desires. What it can do, when it is purified from all practical taint, is to help us to understand the general aspects of the world and the logical analysis of familiar but complex things. Through this achievement, by the suggestion of fruitful hypotheses, it may be indirectly useful in other sciences, notably mathematics, physics, and psychology. But a genuinely scientific philosophy cannot hope to appeal to any except those who have the wish to understand, to escape from intellectual bewilderment. It offers, in its own domain, the kind of satisfaction which the other sciences offer. But it does not offer, or attempt to offer, a solution of the problem of human destiny, or of the destiny of the universe.”

„although fully developed mysticism is rare in the West, some tincture of it colours the thoughts of many people, particularly as regards matters on which they have strong convictions not based on evidence. In all who seek passionately for the fugitive and difficult goods, the conviction is almost irresistible that there is in the world something deeper, more significant, than the multiplicity of little facts chronicled and classified by science. Behind the veil of these mundane things, they feel, something quite different obscurely shimmers, shining forth clearly in the great moments of illumination, which alone give anything worthy to be called real knowledge of truth. To seek such moments, therefore, is to them the way of wisdom, rather than, like the man of science, to observe coolly, to analyse without emotion, and to accept without question the equal reality of the trivial and the important.”

„Instinct, intuition, or insight is what first leads to the beliefs which subsequent reason confirms or confutes; but the confirmation, where it is possible, consists, in the last analysis, of agreement with other beliefs no less instinctive. Reason is a harmonising, controlling force rather than a creative one. Even in the most purely logical realms, it is insight that first arrives at what is new. Where instinct and reason do sometimes conflict is in regard to single beliefs, held instinctively, and held with such determination that no degree of inconsistency with other beliefs leads to their abandonment. Instinct, like all human faculties, is liable to error. Those in whom reason is weak are often unwilling to admit this as regards themselves, though all admit it in regard to others. Where instinct is least liable to error is in practical matters as to which right judgment is a help to survival; friendship and hostility in others, for instance, are often felt with extraordinary discrimination through very careful disguises. But even in such matters a wrong impression may be given by reserve or flattery; and in matters less directly practical, such as philosophy deals with, very strong instinctive beliefs may be wholly mistaken, as we may come to know through their perceived inconsistency with other equally strong beliefs. “It is such considerations that necessitate the harmonising mediation of reason, which tests our beliefs by their mutual compatibility, and examines, in doubtful cases, the possible sources of error on the one side and on the other. In this there is no opposition to instinct as a whole, but only to blind reliance upon some one interesting aspect of instinct to the exclusion of other more commonplace but not less trustworthy aspects. It is such onesidedness, not instinct itself, that reason aims at correcting.”

„the ethical interests which have often inspired philosophers must remain in the background: some kind of ethical interest may inspire the whole study, but none must obtrude in the detail or be expected in the special results which are sought.”

„The modern physicist, on the contrary, though he has no wish to deny that the earth is admirable, is not concerned, as physicist, with its ethical attributes: he is merely concerned to find out facts, not to consider whether they are good or bad.”

„It is a commonplace that happiness is not best achieved by those who seek it directly; and it would seem that the same is true of the good. In thought, at any rate, those who forget good and evil and seek only to know the facts are more likely to achieve good than those who view the world through the distorting medium of their own desires.”

„the new facts have brought new powers; man's physical control over natural forces has been increasing with unexampled rapidity, and promises to increase in the future beyond all easily assignable limits. Thus alongside of despair as regards ultimate theory there is an immense optimism as regards practice: what man can do seems almost boundless. The old fixed limits of human power, such as death, or the dependence of the race on an equilibrium of cosmic forces, are forgotten, and no hard facts are allowed to break in upon the dream of omnipotence. No philosophy is tolerated which sets bounds to man's capacity of gratifying his wishes; and thus the very despair of theory is invoked to silence every whisper of doubt as regards the possibilities of practical achievement.”

„The philosophy, therefore, which is to be genuinely inspired by the scientific spirit, must deal with somewhat dry and abstract matters, and must not hope to find an answer to the practical problems of life. To those who wish to understand much of what has in the past been most difficult and obscure in the constitution of the universe, it has great rewards to offer—triumphs as noteworthy as those of Newton and Darwin, and as important in the long run, for the moulding of our mental habits. And it brings with it—as a new and powerful method of investigation always does—a sense of power and a hope of progress more reliable and better grounded than any that rests on hasty and fallacious generalisation as to the nature of the universe at large. Many hopes which inspired philosophers in the past it cannot claim to fulfil; but other hopes, more purely intellectual, it can satisfy more fully than former ages could have deemed possible for human minds.”

„The question which then arises is: What is the principle of inference by which we pass from past sunrises to future ones? The answer given by Mill is that the inference depends upon the law of causation. Let us suppose this to be true; then what is the reason for believing in the law of causation? There are broadly three possible answers: (1) that it is itself known a priori; (2) that it is a postulate; (3) that it is an empirical generalisation from past instances in which it has been found to hold. The theory that causation is known a priori cannot be definitely refuted, but it can be rendered very unplausible by the mere process of formulating the law exactly, and thereby showing that it is immensely more complicated and less obvious than is generally supposed. The theory that causation is a postulate, i.e. that it is something which we choose to assert although we know that it is very likely false, is also incapable of refutation; but it is plainly also incapable of justifying any use of the law in inference. We are thus brought to the theory that the law is an empirical generalisation, which is the view held by Mill.”

„A method of proof which, when used as directed, gives sometimes truth and sometimes falsehood—as the method of simple enumeration does—is obviously not a valid method, for validity demands invariable truth. Thus, if simple enumeration is to be rendered valid, it must not be stated as Mill states it. We shall have to say, at most, that the data render the result probable. Causation holds, we shall say, in every instance we have been able to test; therefore it probably holds in untested instances. There are terrible difficulties in the notion of probability, but we may ignore them at present. We thus have what at least may be a logical principle, since it is without exception. If a proposition is true in every instance that we happen to know of, and if the instances are very numerous, then, we shall say, it becomes very probable, on the data, that it will be true in any further instance. This is not refuted by the fact that what we declare to be probable does not always happen, for an event may be probable on the data and yet not occur. It is, however, obviously capable of further analysis, and of more exact statement. We shall have to say something like this: that every instance of a proposition[10] being true increases the probability of its being true in a fresh instance, and that a sufficient number of favourable instances will, in the absence of instances to the contrary, make the probability of the truth of a fresh instance approach indefinitely near to certainty. Some such principle as this is required if the method of simple enumeration is to be valid. But this brings us to our other question, namely, how is our principle known to be true? Obviously, since it is required to justify induction, it cannot be proved by induction; since it goes beyond the empirical data, it cannot be proved by them alone; since it is required to justify all inferences from empirical data to what goes beyond them, it cannot itself be even rendered in any degree probable by such data. Hence, if it is known, it is not known by experience, but independently of experience. I do not say that any such principle is known: I only say that it is required to justify the inferences from experience which empiricists allow, and that it cannot itself be justified empirically. A similar conclusion can be proved by similar arguments concerning any other logical principle. Thus logical knowledge is not derivable from experience alone, and the empiricist's philosophy can therefore not be accepted in its entirety, in spite of its excellence in many matters which lie outside logic.”

„Take (say) the series of propositions, “Socrates drank the hemlock,”

„Coleridge drank the hemlock,” “Coleridge drank opium,” “Coleridge ate opium.”

„this thing is round, and red, and so on.”

„this,” but a relation of “this” and “that.”

„Everyone knows that to read an author simply in order to refute him is not the way to understand him; and to read the book of Nature with a conviction that it is all illusion is just as unlikely to lead to understanding. If our logic is to find the common world intelligible, it must not be hostile, but must be inspired by a genuine acceptance such as is not usually to be found among metaphysicians.”

„As logicians, therefore, we may admit the possibility of the mystic's world, while yet, so long as we do not have his insight, we must continue to study the everyday world with which we are familiar. But when he contends that our world is impossible, then our logic is ready to repel his attack. And the first step in creating the logic which is to perform this service is the recognition of the reality of relations.”

„When it simply assigns a quality to a thing, it has only two constituents, the thing and the quality. When it consists of a relation between two things, it has three constituents, the things and the relation. When it consists of a relation between three things, it has four constituents, and so on. The constituents of facts, in the sense in which we are using the word “fact,”

„When we were discussing atomic facts, we saw that we should be able, theoretically, to infer all other truths by logic if we knew all atomic facts and also knew that there were no other atomic facts besides those we knew. The knowledge that there are no other atomic facts is positive general knowledge; it is the knowledge that “all atomic facts are known to me,” or at least “all atomic facts are in this collection”

„Philosophy may be approached by many roads, but one of the oldest and most travelled is the road which leads through doubt as to the reality of the world of sense.”

„Universal scepticism, though logically irrefutable, is practically barren; it can only, therefore, give a certain flavour of hesitancy to our beliefs, and cannot be used to substitute other beliefs for them.”

„the immediate facts perceived by sight or touch or hearing do not need to be proved by argument, but are completely self-evident. Psychologists, however, have made us aware that what is actually given in sense is much less than most people would naturally suppose, and that much of what at first sight seems to be given is really inferred. This applies especially in regard to our space-perceptions. For instance, we instinctively infer the “real”

„Psychologically, a belief may be called derivative whenever it is caused by one or more other beliefs, or by some fact of sense which is not simply what the belief asserts. Derivative beliefs in this sense constantly arise without any process of logical inference, merely by association of ideas or some equally extra-logical process. From the expression of a man's face we judge as to what he is feeling: we say we see that he is angry, when in fact we only see a frown. We do not judge as to his state of mind by any logical process: the judgment grows up, often without our being able to say what physical mark of emotion we actually saw. In such a case, the knowledge is derivative psychologically; but logically it is in a sense primitive, since it is not the result of any logical deduction.”

„Verification consists always in the occurrence of an expected sense-datum.”

„The assumption that sensible objects persist after they have ceased to be sensible—for example, that the hardness of a visible body, which has been discovered by touch, continues when the body is no longer touched—may be replaced by the statement that the effects of sensible objects persist, i.e. that what happens now can only be accounted for, in many cases, by taking account of what happened at an earlier time. Everything that one man, by his own personal experience, can verify in the account of the world given by common sense and physics, will be explicable by some such means, since verification consists merely in the occurrence of an expected sense-datum. But what depends upon testimony, whether heard or read, cannot be explained in this way, since testimony depends upon the existence of minds other than our own, and thus requires a knowledge of something not given in sense. “But before examining the question of our knowledge of other minds, let us return to the question of the thing-in-itself, namely, to the theory that what exists at times when we are not perceiving a given sensible object is something quite unlike that object, something which, together with us and our sense- organs, causes our sensations, but is never itself given in sensation. The thing-in-itself, when we start from common-sense assumptions, is a fairly natural outcome of the difficulties due to the changing appearances of what is supposed to be one object. It is supposed that the table (for example) causes our sense-data of sight and touch, but must, since these are altered by the point of view and the intervening medium, be quite different from the sense-data to which it gives rise.”

„Objects of sense are called “real”

„Each mind sees at each moment an immensely complex three- dimensional world; but there is absolutely nothing which is seen by two minds simultaneously. When we say that two people see the same thing, we always find that, owing to difference of point of view, there are differences, however slight, between their immediate sensible objects. (I am here assuming the validity of testimony, but as we are only constructing a possible theory, that is a legitimate assumption.) The three-dimensional world seen by one mind therefore contains no place in common with that seen by another, for places can only be constituted by the things in or around them. Hence we may suppose, in spite of the differences between the different worlds, that each exists entire exactly as it is perceived, and might be exactly as it is even if it were not perceived. We may further suppose that there are an infinite number of such worlds which are in fact unperceived. If two men are sitting in a room, two somewhat similar worlds are perceived by them; if a third man enters and sits between them, a third world, intermediate between the two previous worlds, begins to be perceived. It is true that we cannot reasonably suppose just this world to have existed before, because it is conditioned by the sense-organs, nerves, and brain of the newly arrived man; but we can reasonably suppose that some aspect of the universe existed from that point of view, though no one was perceiving it. The system consisting of all views of the universe perceived and unperceived, I shall call the system of “perspectives”; I shall confine the expression “private worlds”

„The minds of other people are among our data, in the very wide sense in which we used the word at first. That is to say, when we first begin to reflect, we find ourselves already believing in them, not because of any argument, but because the belief is natural to us. It is, however, a psychologically derivative belief, since it results from observation of people's bodies; and along with other such beliefs, it does not belong to the hardest of hard data, but becomes, under the influence of philosophic reflection, just sufficiently questionable to make us desire some argument connecting it with the facts of sense. The obvious argument is, of course, derived from analogy. Other people's bodies behave as ours do when we have certain thoughts and feelings; hence, by analogy, it is natural to suppose that such behaviour is connected with thoughts and feelings like our own. Someone says, “Look out!”

„Why should we suppose that, when ice melts, the water which replaces it is the same thing in a new form? Merely because this supposition enables us to state the phenomena in a way which is consonant with our prejudices. What we really know is that, under certain conditions of temperature, the appearance we call ice is replaced by the appearance we call water. We can give laws according to which the one appearance will be succeeded by the other, but there is no reason except prejudice for regarding both as appearances of the same substance. One task, if what has just been said is correct, which confronts us in trying to connect the world of sense with the world of physics, is the task of reconstructing the conception of matter without the a priori beliefs which historically gave rise to it. In spite of the revolutionary results of modern physics, the empirical successes of the conception of matter show that there must be some legitimate conception which fulfils roughly the same functions. The time has hardly come when we can state precisely what this legitimate conception is, but we can see in a general way what it must be like. For this purpose, it is only necessary to take our ordinary common-sense statements and reword them without the assumption of permanent substance. We say, for example, that things change gradually—sometimes very quickly, but not without passing through a continuous series of intermediate states. What this means is that, given any sensible appearance, there will usually be, if we watch, a continuous series of appearances connected with the given one, leading on by imperceptible gradations to the new appearances which common-sense regards as those of the same thing.”

„For a proposition to be verifiable, it is not enough that it should be true, but it must also be such as we can discover to be true. Thus verifiability depends upon our capacity for acquiring knowledge, and not only upon the objective truth.”

„different senses have different spaces. The space of sight is quite different from the space of touch: it is only by experience in infancy that we learn to correlate them. In later life, when we see an object within reach, we know how to touch it, and more or less what it will feel like; if we touch an object with our eyes shut, we know where we should have to look for it, and more or less what it would look like. But this knowledge is derived from early experience of the correlation of certain kinds of touch-sensations with certain kinds of sight- sensations. The one space into which both kinds of sensations fit is an intellectual construction, not a datum. And besides touch and sight, there are other kinds of sensation which give other, though less important spaces: these also have to be fitted into the one space by means of experienced correlations. And as in the case of things, so here: the one all-embracing space, though convenient as a way of speaking, need not be supposed really to exist. All that experience makes certain is the several spaces of the several senses, correlated by empirically discovered laws. The one space may turn out to be valid as a logical construction, compounded of the several spaces, but there is no good reason to assume its independent metaphysical reality.”

„A relation is said to be “symmetrical”

„Mathematicians have distinguished different degrees of continuity, and have confined the word “continuous,”

„Every distance, however small, is traversed by passing through all the infinite series of positions between the two ends of the distance.”

„When any nerve is stimulated, so as to cause a sensation, the sensation does not cease instantaneously with the cessation of the stimulus, but dies away in a short finite time. A flash of lightning, brief as it is to our sight, is briefer still as a physical phenomenon: we continue to see it for a few moments after the light-waves have ceased to strike the eye. Thus in the case of a physical motion, if it is sufficiently swift, we shall actually at one instant see the moving body throughout a finite portion of its course, and not only at the exact spot where it is at that instant. Sensations, however, as they die away, grow gradually fainter; thus the sensation due to a stimulus which is recently past is not exactly like the sensation due to a present stimulus. It follows from this that, when we see a rapid motion, we shall not only see a number of positions of the moving body simultaneously, but we shall see them with different degrees of intensity—the present position most vividly, and the others with diminishing vividness, until sensation fades away into immediate memory. This state of things accounts fully for the perception of motion. A motion is perceived, not merely inferred, when it is sufficiently swift for many positions to be sensible at one time; and the earlier and later parts of one perceived motion are distinguished by the less and greater vividness of the sensations.”

„There can never be two facts concerning the same thing.”

„A space may be halved, and then halved again, and so on ad infinitum, and at every stage of the process the parts are still spaces, not points.”

„We saw that, accepting the view that a length is composed of points, the existence of incommensurables proves that every finite length must contain an infinite number of points. In other words, if we were to take away points one by one, we should never have taken away all the points, however long we continued the process. The number of points, therefore, cannot be counted, for counting is a process which enumerates things one by one. The property of being unable to be counted is characteristic of infinite collections, and is a source of many of their paradoxical qualities. So paradoxical are these qualities that until our own day they were thought to constitute logical contradictions. A long line of philosophers, from Zeno[28] to M. Bergson, have based much of their metaphysics upon the supposed impossibility of infinite collections. Broadly speaking, the difficulties were stated by Zeno, and nothing material was added until we reach Bolzano's Paradoxien des Unendlichen, a little work written in 1847–8, and published posthumously in 1851. Intervening attempts to deal with the problem are futile and negligible. The definitive solution of the difficulties is due, not to Bolzano, but to Georg Cantor, whose work on this subject first appeared in 1882.”

„The contention that time is unreal and that the world of sense is illusory must, I think, be regarded as based upon fallacious reasoning. Nevertheless, there is some sense—easier to feel than to state—in which time is an unimportant and superficial characteristic of reality. Past and future must be acknowledged to be as real as the present, and a certain emancipation from slavery to time is essential to philosophic thought. The importance of time is rather practical than theoretical, rather in relation to our desires than in relation to truth. A truer image of the world, I think, is obtained by picturing things as entering into the stream of time from an eternal world outside, than from a view which regards time as the devouring tyrant of all that is. Both in thought and in feeling, to realise the unimportance of time is the gate of wisdom. But unimportance is not unreality; and therefore what we shall have to say about Zeno's arguments in support of Parmenides must be mainly critical.”

„Consider, for example, all the fractions less than 1, arranged in order of magnitude. Between any two of them, there are others, for example, the arithmetical mean of the two. Thus no two fractions are consecutive, and the total number of them is infinite.”

„A single collection of three things might conceivably be described as “a plurality thought as held together and closed, and to that extent as a unity”

„There are two respects in which the infinite numbers that are known differ from finite numbers: first, infinite numbers have, while finite numbers have not, a property which I shall call reflexiveness; secondly, finite numbers have, while infinite numbers have not, a property which I shall call inductiveness. Let us consider these two properties successively. (1) Reflexiveness.—A number is said to be reflexive when it is not increased by adding 1 to it. It follows at once that any finite number can be added to a reflexive number without increasing it. This property of infinite numbers was always thought, until recently, to be self-contradictory; but through the work of Georg Cantor it has come to be recognised that, though at first astonishing, it is no more self-contradictory than the fact that people at the antipodes do not tumble off. In virtue of this property, given any infinite collection of objects, any finite number of objects can be added or taken away without increasing or diminishing the number of the collection.”

„The number of points is the same in a long line and in a short one, being in fact the same as the number of points in all space. The greater and less of metrical geometry involves the new metrical conception of congruence, which cannot be developed out of arithmetical considerations alone. But this question has not the fundamental importance which belongs to the arithmetical theory of infinity.”

„(2) Non-inductiveness.—The second property by which infinite numbers are distinguished from finite numbers is the property of non-inductiveness. This will be best explained by defining the positive property of inductiveness which characterises the finite numbers, and which is named after the method of proof known as “mathematical induction.”

„for example, the property of being greater than 99 is hereditary in the series of finite numbers; and generally, a property is hereditary in this series when, given any number that possesses the property, the next number must always also possess it. It will be seen that a hereditary property, though it must belong to all the finite numbers greater than a given number possessing the property, need not belong to all the numbers less than this number. For example, the hereditary property of being greater than 99 belongs to 100 and all greater numbers, but not to any smaller number. Similarly, the hereditary property of being called Jones belongs to all the descendants (in the direct male line) of those who have this property, but not to all their ancestors, because we reach at last a first Jones, before whom the ancestors have no surname. It is obvious, however, that any hereditary property possessed by Adam must belong to all men; and similarly any hereditary property possessed by 0 must belong to all finite numbers. This is the principle of what is called “mathematical induction.”

„The unity which philosophers rightly feel to be necessary for the assertion of a number is the unity of the general term, and it is the general term which is the proper subject of number. And this applies equally when there is one object or none which falls under the general term. “Satellite of the earth” is a term only applicable to one object, namely, the moon. But “one”

„In the third or fourth century B.C. there lived a Chinese philosopher named Hui Tzŭ, who maintained that “a bay horse and a dun cow are three; because taken separately they are two, and taken together they are one: two and one make three.”

„If the theory that classes are merely symbolic is accepted, it follows that numbers are not actual entities, but that propositions in which numbers verbally occur have not really any constituents corresponding to numbers, but only a certain logical form which is not a part of propositions having this form. This is in fact the case with all the apparent objects of logic and mathematics. Such words as or, not, if, there is, identity, greater, plus, nothing, everything, function, and so on, are not names of definite objects, like “John”

„Premisses are thus quite different from data—they are simpler, more precise, and less infected with logical redundancy.”

„A causal law, we said, allows us to infer the existence of one thing (or event) from the existence of one or more others. The word “thing”

„It is to be observed that what is constant in a causal law is not the object or objects given, nor yet the object inferred, both of which may vary within wide limits, but the relation between what is given and what is inferred. The principle, “same cause, same effect,”

„Since all known things are in time, a causal law must take account of temporal relations. It will be part of the causal law to state a relation of succession or coexistence between the thing given and the thing inferred. When we hear thunder and infer that there was lightning, the law states that the thing inferred is earlier than the thing given. Conversely, when we see lightning and wait expectantly for the thunder, the law states that the thing given is earlier than the thing inferred. When we infer a man's thoughts from his words, the law states that the two are (at least approximately) simultaneous. If a causal law is to achieve the precision at which science aims, it must not be content with a vague earlier or later, but must state how much earlier or how much later. That is to say, the time-relation between the thing given and the thing inferred ought to be capable of exact statement; and usually the inference to be drawn is different according to the length and direction of the interval. “A quarter of an hour ago this man was alive; an hour hence he will be cold.”

„Whenever things occur in certain relations to each other (among which their time-relations must be included), then a thing having a fixed relation to these things will occur at a date fixed relatively to their dates.”

„The first step is the discovery of approximate unanalysed uniformities of sequence or coexistence. After lightning comes thunder, after a blow received comes pain, after approaching a fire comes warmth; again, there are uniformities of coexistence, for example between touch and sight, between certain sensations in the throat and the sound of one's own voice, and so on. Every such uniformity of sequence or coexistence, after it has been experienced a certain number of times, is followed by an expectation that it will be repeated on future occasions, i.e. that where one of the correlated events is found, the other will be found also. The connection of experienced past uniformity with expectation as to the future is just one of those uniformities of sequence which we have observed to be true hitherto. This affords a psychological account of what may be called the animal belief in causation, because it is something which can be observed in horses and dogs, and is rather a habit of acting than a real belief. So far, we have merely repeated Hume, who carried the discussion of cause up to this point, but did not, apparently, perceive how much remained to be said.”

„What does seem, however, to be shown by scientific experience is this: that where an observed uniformity fails, some wider uniformity can be found, embracing more circumstances, and subsuming both the successes and the failures of the previous uniformity. Unsupported bodies in air fall, unless they are balloons or aeroplanes; but the principles of mechanics give uniformities which apply to balloons and aeroplanes just as accurately as to bodies that fall.”

„The principle involved is the principle of induction, which, if it is true, must be an a priori logical law, not capable of being proved or disproved by experience. It is a difficult question how this principle ought to be formulated; but if it is to warrant the inferences which we wish to make by its means, it must lead to the following proposition: “If, in a great number of instances, a thing of a certain kind is associated in a certain way with a thing of a certain other kind, it is probable that a thing of the one kind is always similarly associated with a thing of the other kind; and as the number of instances increases, the probability approaches indefinitely near to certainty.”

„I come now to the question how the conception of causal laws which we have arrived at is related to the traditional conception of cause as it occurs in philosophy and common sense. Historically, the notion of cause has been bound up with that of human volition. The typical cause would be the fiat of a king. The cause is supposed to be “active,” the effect “passive.”

„Not only do memory and hope make a difference in our feelings as regards past and future, but almost our whole vocabulary is filled with the idea of activity, of things done now for the sake of their future effects.”

„But from the point of view of Brutus, the desire, which comes at the beginning, is what makes the whole series interesting. We feel that if his desires had been different, the effects which he in fact produced would not have occurred. This is true, and gives him a sense of power and freedom. It is equally true that if the effects had not occurred, his desires would have been different, since being what “the desires are determined by their consequences just as much as the consequences by the desires; but as we cannot (in general) know in advance the consequences of our desires without knowing our desires, this form of inference is uninteresting as applied to our own acts, though quite vital as applied to those of others. Thus the desires are determined by their consequences just as much as the consequences by the desires; but as we cannot (in general) know in advance the consequences of our desires without knowing our desires, this form of inference is uninteresting as applied to our own acts, though quite vital as applied to those of others.”

„A cause is an event or group of events, of some known general character, and having a known relation to some other event, called the effect; the relation being of such a kind that only one event, or at any rate only one well-defined sort of event, can have the relation to a given cause. It is customary only to give the name “effect”

„the strict, certain, universal law of causation which philosophers advocate is an ideal, possibly true, but not known to be true in virtue of any available evidence. What is actually known, as a matter of empirical science, is that certain constant relations are observed to hold between the members of a group of events at certain times, and that when such relations fail, as they sometimes do, it is usually possible to discover a new, more constant relation by enlarging the group. Any such constant relation between events of specified kinds with given intervals of time between them is a “causal law.”

„We do not like to think that other people, if they knew enough, could predict our actions, though we know that we can often predict those of other people, especially if they are elderly.”

„the attraction which the sun will exert on the earth is not only known at distances for which it has been observed, but at all distances, because it is known to vary as the inverse square of the distance. In fact, what is found to be repeated is always the relation of cause and effect, not the cause itself; all that is necessary as regards the cause is that it should be of the same kind (in the relevant respect) as earlier causes whose effects have been observed. Another respect in which Bergson's statement of causation is inadequate is in its assumption that the cause must be one event, whereas it may be two or more events, or even some continuous process. The substantive question at issue is whether mental events are determined by the past. Now in such a case as the repeated reading of a poem, it is obvious that our feelings in reading the poem are most emphatically dependent upon the past, but not upon one single event in the past. All our previous readings of the poem must be included in the cause. But we easily perceive a certain law according to which the effect varies as the previous readings increase in number, and in fact Bergson himself tacitly assumes such a law. We decide at last not to read the poem again, because we know that this time the effect would be boredom. We may not know all the niceties and shades of the boredom we should feel, but we know enough to guide our decision, and the prophecy of boredom is none the less true for being more or less general. Thus the kinds of cases upon which Bergson relies are insufficient to show the impossibility of prediction in the only sense in which prediction has practical or emotional interest. We may therefore leave the consideration of his arguments and address ourselves to the problem directly. The law of causation, according to which later events can theoretically be predicted by means of earlier events, has often been held to be a priori, a necessity of thought, a category without which science would be impossible. These claims seem to me excessive. In certain directions the law has been verified empirically, and in other directions there is no positive evidence against it. But science can use it where it has been found to be true, without being forced into any assumption as to its truth in other fields. We cannot, therefore, feel any a priori certainty that causation must apply to human volitions. The question how far human volitions are subject to causal laws is a purely empirical one. Empirically it seems plain that the great majority of our volitions have causes, but it cannot, on this account, be held necessarily certain that all have causes. There are, however, precisely the same kinds of reasons for regarding it as probable that they all have causes as there are in the case of physical events.”

„A method of proof which, when used as directed, gives sometimes truth and sometimes falsehood—as the method of simple enumeration does—is obviously not a valid method, for validity demands invariable truth. Thus, if simple enumeration is to be rendered valid, it must not be stated as Mill states it. We shall have to say, at most, that the data render the result probable. Causation holds, we shall say, in every instance we have been able to test; therefore it probably holds in untested instances. There are terrible difficulties in the notion of probability, but we may ignore them at present. We thus have what at least may be a logical principle, since it is without exception. If a proposition is true in every instance that we happen to know of, and if the instances are very numerous, then, we shall say, it becomes very probable, on the data, that it will be true in any further instance. This is not refuted by the fact that what we declare to be probable does not always happen, for an event may be probable on the data and yet not occur. It is, however, obviously capable of further analysis, and of more exact statement. We shall have to say something like this: that every instance of a proposition[10] being true increases the probability of its being true in a fresh instance, and that a sufficient number of favourable instances will, in the absence of instances to the contrary, make the probability of the truth of a fresh instance approach indefinitely near to certainty. Some such principle as this is required if the method of simple enumeration is to be valid. A similar conclusion can be proved by similar arguments concerning any other logical principle. Thus logical knowledge is not derivable from experience alone, and the empiricist's philosophy can therefore not be accepted in its entirety, in spite of its excellence in many matters which lie outside logic.”

„The assumption that sensible objects persist after they have ceased to be sensible—for example, that the hardness of a visible body, which has been discovered by touch, continues when the body is no longer touched—may be replaced by the statement that the effects of sensible objects persist, i.e. that what happens now can only be accounted for, in many cases, by taking account of what happened at an earlier time. Everything that one man, by his own personal experience, can verify in the account of the world given by common sense and physics, will be explicable by some such means, since verification consists merely in the occurrence of an expected sense-datum. But what depends upon testimony, whether heard or read, cannot be explained in this way, since testimony depends upon the existence of minds other than our own, and thus requires a knowledge of something not given in sense. “But before examining the question of our knowledge of other minds, let us return to the question of the thing-in-itself, namely, to the theory that what exists at times when we are not perceiving a given sensible object is something quite unlike that object, something which, together with us and our sense- organs, causes our sensations, but is never itself given in sensation. “Objects of sense are called “real”

„The minds of other people are among our data, in the very wide sense in which we used the word at first. That is to say, when we first begin to reflect, we find ourselves already believing in them, not because of any argument, but because the belief is natural to us. It is, however, a psychologically derivative belief, since it results from observation of people's bodies; and along with other such beliefs, it does not belong to the hardest of hard data, but becomes, under the influence of philosophic reflection, just sufficiently questionable to make us desire some argument connecting it with the facts of sense. “Why should we suppose that, when ice melts, the water which replaces it is the same thing in a new form? Merely because this supposition enables us to state the phenomena in a way which is consonant with our prejudices. What we really know is that, under certain conditions of temperature, the appearance we call ice is replaced by the appearance we call water. We can give laws according to which the one appearance will be succeeded by the other, but there is no reason except prejudice for regarding both as appearances of the same substance. One task, if what has just been said is correct, which confronts us in trying to connect the world of sense with the world of physics, is the task of reconstructing the conception of matter without the a priori beliefs which historically gave rise to it. In spite of the revolutionary results of modern physics, the empirical successes of the conception of matter show that there must be some legitimate conception which fulfils roughly the same functions. The time has hardly come when we can state precisely what this legitimate conception is, but we can see in a general way what it must be like. For this purpose, it is only necessary to take our ordinary common-sense statements and reword them without the assumption of permanent substance. We say, for example, that things change gradually—sometimes very quickly, but not without passing through a continuous series of intermediate states. What this means is that, given any sensible appearance, there will usually be, if we watch, a continuous series of appearances connected with the given one, leading on by imperceptible gradations to the new appearances which common-sense regards as those of the same thing.”

„active,” the effect “passive.”