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[Bertrand Russell, in keeping with the tradition of modern philosophy, devoted most of his philosophical energies to developing a theory of knowledge. In his book, Confessions of a Philosopher Bryan Magee highly recommended the following five books from among Russell’s massive output: The Problems of Philosophy, 1912; Our Knowledge of the External World, 1914; An Inquiry into Meaning and Truth, 1940; Human Knowledge: Its Scope and Limits, 1948; My Philosophical Development, 1959. My excerpts from these books can be found below. Interestingly, Magee panned Russell’s History of Western Philosophy, 1946, which he claimed was overrated. He explains: ‘Its account of every important philosopher’s work is inadequate even given its limitations of space. The treatment throughout is superficial, not to say flip, and although this sort of thing can be highly enjoyable in ordinary conversation it is not acceptable when introducing beginners to the subject.’ Apparently Russell was lecturing in the United States, needed money, and threw the book together from his lecture notes. Magee liked and respected Russell, visited him a number of times, and devoted a whole chapter of his book to the great man. However, his appraisal of Russell’s legacy is as follows, ‘Just as in mathematical logic [Russell] had devoted several years of hard, independent and deeply original thinking to work that had already been done by Frege, so in general philosophy it took him the whole of a magnificent career to reach the conclusion that empiricism is fundamentally inadequate for a reason given by Kant. The bitterest irony of all is that the philosopher to whom Kant himself directly owed this insight was Hume.’ Nevertheless, ‘there is both pleasure and profit to be got from reading Russell,’ an opinion with which I enthusiastically agree. To those put off by Russell’s implacable hostility to religion, his messy personal life, and his many foolish public utterances—his onetime friend Alastair Cooke said he had a first rate mind, but lacked horse sense—I would make the case for reading certain of his works in this way. Russell deserves our attention and respect, not because he is the father of modern philosophical analysis, nor because he was by all accounts a man of remarkable intelligence, nor because he was one of the greatest logicians of all time. These qualities and accomplishments recommend him, but they are not sufficient grounds for trusting him. The reason, I believe, that reading Russell can be so fruitful is that he arrived at conclusions diametrically opposed to those which he had hoped for. And that means that there was nothing but thought and a passion for truth to drive him the way he went.]

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The Problems of Philosophy

by Bertrand Russell, 1912

Is there any knowledge in the world which is so certain that no reasonable man could doubt it? This question, which at first sight might not seem difficult, is really one of the most difficult that can be asked.

Berkeley [shows] that the existence of matter is capable of being denied without absurdity, and that if there are any things that exist independently of us they cannot be the immediate objects of our sensations.

‘I think, therefore I am’ says rather more than is strictly certain. It might seem as though we were quite sure of being the same person today as we were yesterday, and this is no doubt true in some sense. But the real Self is as hard to arrive at as the real table, and does not seem to have that absolute, convincing certainty that belongs to particular experiences.

All knowledge must be built up upon our instinctive beliefs, and if these are rejected, nothing is left.

We cannot have reason to reject a belief except on the ground of some other belief.

Do any number 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 tomorrow, 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.

The inductive principle is 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.

When we see what looks like our best friend approaching us, we have no reason to suppose that his body is not inhabited by the mind of our worst enemy or of some total stranger.

Knowledge as to what is intrinsically of value is a priori in the same sense in which logic is a priori, namely in the sense that the truth of such knowledge can be neither proved nor disproved by experience.

There is no reasoning which, starting from some simpler self-evident principle, leads us to the principle of induction as its conclusion.

All a priori knowledge deals exclusively with the relations of universals.

Logical principles are known to us, and cannot be themselves proved by experience, since all proof presupposes them.

Our immediate knowledge of truths may be called intuitive knowledge, and the truths so known may be called self-evident truths.

All our knowledge of truths depends upon our intuitive knowledge.

It is felt by many that a belief for which no reason can be given is an unreasonable belief. In the main, this view is just... But let us imagine some insistent Socrates, who, whatever reason we give him, continues to demand a reason for the reason. We must sooner or later, and probably before very long, be driven to a point where we cannot find any further reason, and where it becomes almost certain that no further reason is even theoretically discoverable. Starting with the common beliefs of daily life, we can be driven back from point to point, until we come to some general principle, which seems luminously evident, and is not itself capable of being deduced from anything more evident.

I am absolutely certain that half a minute ago I was sitting in the same chair in which I am sitting now. Going backward over the day, I find things of which I am quite certain, other things of which I am almost certain, other things of which I can become certain by thought and by calling up attendant circumstances, and some things of which I am by no means certain.

One important point about self-evidence is made clear by the case of memory, and that is, that self-evidence has degrees: it is not a quality which is simply present or absent, but a quality which may be more or less present, in gradations ranging from absolute certainty down to an almost imperceptible faintness.

Truth and falsehood are properties of beliefs and statements: hence a world of mere matter, since it would contain no beliefs or statements, would also contain no truth or falsehood.

When we speak of philosophy as a criticism of knowledge, it is necessary to impose a certain limitation. If we adopt the attitude of the complete sceptic, placing ourselves wholly outside all knowledge, and asking, from this outside position, to be compelled to return within the circle of knowledge, we are demanding what is impossible, and our scepticism can never be refuted. For all refutation must begin with some piece of knowledge which the disputants share; from blank doubt, no argument can begin. Hence the criticism of knowledge which philosophy employs must not be of this destructive kind, if any result is to be achieved. Against this absolute scepticism, no logical argument can be advanced. But it is not difficult to see that scepticism of this kind is unreasonable. Descartes’s ‘methodical doubt,’ with which modern philosophy began, is not of this kind, but is rather the kind of criticism which we are asserting to be the essence of philosophy. His ‘methodical doubt’ consisted in doubting whatever seemed doubtful; in pausing, with each apparent piece of knowledge, to ask himself whether, on reflection, he could feel certain that he really knew it. This is the kind of criticism which constitutes philosophy. Some knowledge, such as knowledge of the existence of our sense-data, appears quite indubitable, however calmly and thoroughly we reflect upon it. In regard to such knowledge, philosophical criticism does not require that we should abstain from belief. But there are beliefs—such, for example, as the belief that physical objects exactly resemble our sense-data—which are entertained until we begin to reflect, but are found to melt away when subjected to a close inquiry. Such beliefs philosophy will bid us reject, unless some new line of argument is found to support them. But to reject the beliefs which do not appear open to any objections, however closely we examine them, is not reasonable, and is not what philosophy advocates.

The criticism aimed at, in a word, is not that which, without reason, determines to reject, but that which considers each piece of apparent knowledge on its merits, and retains whatever still appears to be knowledge when this consideration is completed. That some risk of error remains must be admitted, since human beings are fallible. Philosophy may claim justly that it diminishes the risk of error, and that in some cases it renders the risk so small as to be practically negligible. To do more than this is not possible in a world where mistakes must occur; and more than this no prudent advocate of philosophy would claim to have performed.

Truth consists in some form of correspondence between belief and fact. It is, however, by no means an easy matter to discover a form of correspondence to which there are no irrefutable objections.

Beliefs depend on minds for their existence, but do not depend on minds for their truth.

‘Knowledge’ is not a precise conception: it merges into ‘probable opinion,’ as we shall see more fully in the course of the present chapter. A very precise definition, therefore, should not be sought, since any such definition must be more or less misleading.

The chief difficulty in regard to knowledge does not arise over derivative knowledge, but over intuitive knowledge. So long as we are dealing with derivative knowledge, we have the test of intuitive knowledge to fall back upon. But in regard to intuitive beliefs, it is by no means easy to discover any criterion by which to distinguish some as true and others as erroneous. In this question it is scarcely possible to reach any very precise result: all our knowledge of truths is infected with some degree of doubt, and a theory which ignored this fact would be plainly wrong.

What we firmly believe, if it is true, is called knowledge, provided it is either intuitive or inferred (logically or psychologically) from intuitive knowledge from which it follows logically. What we firmly believe, if it is not true, is called error. What we firmly believe, if it is neither knowledge nor error, and also what we believe hesitatingly, because it is, or is derived from, something which has not the highest degree of self-evidence, may be called probable opinion. Thus the greater part of what would commonly pass as knowledge is more or less probable opinion.

In regard to probable opinion, we can derive great assistance from coherence, which we rejected as the definition of truth, but may often use as a criterion. A body of individually probable opinions, if they are mutually coherent, become more probable than any one of them would be individually. It is in this way that many scientific hypotheses acquire their probability.

If our dreams, night after night, were as coherent one with another as our days, we should hardly know whether to believe the dreams or the waking life. As it is, the test of coherence condemns the dreams and confirms the waking life. But this test, though it increases probability where it is successful, never gives absolute certainty, unless there is certainty already at some point in the coherent system.

Our Knowledge of the External World

by Bertrand Russell, 1914

Philosophy, from the earliest times, has made greater claims, and achieved fewer results, than any other branch of learning. Ever since Thales said that all is water, philosophers have been ready with glib assertions about the sum-total of things; and equally glib denials have come from other philosophers ever since Thales was contradicted by Anaximander. I believe that the time has now arrived when this unsatisfactory state of things can be brought to an end.

Bergson, under the name of “intuition,” has raised instinct to the position of sole arbiter of metaphysical truth. But in fact the opposition of instinct and reason is mainly illusory. 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 harmonizing, controlling force rather than a creative one. Even in the most purely logical realms, it is insight that first arrives at what is new.

Let us next imagine whether intuition possesses any such infallibility as Bergson claims for it. The best instance of it, according to him is our acquaintance with ourselves; yet self-knowledge is proverbially rare and difficult. Most men, for example, have in their nature meannesses, vanities, and envies of which they are quite unconscious, though even their best friends can perceive them without any difficulty. It is true that intuition has a convincingness which is lacking to intellect: while it is present, it is almost impossible to doubt its truth. But if it should appear, on examination, to be at least as fallible as intellect, its greater subjective certainty becomes a demerit, making it only the more irresistibly deceptive. Apart from self-knowledge, one of the most notable examples of intuition is the knowledge people believe themselves to possess of those with whom they are in love: the wall between different personalities seems to become transparent, and people think they see into another soul as into their own. Yet deception in such cases is constantly practised with success; and even where there is no intentional deception, experience gradually proves, as a rule, that the supposed insight was illusory, and that the slower, more groping methods of the intellect are in the long run more reliable.

While admitting that doubt is possible with regard to all our common knowledge, we must nevertheless accept that knowledge in the main if philosophy is to be possible at all. There is not any superfine brand of knowledge, obtainable by the philosopher, which can give us a standpoint from which to criticize the whole of the knowledge of daily life. The most that can be done is to examine and purify our common knowledge by an internal scrutiny, assuming the canons by which it has been obtained, and applying them with more care and with more precision. Philosophy cannot boast of having achieved such a degree of certainty that it can have authority to condemn the facts of experience and the laws of science. The philosophic scrutiny, therefore, though sceptical in regard to every detail, is not sceptical as regards the whole.

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. There may or may not be a possible deduction leading to the same result, but whether there is or not, we certainly do not employ it. If we call a belief “logically primitive” when it is not actually arrived at by a logical inference, then innumerable beliefs are logically primitive which psychologically are derivative.

When we reflect upon the beliefs which are logically but not psychologically primitive, we find that, unless they can on reflection be deduced by a logical process from beliefs which are also psychologically primitive, our confidence in their truth tends to diminish the more we think about them. We naturally believe, for example, that tables and chairs, trees and mountains, are still there when we turn our backs upon them. I do not wish for a moment to maintain that this is certainly not the case, but I do maintain that the question whether it is the case is not to be settled offhand on any supposed ground of obviousness. The belief that they persist is, in all men except a few philosophers, logically primitive, but it is not psychologically primitive; psychologically, it arises only through our having seen those tables and chairs, trees and mountains. As soon as the question is seriously raised whether, because we have seen them, we have a right to suppose that they are there still, we feel that some kind of argument must be produced, and that if none is forthcoming, our belief can be no more than a pious opinion. We do not feel this as regards the immediate objects of sense: there they are, and as far as their momentary existence is concerned, no further argument is required. There is accordingly more need of justifying our psychologically derivative beliefs than of justifying those that are primitive.

The hardest of hard data are of two sorts: the particular facts of sense, and the general truths of logic. The more we reflect upon these, the more we realize exactly what they are, and exactly what a doubt concerning them really means, the more luminously certain do they become. Verbal doubt concerning even these is possible, but verbal doubt may occur when what is nominally being doubted is not really in our thoughts, and only words are actually present to our minds. Real doubt, in these two cases, would, I think, be pathological. At any rate, to me they seem quite certain, and I shall assume that you agree with me in this. Without this assumption, we are in danger of falling into that universal scepticism which, as we saw, is as barren as it is irrefutable. If we are to continue philosophizing, we must make our bow to the sceptical hypothesis, and, while admitting the elegant terseness of its philosophy, proceed to the consideration of other hypotheses which, though perhaps not certain, have at least as good a right to our respect as the hypothesis of the sceptic.

Another form in which the question is often put is: “Can we know of the existence of any reality which is independent of ourselves?” This form of the question suffers from the ambiguity of the two words “independent” and “self.” To take the Self first: the question as to what is to be reckoned part of the Self and what is not, is a very difficult one. Among many other things which we may mean by the Self, two may be selected as specially important, namely (1) the bare subject which thinks and is aware of objects, (2) the whole assemblage of things that would necessarily cease to exist if our lives came to an end. The bare subject, if it exists at all, is an inference, and is not part of the data; therefore, this meaning of Self may be ignored in our present inquiry. The second meaning is difficult to make precise, since we hardly know what things depend upon our lives for their existence. And in this form, the definition of Self introduces the word “depend,” which raises the same questions as are raised by the word “independent.” Let us therefore take up the word “independent,” and return to the Self later.

When we hear certain noises, which are those we should utter if we wished to express a certain thought, we assume that that thought, or one very like it, has been in another mind, and has given rise to the expression which we hear. If at the same time we see a body resembling our own, moving its lips as we move ours when we speak, we cannot resist the belief that it is alive, and that the feelings inside it continue when we are not looking at it. When we see our friend drop a weight upon his toe, and hear him say—what we should say in similar circumstances, the phenomena can no doubt be explained without assuming that he is anything but a series of shapes and noises seen and heard by us, but practically no man is so infected with philosophy as not to be quite certain that his friend has felt the same kind of pain as he himself would feel. We will consider the legitimacy of this belief presently; for the moment, I only wish to point out that it needs the same kind of justification as our belief that the moon exists when we do not see it, and that, without it, testimony heard or read is reduced to noises and shapes, and cannot be regarded as evidence of the facts which it reports. The verification of physics which is possible at our present level is, therefore, only that degree of verification which is possible by one man’s unaided observations, which will not carry us very far towards the establishment of a whole science.

It must be conceded to begin with that the argument in favour of the existence of other people’s minds cannot be conclusive. A phantasm of our dreams will appear to have a mind—a mind to be annoying, as a rule. It will give unexpected answers, refuse to conform to our desires, and show all those other signs of intelligence to which we are accustomed in the acquaintances of our waking hours. And yet, when we are awake, we do not believe that the phantasm was, like the appearances of people in waking life, representative of a private world to which we have no direct access. If we are to believe this of the people we meet when we are awake, it must be on some ground short of demonstration, since it is obviously possible that what we call waking life may be only an unusually persistent and recurrent nightmare. It may be that our imagination brings forth all that other people seem to say to us, all that we read in books, all the daily, weekly, monthly, and quarterly journals that distract our thoughts, all the advertisements of soap and all the speeches of politicians. This may be true, since it cannot be shown to be false, yet no one can really believe it. Is there any logical ground for regarding this possibility as improbable? Or is there nothing beyond habit and prejudice?

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 hypothesis that other people have minds must, I think, be allowed to be not susceptible of any very strong support from the analogical argument. At the same time, it is a hypothesis which systematizes a vast body of facts and never leads to any consequences which there is reason to think false. There is therefore nothing to be said against its truth, and good reason to use it as a working hypothesis. When once it is admitted, it enables us to extend our knowledge of the sensible world by testimony, and thus leads to the system of private worlds which we assumed in our hypothetical construction. In actual fact, whatever we may try to think as philosophers, we cannot help believing in the minds of other people, so that the question whether our belief is justified has a merely speculative interest. And if it is justified, then there is no further difficulty of principle in that vast extension of our knowledge, beyond our own private data, which we find in science and common sense.

There is some sense—easier to feel than to state—in which time is an unimportant and superficial characteristic of reality.

The view that the law of causality is a priori cannot, I think, be maintained by anyone who realizes what a complicated principle it is. In the form which states that “every event has a cause” it looks simple; but on examination, “cause” is merged in “causal law,” and the definition of a “causal law” is found to be far from simple.

We do not think we were necessarily not free in the past, merely because we can now remember our past volitions. Similarly, we might be free in the future, even if we could now see what our future volitions were going to be. Freedom, in short, in any valuable sense, demands only that our volitions shall be, as they are, the result of our own desires, not of an outside force compelling us to will what we would rather not will. Everything else is confusion of thought, due to the feeling that knowledge compels the happening of what it knows when this is future, though it is at once obvious that knowledge has no such power in regard to the past. Free will, therefore, is true in the only form which is important; and the desire for other forms is a mere effect of insufficient analysis.

It is necessary to practise methodological doubt, like Descartes, in order to loosen the hold of mental habits; and it is necessary to cultivate logical imagination, in order to have a number of hypotheses at command, and not to be the slave of the one which common sense has rendered easy to imagine. These two processes, of doubting the familiar and imagining the unfamiliar, are correlative, and form the chief part of the mental training required for a philosopher.

The naive beliefs which we find in ourselves when we first begin the process of philosophic reflection may turn out, in the end, to be almost all capable of a true interpretation; but they ought all, before being admitted into philosophy, to undergo the ordeal of sceptical criticism. Until they have gone through this ordeal, they are mere blind habits, ways of behaving rather than intellectual convictions.

So meagre was the logical apparatus [in the past] that all the hypotheses philosophers could imagine were found to be inconsistent with the facts. Too often this state of things led to the adoption of heroic measures, such as a wholesale denial of the facts, when an imagination better stocked with logical tools would have found a key to unlock the mystery. It is in this way that the study of logic becomes the central study in philosophy: it gives the method of research in philosophy, just as mathematics gives the method in physics. And as physics, which from Plato to the Renaissance, was as unprogressive, dim, and superstitious as philosophy, became a science through Galileo’s fresh observation of facts and subsequent mathematical manipulation, so philosophy, in our own day, is becoming scientific through the simultaneous acquisition of new facts and logical methods.

The one and only condition, I believe, which is necessary in order to secure for philosophy in the near future an achievement surpassing all that has hitherto been accomplished by philosophers, is the creation of a school of men with scientific training and philosophical interests, unhampered by the traditions of the past, and not misled by the literary methods of those who copy the ancients in all except their merits.

An Inquiry into Meaning and Truth

by Bertrand Russell, 1940

We all start from “naive realism,” i.e., the doctrine that things are what they seem. We think that grass is green, that stones are hard, and that snow is cold. But physics assures us that the greenness of grass, the hardness of stones, and the coldness of snow, are not the greenness, hardness, and coldness that we know in our own experience, but something very different. The observer, when he seems to himself to be observing a stone, is really, if physics is to be believed, observing the effects of the stone upon himself.

It is argued that, on the basis of a single experience, a number of verbal statements are justified. The character of such statements is investigated, and it is contended that they must always be confined to matters belonging to the biography of the observer; they can be such as “I see a canoid patch of colour,” but not such as “there is a dog.” Statements of this latter kind always involve, in their justification, some element of inference.

Attempts have been made to define “truth” in terms of “knowledge,” or of concepts, such as “verifiability,” which involve “knowledge.” Such attempts, if carried out logically, lead to paradoxes which there is no reason to accept. I conclude that “truth” is the fundamental concept, and that “knowledge” must be defined in terms of “truth,” not vice versa. This entails the consequence that a proposition may be true although we can see no way of obtaining evidence either for or against it. It involves also a partial abandonment of the complete metaphysical agnosticism that is favoured by the logical positivists.

People who have learnt a certain language have acquired an impulse to use certain words on certain occasions, and this impulse, when it has been acquired, is strictly analogous to the impulse to cry when hurt.

One of the things that have seemed puzzling about language is that, in ordinary speech, sentences are true or false, but single words are neither. In the object-language this distinction does not exist. Every single word of this language is capable of standing alone, and, when it stands alone, means that it is applicable to the present datum of perception.

I do not like to use the word “perception” for the complete experience consisting of a sensory core supplemented by expectations, because the word “perception” suggests too strongly that the beliefs involved are true. I will therefore use the phrase “perceptive experience.” Thus whenever I think I see a cat, I have the perceptive experience of “seeing a cat,” even if, on this occasion, no physical cat is present.

The question of data has been, mistakenly I think, mixed up with the question of certainty. The essential characteristic of a datum is that it is not inferred. It may not be true, and we may not feel certain that it is true. The most obvious example is memory. We know that memory is fallible, but there are many things that we believe, though not with complete assurance, on the basis of memory alone. Another example is derived from faint perceptions. Suppose you are listening to a sound which is gradually growing more distant, for example, a receding airplane. At one time, you are sure that you hear it; at a later time, you are sure that you do not hear it. At certain intermediate times, you think that you still hear it, but cannot be sure; at these times you have an uncertain datum. I am prepared to concede that all data have some uncertainty, and should therefore, if possible, be confirmed by other data. But unless these other data had some degree of independent credibility, they would not confirm the original data.

We assume that perception can cause knowledge, although it may cause error if we are logically careless. Without this fundamental assumption, we should be reduced to complete scepticism as regards the empirical world. No arguments are logically possible either for or against complete scepticism, which must be admitted to be one among possible philosophies. It is, however, too short and simple to be interesting. I shall, therefore, without more ado, develop the opposite hypothesis, according to which beliefs caused by perception are to be accepted unless there are positive grounds for rejecting them.

Empiricism, as a theory of knowledge, is self-refuting. For, however it may be formulated, it must involve some general proposition about the dependence of knowledge upon experience; and any such proposition, if true, must have as a consequence that itself cannot be known [empirically]. While, therefore, empiricism may be true, it cannot, if true, be know to be so.

Lamb, in an altercation with a Billingsgate fish-wife, called her a she-parallelogram, and produced a greater effect than he could have done by any more significant abuse; this was because she did not know his sentence to be nonsense. Many religious people are much affected by such sentences as “God is one,” which are syntactically faulty, and must be regarded by the logician as strictly meaningless. (The correct phrase would be “There is only one God.”)

Suppose a man who thinks that “cat” means the kind of animal that other people call “dog.” If he sees a Great Dane and says “there is a cat,” he is believing a true proposition, but uttering an incorrect one. It would seem, therefore, that “correct” cannot be used in defining “true,” since “correct” is a social concept, but “true” is not.

Perhaps this difficulty could be overcome. When our man says “there is a cat,” what would ordinarily be called his “thought” is true, but the “thought” that he causes in his hearer is untrue. His implicit behaviour will be appropriate, in the sense that he will (for example) expect the animal to bark and not mew, but the hearer’s implicit behaviour will, in the same sense, be inappropriate. The speaker and the hearer use different languages (at least so far as the words “cat” and “dog” are concerned). I think that, in fundamental discussions of language, its social aspect should be ignored, and a man should always be supposed to be speaking to himself—or, what comes to the same thing, to a man whose language is precisely identical with his own. This eliminates the concept of “correctness.” What remains—if a man is to be able to interpret notes written by himself on previous occasions—is constancy in his own use of words: we must suppose that he uses the same language today as he used yesterday. In fact, the whole residuum of what was to have been done by the concept of “correctness” is this: speaker and hearer (or writer and reader) must use the same language, i.e. have the same interpretative habits.

Language serves three purposes: (1) to indicate facts, (2) to express the state of the speaker, (3) to alter the state of the hearer. These three purposes are not always all present. If, when alone, I prick my finger and say “ouch,” only (2) is present. Imperative, interrogative, and optative sentences involve (2) and (3), but not (1). Lies involve (3), and, in a sense, (1), but not (2). Exclamatory statements made in solitude, or without regard to a hearer, involve (1) and (2), but not (3). Single words may involve all three, for instance if I find a corpse in the street and shout “murder!”

We agreed in the last chapter that an indicative sentence “expresses” a state of the speaker, and “indicates” a fact or fails to do so. The problem of truth and falsehood has to do with “indication.” It appeared that truth and falsehood apply primarily to beliefs, and only derivatively to sentences as “expressing” beliefs.

It will be seen that the relation of a belief or a sentence to what it indicates, i.e. to its verifier (if any), is often somewhat remote and causal. Also that, although to “know” a verifier means to perceive it, we must, unless our knowledge is to be unbelievably depleted, know the truth of many sentences whose verifiers cannot be perceived. Such sentences, however, always contain a variable where the name of the verifier would occur if our perceptive faculties were sufficiently extensive.

In the present chapter, I wish to discuss, not knowledge, but truth. What I know must be true, but truth is wider than knowledge in two respects. First, there are true sentences (if we accept the law of excluded middle) as to which we have no opinion whatever; second, there are true sentences which we believe and yet do not know, because we have arrived at them from faulty reasoning. I once met a Christadelphian who held, on grounds derived from the Book of Revelation, that there would shortly be trouble in Egypt. There was. His belief was true, but not knowledge.

“True” and “false,” we decided, are predicates, primarily, of beliefs, and derivatively of sentences. I suggest that “true” is a wider concept than “verifiable,” and, in fact, cannot be defined in terms of verifiability.

The simplest form of the argument for the physical world is the argument that “things” exist when I do not see them—or rather, to avoid Berkeley, when no one sees them. Suppose, for example, that I keep my cheque-book in a drawer, so that it affects no one’s senses except when the drawer is open. Why do I believe that it is there when the drawer is shut, and even when no one sees the drawer?

Some philosophers might argue that, when I say “the book is in the drawer,” I only mean “if anyone opens the drawer he will see it”—where “opening the drawer” must be interpreted as an experience, not as something done to a permanent drawer. This view, right or wrong, is one which would only occur to a philosopher, and is not the one I wish to discuss. What I wish to discuss is the view that something—which may be called the book—is occurring when no one sees it. I do not wish to discuss whether the view is true, but what kind of influence is involved in supposing it true.

Unsophisticated common sense supposes that the book, just as it appears when seen, is there all the time. This we know to be false. The book which can exist unseen must, if it exists, be the sort of thing that physics says it is, which is quite unlike what we see. What we more or less know is that, if we fulfil certain conditions, we shall see the book. We believe that the causes of this experience lie only partly within ourselves; the causes external to ourselves are what lead us to belief in the book. This requires belief in a kind of cause which completely and essentially transcends experience.

We now have to ask ourselves: is there a sense in which a proposition may be true although it cannot be known? Take, say, “in the invisible part of the moon there is a mountain of which the height is between 6,000 and 7,000 metres.” Common sense would say unhesitatingly that this proposition is either true or false, but many philosophers have theories of truth which make this doubtful.

“Had we but world enough and time,” we could dispense with general propositions. Instead of “all men are mortal,” we could say “Socrates is mortal,” “Plato is mortal,” and so on. In fact, however, this would take too long, and our vocabulary of names is insufficient. We must therefore use general propositions.

Let us consider some case where we seem more certain of the truth of our general proposition, say “all dodos are mortal.” We know this, it may be said, because all dodos are dead. It might be objected that perhaps there are dodos in other planets, or that evolution, having produced the dodo once, may produce it again, and next time may make it immortal, like the phoenix. We will therefore amend our general proposition, and say only: “all dodos living on the surface of the earth before 1940 were mortal.” This seems fairly indubitable.

We could be said to “know” a proposition if it is in fact true and we believe it on the best available evidence. But if this evidence is not conclusive, we shall never know whether the proposition is in fact true, and shall therefore never know whether we know it. It is hoped that inductive evidence may make an empirical generalization probable. This takes us, however, into a region that lies outside the scope of the present work, and I shall therefore say no more on the subject.

The theory of truth-functions is the most elementary part of mathematical logic, and concerns everything that can be said about propositions by means of “or” and “not.”

We have to consider, in this chapter and the next, whether to sacrifice the law of excluded middle or to attempt a definition of truth which is independent of knowledge. The difficulties of either view are appalling. If we define truth in relation to knowledge, logic collapses, and much hitherto accepted reasoning, including large parts of mathematics, must be rejected as invalid. But if we adhere to the law of excluded middle, we shall find ourselves committed to a realist metaphysic which may seem, in the spirit if not in the letter, incompatible with empiricism. The question is fundamental, and of the greatest importance.

Brouwer argues that “true” is a useless conception unless we have ways of discovering whether a proposition is true or not. He therefore substitutes “verifiable” for “true,” and he does not call a proposition “false” unless its contradictory is verifiable. There thus remains an intermediate class of propositions, which are syntactically correct, but neither verifiable nor the contradictories of verifiable propositions. This intermediate class Brouwer refuses to call either true or false, and in regard to them he regards the law of excluded middle as mistaken.

No one has yet gone so far as to define “truth” as “what is known”; the epistemological definition of “truth” is “what can be known.” The word “verifiable” is commonly used, and a proposition is verifiable if it can be verified. This at once introduces difficulties, since possibility is an awkward concept.

When we say “all men are mortal,” are we saying anything, or are we making meaningless noises? I am not asking whether the sentence is true, but whether it is significant.

Epistemological scepticism has a logical foundation, namely the principle that it is never possible to deduce the existence of something from the existence of something else. This principle must be stated more clearly, and without the use of the word “existence.” Let us take an illustration. You look out of the window, and observe that you can see three houses. You turn back into the room and say “three houses are visible from the window.” The kind of sceptic that I have in mind would say “you mean three houses were visible.” You would reply “but they can’t have vanished in this little moment.” You might look again and say “yes, there they are still.” The sceptic would retort: “I grant that when you looked again they were there again, but what makes you think they had been there in the interval?” You would only be able to say “because I see them whenever I look.” The sceptic would say “then you ought to infer that they are caused by your looking.” You will never succeed in getting any evidence against this view, because you can’t find out what the houses look like when no one is looking at them.

Our logical principle may be stated as follows: “no proposition about what occurs in one part of space-time logically implies any proposition about what occurs in another part of space-time.” If the reference to space-time is thought unduly suggestive of physicalism, it can easily be eliminated. We may say: “the perceptive propositions derivable from one perceived event never logically imply any proposition about any other event.” I do not think this can be questioned by any one who understands the logic of truth-functions.

But outside pure mathematics the important kinds of inference are not logical; they are analogical and inductive. Now the kind of partial sceptic whom we have been having in mind allows such inferences, for he accepts physicalism whenever it enables us to prophesy our own future percepts. He will allow the man measuring the velocity of sound to say “in five seconds I shall see the flag wave”; he will only not allow him to say “in five seconds the flag will wave.” These two inferences, however, are exactly on a level as regards induction and analogy, without which science, however interpreted, becomes impossible. Our logical foundation thus becomes irrelevant, and we have to consider whether induction and analogy can ever make it probable that there are unperceived events.

Although the above discussion has been so far very inconclusive, I find myself believing, at the end of it, that truth and knowledge are different, and that a proposition may be true although no method exists of discovering that it is so. In that case, we may accept the law of excluded middle. We shall define “truth” by reference to “events” (I am speaking of non-logical truth), and “knowledge” by relation to “percepts.” Thus “truth” will be a wider conception than “knowledge.” It would be a practically useless conception, but for the fact that knowledge has very vague boundaries. When we embark upon an investigation, we assume that the propositions concerning which we are inquiring are either true or false; we may find evidence, or we may not. Before the spectroscope, it would have seemed impossible ever to ascertain the chemical constitution of the stars; but it would have been a mistake to maintain that they neither do nor do not contain the elements we know. At present, we do not know whether there is life elsewhere in the universe, but we are right to feel sure that there either is or is not. Thus we need “truth” as well as “knowledge,” because the boundaries of knowledge are uncertain, and because, without the law of excluded middle, we could not ask the questions that give rise to discoveries.

To sum up the result of this long discussion: what we called the epistemological theory of truth, if taken seriously, confines “truth” to propositions asserting what I now perceive or remember. Since no one is willing to adopt so narrow a theory, we are driven to the logical theory of truth, involving the possibility of events that no one experiences and of propositions that are true although there can never be any evidence in their favour. Facts are wider (at least possibly) than experiences. A “verifiable” proposition is one having a certain kind of correspondence with an experience; a “true” proposition is one having exactly the same kind of correspondence with a fact—except that the simplest type of correspondence, that which occurs in judgments of perception, is impossible in the case of all other judgments, since these involve variables. Since an experience is a fact, verifiable propositions are true; but there is no reason to suppose that all true propositions are verifiable. If, however, we assert positively that there are true propositions that are not verifiable, we abandon pure empiricism. Pure empiricism, finally, is believed by no one, and if we are to retain beliefs that we all regard as valid, we must allow principles of inference which are neither demonstrative nor derivable from experience.

What [Carnap] calls “meaning” is what I have called “significance,” i.e. it is a property of sentences.

Given the experience necessary for the understanding of the name “a” and the predicate “P”, we can understand the sentence “a has the predicate P” without the need of any experience corresponding to this sentence; and when I say that we can understand the sentence, I do not mean that we know how to find out whether it is true. If you say “Mars contains inhabitants as mad and wicked as those of our planet,” I understand you, but I do not know how to find out whether what you say is true.

When it is said that “the meaning of a proposition is the method of its verification,” this omits the propositions that are most nearly certain, namely judgments of perception. For these there is no “method of verification,” since it is they that constitute the verification of all other empirical propositions that can be in any degree known. If [Moritz] Schlick were right, we should be committed to an endless regress, for propositions are verified by means of other propositions, which, in turn, must derive their meaning from the way in which they are verified by yet other propositions, and so on ad infinitum. All those who make “verification” fundamental overlook the real problem, which is the relation between words and non-verbal occurrences in judgements of perception.

The view of Carnap, which allows the concept of “thing” in the statement of factual premises, seems to me to ignore Berkeley and Hume, not to say Heraclitus. You cannot step twice into the same river, because fresh waters are continually flowing in upon you; but the difference between a river and a table is only a matter of degree. Carnap might admit that a river is not a “thing”; the same arguments should convince him that a table is not a “thing.”

It is obvious that, if nothing can be learnt from one observation, then nothing can be learnt from many observations. Therefore our first question must be: “what can be learnt from one observation?” What can be learnt from one observation cannot contain words applicable to classes of things, such as “paper” and “table.” We saw in an earlier chapter that “there is a dog” cannot be a factual premise, but “there is a canoid patch of colour” can be. A factual premise must not contain words which are condensed inductions, such as “dog,” “paper,” “table.”

Factual premises may not be certain, but there is nothing more certain by which they can be shown to be false.

When Newton’s theory of gravitation was replaced by Einstein’s, a certain vagueness in Newton’s concept of acceleration was removed, but almost all the assertions implied by Newton’s theory remained true. I should say that this is an illustration of what always happens when an old theory gives way to a better one: the old assertions failed to be definitely true or false, both because they were vague, and because they were many masquerading as one, some of the many being true and some false. But I do not see how to state the improvement except in terms of the two ideals of precision and truth.

I think that all judgments of perception involve analysis of a perceptual whole; what is given is a pattern, and the realization that it consists of interrelated objects results from analysis.

In the present chapter I propose to consider whether anything, and, if so, what, can be inferred from the structure of language as to the structure of the world. There has been a tendency, especially among logical positivists, to treat language as an independent realm, which can be studied without regard to non-linguistic occurrences. To some extent, and in a limited field, this separation of language from other facts is possible; the detached study of logical syntax has undoubtedly yielded valuable results. But I think it is easy to exaggerate what can be achieved by syntax alone. There is, I think, a discoverable relation between the structure of sentences and the structure of the occurrences to which the sentences refer. I do not think the structure of non-verbal facts is wholly unknowable, and I believe that, with sufficient caution, the properties of language may help us to understand the structure of the world.

Assuming that we can get rid of all universals except similarity, it remains to be considered whether similarity itself could be explained away.

We will consider this in the simplest possible case. Two patches of red (not necessarily of exactly the same shade) are similar, and so are two instances of the word “red.” Let us suppose that we are being shown a number of coloured discs and asked to name their colours—say in a test for colour-blindness. We are shown two red discs in succession, and each time we say “red.” We have been saying that, in the primary language, similar stimuli produce similar reactions; our theory of meaning has been based on this. In our case, the two discs are similar, and the two utterances of the word “red” are similar. Are we saying the same thing about the discs and about the utterances when we say the discs are similar and when we say the utterances are similar? or are we only saying similar things? In the former case, similarity is a true universal; in the latter case, not. The difficulty, in the latter case, is the endless regress; but are we sure that this difficulty is insuperable? We shall say, if we adopt this alternative: if A and B are perceived to be similar, and C and D are also perceived to be similar, that means that AB is a whole of a certain kind and CD is a whole of the same kind; i.e., since we do not want to define the kind by a universal, AB and CD are similar wholes. I do not see how we are to avoid an endless regress of the vicious kind if we attempt to explain similarity in this way.

I conclude, therefore, though with hesitation, that there are universals, and not merely general words. Similarity, at least, will have to be admitted; and in that case it seems hardly worth while to adopt elaborate devices for the exclusion of other universals.

It should be observed that the above argument only proves the necessity of the word “similar,” not of the word “similarity.”

Some propositions containing the word “similarity” can be replaced by equivalent propositions containing the word “similar,” while others cannot. These latter need not be admitted. Suppose, for example, I say “similarity exists.” If “exists” means what it does when I say “the President of the United States exists,” my statement is nonsense. What I can mean may, to begin with, be expressed in the statement: “there are occurrences which require for their verbal description sentences of the form ‘a is similar to b’.” But this linguistic fact seems to imply a fact about the occurrences described, namely the sort of fact that is asserted when I say “a is similar to b.” When I say “similarity exists,” it is this fact about the world, not a fact about language, that I mean to assert. The word “yellow” is necessary because there are yellow things; the word “similar” is necessary because there are pairs of similar things. And the similarity of two things is as truly a non-linguistic fact as the yellowness of one thing.

We have arrived, in this chapter, at a result which has been, in a sense, the goal of all our discussions. The result I have in mind is this: that complete metaphysical agnosticism is not compatible with the maintenance of linguistic propositions. Some modern philosophers hold that we know much about language, but nothing about anything else. This view forgets that language is an empirical phenomenon like another, and that a man who is metaphysically agnostic must deny that he knows when he uses a word. For my part, I believe that, partly by means of the study of syntax, we can arrive at considerable knowledge concerning the structure of the world.

Human Knowledge: Its Scope and Limits

by Bertrand Russell, 1948

Fact, Belief, Truth, and Knowledge

The purpose of this chapter is to state in dogmatic form certain conclusions which follow from previous discussion, together with the fuller discussions of “An Inquiry into Meaning and Truth.” More particularly, I wish to give meanings, as definite as possible, to the four words in the title of this chapter. I do not mean to deny that the words are susceptible of other equally legitimate meanings, but only that the meanings which I shall assign to them represent important concepts, which, when understood and distinguished, are useful in many philosophical problems, but when confused are a source of inextricable tangles.

A. Fact

"Fact,” as I intend the term, can only be defined ostensively. Everything that there is in the world I call a “fact.” The sun is a fact; Caesar’s crossing of the Rubicon was a fact; if I have toothache, my toothache is a fact. If I make a statement, my making it is a fact, and if it is true there is a further fact in virtue of which it is true, but not if it is false. The butcher says: “I’m sold out, and that’s a fact”; immediately afterwards, a favoured customer arrives, and gets a nice piece of lamb from under the counter. So the butcher told two lies, one in saying he was sold out, and the other in saying that his being sold out was a fact. Facts are what make statements true or false. I should like to confine the word “fact” to the minimum of what must be known in order that the truth or falsehood of any statement may follow analytically from those asserting that minimum. For example, if “Brutus was a Roman” and “Cassius was a Roman” each assert a fact, I should not say the “Brutus and Cassius were Romans” asserted a new fact. We have seen that the questions whether there are negative facts and general facts raise difficulties. These niceties, however, are largely linguistic.

I mean by a “fact” something which is there, whether anybody thinks so or not. If I look up a railway time-table and find that there is a train to Edinburgh at 10 a.m., then, if the time-table is correct, there is an actual train, which is a “fact.” The statement in the time-table is itself a “fact,” whether true or false, but it only states a fact if it is true, i.e. if there really is a train. Most facts are independent of our volitions; that is why they are called “hard,” “stubborn,” or “inescapable.” Physical facts, for the most part, are independent, not only of our volitions, but even our existence.

The whole of our cognitive life is, biologically considered, part of the process of adaptation to facts. This process is one which exists, in a greater or less degree, in all forms of life, but is not commonly called “cognitive” until it reaches a certain level of development. Since there is no sharp frontier anywhere between the lowest animal and the most profound philosopher, it is evident that we cannot say precisely at what point we pass from mere animal behaviour to something deserving to be dignified by the name of “knowledge.” But at every stage there is adaptation, and that to which the animal adapts itself is the environment of fact.

B. Belief

“Belief.” which we have next to consider, has an inherent and inevitable vagueness, which is due to the continuity of mental development from the amoeba to homo sapiens. In its most developed form, which is that most considered by philosophers, it is displayed by the assertion of a sentence. After sniffing for a time, you exclaim: “Good heavens! the house is on fire.” Or, when a picnic is in contemplation, you say: “Look at those clouds: there will be rain.” Or, in a train, you try to subdue an optimistic fellow-passenger by observing: “Last time I did this journey we were three hours late.” Such remarks, if you are not lying, express beliefs. We are so accustomed to the use of words for expressing beliefs that it may seem strange to speak of “belief” in cases where there are no words. But it is clear that even when words are used they are not of the essence of the matter. The smell of burning first makes you believe that the house is on fire, and then the words come, not as being the belief, but as a way of putting it into a form of behaviour in which it can be communicated to others. I am thinking, of course, of beliefs that are not very complicated or refined. I believe that the angles of a polygon add up to twice as many right angles as the figure has sides diminished by four right angles, but a man would need super-human mathematical intuition to be able to believe this without words. But the simpler kind of belief, especially when it calls for action, may be entirely unverbalized. When you are travelling with a companion, you may say: “We must run; the train is just going to start.” But if you are alone you may have the same belief, and run just as fast, without any words passing through your head.

I propose, therefore, to treat belief as something that can be pre-intellectual, and can be displayed in the behaviour of animals. I incline to think that, on occasion, a purely bodily state may deserve to be called a “belief.” For example, if you walk into your room in the dark, and someone has put a chair in an unusual place, you may bump into it, because your body believed there was no chair there. But the parts played by mind and body respectively in belief are not very important to separate for our present purposes. A belief, as I understand the term, is a certain kind of state of body or mind or both. To avoid verbiage, I shall call it a state of an organism, and ignore the distinction of bodily and mental factors.

One characteristic of a belief is that it has external reference, in the sense defined in a previous chapter. The simplest case, which can be observed behaviouristically, is when, owing to conditioned reflex, the presence of A causes behaviour appropriate to B. This covers the important case of acting on information received: here the phrase heard is A, and what it signifies is B. Somebody says “look out, there’s a car coming,” and you act as you would if you saw the car. In this case you are believing what is signified by the phrase “a car is coming.”

Any state of an organism which consists in believing something can, theoretically, be fully described without mentioning the something. When you believe “a car is coming,” your belief consists in a certain state of the muscles, sense-organs, and emotions, together perhaps with certain visual images. All this, and whatever else may go to make up your belief, could in theory, be fully described by a psychologist and physiologist working together, without their ever having to mention anything outside your mind and body. Your state, when you believe that a car is coming, will be very different in different circumstances. You may be watching a race, and wondering whether the car on which you have put your money will win. You may be waiting for the return of your son from captivity in the Far East. You may be trying to escape from the police. You may be suddenly roused from absent-mindedness while crossing the street. But although your total state will not be the same in these various cases, there will be something in common among them, and it is this something which makes them all instances of the belief that a car is coming. A belief, we may say, is a collection of states of an organism bound together by all having, in whole or part, the same external reference.

In an animal or a young child, believing is shown by an action or series of actions. The beliefs of the hound about the fox are shown by his following the scent. But in human beings, as a result of language and of the practice of suspended reactions, believing often becomes a more or less static condition, consisting perhaps in pronouncing or imagining appropriate words, together with one of the feelings that constitute different kinds of belief. As to these, we may enumerate: first, the kind of belief that consists in filling out sensation by animal inferences; second, memory; third, expectation; fourth, the kind of belief generated unreflectingly by testimony; and fifth, the kind of belief resulting from conscious inference. Perhaps this list is both incomplete and in part redundant, but certainly perception, memory, and expectation differ as to the kinds of feeling involved. “Belief,” therefore, is a wide generic term, and a state of believing is not sharply separated from cognate states which would not naturally be described as believings.

The question what it is that is believed when an organism is in a state of believing is usually somewhat vague. The hound pursuing a scent is unusually definite, because his purpose is simple and he has no doubt as to the means; but a pigeon hesitating whether to eat out of your hand is in a much more vague and complex condition. Where human beings are concerned, language gives an illusory appearance of precision; a man may be able to express his belief in a sentence, and it is then supposed that the sentence is what he believes. But as a rule this is not the case. If you say “look, there is Jones,” you are believing something, and expressing your belief in words, but what you are believing has to do with Jones, not with the name “Jones.” You may, on another occasion, have a belief which is concerned with words. “Who is that very distinguished man who has just come in? That is Sir Theophilus Thwackum.” In this case it is the name you want. But as a rule in ordinary speech the words are, so to speak, transparent; they are not what is believed, any more than a man is the name by which he is called.

When words merely express a belief which is about what the words mean, the belief indicated by the words is lacking in precision to the degree that the meaning of the words is lacking in precision. Outside logic and pure mathematics, there are no words of which the meaning is precise, not even such words as “centimetre” and “second.” Therefore even when a belief is expressed in words having the greatest degree of precision of which empirical words are capable, the question as to what it is that is believed is still more or less vague.

This vagueness does not cease when a belief is what may be called “purely verbal,” i.e. when what is believed is that a certain sentence is true. This is the sort of belief acquired by schoolboys whose education has been on old-fashioned lines. Consider the difference in the schoolboy’s attitude to “William the Conqueror, 1066” and “next Wednesday will be a whole holiday.” In the former case, he knows that that is the right form of words, and cares not a pin for their meaning; in the latter case, he acquires a belief about next Wednesday, and cares not a pin what words you use to generate his belief. The former belief, but not the latter, is “purely verbal.”

If I were to say that the schoolboy is believing that the sentence “William the Conqueror, 1066” is “true,” I should have to add that his definition of “truth” is purely pragmatic: a sentence is “true” if the consequences of uttering it in the presence of a master are pleasant; if they are unpleasant, it is “false.”

Forgetting the schoolboy, and resuming our proper character as philosophers, what do we mean when we say that a certain sentence is “true”? I am not yet asking what is meant by “true”; this will be our next topic. For the moment I am concerned to point out that, however “true” may be defined, the significance of “this sentence is true” must depend upon the significance of the sentence, and is therefore vague in exactly the degree in which there is vagueness in the sentence which is said to be true. We do not therefore escape from vagueness by concentrating attention on purely verbal beliefs.

Philosophy, like science, should realize that, while complete precision is impossible, techniques can be invented which gradually diminish the area of vagueness or uncertainty. However admirable our measuring apparatus may be, there will always remain some lengths concerning which we are in doubt whether they are greater than, less than, or equal to, a metre; but there is no known limit to the refinements by which the number of such doubtful lengths can be diminished. Similarly, when a belief is expressed in words, there will always remain a band of possible circumstances concerning which we cannot say whether they would make the belief true or false, but the breadth of this band can be indefinitely diminished, partly by improved verbal analysis, partly be a more delicate technique in observation. Whether complete precision is or is not theoretically possible depends upon whether the physical world is discrete or continuous.

Let us now consider the case of a belief expressed in words all of which have the greatest attainable degree of precision. Suppose, for the sake of concreteness, that I believe the sentence: “My height is greater that 5 ft. 8 ins. and less that 5 ft. 9 ins.” Let us call this sentence “S”. I am not yet asking what would make this sentence true, or what would entitle me to say that I know it; I am asking only: “What is happening in me when I have the belief which I express by the sentence S?” There is obviously no one correct answer to this question. All that can be said definitely is that I am in a state such as, if certain further things happen, will give me a feeling which might be expressed by the words “quite so,” and that, now, while these things have not yet happened, I have the idea of their happening combined with the feeling expressed by the word “yes.” I may, for instance, imagine myself standing against a wall on which there is a scale of feet and inches, and in imagination see the top of my head between two marks on this scale, and towards this image I may have the feeling of assent. We may take this as the essence of what may be called “static” belief, as opposed to belief shown by action: static belief consists in an idea or image combined with a yes-feeling.

C. Truth

I come now to the definition of “truth” and “falsehood.” Certain things are evident. Truth is a property of beliefs, and derivatively of sentences which express beliefs. Truth consists in a certain relation between a belief and one or more facts other than the belief. When this relation is absent, the belief is false. A sentence may be called “true” or “false” even if no one believes it, provided that, if it were believed, the belief would be true or false as the case may be.

So much, I say, is evident. But what is not evident is the nature of the relation between belief and fact that is involved, or the definition of the possible fact that will make a given belief true, or the meaning of “possible” in this phrase. Until these questions are answered we have no adequate definition of “truth.”

Let us begin with the biologically earliest form of belief, which is to be seen among animals as among men. The compresence of two kinds of circumstance, A and B, if it has been frequent or emotionally interesting, is apt to have the result that, when A is sensibly present, the animal reacts as it formerly reacted to B, or at any rate displays some part of this reaction. In some animals this connection may be sometimes innate, and not the result of experience. But however the connection may be brought about, when the sensible presence of A causes acts appropriate to B, we may say that the animal “believes” B to be in the environment, and that the belief is “true” if B is in the environment. If you wake a man up in the middle of the night and shout “fire!” he will leap from his bed even if he does not yet see or smell fire. His action is evidence of a belief which is “true” if there is fire, and “false” otherwise. Whether his belief is true depends upon a fact which may remain outside his experience. He may escape so fast that he never acquires sensible evidence of the fire; he may fear that he will be suspected of incendiarism and flee the country, without ever inquiring whether there was a fire or not; nevertheless his belief remains true if there was the fact (namely fire) which constituted its external reference or significance, and if there was not such a fact his belief remained false even if all his friends assured him that there had been a fire.

The difference between a true and false belief is like that between a wife and a spinster: in the case of a true belief there is a fact to which it has a certain relation, but in the case of a false belief there is no such fact. To complete our definition of “truth” and “falsehood” we need a description of the fact which would make a given belief true, this description being one which applies to nothing if the belief is false. Given a woman of whom we do not know whether she is married or not, we can frame a description which will apply to her husband if she has one, and to nothing if she is a spinster. Such a description would be: “the man who stood beside her in a church or registry office while certain words were pronounced.” In like manner we want a description of the fact or facts which, if they exist, make a belief true. Such fact or facts I call the “verifier” of the belief.

What is fundamental in this problem is the relation between sensations and images, or, in Hume’s terminology, between impressions and ideas. We have considered in a previous chapter the relation of an idea to its prototype, and have seen how “meaning” develops out of this relation. But given meaning and syntax, we arrive at a new concept, which I call “significance,” and which is characteristic of sentences and of complex images. In the case of single words used in an exclamatory manner, such as “fire!” or “murder!” meaning and significance coalesce, but in general they are distinct. The distinction is made evident by the fact that words must have meaning if they are to serve a purpose, but a string of words does not necessarily have significance. Significance is a characteristic of all sentences that are not nonsensical, and not only of sentences in the indicative, but also of such as are interrogative, imperative, or optative. For present purposes, however, we may confine ourselves to sentences in the indicative. Of these we may say that the significance consists in the description of the fact which, if it exists, will make the sentence true. It remains to define this description.

Let us take an illustration. Jefferson had a belief expressed in the words: “There are mammoths in North America.” This belief might have been true even if no one had seen one of these mammoths; there might, when he expressed the belief, have been just two in an uninhabited part of the Rocky Mountains, and they might soon afterwards have been swept by a flood down the Colorado River into the sea. In that case, in spite of the truth of his belief, there would have been no evidence for it. The actual mammoths would have been facts, and would have been, in the above sense, “verifiers” of the belief. A verifier which is not experienced can often be described, if it has a relation known by experience to something known by experience; it is in this way that we understand such a phrase as “the father of Adam,” which describes nothing. It is in this way that we understand Jefferson’s belief about mammoths: we know the sort of facts that would have made his belief true, that is to say, we can be in a state of mind such that, if we had seen mammoths, we should have exclaimed: “Yes, that’s what I was thinking of.”

The significance of a sentence results from the meanings of its words together with the laws of syntax. Although meanings must be derived from experience, significance need not. I know from experience the meaning of “man” and the meaning of “wings,” and therefore the significance of the sentence “There is a winged man,” although I have no experience of what this sentence signifies. The significance of a sentence may always be understood as in some sense a description. When this description describes a fact, the sentence is “true”; otherwise it is “false.”

It is important not to exaggerate the part played by convention. So long as we are considering beliefs, not the sentences in which they are expressed, convention plays no part at all. Suppose you are expecting to meet some person of whom you are fond, and whom you have not seen for some time. Your expectation may be quite wordless, even if it is detailed and complex. You may hope that he will be smiling, you may recall his voice, his gait, the expression of his eyes; your total expectation may be such as only a good painter could express, in paint, not in words. In this case you are expecting an experience of your own, and the truth or falsehood of your expectation is covered by the relation of idea and impression: your expectation is “true” if the impression, when it comes, is such that it might have been the prototype of your previous idea if the time-order had been reversed. This is what we express when we say: “That is what I expected to see.” Convention is concerned only in the translation of belief into language, or (if we are told something) of language into belief. Moreover the correspondence of language and belief, except in abstract matters, is usually by no means exact: the belief is richer in detail and context than the sentence, which picks out only certain salient features. You say “I shall see him soon,” but you think “I shall see him smiling, but looking older, friendly, but shy, with his hair untidy and his shoes muddy”—and so on, through an endless variety of detail of which you may be only half aware.

The case of an expectation is the simplest from the point of view of defining truth and falsehood, for in this case the fact upon which truth or falsehood depends is about to be experienced. Other cases are more difficult. Memory, form the standpoint of our present problem, is closely analogous to expectation. A recollection is an idea, while the fact recollected was an impression; the memory is “true” if the recollection has to the fact that kind of resemblance which exists between an idea and its prototype.

Consider, next, such a statement as “you have a toothache.” In any belief concerning another person’s experience there may be the same sort of extra-verbal richness that we have seen to be frequent in regard to expectations of our own experiences; you may, having recently had toothache, feel sympathetically the throbbing pangs that you imagine your friend to be suffering. Whatever wealth or paucity of imagination you may bring to bear, it is clear that your belief is “true” in proportion as it resembles the fact of your friend’s toothache—the resemblance being again of the sort that can subsist between idea and prototype.

But when we pass on to something which no one experiences or has experienced, such as the interior of the earth, or the world before life began, both belief and truth become more abstract than in the above cases. We must now consider what can be meant by “truth” when the verifying fact is experienced by no one.

Anticipating coming discussions, I shall assume that the physical world, as it is independently of perception, can be known to have a certain structural similarity to the world of our percepts, but cannot be known to have any qualitative similarity. And when I say that it has structural similarity, I am assuming that the ordering relations in terms of which the structure is defined are spatio-temporal relations such as we know in our own experience. Certain facts about the physical world, therefore—those facts, namely, which consist of space-time structure—are such as we can imagine. On the other hand, facts as to the qualitative character of physical occurrences are, presumably, such as we cannot imagine.

Now while there is no difficulty in supposing that there are unimaginable facts, there cannot be beliefs, other than general beliefs, of which the verifiers would be unimaginable. This is an important principle, but if it is not to lead us astray a little care is necessary as regards certain logical points. The first of these is that we may know a general proposition although we do not know any instance of it. On a large pebbly beach you may say, probably with truth: “There are pebbles on this beach which no one will ever have noticed.” It is quite certainly true that there are finite integers which no one will ever have thought of. But it is self-contradictory to suppose such propositions established by giving instances of their truth. This is only an application of the principle that we can understand statements about all or some of the members of a class without being able to enumerate the members. We understand the statement “all men are mortal” just as completely as we should if we could give a complete list of men; for to understand this statement we need only understand the concepts “man” and “mortal” and what is meant by being an instance of them.

Now take the statement: “There are facts which I cannot imagine.” I am not considering whether this statement is true; I am only concerned to show that it is intelligible. Observe, in the first place, that if it is not intelligible, its contradictory must also be not intelligible, and therefore not true, though also not false. Observe, in the second place, that to understand the statement it is unnecessary to be able to give instances, any more than of the unnoticed pebbles or the numbers that are not thought of. All that is necessary is to understand the words and the syntax, which we do. The statement is therefore intelligible; whether it is true is another matter.

Take, now, the following statement: “There are electrons, but they cannot be perceived.” Again I am not asking whether the statement is true, but what is meant by supposing it true or believing it to be true. “Electron” is a term defined by means of causal and spatio-temporal relations to events that we experience, and to other events related to them in ways of which we have experience. We have experience of the relation “parent,” and can therefore understand the relation “great-great-great-grandparent,” although we have no experience of this relation. In like manner we can understand sentences containing the word “electron,” in spite of not perceiving anything to which this word is applicable. And when I say we can understand such sentences, I mean that we can imagine facts which would make them true.

The peculiarity, in such cases, is that we can imagine general circumstances which would verify our belief, but cannot imagine the particular facts which are instances of the general fact. I cannot imagine any particular fact of the form: “n is a number which will never have been thought of,” for, whatever value I give to n, my statement becomes false by the very fact of my giving that value. But I can quite well imagine the general fact which gives truth to the statement: “There are numbers which will never have been thought of.” The reason is that general statements are concerned with intensions, and can be understood without any knowledge of the corresponding extensions.

Beliefs as to what is not experienced, as the above discussion has shown, are not as to unexperienced individuals, but as to classes of which no member is experienced. A belief must always be capable of being analyzed into elements that experience has made intelligible, but when a belief is set out in logical form it often suggests a different analysis, which would seem to involve components not known by experience. When such psychologically misleading analysis is avoided, we can say, quite generally: Every belief which is not merely an impulse to action is in the nature of a picture, combined with a yes-feeling or a no-feeling; in the case of a yes-feeling it is “true” if there is a fact having to the picture the kind of similarity that a prototype has to an image; in the case of a no-feeling it is “true” if there is no such fact. A belief which is not true is called “false.”

This is a definition of “truth” and “falsehood.”

D. Knowledge

I come now to the definition of “knowledge.” As in the cases of “belief” and “truth,” there is a certain inevitable vagueness and inexactitude in the conception. Failure to realize this has led, it seems to me, to important errors in the theory of knowledge. Nevertheless, it is well to be as precise as possible about the unavoidable lack of precision in the definition of which we are in search.

It is clear that knowledge is a sub-class of true beliefs: every case of knowledge is a case of true belief, but not vice versa. It is very easy to give examples of true beliefs that are not knowledge. There is the man who looks at a clock which is not going, though he thinks it is, and who happens to look at it at the moment when it is right; this man acquires a true belief as to the time of day, but cannot be said to have knowledge. There is the man who believes, truly, that the last name of the Prime Minister in 1906 began with a B, but who believes this because he thinks that Balfour was Prime Minister then, whereas in fact it was Campbell-Bannerman. There is the lucky optimist who, having bought a ticket for a lottery, has an unshakeable conviction that he will win, and, being lucky, does win. Such instances can be multiplied indefinitely, and show that you cannot claim to have known merely because you turned out to be right.

What character in addition to truth must a belief have in order to count as knowledge? The plain man would say there must be sound evidence to support the belief. As a matter of common sense this is right in most of the cases in which doubt arises in practice, but if intended as a complete account of the matter it is very inadequate. “Evidence” consists, on the one hand, of certain matters of fact that are accepted as indubitable, and, on the other hand, of certain principles by means of which inferences are drawn from the matters of fact. It is obvious that this process is unsatisfactory unless we know the matters of fact and the principles of inference not merely by means of evidence, for otherwise we become involved in a vicious circle or an endless regress. We must therefore concentrate our attention on the matters of fact and the principles of inference. We may then say that what is known consists, first, of certain matters of fact and certain principles of inference, neither of which stands in need of extraneous evidence, and secondly, of all that can be ascertained by applying the principles of inference to the matters of fact. Traditionally, the matters of fact are those given in perception and memory, while the principles of inference are those of deductive and inductive logic.

There are various unsatisfactory features in this traditional doctrine, though I am not at all sure that, in the end, we can substitute anything very much better. In the first place, the doctrine does not give an intensional definition of “knowledge,” or at any rate not a purely intensional definition; it is not clear what there is in common between facts of perception and principles of inference. In the second place, as we shall see in Part III, it is very difficult to say what are facts of perception. In the third place, deduction has turned out to be much less powerful than was formerly supposed; it does not give new knowledge, except as to new forms of words for stating truths in some sense already known. In the fourth place, the methods of inference that may be called in a broad sense “inductive” have never been satisfactorily formulated; when formulated, even if completely true, they only give probability to their conclusions; moreover, in any possibly accurate form, they lack self-evidence, and are only to be believed, if at all, because they seem indispensable in reaching conclusions that we all accept.

There are, broadly speaking, three ways that have been suggested for coping with the difficulties in defining “knowledge.” The first, and oldest, is to emphasize the concept of “self-evidence.” The second is to abolish the distinction between premises and conclusions, and to say that knowledge is constituted by the coherence of a whole body of beliefs. The third and most drastic is to abandon the concept of “knowledge” altogether and substitute “beliefs that promote success”—and here “success” may perhaps be interpreted biologically. We may take Descartes, Hegel, and Dewey as protagonists of these three points of view.

Descartes holds that whatever I conceive clearly and distinctly is true. He believes that, from this principle, he can derive not only logic and metaphysics, but also matters of fact, at least in theory. Empiricism has made such a view impossible; we do not think that even the utmost clarity in our thoughts would enable us to demonstrate the existence of Cape Horn. But this does not dispose of the concept of “self-evidence”: we may say that what he says applies to conceptual evidence, but that there is also perceptual evidence, by means of which we come to know matters of fact. I do not think we can entirely dispense with self-evidence. If you slip on a piece of orange peel and hit your head with a bump on the pavement, you will have little sympathy with a philosopher who tries to persuade you that it is uncertain whether you are hurt. Self-evidence also makes you accept the argument that if all men are mortal and Socrates is a man, then Socrates is mortal. I do not know whether self-evidence is anything except a certain firmness of conviction; the essence of it is that, where it is present, we cannot help believing. If, however, self-evidence is to be accepted as a guarantee of truth, the concept must be carefully distinguished from others that have a subjective resemblance to it. I think we must bear it in mind as relevant to the definition of “knowledge,” but as not in itself sufficient.

Another difficulty about self-evidence is that it is a matter of degree. A clap of thunder is indubitable, but a very faint noise is not; that you are seeing the sun on a bright day is self-evident, but a vague blur in a fog may be imaginary; a syllogism in Barbara is obvious, but a difficult step in a mathematical argument may be very hard to “see.” It is only for the highest degree of self-evidence that we should claim the highest degree of certainty.

The coherence theory and the instrumentalist theory are habitually set forth by their advocates as theories of truth. As such they are open to certain objections which I have urged elsewhere. I am considering them now, not as theories of truth, but as theories of knowledge. In this form there is more to be said for them.

Let us ignore Hegel, and set forth the coherence theory of knowledge for ourselves. We shall have to say that sometimes two beliefs cannot both be true, or, at least, that we sometimes believe this. If I believe simultaneously that A is true, that B is true, and that A and B cannot both be true, I have three beliefs which do not form a coherent group. In that case at least one of the three must be mistaken. The coherence theory in its extreme form maintains that there is only one possible group of mutually coherent beliefs, which constitute the whole of knowledge and the whole of truth. I do not believe this; I hold, rather, to Leibnitz’s multiplicity of possible worlds. But in a modified form it will say that all, or nearly all, of what passes for knowledge is in a greater or less degree uncertain; that, if principles of inference are among the prima facie materials of knowledge, then one piece of prima facie knowledge may be inferrible from another, and thus acquires more credibility than it had on its own account. It may thus happen that a body of propositions, each of which has only a moderate degree of credibility on its own account, may collectively have a very high degree of credibility. But this argument depends upon the possibility of varying degrees of intrinsic credibility, and is therefore not a pure coherence theory. I shall consider this matter in more detail in Part V.

With respect to the theory that we should substitute for “knowledge” the concept “beliefs that promote success,” it is sufficient to point out that it derives whatever plausibility it may possess from being half-hearted. It assumes that we can know (in the old-fashioned sense) what beliefs promote success, for if we cannot know this the theory is useless in practice, whereas its purpose is to glorify practice at the expense of theory. In practice, obviously, it is often very difficult to know what beliefs promote success, even if we have an adequate definition of “success.”

The conclusion to which we seem to be driven is that knowledge is a matter of degree. The highest degree is found in facts of perception, and in the cogency of very simple arguments. The next highest degree is in vivid memories. When a number of beliefs are each severally in some degree credible, they become more so if they are found to cohere as a logical whole. General principles of inference, whether deductive or inductive, are usually less obvious than many of their instances. Towards the end of our inquiry I shall return to the definition of “knowledge,” and shall then attempt to give more precision and articulation to the above suggestions. Meanwhile let us remember that the question “what do we mean by ‘knowledge’?” is not one to which there is a definite and unambiguous answer, any more than to the question “what do we mean by ‘baldness’?”


Our knowledge of facts, in so far as it is not inferential, has two sources, sensation and memory. Of these, sensation is the more fundamental, since we can only remember what has been a sensible experience. But although sensation is a source of knowledge, it is not itself, in any usual sense, knowledge. When we speak of “knowledge,” we generally imply a distinction between the knowing and what is known, but in sensation there is no such distinction. “Perception,” as the word is used by most psychologists, is of the nature of knowledge, but it is so because of the adjuncts which are added to pure sensation by experience, or, possibly, by congenital dispositions. But these adjuncts can only count as “knowledge” if there are connections between the sensation and other facts outside my momentary mental state, and these connections must be suitably related to the connection between the pure sensation and the rest of the mental state called a perceiving. The passage from sensation to perception, therefore, involves connections between facts, not only facts. It involves these, however, only if perception is to be regarded as a form of knowledge; as a psychological occurrence, perception is a mere fact, but one which might not be veridical as regards what it adds to sensation. It is only veridical if there are certain connections among facts, e.g. between the visual appearance of iron and hardness.

The purely logical analysis of “dogs bark” soon reaches complexities which make it incredible that ordinary folk can seem to understand anything so remote, mysterious, and universal. The first stage, for the logician, is to substitute: “Whatever x may be, either x is not a dog or x barks.” But since dogs only bark sometimes, you have to substitute for “x barks” the statement “there is a time t at which x barks.” Then you must substitute one or other of the two alternative definitions of “t” given in Part IV. In the end you will arrive at a statement of enormous length, not only about dogs, but about everything in the universe, and so complicated that it cannot be understood except by a person with a considerable training in mathematical logic. But suppose you have to explain your statement “dogs bark” to such a person, but as he is a foreigner with only a mathematician’s knowledge of English, he does not know the word “dog” or the word “bark.” What will you do? You will certainly not go through the above logical rigmarole. You will point to your dog and say “dog”; you will then excite him till he barks and say “bark.” The foreigner will then understand you, although, as a logician, he has no business to do so. This makes it clear that the psychology of general propositions is something very different from their logic. The psychology is what does take place when we believe them; the logic is perhaps what ought to take place if we were logical saints.

The hypothesis that the starry heavens exist at all times, and the hypothesis that they only exist when I see them, are exactly identical in all those of their consequences that I can test. It is specially in such cases that meaning is identified with verification, and that, therefore, the two hypotheses are said to have the same significance. And it is this that I am specially concerned to deny. Perhaps the most obvious case is other people’s minds. The hypothesis that there are other people, having thoughts and feelings more or less like my own, does not have the same significance as the hypothesis that other people are only parts of my dreams, and yet the verifiable consequences of the two hypotheses are identical. We all feel love and hate, sympathy and antipathy, admiration and contempt, for what we believe to be real people. The emotional consequences of this belief are very different from those of solipsism, though the verifiable consequences are not. I should say that two beliefs whose emotional consequences differ have substantially distinct significations.

Belief in the external causation of certain kinds of experience is primitive, and is, in a certain sense, implicit in animal behaviour. It is involved in the concept of “perception.” When you “perceive” a table or a person, the sun or the moon, the noise of an explosion or the smell of a bad drain, it is, for common sense, because what you are perceiving is there to be perceived. If you think you are perceiving an object which in fact is not there, you are dreaming, or suffering a hallucination, or misinterpreting a sensation. But it is assumed that such occurrences are sufficiently uncommon, or sufficiently queer, to be incapable of deceiving permanently anybody but a lunatic. Most perceptions, at most times, are taken to be either trustworthy or only momentarily deceptive; persons whose professed perceptions threaten our security by their strangeness are locked up in asylums. Thus common sense, by the help of the law, succeeds in preserving its belief that what seem like perceptions usually have external causes which more or less resemble their effects in perception. I think that common sense is in the right in this belief, except that the resemblance between perception and object is probably less than common sense supposes.

I come now to another application of the concept of identical structures. We all believe that we live in a common world, peopled not only by sentient beings like ourselves, but also by physical objects. I say we all believe this, in spite of the fact that some philosophers have pretended to doubt it. There are on the one hand solipsists who maintain that they alone exist, and make desperate efforts to make others agree with them. Then there are philosophers who hold that all reality is mental, and that while the feelings we experience when we look at the sun are real, the sun itself is a fiction. And as a development of this view there is the theory of Leibnitz, according to which the world consists of monads that never interact, and perception is in no degree due to the action of the outer world upon the percipient. In this view we may be said to be all dreaming, but the dreams that we all have are identical in structure. These different views, I say, have been advocated by different philosophers, and I do not think that any of them can be disproved. On the other hand, none of them can be proved, and, what is more, none of them can be believed, not even by their advocates.

My Philosophical Development

by Bertrand Russell, 1959

I returned to England in June 1944, after three weeks on the Atlantic. Trinity had awarded me a five-years lectureship and I chose as the subject of my annual course, ‘Non-Demonstrative Inference.’ I had become increasingly aware of the very limited scope of deductive inference as practised in logic and pure mathematics. I realized that all the inferences used both in common sense and in science are of a different sort from those in deductive logic, and are such that, when the premises are true and the reasoning correct, the conclusion is only probable.

I found the subject of non-demonstrative inference much larger and much more interesting than I had expected. I found that it had in most discussions been unduly confined to the investigation of induction. I came to the conclusion that inductive arguments, unless they are confined within the limits of common sense, will lead to false conclusions much more often than to true ones. The limitations imposed by common sense are easy to feel but very difficult to formulate. In the end, I came to the conclusion that, although scientific inference needs indemonstrable extra-logical principles, induction is not one of them. It has a part to play, but not as a premise.

Another conclusion which was forced upon me was that not only science, but a great deal that no one sincerely doubts to be knowledge, is impossible if we only know what can be experienced and verified. I felt that much too much emphasis had been laid upon experience, and that, therefore, empiricism as a philosophy must be subjected to important limitations.

I found that, for lack of analysis, people had admitted blocks of non-demonstrative inference because they had a subjective prejudice in favour of certain kinds of knowledge, and had rejected other blocks on account of a contrary prejudice.

A very great deal of what we all unquestioningly accept as knowledge depends upon testimony, and testimony, in turn, depends upon the belief that there are other minds besides our own. To common sense, the existence of other minds does not appear open to doubt, and I do not myself see any reason to disagree with common sense on this point. But, undoubtedly, it is through experiences of my own that I am led to believe in the minds of others; and, undoubtedly, as a matter of pure logic, it would be possible for me to have these experiences even if other minds did not exist.

Unless we are to land ourselves in preposterous paradoxes, we shall find it necessary to admit that we may know such propositions as ‘all A is B’ or ‘some A is B,’ without being able to give any instance of A—e.g., ‘all the numbers that I have never thought of and never shall think of are greater than a thousand.’ Although this proposition is undeniable, I should contradict myself if I attempted to give an instance.

I do not think it is possible to get anywhere if we start from scepticism. We must start from a broad acceptance of whatever seems to be knowledge and is not rejected for some specific reason. Hypothetical scepticism is useful in logical dissection. It enables us to see how far we can get without this or that premise—as, for example, we can inquire how much of geometry is possible without the axiom of parallels. But it is only for such purposes that hypothetical scepticism is useful.

It is to be observed that, without the introduction of principles, no suggested collection of facts, or supposed facts, is either coherent or inconsistent, since no two facts can either imply or contradict each other except in virtue of some extralogical principle.

In the transition from crude fact to science, we need forms of inference additional to those of deductive logic. Traditionally, it was supposed that induction would serve this purpose, but this was an error, since it can be shown that the conclusions of inductive inferences from true premises are more often false than true.

The accusation of metaphysics has become in philosophy something like the accusation of being a security risk in the public service. I do not for my part know what is meant by the word ‘metaphysics.’ The only definition I have found that fits all cases is: ‘a philosophical opinion not held by the present author.’

Remarks on Russell’s Thought by Alan Wood

Philosophical argument, strictly speaking, consists mainly of an endeavour to cause the reader to perceive what has been perceived by the author. The argument, in short, is not of the nature of proof, but of exhortation.

Look, can’t you see what I see?

The love of system, of perhaps the inmost essence of the intellectual impulse.

Russell’s philosophy was a battleground on which he fought a losing battle against himself; sometimes going one way, sometimes another; and he covered the whole field before reaching conclusions usually diametrically opposed to those which he had hoped for.

To the question ‘Does analysis mean falsification?’ I believe the only correct answer is ‘Yes, if you don’t know what you are doing.’

The general trend of Russell’s thought led to results directly opposite to those he hoped to reach.

Any hostile critic can collect an easy crop of verbal inconsistencies from many a great thinker if he is unsympathetic to the problems presented by difficult subject matter.

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