Knowledge, Error, and Probable Belief

The question as to what we mean by truth and falsehood, which we considered in the preceding chapter, is of much less interest than the question as to how we can know what is true and what is false. This question will occupy us in the present chapter. There can be no doubt that some of our beliefs are erroneous; thus we are led to inquire what certainty we can ever have that such and such a belief is not erroneous. In other words, can we ever know anything at all, or do we merely sometimes by good luck believe what is true? Before we can attack this question, we must, however, first decide what we mean by 'knowing', and this question is not so easy as might be supposed.

In the previous chapter, we considered what we mean by truth and falsehood. But how we can know what is true and what is false is a much more interesting question. We will explore this question in the present chapter. There is no doubt that some of our beliefs are mistaken. So we must ask how we can ever be certain that a particular belief is not mistaken. In other words, can we ever know anything at all? Or do we sometimes just happen to believe what is true? Before we can tackle this question, however, we must first decide what we mean by 'knowing'. Defining 'knowing' is not as easy as it might seem.

At first sight we might imagine that knowledge could be defined as 'true belief'. When what we believe is true, it might be supposed that we had achieved a knowledge of what we believe. But this would not accord with the way in which the word is commonly used. To take a very trivial instance: If a man believes that the late Prime Minister's last name began with a B, he believes what is true, since the late Prime Minister was Sir Henry Campbell Bannerman. But if he believes that Mr. Balfour was the late Prime Minister, he will still believe that the late Prime Minister's last name began with a B, yet this belief, though true, would not be thought to constitute knowledge. If a newspaper, by an intelligent anticipation, announces the result of a battle before any telegram giving the result has been received, it may by good fortune announce what afterwards turns out to be the right result, and it may produce belief in some of its less experienced readers. But in spite of the truth of their belief, they cannot be said to have knowledge. Thus it is clear that a true belief is not knowledge when it is deduced from a false belief.

At first, we might think knowledge could be defined as 'true belief'. When what we believe is true, we might suppose we have knowledge of what we believe. But this definition would not match how the word is commonly used. Take a very simple example: A man might believe that the previous Prime Minister's last name began with a B. His belief is true, since the previous Prime Minister was Sir Henry Campbell Bannerman. But suppose he believes that Mr. Balfour was the previous Prime Minister. He will still believe that the previous Prime Minister's last name began with a B. Yet this belief, though true, would not count as knowledge. A newspaper might make an informed prediction and announce a battle's result before receiving any telegram reporting the outcome. By luck, the newspaper may announce what later turns out to be the correct result. The report may lead some of its less experienced readers to believe that result. But although their belief is true, those readers cannot be said to have knowledge. So a true belief is clearly not knowledge when it is drawn from a false belief.

In like manner, a true belief cannot be called knowledge when it is deduced by a fallacious process of reasoning, even if the premisses from which it is deduced are true. If I know that all Greeks are men and that Socrates was a man, and I infer that Socrates was a Greek, I cannot be said to know that Socrates was a Greek, because, although my premisses and my conclusion are true, the conclusion does not follow from the premisses.

Similarly, a true belief cannot be called knowledge if it comes from faulty reasoning, even when the premises are true. Suppose I know that all Greeks are men and that Socrates was a man. If I conclude that Socrates was a Greek, I cannot be said to know that Socrates was a Greek. This is because, although my premises and conclusion are true, the conclusion does not follow from the premises.

But are we to say that nothing is knowledge except what is validly deduced from true premisses? Obviously we cannot say this. Such a definition is at once too wide and too narrow. In the first place, it is too wide, because it is not enough that our premisses should be true, they must also be known. The man who believes that Mr. Balfour was the late Prime Minister may proceed to draw valid deductions from the true premiss that the late Prime Minister's name began with a B, but he cannot be said to know the conclusions reached by these deductions. Thus we shall have to amend our definition by saying that knowledge is what is validly deduced from known premisses. This, however, is a circular definition: it assumes that we already know what is meant by 'known premisses'. It can, therefore, at best define one sort of knowledge, the sort we call derivative, as opposed to intuitive knowledge. We may say: 'Derivative knowledge is what is validly deduced from premisses known intuitively'. In this statement there is no formal defect, but it leaves the definition of intuitive knowledge still to seek.

But should we say that only conclusions validly deduced from true premises count as knowledge? Clearly, we cannot. Such a definition is both too broad and too narrow. First, it is too broad because our premises must not only be true. They must also be known. A man who believes that Mr. Balfour was the previous Prime Minister may make valid deductions from a true premise. That premise is that the previous Prime Minister's name began with a B. But we cannot say that he knows the conclusions he reaches through these deductions. So we must revise our definition: knowledge is what is validly deduced from known premises. But this definition is circular. It assumes we already know what 'known premises' means. So, at best, the definition can describe only one kind of knowledge. We call this kind derivative knowledge, as opposed to intuitive knowledge. We may say: 'Derivative knowledge is what is validly deduced from premises known intuitively'. This statement has no formal flaw, but we still need a definition of intuitive knowledge.

Leaving on one side, for the moment, the question of intuitive knowledge, let us consider the above suggested definition of derivative knowledge. The chief objection to it is that it unduly limits knowledge. It constantly happens that people entertain a true belief, which has grown up in them because of some piece of intuitive knowledge from which it is capable of being validly inferred, but from which it has not, as a matter of fact, been inferred by any logical process.

For now, let us set aside the question of intuitive knowledge and consider the definition of derivative knowledge suggested above. The main objection to this definition is that it limits knowledge too narrowly. People often hold a true belief that has developed because of some piece of intuitive knowledge. The belief could be validly inferred from that intuitive knowledge. But in fact, they have not arrived at the belief through any logical process.

Take, for example, the beliefs produced by reading. If the newspapers announce the death of the King, we are fairly well justified in believing that the King is dead, since this is the sort of announcement which would not be made if it were false. And we are quite amply justified in believing that the newspaper asserts that the King is dead. But here the intuitive knowledge upon which our belief is based is knowledge of the existence of sense-data derived from looking at the print which gives the news. This knowledge scarcely rises into consciousness, except in a person who cannot read easily. A child may be aware of the shapes of the letters, and pass gradually and painfully to a realization of their meaning. But anybody accustomed to reading passes at once to what the letters mean, and is not aware, except on reflection, that he has derived this knowledge from the sense-data called seeing the printed letters. Thus although a valid inference from the-letters to their meaning is possible, and could be performed by the reader, it is not in fact performed, since he does not in fact perform any operation which can be called logical inference. Yet it would be absurd to say that the reader does not know that the newspaper announces the King's death.

Consider, for example, the beliefs we form through reading. If newspapers announce the King's death, we are fairly well justified in believing that the King is dead. Such an announcement would not be made if it were false. And we are fully justified in believing that the newspaper says the King is dead. But our belief rests on intuitive knowledge of the existence of sense-data from looking at the printed news. We are barely conscious of this knowledge, except when we have difficulty reading. A child may notice the shapes of the letters and slowly struggle to understand their meaning. But experienced readers move straight to the letters' meaning. Only on reflection do they realize that their knowledge comes from the sense-data of seeing the printed letters. So although readers could make a valid inference from the letters to their meaning, they do not actually do so. They could make that inference, but in fact they perform no mental operation that could be called logical inference. Yet it would be absurd to say that readers do not know that the newspaper announces the King's death.

We must, therefore, admit as derivative knowledge whatever is the result of intuitive knowledge even if by mere association, provided there is a valid logical connexion, and the person in question could become aware of this connexion by reflection. There are in fact many ways, besides logical inference, by which we pass from one belief to another: the passage from the print to its meaning illustrates these ways. These ways may be called 'psychological inference'. We shall, then, admit such psychological inference as a means of obtaining derivative knowledge, provided there is a discoverable logical inference which runs parallel to the psychological inference. This renders our definition of derivative knowledge less precise than we could wish, since the word 'discoverable' is vague: it does not tell us how much reflection may be needed in order to make the discovery. But in fact '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.

We must therefore accept as derivative knowledge anything that results from intuitive knowledge, even through mere association, under two conditions. There must be a valid logical connection, and the person must be able to recognize that connection through reflection. In fact, there are many ways besides logical inference to move from one belief to another. Moving from printed words to their meaning illustrates these other ways. These ways may be called 'psychological inference'. We will therefore accept such psychological inference as a way to gain derivative knowledge, provided a parallel logical inference can be discovered. This makes our definition of derivative knowledge less precise than we would like, because the word 'discoverable' is vague. The word does not tell us how much reflection may be needed to discover the logical connection. But in fact, 'knowledge' is not a precise concept. It shades into 'probable opinion', as we will see more fully later in this chapter. We should therefore not seek a very precise definition, since any such definition must be misleading to some extent.

The chief difficulty in regard to knowledge, however, 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. Something may be done, however, to mitigate the difficulties of the question.

The main difficulty with knowledge, however, concerns intuitive knowledge, not knowledge derived from it. As long as we are dealing with derived knowledge, we can fall back on intuitive knowledge to test it. But with intuitive beliefs, finding any test to distinguish true beliefs from false ones is far from easy. We can hardly reach a very precise conclusion on this question. All our knowledge of truths carries some degree of doubt, and any theory that ignored this doubt would be clearly wrong. However, we can do something to make these difficulties less severe.

Our theory of truth, to begin with, supplies the possibility of distinguishing certain truths as self-evident in a sense which ensures infallibility. When a belief is true, we said, there is a corresponding fact, in which the several objects of the belief form a single complex. The belief is said to constitute knowledge of this fact, provided it fulfils those further somewhat vague conditions which we have been considering in the present chapter. But in regard to any fact, besides the knowledge constituted by belief, we may also have the kind of knowledge constituted by perception (taking this word in its widest possible sense). For example, if you know the hour of the sunset, you can at that hour know the fact that the sun is setting: this is knowledge of the fact by way of knowledge of truths; but you can also, if the weather is fine, look to the west and actually see the setting sun: you then know the same fact by the way of knowledge of things.

To begin with, our theory of truth lets us distinguish certain truths as self-evident in a sense that guarantees infallibility. We said that when a belief is true, a corresponding fact exists. In that fact, the various objects of the belief form a single complex whole. The belief counts as knowledge of this fact if it meets the further, somewhat vague conditions discussed in this chapter. But for any fact, besides knowledge through belief, we may also have knowledge through perception. Here, “perception” is taken in its widest possible sense. For example, if you know when the sun sets, you can know at that hour that the sun is setting. This is knowledge of the fact through knowledge of truths. But if the weather is fine, you can also look west and actually see the setting sun. You then know the same fact through knowledge of things.

Thus in regard to any complex fact, there are, theoretically, two ways in which it may be known: (1) by means of a judgement, in which its several parts are judged to be related as they are in fact related; (2) by means of acquaintance with the complex fact itself, which may (in a large sense) be called perception, though it is by no means confined to objects of the senses. Now it will be observed that the second way of knowing a complex fact, the way of acquaintance, is only possible when there really is such a fact, while the first way, like all judgement, is liable to error. The second way gives us the complex whole, and is therefore only possible when its parts do actually have that relation which makes them combine to form such a complex. The first way, on the contrary, gives us the parts and the relation severally, and demands only the reality of the parts and the relation: the relation may not relate those parts in that way, and yet the judgement may occur.

Thus, in theory, any complex fact can be known in two ways: (1) through a judgment that its parts are related as they actually are. (2) Through acquaintance with the complex fact itself. This acquaintance may broadly be called perception, though it is by no means limited to objects of the senses. Notice that the second way of knowing a complex fact, through acquaintance, is possible only when that fact really exists. The first way, however, can be mistaken, like all judgment. The second way gives us the complex whole. So acquaintance is possible only when the parts actually have the relationship that combines them into that complex whole. The first way, by contrast, gives us the parts and the relationship separately. It requires only that the parts and the relationship exist. The relationship may not connect those parts in that way, yet the judgment may still occur.

It will be remembered that at the end of Chapter XI we suggested that there might be two kinds of self-evidence, one giving an absolute guarantee of truth, the other only a partial guarantee. These two kinds can now be distinguished.

Recall that at the end of Chapter XI, we suggested there might be two kinds of self-evidence. One gives an absolute guarantee of truth, while the other gives only a partial guarantee. We can now distinguish between these two kinds.

We may say that a truth is self-evident, in the first and most absolute sense, when we have acquaintance with the fact which corresponds to the truth. When Othello believes that Desdemona loves Cassio, the corresponding fact, if his belief were true, would be 'Desdemona's love for Cassio'. This would be a fact with which no one could have acquaintance except Desdemona; hence in the sense of self-evidence that we are considering, the truth that Desdemona loves Cassio (if it were a truth) could only be self-evident to Desdemona. All mental facts, and all facts concerning sense-data, have this same privacy: there is only one person to whom they can be self-evident in our present sense, since there is only one person who can be acquainted with the mental things or the sense-data concerned. Thus no fact about any particular existing thing can be self-evident to more than one person. On the other hand, facts about universals do not have this privacy. Many minds may be acquainted with the same universals; hence a relation between universals may be known by acquaintance to many different people. In all cases where we know by acquaintance a complex fact consisting of certain terms in a certain relation, we say that the truth that these terms are so related has the first or absolute kind of self-evidence, and in these cases the judgement that the terms are so related must be true. Thus this sort of self-evidence is an absolute guarantee of truth.

We may call a truth self-evident in the first and most absolute sense when we directly know the corresponding fact. Othello believes that Desdemona loves Cassio. If his belief were true, the corresponding fact would be 'Desdemona's love for Cassio'. No one except Desdemona could directly know this fact. So, in the sense of self-evidence we are considering, this truth could be self-evident only to Desdemona, if it were true. All mental facts and all facts about sense-data are private in the same way. Such facts can be self-evident, in our present sense, to only one person. Only one person can directly know the mental things or sense-data involved. Thus no fact about any particular existing thing can be self-evident to more than one person. On the other hand, facts about universals are not private in this way. Many minds may directly know the same universals. So many different people may directly know a relation between universals. Sometimes we directly know a complex fact consisting of certain terms standing in a certain relation. In all such cases, the truth that these terms stand in this relation has the first, absolute kind of self-evidence. In these cases, the judgment that the terms stand in this relation must be true. Thus this kind of self-evidence is an absolute guarantee of truth.

But although this sort of self-evidence is an absolute guarantee of truth, it does not enable us to be absolutely certain, in the case of any given judgement, that the judgement in question is true. Suppose we first perceive the sun shining, which is a complex fact, and thence proceed to make the judgement 'the sun is shining'. In passing from the perception to the judgement, it is necessary to analyse the given complex fact: we have to separate out 'the sun' and 'shining' as constituents of the fact. In this process it is possible to commit an error; hence even where a fact has the first or absolute kind of self-evidence, a judgement believed to correspond to the fact is not absolutely infallible, because it may not really correspond to the fact. But if it does correspond (in the sense explained in the preceding chapter), then it must be true.

But although this kind of self-evidence guarantees truth, it does not make us absolutely certain that any particular judgement is true. Suppose we first perceive the sun shining, a complex fact, and then form the judgement 'the sun is shining'. To move from perception to judgement, we must analyse the complex fact we perceive. We have to separate 'the sun' and 'shining' as parts of the fact. We can make a mistake in this process. So even when a fact has the first, absolute kind of self-evidence, a judgement believed to match that fact is not infallible. The judgement may not actually correspond to the fact. But if the judgement does correspond to the fact (in the sense explained in the preceding chapter), it must be true.

The second sort of self-evidence will be that which belongs to judgements in the first instance, and is not derived from direct perception of a fact as a single complex whole. This second kind of self-evidence will have degrees, from the very highest degree down to a bare inclination in favour of the belief. Take, for example, the case of a horse trotting away from us along a hard road. At first our certainty that we hear the hoofs is complete; gradually, if we listen intently, there comes a moment when we think perhaps it was imagination or the blind upstairs or our own heartbeats; at last we become doubtful whether there was any noise at all; then we think we no longer hear anything, and at last we know we no longer hear anything. In this process, there is a continual gradation of self-evidence, from the highest degree to the least, not in the sense-data themselves, but in the judgements based on them.

The second kind of self-evidence belongs primarily to judgments themselves. It does not come from directly perceiving a fact as a single complex whole. This kind of self-evidence varies in degree, from the highest certainty to a slight inclination to accept a belief. Take, for example, a horse trotting away from us along a hard road. At first, we are completely certain that we hear its hooves. Gradually, if we listen closely, a moment comes when we think perhaps we imagined the sound. Or perhaps we heard the window blind upstairs or our own heartbeats. Eventually, we become unsure whether there was any sound at all. Then we think we no longer hear anything, and finally we know we no longer hear anything. Throughout this process, the degree of self-evidence changes continuously, from the highest degree to the lowest. This change is not in the sense-data themselves, but in the judgments based on them.

Or again: Suppose we are comparing two shades of colour, one blue and one green. We can be quite sure they are different shades of colour; but if the green colour is gradually altered to be more and more like the blue, becoming first a blue-green, then a greeny-blue, then blue, there will come a moment when we are doubtful whether we can see any difference, and then a moment when we know that we cannot see any difference. The same thing happens in tuning a musical instrument, or in any other case where there is a continuous gradation. Thus self-evidence of this sort is a matter of degree; and it seems plain that the higher degrees are more to be trusted than the lower degrees.

Or take another example: Suppose we are comparing two shades of colour, one blue and one green. We can be quite sure the two shades are different. But suppose the green gradually changes to look more and more like the blue. It becomes first blue-green, then greenish-blue, then blue. At some point, we will be unsure whether we can see any difference. Then we will reach a point when we know we cannot see any difference. The same thing happens when tuning a musical instrument, or whenever there is a continuous, gradual change. So self-evidence of this kind comes in degrees. And it seems clear that higher degrees of self-evidence are more trustworthy than lower degrees.

In derivative knowledge our ultimate premisses must have some degree of self-evidence, and so must their connexion with the conclusions deduced from them. Take for example a piece of reasoning in geometry. It is not enough that the axioms from which we start should be self-evident: it is necessary also that, at each step in the reasoning, the connexion of premiss and conclusion should be self-evident. In difficult reasoning, this connexion has often only a very small degree of self-evidence; hence errors of reasoning are not improbable where the difficulty is great.

In knowledge gained through reasoning, our basic premises must be self-evident to some degree. So must the connection between those premises and the conclusions drawn from them. Consider, for example, a line of reasoning in geometry. The axioms we start from must be self-evident, but that is not enough. At every step, the connection between premise and conclusion must also be self-evident. In difficult reasoning, this connection is often self-evident only to a very small degree. So errors in reasoning are not unlikely when the difficulty is great.

From what has been said it is evident that, both as regards intuitive knowledge and as regards derivative knowledge, if we assume that intuitive knowledge is trustworthy in proportion to the degree of its self-evidence, there will be a gradation in trustworthiness, from the existence of noteworthy sense-data and the simpler truths of logic and arithmetic, which may be taken as quite certain, down to judgements which seem only just more probable than their opposites. 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.

From what we have said, the following is clear about both intuitive knowledge and knowledge derived from it. Suppose intuitive knowledge is trustworthy in proportion to how self-evident it is. Then knowledge will have varying degrees of trustworthiness. At one end are the existence of notable sense-data and the simpler truths of logic and arithmetic. These may be taken as completely certain. At the other end are judgments that seem only slightly more probable than their opposites. A firm belief, if true, is called knowledge, provided it meets one of two conditions. The belief must either be intuitive or be inferred, logically or psychologically, from intuitive knowledge that logically implies it. A firm belief, if untrue, is called error. A firm belief that is neither knowledge nor error may be called probable opinion. The same term may apply to beliefs we hold hesitantly because their basis is not self-evident to the highest degree. Such beliefs may themselves lack the highest degree of self-evidence, or they may derive from something that lacks it. Thus, most of what would commonly be accepted as knowledge is probable opinion, to varying degrees.

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. They fit into a coherent system of probable opinions, and thus become more probable than they would be in isolation. The same thing applies to general philosophical hypotheses. Often in a single case such hypotheses may seem highly doubtful, while yet, when we consider the order and coherence which they introduce into a mass of probable opinion, they become pretty nearly certain. This applies, in particular, to such matters as the distinction between dreams and waking life. 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. Thus the mere organization of probable opinion will never, by itself, transform it into indubitable knowledge.

When assessing probable beliefs, we can get great help from coherence. We rejected coherence as the definition of truth, but we may often use it as a criterion. If individually probable beliefs fit together coherently, they become more probable than any one would be on its own. Many scientific hypotheses gain their probability in this way. They fit into a coherent system of probable beliefs, becoming more probable than they would be in isolation. The same applies to general philosophical hypotheses. Often, such hypotheses may seem highly doubtful in a single case. Yet they become almost certain when we consider the order and coherence they bring to many probable beliefs. This applies particularly to matters such as the distinction between dreams and waking life. Suppose our dreams, night after night, were as coherent with one another as our days are. We would hardly know whether to believe our dreams or our waking life. As things stand, the test of coherence rejects dreams and supports waking life. But although this test increases probability when it succeeds, it never gives absolute certainty. It can do so only if something within the coherent system is already certain. So simply organizing probable beliefs will never, by itself, turn them into knowledge beyond doubt.