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Series I

Lecture 3: Belief and Knowledge

The Contrast between Belief and Knowledge

So much for various uses of the verb ‘to know’. We must bear them in mind when we consider the relations between belief and knowledge. Belief is often contrasted with knowledge, as in ‘I do not know where he lives, but I believe he lives in Bradford’. Knowledge is what we aim at in all our enquiries and investigations. But often we cannot get it. Belief is a second best. It is not what we wanted, but it is better than nothing. It may of course be held that knowledge is itself definable in terms of belief, and we shall consider this view later. But anyone who accepts it will still have to distinguish between the sort of belief which amounts to knowledge and the sort which does not. There will still be a contrast between knowledge and ‘mere’ belief. And some reasonable beliefs, beliefs held on good but not conclusive evidence, will have to be counted as ‘mere’ beliefs, and contrasted with knowledge, even when the propositions believed are in fact true.

To discuss the contrast between knowledge and belief, let us consider each of the different kinds of knowledge which can be distinguished. Let us first consider the usage in which the verb ‘to know’ governs an accusative (knowledge by acquaintance). The verb ‘to believe’ may govern an accusative too. We may believe a person.1 He told us that the bus would arrive at 10.30, and we believed him, though actually it arrived half an hour earlier and we missed it. But there is no contrast here between believing and knowing. Believing a person is not a second-best substitute for knowing him. It amounts only to believing what he says or writes or otherwise conveys, e.g. by means of a signal or a gesture. Again, I cannot believe, or disbelieve, an inanimate object, though inanimate objects, as well as persons, may be known by acquaintance, at least in the ordinary everyday use of the verb ‘to know’ with an accusative. One cannot even believe a cat or a dog, though in some circumstances one might trust it or rely on it; (a blind man trusts his guide-dog, and I may trust my cat to miaow if he gets shut up in the attic or the cellar). I think we cannot even believe a parrot or a raven which talks, not even if it utters indicative sentences. One assumes that its utterances have no relation to facts and do not even purport to be true. The most we can do is to draw inferences from these utterances. According to an Indian story, one could infer that a certain house belonged to the philosopher Sankara, because all the parrots in the trees around it were saying ‘The Vedas are infallible’. (Someone who wished to visit Sankara asked how to find his house, and this was the advice he received.)

There is no contrast, then, between knowing a person by acquaintance and believing him. What is contrasted with knowing an entity by acquaintance is believing propositions about it or him. The propositions we believe about an entity may be very numerous, and it might be that all of them are true. Still, such belief is a poor substitute for knowledge by acquaintance, though better than nothing. It is indeed a third best. The second best, in this case, is knowledge by description. But sometimes we only believe that there is something to which such and such a description applies; and even when we do know this, we may only believe and not know that there is only one thing to which the description applies. I may believe that there is only one person to whom the description, ‘being your brother’, applies, when in fact you have two brothers. It may well be that much of the knowledge by description which we ordinarily claim to have is belief rather than knowledge, if only because so much of it depends on testimony1, spoken or written, and the reliability of the testimony is often taken for granted without much or any investigation.

As we now see, the contrast between belief and knowledge is most obvious when we compare belief ‘that’ with knowing ‘that’, knowledge of facts or truths (knowledge by description is a special case of this). We often believe that p, when we do not know that p is true. Such belief ‘that’ may fairly be called a second-best. Very often, knowledge ‘that’ is not available, through lack of time or lack of conclusive evidence. I cannot know that William will answer my letter by return of post. I cannot even know that he will get it. But I believe that he will. The post office is a fairly efficient organization, though not infallible. I also believe that he will answer by return of post, because I asked him to; he is a kind-hearted person and businesslike rather than otherwise. Of course, he may be ill or incapacitated or away from home; but if he were, the chances are that I should have heard about it. So I can believe with some confidence, though not with complete conviction, that he will answer my letter by return of post, and that his answer will reach me at breakfast time on the day after tomorrow. This belief, though inferior to the knowledge I should like to have, is much better than nothing. It gives me some guidance in my inferences and my actions. I can make plans ‘on the assumption that’ the answer will come the day after tomorrow. I do not just have to wait and see, although my plans are made with some reservations.

Belief and Knowing ‘How To’

Knowing ‘how to’, despite its importance in other contexts, does not seem to be contrasted in any obvious way with belief. It is true that in the practical sphere, as in the cognitive, there is a contrast between knowing and making a mistake. Moreoever, in both spheres alike one may forget what one formerly knew, and in both alike the forgetting may be either permanent or temporary. A man may forget how to tie a bow-tie, though he once knew how to do it. Or on a particular occasion, when he is ill or in a great hurry or very tired, he cannot remember how to do it, though ordinarily he can. But there is no contrast here between knowing and believing. There is no such thing as ‘believing how to tie a bow-tie’ or ‘merely believing how to do it’, as opposed to knowing how to do it. And though we do speak of thinking how to do something, this is not at all like thinking ‘that’. ‘Thinking that p’ is a familiar way of expressing a mild degree of belief (opinion as opposed to conviction). But thinking ‘how to’ is a state of wondering or questioning.

It is true that if someone is asked whether he knows ‘how to’ do something, he may reply ‘No, but I believe (or think) one does it by taking off the casing and tightening up a nut which one finds inside’. But this is a case of believing that. He believes that the correct way of doing it is so-and-so. Or he might answer, more oddly. ‘I believe I know how to do it, but I am not sure.’ But this again is believing that. He believes that he has acquired a certain sort of skill or proficiency, but he is not quite sure that he has.

If we wish to find a second-best substitute for knowing how, related to knowing how as ‘belief that’ is related to ‘knowledge that’, the most hopeful candidate, perhaps, is ‘having an idea (or some idea) how to do it’. Does Watson know how to get an aircraft out of a spin? No, not quite, but he has some idea how to do it. Having an idea how to do something might be described as an imperfect or half-baked skill. It has the same practical character which knowing how has. Like knowing how, it manifests itself in actual performances, but not all of them are successful. If a person has some idea how to get out of a spin, without knowing how to, he will get out of it on three occasions out of five, perhaps, but on the other two he will only be saved from death by the intervention of the instructor. And even on the three more fortunate occasions, he will probably make some bungling movements with the control stick or the rudder-pedal before success is achieved.

Like knowing how, ‘having some idea how’ may be inarticulate. A man who knows how to do something may be quite unable to tell us, or himself, how he does it. A man who has some idea how to do it is perhaps more likely to be able to tell us how he tries to do it; and this may be why the word ‘idea’ is used. When a skill is only half-learned, we are more likely to give ourselves verbal instructions. To put it otherwise, a half-learned skill is more likely to be ‘conscious’ than a fully-learned one. But still, it need not be. The beginner in bicycling has difficulty in learning to mount his bicycle. If all goes well, a time comes when he succeeds more often than not. We then say he has some idea how to do it, and so does he. But he is very unlikely to be able to describe the bodily movements and muscular adjustments that he makes.

Even so, the relation between knowing how to do something and having some idea how to do it is not altogether parallel to the relation between knowing ‘that’ and believing ‘that’. It corresponds rather to the relation between knowing all about something and knowing a little about it. When I believe that p, the propositions I believe may be completely false—‘nowhere near the truth’ as we say. I believe it will be raining by lunchtime to-day, and in fact the weather remains fine for the rest of the week. (If rain had begun to fall at 2.15 p.m. to-day, you might have said that my forecast was ‘wrong but not so very far wrong’.) But when a man has some idea how to do something, he is not completely devoid of skill, and his performances are not wholly different from those of the man who knows how to do it. What he does is not wholly wrong; it is only partly wrong, even though he may not succeed in achieving the end he aimed at. But some of our beliefs are wholly wrong.

Belief ‘In’

The attempt to pair off the various uses of ‘know’ with corresponding uses of ‘believe’ breaks down in the case of knowing how to. There is no ‘believing how to’. We meet with a similar difficulty when we consider ‘believing in’, but this time it is the other way round. There is no ‘knowing in’ to serve as the optimum for which believing in would be a second-best or inferior substitute.

‘Believing in’ is an important concept, especially (but not only) in the philosophy of religion. It is also a complex and baffling one. We shall have to discuss it in detail later.2 Here we are only concerned with its relation to knowledge.

There is a sense of ‘believing in’ which seems to be reducible quite straightforwardly to ‘believing that’. Surely believing in fairies amounts just to believing that there are fairies, and believing in the possibility of interplanetary travel is just believing that interplanetary travel is possible? Yet even in these examples there is perhaps some residue which the ‘believing that’ analysis leaves out. This residue might be described rather vaguely as ‘attaching importance to’. It becomes more obvious if we consider another example, believing in representative government. This does not consist merely in believing that there is such a form of government. It is a valuational attitude as well. The believer in representative government is in favour of that form of government, indeed, strongly in favour of it, and he uses the ‘believe in’ phraseology to express this favourable attitude. This valuational aspect of ‘believing in’ comes still more clearly into view when we consider belief in God.

We must also notice that when the object of ‘belief in’ is a human being, we may both believe in him and know him by acquaintance—at least in the ordinary everyday sense of ‘know’. The belief in Winston Churchill which most Englishmen had during the Second World War existed in those who knew him by acquaintance as well as in those who did not. It may be, however, that many of those who know a person only by description may believe in him firmly, while those who know him by acquaintance have little belief in him or none at all. Probably the Duke of Monmouth was in this unfortunate situation in 1685 and it helped to make his rebellion the tragic failure that it was.

It seems, then, that there is no neat and tidy way of contrasting belief in a person with knowledge of him by acquaintance. It would be an over-simplification to regard such ‘belief in’ as an inferior substitute for knowledge by acquaintance, and an even worse one to regard it as an inferior substitute for knowledge ‘that’.

The Relation between Belief and Knowledge

Before we could discuss the relation between belief and knowledge we had to distinguish between different senses of the word ‘knowledge’, and it turns out that the word ‘belief’ has several different senses too. Until we have considered these distinctions, we do not clearly understand what question we are trying to answer. Perhaps we can now formulate it a little more clearly.

I may remind you (I ought to have done so before) that the first distinction we considered was between the dispositional and the active or occurrent sense of the verb ‘to know’. Now this distinction, if applicable at all, applies both to knowledge and to belief. In both cases alike it is a highly controversial one, and in both the controversy is important. The difference between the traditional occurrence analysis of belief and the modern dispositional analysis is indeed one of the main themes of these lectures. But the distinction between ‘dispositional’ and ‘active’ (or ‘occurrent’) has little relevance to the questions we are now to discuss, if only because it cuts across the distinction between belief and knowledge itself. It cuts across many other distinctions too, for example that between hope and fear, or between love and hate. We might say that its domain is hardly narrower than the whole of the philosophy of mind.

If the disposition-act distinction be omitted, we are left with three senses of the word ‘know’ (four if you do not count knowledge by description as simply a special case of ‘knowledge that’) and three of the word ‘believe’. They may be tabulated thus:



1. Knowledge by acquaintance.

1. Believing a person.

2. Knowledge ‘that’ (knowledge of facts or truths).

2. Belief ‘that’.

3. Knowledge ‘how to’.

3. Belief ‘in’.

As we saw, we are accustomed to contrast belief with knowledge, and to think of it as an inferior substitute for knowledge. Even if we hold that knowledge is itself definable, somehow, in terms of belief (a view we shall consider presently) we still contrast knowledge with ‘mere’ belief, and the belief which does not amount to knowledge is still regarded as an inferior substitute for the belief which does. But it turns out that this contrast, this relation between an optimum and an inferior substitute, does not apply wholesale, to any sense you like of the word ‘know’ and any sense you like of the word ‘believe’. Knowing how to does not seem to be contrasted with any of the sense of ‘believe’. Believing a person is not contrasted with knowing him by acquaintance, as considerations of syntactical symmetry might lead us to expect. Its ‘opposite number’, on the knowledge side, if it has one, is knowing that the person's statements are true. And believing ‘in’ is only contrasted with knowledge where the belief in A is reducible without remainder to the belief that A exists (believing in fairies, for example).

The contrast between knowledge and belief is most obvious and most direct when we compare ‘knowledge that’ with ‘belief that’. There is also an indirect or two-stage contrast between knowledge by acquaintance and ‘belief that’. First, knowledge by acquaintance is contrasted with knowledge by description, which is a second-best substitute for it, and is itself a special case of ‘knowledge that’. Then, in its turn, this knowledge that a certain description applies to one and only one entity is contrasted with the belief that it so applies, which is a third best.

The conclusion suggested by our discussion is this. When we enquire into the relation between belief and knowledge, we are mainly concerned with the relation between belief that and knowledge that. In Russell's later terminology we are comparing two ‘propositional attitudes’; and they may, of course, be attitudes to the same proposition. If we contrast belief with knowledge and think of it as an inferior substitute for knowledge, the contrast is primarily between ‘knowledge that’ and ‘belief that’. Again, if we define knowledge in terms of belief, we are defining ‘knowledge that’ in terms of ‘belief that’; and the contrast which remains is one between ‘knowledge that’ and mere ‘belief that’, or between the sort of ‘belief that’ which amounts to ‘knowledge that’ and the sort which does not. Let us turn then, to the distinction between ‘belief that’ and ‘knowledge that’. What are we to say about it?

Belief ‘That’ and Knowledge ‘That’

We may begin our discussion with a platitude, since one of the chief occupational hazards of a philosopher is neglect of the obvious. If someone knows that p, then p is true. Of course, he may say he knows this, or claim to know it, or others may say of him that he knows it, and p may nevertheless be false. But if he—or anyone else—does know that p, this entails that p is true. It is a contradiction to say ‘John knew that it was raining, but it wasn't’. Moreoever, it is a contradiction to say ‘He knew that it is raining, but perhaps it wasn't’. It is even a contradition to say ‘He knew that it was raining and perhaps it was’. If he did know that it was raining, it just was raining, and there was no ‘perhaps’ about it.

But believing that p does not have these consequences. There is no contradiction whatever in saying ‘John believes that p, but p is false’. And no matter how many people believe that p, p may still be false.

Might it be that p is not even false? Could one believe what is called a ‘meaningless proposition’? It is not easy to see how anyone could. For surely there would be nothing to believe? Yet there is a too-familiar state which we describe as ‘believing what one does not understand’; a strange feat certainly, but we all seem to be capable of it.

Moreover, there seems to be some sense in which we can sincerely claim to believe a proposition which we do not in fact believe, as we can sincerely claim to know what we do not in fact know. There are some awkward questions here which we shall have to consider later. But we may neglect them now, because they are not very relevant to our present topic. Let us assume that our believer really does believe what he says he believes and that what he believes is at least false (not meaningless). The important point at present is that it need not be true, no matter how firmly he believes it, not even if everyone else believes it too.

It is also important to point out that reasonable beliefs are no exception to this rule. Reasonable beliefs may perfectly well be mistaken. A reasonable belief is one which is in accordance with the evidence. If the relevant facts which are known to me are more favourable to p than to not p, then it will be reasonable for me to believe p. But unless the evidence is conclusive (i.e. is sufficient to make p certain), it is still possible that p may be false after all. Before Australia was discovered, for example, it was reasonable for Europeans to believe that all adult swans are white. They had a good deal of evidence for believing so. But this proposition eventually turned out to be false.

On the other hand, an unreasonable belief (one held on very weak evidence or no evidence at all) may happen to be correct, though it is no credit to the believer if it is. A man believes that this horse will win the race because he likes the sound of its name, or because the race is on Thursday and Thursday is his lucky day. And perhaps the horse does win; the proposition he believes turns out to be true, though his belief was quite unreasonable.

It follows from this, paradoxically, that there is a sense of the word ‘right’ in which it may be right (right and proper) for someone to believe a false proposition—viz. when all the evidence he has is in favour of it—and wrong (improper) to believe a true one: viz. when he has no evidence for it, and a fortiori when the evidence he does have is against it. Sometimes people are praised for holding correct beliefs and condemned for holding mistaken ones. But if we must indulge in praise or blame about such matters, the relevant point is not the correctness or incorrectness of those beliefs, but their reasonableness or unreasonableness in view of the evidence those people had at the time.

We must, therefore, be careful not to equate the two statements ‘X's belief is correct’ (i.e. what he believes is in fact true) ‘X's belief is reasonable, given the evidence which he has.’ But this is a digression. Let us return to the distinction between belief and knowledge.

It might perhaps be suggested that the difference between them is just a difference of degree. As we have seen already, there are many different degrees of belief, ranging all the way from merely suspecting or surmising at the one end, to complete conviction at the other. And ‘knowledge’ (it might be said) is the name we give to the highest degree of belief—believing a proposition with complete conviction, being absolutely sure about it.

Now there may be some connection between knowledge and complete conviction. If tomorrow morning after breakfast I have just a mild opinion that it will rain in about an hour's time, no one would say I knew this—even though it does in fact rain fifty-seven minutes later. But it is perfectly obvious that though complete conviction may be a necessary condition of knowledge, we cannot just identify knowledge with complete conviction. No matter how firmly someone believes a proposition—even if he is absolutely sure of it—it still makes sense to say that what he believes is false; and quite often it is in fact false. I may be absolutely convinced that to-day is Tuesday, and yet I may be mistaken. There was a time, presumably, when all mankind were absolutely sure that the earth is flat, but nevertheless this proposition which they were absolutely sure of is false.

It is true, no doubt, that when a man is absolutely convinced of something he may say ‘I know it’. He will also act as if he knew it. Being absolutely convinced that today is Tuesday, I take an early bus and go off into the country for the day. I do so without any hesitation or qualm, just as I should if I knew that to-day is Tuesday, and therefore knew that I do not have to lecture this morning. But saying you know (or claiming to know) is one thing, and knowing is another. Again, it is only too obvious that a man may act as if he knew that his spectacles are in his pocket, when in fact he has left them on the dressing table in his bedroom. Lost among a maze of footpaths, he unhesitatingly opens his map, only to find that the cannot read it. It is also true (and perhaps more interesting) that there is something ‘linguistically odd’ or even absurd in saying, ‘I am convinced (absolutely sure) that to-day is Saturday, but I may be mistaken,’ just as it is absurd to say ‘I know that it is Saturday, but I may be mistaken’. ‘Such is my firm and unshakable conviction. But of course I may be wrong.’ Those two remarks together amount to something like a contradiction.

We notice, however, that this only applies to conviction statements in the first person singular and the present tense. There is no absurdity at all in saying ‘Jones is absolutely convinced that p, but he may be mistaken’; and there is no absurdity in saying ‘I was absolutely convinced that p a week ago, but I may have been mistaken’. Whereas with statements of the form ‘X knows that p but he may be mistaken’ there is no such distinction. Statements of this form are absurd whatever tense they are made in, and whether they are in the first person or not.

Then what kind of absurdity is there in saying ‘I am absolutely convinced that p, but I may be mistaken’ or ‘I am perfectly sure that p, but perhaps p is false after all’? Only this, that absolute conviction, so long as one has it, prevents one from considering the possibility that one may be mistaken, or at any rate prevents one from taking this possibility seriously (attaching any appreciable probability to it). If someone states that he does attach some probability, even a small one, to the possibility that p may be false, this does not exactly contradict his previous statement that he is absolutely convinced of p; but it does show that one or other of his two statements cannot be sincere. This oddity which there is in the two statements taken together is moral rather than logical. Nevertheless, it is in fact perfectly possible that p may be false, even though the man who is convinced is thereby prevented from considering this possibility seriously so long as his state of absolute conviction remains. On the ‘performatory’ view, a man who says ‘I am absolutely convinced that p, but I may be mistaken’ is at once giving a guarantee and withdrawing it.3 (Cf ‘I promise to come, but I probably shall not come’ ‘You must not be at all surprised if I don't’.)

Thus it is quite impossible just to equate knowledge with complete conviction—to say that knowledge just is the highest possible degree of belief.

Can Knowledge Be Defined in Terms of Belief?

Does it follow from this that belief and knowledge differ in kind and not in degree? Shall we say that there are just two quite different states of mind in which we can be: one which is infallible or incapable of being erroneous, namely, a state of knowledge; and another which is fallible or corrigible, namely a state of belief—regardless of the degree of firmness or strength with which the belief is held?

In the past, some philosophers have regarded the distinction between knowledge and belief in this way. But most contemporary philosophers would reject any such view. They would admit that there is a difference, and a very important one, between knowing that something is the case and merely believing that it is the case, without knowing that it is. But they would say the distinction is more like that between success and failure, and is not a distinction between two states of mind at all. So far as their state of mind goes, there need be no difference whatever between the man who knows something and the man who believes something without knowing it. The man who knows something is absolutely sure about it; and the man who merely believes something without knowing it may also be absolutely sure about it. He too may have the highest degree of belief—complete conviction.

As to the contention that knowledge is infallible or incorrigible, this (it would be said) is no more than a matter of definition—a tautology if you like. The verb ‘to know’ is so used that if someone is sure of something and turns out to be mistaken, we do not call this knowledge. It is as if someone argued that the man who, without a handicap, wins the race cannot fail to run faster than the others. The truth is, that if he had not run faster than the others, we should not call him the winner. On this view, the difference between the man who knows and the man who only believes is like the difference between the winner of the race and the other competitors who ran but do not win.

Let us consider this view further. At first sight, it looks rather like a proposal to identify knowledge with correct belief (what Plato called ortheÒ doxa). But of course this would not give us all we want. Even correct belief, we usually think, need not be knowledge. On Saturday I may have believed that Sunday would be a fine day. And perhaps it is a fine day. But if I believed this on Saturday merely because Old Moore's Almanac said so, or merely because I wanted Sunday to be fine, we would hardly say that this belief of mine amounted to knowledge. If we wish to say that knowledge is to be defined, somehow, in terms of correct belief, we shall certainly have to add something about the grounds of the belief. It is not enough that the proposition believed is in fact true; it is also necessary that there should be good reasons for the belief. Plato himself suggests in the Theaetetus that knowledge can be defined as ortheÒdoxa meta logou (‘correct belief with a reason’).4

Moreover, even though someone's belief is correct, and he does have good reasons for holding it, we should not necessarily be willing to say that we knew. I go down to the station to catch a train. The man in the ticket office tells me that this particular train is always five minutes late. I take his word for it and go off to the refreshment room for a cup of coffee. And sure enough, the train is five minutes late. Here I have a fairly good reason for my belief, and what I believe is in fact true. But we should hardly say I knew that the train would be five minutes late.

Again, I believe that within the next minutes at least one human being will walk past the front door of the Examination Schools. Actually, we will suppose, two people do walk past during that minute, so my belief was correct. Moreover, I had a good reason for holding it, namely my past observations of the degree of crowdedness of this part of the High Street at this hour of the morning on weekdays. But we should hardly be willing to say I knew that at least one human being would walk past during that minute, though certainly I had some evidence (quite good evidence) for believing so, and my belief was in fact correct. My reason for believing was a good reason, but not a conclusive one.

What we require, before we are willing to use the honorific word ‘knowledge’, is that the man's reason for belief should be not merely good but conclusive—sufficient to make the proposition certain. (It need not of course be conclusive in the deductive way.)

So far, we have been trying to work out the conception of knowledge one is committed to, if one starts from the assumption that there need be no difference between the state of mind of the man who knows, and the state of mind of the man who merely believes without knowing. The definition of the term ‘knowledge’ which this way of looking at the matter leads us to can now be given.

A knows that p’, we shall have to say, is equivalent to the following:

  1. A believes that p with full conviction (is completely sure about it).’
  2. p is in fact true.’
  3. A has conclusive reasons for believing it: not merely good reasons, but reasons sufficient to establish or certify the proposition p.’

But now suppose that any of these three conditions fails to be satisfied. If a man believes with less than full conviction, or if what he believes is false, or if he believes with no reason at all, or with reasons which are good but not conclusive, then we shall say that he is ‘merely’ believing, and does not know—though if he has good though not conclusive reasons, his belief will still be a reasonable one, provided the strength of it is no greater than those reasons justify.

It will be noticed that, according to this definition, the distinction between knowledge and belief which falls short of knowledge is partly one of degree: (1) in the degree of conviction, since if a man believes with something less than complete sureness we refuse to say that he knows; (2) in respect of the strength of the evidence or of the reasons for believing.

On the other hand, it is also required, of course, that the proposition believed should be true. And this is not a matter of degree. Moreover, the distinction between conclusive reasons and reasons which are good but non-conclusive is not wholly a difference of degree, but only partly. Conclusive evidence is not merely stronger than evidence which is good but not conclusive (though it is of course stronger). There is also the difference that conclusive evidence settles the question, while evidence which is less than conclusive does not. And this is not just a difference of degree. Here again, it is more like the difference between success and failure; between winning the prize and failing to win it; between hitting the bull's eye and getting on to some other part of the target.

What shall we say about this account of the difference between knowledge and belief? (Strictly speaking, of course, it is a way of distinguishing between belief which amounts to knowledge and belief which falls short of knowledge: or if you like, it is a way of distinguishing not so much between knowledge and belief, but rather between knowledge and mere belief.)

We must admit that this way of drawing the distinction does fit many of the cases very well. For example, a very great deal of our knowledge, what we all agree to call knowledge, comes from testimony5—including written testimony—documents, etc.

Most of our geographical knowledge, and the whole of our historical knowledge, is of this kind, e.g. our knowledge that there is such a country as Australia, or that there are lions in Africa, or that there was an Emperor of the French called Napoleon III. The same applies to the knowledge we get from testimony about quite recent events which are beyond the range of our immediate observation. For instance, by reading to-day's newspaper we ‘learn’ (come to know) that the Prime Minister made a speech at Bradford yesterday. (If you like, this latter is a kind of short-range historical knowledge.) Again, it could be argued that our inductive knowledge is of the kind this theory requires: that we find out—come to know—what the laws of nature are by a process of accumulating evidence, until the stage comes when the evidence is sufficient to establish such and such a generalisation or make it certain.

Some Difficulties in the Proposed Definition

Nevertheless there is one feature of this definition of knowledge which gets us into difficulty. It does require that if someone knows that p, the question ‘How does he know?’ always makes sense. According to the definition, he must have reasons (and moreover, sufficient or conclusive reasons) for accepting the proposition p, if we are to say he knows that p. He need not necessarily be able to put those reasons into words. But he must have them. He must have evidence sufficient to establish or certify the proposition p.

But surely there are some cases of knowledge where the question ‘How do you know?’ has no application? Consider what may be called propositions describing present experiences: e.g. ‘There is something brown in my present visual field’, ‘I am now picturing (imagining) the front of Blackwell's bookshop in Oxford’, ‘I am wondering what the time is’, or ‘I have a headache’.

Now when someone makes a statement of this sort the question ‘How do you know?’ does not apply. How do I know that there is something brown in my present visual field? I do know this. But the word ‘how’ does not apply, if it is a demand for reasons, as it is when you ask ‘How do you know that lunch is at 12.30?’. The only answer I could make to your question is ‘I just notice that there is something brown in my present visual field, or that I am wondering what the time is, or that I have a headache’. Or more technically, I could say ‘I just know this by inspection’ or ‘I know it immediately’—that is, without having reasons and without the need of any reasons.

The same applies to some statements describing past experiences. I know that I have often had a headache in the past. How do I know this? I just remember it. And when I say ‘I remember it’ I am not giving my evidence for the proposition. My knowledge, here again, is immediate; and in so far as I am telling you how I know, the word ‘how’ refers only to the kind of knowledge which it is, namely memory-knowledge, not to my reasons for the proposition I claim to know.

To put the point in another way, the definition of knowledge we are examining appears to assume that all knowledge is inferential (or ‘mediate’). For when we know that p, we always have to have reasons for accepting p, according to this definition, and moreover, they have to be sufficient or conclusive reasons. But it seems perfectly plain that there is in fact some knowledge which is not inferential at all.

Moreover, it could be argued that there must be some non-inferential (immediate) knowledge, if inferential knowledge itself is to be possible. Unless there were some propositions which we just know to be true, without having and without needing any reasons—some cases where it makes no sense to ask ‘What was your reason?’ or ‘How do you know?’—unless this were so, the other sort of knowledge, when it does make sense to ask for reasons, could not possibly exist.

There is another question which we should consider. If I do have reasons for accepting a proposition p (either conclusive ones, or merely reasons which are good but not conclusive) what do these reasons consist of? Sometimes they are other propositions which I likewise accept because I have good reasons for accepting them. How do I know that lunch is at 12.30? ‘Well,’ I may say ‘the College Porter told me, and I saw a notice on the notice board outside the Common Room.’ But how do I know that the Porter did tell me this, and that there was this notice outside the Common Room? Well, I just remember having certain visual and auditory experiences. I knew I was having them at the time, and for this knowledge no reason could be given, and none could be demanded. And I know now that I did have them; and I know this, not because of any reasons, but just by remembering it or recalling it.

We get into a rather similar difficulty if we turn to another point in the definition of knowing which I am examining. If we wish to define knowledge in terms of belief (of being sure), we have to use the word ‘true’ in our definition, because ‘John knows that p’ does entail that p is true (or if you like, entails that it is actually the case that p). But if we wish to maintain that this definition covers all the sorts of knowledge that there are—that all knowledge consists in being sure for conclusive reasons, of a proposition which is in fact true—we are confronted with a rather awkward difficulty: How do we ever settle the question whether John really does know something which he claims to know? Supposing he does know it, how can we ever find out that he does?

He claims to know that it is raining. We wish to decide whether this claim of his is justified. But in order to settle this question, we must ourselves have means of knowing whether it is raining or not. We must ourselves know whether or not the proposition ‘It is raining’ is in fact true. Unless this proposition is true, his claim to knowledge is unjustified. And how do we ourselves know whether it is raining or not? Not because of any reasons, but just by looking and seeing, or just by feeling the raindrops—just by having certain experiences. Indeed, how do we know that John makes any claim to knowledge at all? (Unless we do know this, there is no question to settle.) We know this by hearing what he says, or seeing what he writes.

In other words, if it is really possible to test people's claims to knowledge—to settle the question whether they really do know something or merely believe it without knowing—it must also be possible, sometimes, for a proposition to be empirically verified or empirically falsified—verified or falsified directly by experience. This direct empirical verification is a kind of knowledge which cannot be defined in terms of belief. Consider what the situation would be if there were not this possibility of direct empirical verification or falsification. It would follow that there might in fact be many instances of knowledge in the world, many people might be sure of propositions which were as a matter of fact true, and might be sure of them for sufficient reasons; and yet neither we nor they could ever discover that there are all these instances of knowledge. For to discover this, it must be possible for us to find out, for ourselves, what propositions are in fact true. And unless some propositions are directly verifiable or falsifiable nothing can ever be found out at all.

There is a similar difficulty about finding out what reasons John has for believing p, or whether he has any. He may in fact have very good ones; but unless we can find out what they are and how good they are, we shall not be able to settle the question whether he does really know what he claims to know. And if we ourselves are sure of something for sufficient reasons and it is in fact true, how do we ourselves know that we are sure of it, that our reasons for believing it are such and such, and that what we are sure of is as a matter of fact true?

We cannot know these things about other people, or about ourselves either, unless at some stage or other there is a possibility of direct empirical verification or falsification. And as I have said already, this direct empirical verification or falsification is a kind of knowledge (a way of finding something out) for which this definition does not provide. For in this case it is pointless to ask for reasons. And moreover, in this case, the knowledge we have is something quite different from belief of any sort. If you like, it does not consist in accepting a proposition, but rather in noticing some actual event or state of affairs.

This difference, between believing on the one hand and just being aware of something on the other, can be seen quite easily by considering a very commonplace example. You and I are sitting opposite each other in the train at night, and I am wondering whether the train will arrive at Basingstoke on time. I can know that I am wondering about this. You, on the other hand, can believe that I am wondering whether the train will arrive on time. You may believe it very firmly; you may be completely sure of it. You may have very good reasons for your belief too. You may see me looking repeatedly at my watch, and putting my face against the window to look at the dark landscape outside. You may even hear me say ‘I wonder whether we shall catch the connection at Basingstoke’. But is it not obvious that your ‘cognitive situation’ is quite different from mine? When I know that I am wondering whether the train will arrive on time, I am just noticing an experience that I have. But this is not at all what you are doing. You are accepting or assenting to a proposition about me and, as it happens, a true one. You may have good reasons for accepting it. But you are certainly not directly aware of the state of affairs which makes the proposition true; whereas that is just what I am directly aware of.

The difference I am trying to point out would still be there, even if you had conclusive reasons for your belief about me (not merely good ones, but conclusive ones). Whether one ever can have conclusive reasons for such a belief about the experiences of another person is, of course, disputable; in ordinary life we do assume that one can, at least sometimes, but philosophers have often denied it. But suppose you did have conclusive reasons for your belief that I am wondering about this, and that you held your belief with complete conviction. Then you would know that I am wondering about it, according to the definition of ‘knowledge’ which we are examining. But it is still obvious that your knowledge of this mental occurrence in me would be a completely different sort of knowledge from my own. My knowledge is direct and first hand in a way that yours is not. I am noticing an occurrence, whereas you are assenting with conviction to a proposition. In my case it makes no sense to ask for reasons, but in yours it does.


So much for the theory that knowledge consists in having a firm belief on sufficient evidence (for sufficient or conclusive reasons) with regard to a proposition which is in fact true. We must admit that there are some sorts of knowledge, or some usages of the word ‘know’, to which this definition does apply very well: that is, we must admit that there are some sorts of knowledge which can be defined, with suitable precautions, in terms of belief. The precautions are that the following conditions must be satisfied: (a) that the proposition believed is true, (b) that the believer has conclusive reasons for it, (c) that he believes it with full conviction. Moreover, we must admit that with regard to those sorts of knowledge, the distinction between knowing and ‘merely believing’ is partly a difference of degree. To have knowledge, in these cases, you do have to have more evidence (stronger reasons) than you have when you merely believe without knowing, and mere belief perhaps is possible without any evidence at all.

When we say we know that the sun is larger than the moon, or that the Labour Party won the last election, or that there are kangaroos in Australia, or that this rock was brought here by a glacier, or again that water boils at 212° Fahrenheit at sea level—in all these cases we do mean by the word ‘know’ just what the definition says we mean. But I have also tried to show that there is another sort of knowledge—immediate or direct knowledge—which is quite different from this, and cannot be defined in terms of belief at all.

  • 1.

    Cf. above Lecture 1, Introduction, pp. 38–9.

  • 2.

    See Lecture 5, below.

  • 3.

    Series II, Lecture 9.

  • 4.

    See Lecture 1, pp. 30–2.

  • 5.

    Theaetetus, 201 c—d.

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