CHAPTER 7 OF THE PROBLEMS OF PHILLOSPHY THE PROBLEMS OF PHILLOSPHY by Bertrand Russell, CHAPTER 7, ON OUR KNOWLEDGE OF GENERAL PRINCIPLES We saw in the preceding chapter that the principle of induction, while necessary to the validity of all arguments based on experience, is itself not capable of being proved by experience and yet is unhesitatingly believed by everyone, at least in all its concrete applications. In these characteristics the principle of induction does not stand alone. There are a number of other principles which cannot be proved or disproved by experience, but are used in arguments which start from what is experienced. Some of these principles have even greater evidence than the principle of induction, and the knowledge of them has the same degree of certainty as the knowledge of the existence of sense data. They constitute the means of drawing inferences from what is given in sensation, and if what we infer is to be true, it is just as necessary that our principles of inference should be true as it is that our data should be true. The principles of inference are apt to be overlooked because of their very obviousness, the assumption involved is assented to without our realizing that it is an assumption. But it is very important to realize the use of principles in inference if a correct theory of knowledge is to be obtained, for our knowledge of them raises interesting and difficult questions. In all our knowledge of general principles what actually happens is that first of all we realize some particular application of the principle, and then we realize that the particularity is irrelevant, and that there is a generality which may equally truly be affirmed. This is of course familiar in such matters as teaching arithmetic. Two and two or four is first learned in the case of some particular pair of couples, and then in some other particular case and so on, until at last it becomes possible to see that it is true of any pair of couples. The same thing happens with logical principles. Suppose two men are discussing what day of the month it is. One of them says, at least you will admit that if yesterday was the fifteenth, today must be the sixteenth. Yes, says the other, I admit that. And you know, the first continues, that yesterday was the fifteenth, because you dined with Jones, and your diary will tell you that was on the fifteenth. Yes, says the second, therefore today is the sixteenth. Now such an argument is not hard to follow, and if it is granted that its premises are true in fact, no one will deny that the conclusion must also be true. But it depends for its truth upon an instance of a general logical principle. The logical principle is as follows. Suppose it known that if this is true, then that is true. When it is the case that if this is true, that is true, we shall say that this implies that, and that that follows from this. Thus our principle states that if this implies that, and this is true, then that is true. In other words, anything implied by a true proposition is true, or whatever follows from a true proposition is true. This principle is really involved, at least concrete instances of it are involved in all demonstrations. Whenever one thing which we believe is used to prove something else, which we consequently believe, this principle is relevant. If anyone asks, why should I accept the results of valid arguments based on true premises, we can only answer by appealing to our principle. In fact, the truth of the principle is impossible to doubt, and its obviousness is so great that at first sight it seems almost trivial. Such principles, however, are not trivial to the philosopher, for they show that we may have indubitable knowledge which is in no way derived from objects of sense. The above principle is merely one of a certain number of self-evident logical principles. Some, at least of these principles, must be granted before any argument of proof becomes possible. When some of them have been granted, others can be proved, though these others, so long as they are simple, are just as obvious as the principles taking for granted. For no very good reason, three of these principles have been singled out by tradition under the name of laws of thought. They are as follows. One, the law of identity. Whatever is, is. Two, the law of contradiction. Nothing can both be and not be. Three, the law of excluded middle. Everything must either be or not be. These three laws are samples of self-evident logical principles, but are not really more fundamental or more self-evident than various other similar principles. For instance, the one we considered just now, which states that what follows from a true premise is true. The name laws of thought is also misleading, for what is important is not the fact that we think in accordance with these laws, but the fact that things behave in accordance with them. In other words, the fact that when we think in accordance with them, we think truly. But this is a large question to which we must return at a later stage. In addition to the logical principles which enable us to prove from a given premise that something is certainly true, there are other logical principles which enable us to prove from a given premise that there is a greater or less probability that something is true. An example of such principles, perhaps the most important example, is the inductive principle which we considered in the preceding chapter. One of the great historic controversies in philosophy is the controversy between the two schools called, respectively, empiricists and rationalists. The empiricists, who are best represented by the British philosophers Locke, Berkeley and Hume, maintained that all our knowledge is derived from experience. The rationalists, who are represented by the continental philosophers of the 17th century, especially Descartes and Leithnitz, maintained that in addition to what we know by experience, there are certain innate ideas and innate principles which we know independently of experience. It has now become possible to decide with some confidence as to the truth or falsehood of these opposing schools. It must be admitted, for the reasons already stated, that logical principles are known to us and cannot be themselves proved by experience since all proof presupposes them. In this therefore, which was the most important point of the controversy, the rationalists were in the right. On the other hand, even that part of our knowledge which is logically independent of experience, in the sense that experience cannot prove it, is yet elicited and caused by experience. It is on occasion of particular experiences that we become aware of the general laws which their connections exemplify. It would certainly be absurd to suppose that there are innate principles in the sense that babies are born with the knowledge of everything which men know and which cannot be deduced from what is experienced. For this reason, the word innate would not now be employed to describe our knowledge of logical principles. The phrase a priori is less objectionable and is more usual in modern writers. Thus, while admitting that all knowledge is elicited and caused by experience, we shall nevertheless hold that some knowledge is a priori in the sense that the experience which makes us think of it does not suffice to prove it, but merely so directs our attention that we see its truth without requiring any proof from experience. There is another point of great importance in which the empiricists were in the right as against the rationalists. Nothing can be known to exist except by the help of experience. That is to say, if we wish to prove that something of which we have no direct experience exists, we must have among our premises the existence of one or more things of which we have direct experience. Our belief that the emperor of China exists, for example, rests upon testimony, and testimony consists in the last analysis of sense data seen or heard in reading or being spoken to. Rationalist believed that, from general consideration as to what must be, they could deduce the existence of this or that in the actual world. In this belief they seem to have been mistaken. All the knowledge that we can acquire a priori concerning existence seems to be hypothetical. It tells us that if one thing exists, another must exist, or more generally, that if one proposition is true, another must be true. This is exemplified by the principles we have already dealt with, such as, if this is true and this implies that, then that is true, or if this and that have been repeatedly found connected, they will probably be connected in the next instance in which one of them is found. Thus the scope and power of a priori principles is strictly limited. All knowledge that something exists must be in part dependent on experience. When anything is known immediately, its existence is known by experience alone. When anything is proved to exist without being known immediately, both experience and a priori principles must be required in the proof. Knowledge is called empirical when it rests wholly or partly upon experience. Thus all knowledge which asserts existence is empirical, and the only a priori knowledge concerning existence is hypothetical, giving connections among things that exist or may exist, but not giving actual existence. A priori knowledge is not all of the logical kind we have been hitherto considering. Perhaps the most important example of non-logical a priori knowledge is knowledge as to ethical value. I am not speaking of judgments as to what is useful or as to what is virtuous, for such judgments do require empirical premises. I am speaking of judgments as to the intrinsic desirability of things. If something is useful, it must be useful because it secures some hint. The end must, if we have gone far enough, be valuable on its own account, and not merely because it is useful for some further end. Thus all judgments as to what is useful depend upon judgments as to what has value on its own account. We judge, for example, that happiness is more desirable than misery, knowledge than ignorance, goodwill than hatred, and so on. Such judgments must in part at least be immediate and a priori. Like our previous a priori judgments, they may be elicited by experience, and indeed they must be, for it seems not possible to judge whether anything is intrinsically valuable unless we have experienced something of the same kind. But it is fairly obvious that they cannot be proved by experience, for the fact that a thing exists or does not exist cannot prove either that it is good that it should exist or that it is bad. The pursuit of this subject belongs to ethics where the impossibility of deducing what ought to be from what is has to be established. In the present connection it is only important to realize that 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. All pure mathematics is a priori, like logic. This was strenuously denied by the empirical philosophers who maintained that experience was as much the source of our knowledge of arithmetic as of our knowledge of geography. They maintained that by the repeated experience of seeing two things and two other things, and finding that altogether they made four things, we were led by induction to the conclusion that two things and two other things would always make four things altogether. If, however, this was the source of our knowledge that two and two are four, we should proceed differently in persuading ourselves of its truth from the way in which we do actually proceed. In fact, a certain number of instances are needed to make us think of two abstractly rather than of two coins or two books or two people or two of any other specified kind. But as soon as we are able to divest our thoughts of irrelevant particularity, we become able to see the general principle that two and two are four, any one instance is seen to be typical and the examination of other instances becomes unnecessary. The same thing is exemplified in geometry. If we want to prove some property of all triangles, we draw some one triangle and reason about it, but we can avoid making use of any property which it does not share with all other triangles, and thus from our particular case we obtain a general result. We do not in fact feel our certainty that two and two are four increased by fresh instances because as soon as we have seen the truth of this proposition, our certainty becomes so great as to be incapable of growing greater. Moreover, we feel some quality of necessity about the proposition two and two are four, which is absent from even the best attested empirical generalizations. Such generalizations always remain mere facts. We feel that there might be a world in which they were false, though in the actual world they happen to be true. In any possible world, on the contrary, we feel that two and two would be four. This is not a mere fact, but a necessity to which everything actual and possible must conform. The case may be made clearer by considering a genuinely empirical generalization such as all men are mortal. It is plain that we believe this proposition in the first place because there is no known instance of men living beyond a certain age, and in the second place because there seem to be physiological grounds for thinking that an organism such as a man's body must sooner or later wear out. Neglecting the second ground and considering merely our experience of men's mortality, it is plain that we should not be content with one quite clearly understood instance of a man dying, whereas in the case of two and two or four, one instance does suffice, when carefully considered, to persuade us that the same must happen in any other instance. Also, we can be forced to admit, on reflection, that there may be some doubt, however slight, as to whether all men are mortal. This may be made plain by the attempt to imagine two different worlds, in one of which there are men who are not mortal, while in the other two and two make five. When Swift invites us to consider the race of strode bugs who never die, we are able to acquiesce an imagination. But a world where two and two make five seems quite on a different level, we feel that such a world, if there were one, would upset the whole fabric of our knowledge and reduce us to utter doubt. The fact is that in simple mathematical judgments such as two and two or four, and also in many judgments of logic, we can know the general proposition without inferring it from instances, although some instance is usually necessary to make clear to us what the general proposition means. This is why there is real utility in the process of deduction, which goes from the general to the general, or from the general to the particular, as well as in the process of induction, which goes from the particular to the particular, or from the particular to the general. It is an old debate among philosophers whether deduction ever gives new knowledge. We can now see that in certain cases, at least, it does do so. If we already know that two and two always make four, and we know that brown and Jones are two, and so are Robinson and Smith, we can deduce that brown and Jones and Robinson and Smith are four. This is new knowledge not contained in our premises, because the general proposition two and two or four never told us there were such people as brown and Jones and Robinson and Smith, and the particular premises do not tell us that there were four of them, whereas the particular proposition deduced does tell us both these things. But the newness of knowledge is much less certain if we take the stock instance of deduction that is always given in books on logic. Namely, all men are mortal, Socrates is a man, therefore Socrates is mortal. In this case, what we really know beyond reasonable doubt is that certain men A, B, C were mortal, since in fact they have died. If Socrates is one of these men, it is foolish to go the roundabout way through all men are mortal to arrive at the conclusion that probably Socrates is mortal. If Socrates is not one of the men on whom our induction is based, we shall still do better to argue straight from our A, B, C to Socrates than to go round by the general proposition all men are mortal. For the probability that Socrates is mortal is greater on our data than the probability that all men are mortal. This is obvious because if all men are mortal, so is Socrates, but if Socrates is mortal it does not follow that all men are mortal. Hence we shall reach the conclusion that Socrates is mortal with a greater approach to certainty if we make our argument purely inductive than if we go by way of all men are mortal and then use deduction. This illustrates the difference between general propositions known a priori, such as two and two are four, and empirical generalizations such as all men are mortal. In regard to the former, deduction is the right mode of argument, whereas in regard to the latter, induction is always theoretically preferable and warrants a greater confidence in the truth of our conclusion because all empirical generalizations are more uncertain than the instances of them. We have now seen that there are propositions known a priori and that among them are the propositions of logic and pure mathematics as well as the fundamental propositions of ethics. The question which must next occupy us is this. How is it possible that there should be such knowledge? And more particularly, how can there be knowledge of general propositions in cases where we have not examined all the instances and indeed never can examine them all because their number is infinite? These questions which were first brought prominently forward by the German philosopher Kant, 1724 to 1804, are very difficult and historically very important. End of chapter 7. Recording by M. L. Cohen www.mojo.mu411.com Cleveland, Ohio August 2007 The Problems of Philosophy by Bertrand Russell Chapter 8 How a Priory Knowledge is Possible Immanuel Kant is generally regarded as the greatest of the modern philosophers. Though he lived through the Seven Years War and the French Revolution, he never interrupted his teaching of philosophy at Königsberg in East Prussia. His most distinctive contribution was the invention of what he called the critical philosophy, which, assuming as a datum that there is knowledge of various kinds, inquired how such knowledge comes to be possible, and deduced from the answer to this inquiry many metaphysical results as to the nature of the world. Whether these results were valid may well be doubted, but Kant undubitably deserves credit for two things. First, for having perceived that we have a priory knowledge which is not purely analytic—that is, such that the opposite would be self-contradictory—and secondly, for having made evident the philosophical importance of the theory of knowledge. Before the time of Kant it was generally held that whatever knowledge was a priory must be analytic, but this word means will be best illustrated by examples.  The subject spoken about is given as having at least two properties, of which one is singled out to be asserted of it. Such propositions as the above are trivial, and would never be enunciated in real life except by an orator preparing the way for a piece of sophistry. They are called analytic because the predicate is obtained by merely analyzing the subject. Before the time of Kant it was thought that all judgments of which we could be certain a priory were of this kind, that in all of them there was a predicate which was only part of the subject of which it was asserted. If this were so, we should be involved in a definite contradiction if we attempted to deny anything that could be known a priory. A bald man is not bald would assert and deny baldness of the same man and would therefore contradict itself. Thus, according to the philosophers before Kant the law of contradiction which asserts that nothing can at the same time have and not have a certain property suffice to establish the truth of all a priory knowledge. Hume, 1711 to 1776 who preceded Kant, accepting the usual view as to what make knowledge a priory, discovered that in many cases which had previously been supposed analytic and notably in the case of cause and effect, the connection was really synthetic. Before Hume, rationales at least had supposed that the effect could be logically deduced from the cause if only we had sufficient knowledge. Hume argued, correctly as would now be generally admitted, that this could not be done. Hence, he inferred the far more doubtful proposition that nothing could be known a priory about the connection of cause and effect. Kant, who had been educated in the rationalist tradition, was much perturbed by Hume's skepticism and endeavored to find an answer to it. He perceived that not only the connection of cause and effect but all the propositions of arithmetic and geometry are synthetic, that is, not analytic. In all these propositions no analysis of the subject will reveal the predicate. His stock instance was the proposition 7 plus 5 equals 12. He pointed out, quite truly, that 7 and 5 have to be put together to give 12. The idea of 12 was not contained in them nor even in the idea of adding them together. Thus he would lead to the conclusion that all pure mathematics, though a priory, is synthetic, and this conclusion raised a new problem of which he endeavored to find the solution. The question which Kant put at the beginning of his philosophy, namely how is pure mathematics possible, is an interesting and difficult one to which every philosophy which is not purely skeptical must find some answer. The answer of the pure empiricist that our mathematical knowledge is derived by induction from particular instances we have already seen to be inadequate for two reasons. First, that the validity to the inductive principle itself cannot be proved by induction. Secondly, that the general propositions of mathematics, such as 2 and 2 always makes 4, can obviously be known with certainty by consideration of a single instance and gain nothing by enumeration of other cases in which they have been found to be true. Thus our knowledge of the general propositions of mathematics, and the same applies to logic, must be accounted for otherwise than our merely probable knowledge of empirical generalization such as all men are mortal. The problem arises through the fact that such knowledge is general, whereas all experience is particular. It seems strange that we should apparently be able to know some truths in advance about particular things of which we have as yet no experience, but it cannot easily be doubted that logic and arithmetic will apply to such things. We do not know who will be the inhabitants of London a hundred years hence, but we know that any two of them and any other two of them will make four of them. This apparent power of anticipating facts about things of which we have no experience is certainly surprising. Consolution of the problem, though not valid in my opinion, is interesting. It is however very difficult and is differently understood by different philosophers. We can therefore only give the nearest outline of it, and even that will be thought misleading by many exponents of Kant's system. What Kant maintained was that in all our experience there are two elements to be distinguished. The one due to the object, that is to what we have called the physical object, the other due to our own nature. We saw in discussing matter and sense data that the physical object is different from the associated sense data, and that the sense data are to be regarded as resulting from an interaction between the physical object and ourselves. So far we are in agreement with Kant. But what is distinctive of Kant is the way in which he apportions the shares of ourselves and the physical objects respectively. He considers that the crude material given in sensation, the color, hardness, etc., is due to the object and that what we supply is the arrangement in space and time, and all the relations between sense data which result from comparison or from considering one as the cause of the other or in any other way. His chief reason in favor of this view is that we seem to have a priori knowledge as to space and time and causality in comparison, but not as to the actual crude material of sensation. We can be sure, he says, that anything we shall ever experience must show the characteristics affirmed of it in our a priori knowledge because these characteristics are due to our own nature, and therefore nothing can ever come into our experience without acquiring these characteristics. The physical object, which he calls the quote thing in itself, and quote, he regards as essentially unknowable. What can be known is the object as we have it in experience, which he calls quote phenomenon. Kant's thing in itself is identical in definition with the physical object namely it is the cause of sensations. In the properties deduced from the definition it is not identical since Kant held, in spite of some inconsistencies regards cause, that we can know that none of the categories are applicable to the quote thing in itself. The phenomenon, being a joint product of us and the thing in itself, is sure to have those characteristics which are due to us and is therefore sure to conform to our a priori knowledge. Hence this knowledge, though true of all actual impossible experience, must not be supposed to apply outside experience. Thus, in spite of the existence of a priori knowledge, we cannot know anything about the thing in itself or about what is not an actual or possible object of experience. In this way he tried to reconcile and harmonize the contentions of the rationalists with the arguments of the empiricists. Apart from the minor grounds on which Kant's philosophy may be criticized, there is one main objection which seems fatal to any attempt to deal with the problem of a priori knowledge by his method. The thing to be accounted for is our certainty, that the facts must always conform to logic and arithmetic. To say that logic and arithmetic are contributed by us does not account for this, how our nature is as much a fact of the existing world as anything, and there can be no certainty that it will remain constant. It might happen, if Kant is right, that tomorrow our nature would so change as to make two and two become five. This possibility seems never to have occurred to him, yet it is one which utterly destroys the certainty and universality which he is anxious to vindicate for arithmetical propositions. It is true that this possibility, formally, is inconsistent with the Kantian view that time itself is a form imposed by the subject upon phenomenon, so that our real self is not in time and has no tomorrow. But he will still have to suppose that the time order of phenomenon is determined by characteristics of what is behind phenomenon, and this suffices for the substance of our argument. Reflection, moreover, seems to make it clear that if there is any truth in our arithmetical beliefs, they must apply to things equally whether we think of them or not. Two physical objects and two other physical objects must make four physical objects, even if physical objects cannot be experienced. To assert this is certainly within the scope of what we mean when we state that two and two are four. Its truth is just as indubitable as the truth of the assertion that two phenomena and two other phenomena make four phenomena. Thus, constitution unduly limits the scope of a priori propositions in addition to failing in the attempt at explaining their certainty. Apart from the special doctrine's advocates by Kant, it is very common among philosophers to regard what is a priori as in some sense mental, as concerned rather with the way we must think than with any fact of the outer world. We noted in the preceding chapter the three principles commonly called, quote, laws of thought, end quote. The view which led to their being so named is a natural one, but there are strong reasons for thinking that is erroneous. Let us take as an illustration the law of contradiction. This is commonly stated in the form, quote, nothing can both be and not be, end quote, which is intended to express the fact that nothing can at once have and not have a given quality. Thus, for example, if a tree is a beach, it cannot also be not a beach. If my table is rectangular, it cannot also be not rectangular, and so on. Now what makes it natural to call this principle a law of thought is that it is by thought rather than by outward observation that we persuade ourselves of its necessary truth. When we have seen that a tree is a beach, we do not need to look again in order to ascertain whether there's also not a beach. Thought alone makes us know that this is impossible. But the conclusion that the law of contradiction is a law of thought is nevertheless erroneous. What we believe, when we believe the law of contradiction, is not that the mind is so made that it must believe the law of contradiction. This belief is a subsequent result of psychological reflection, which presupposes the belief in the law of contradiction. The belief in the law of contradiction is a belief about things, not only about thoughts. It is not, for example, the belief that if we think a certain tree is a beach, we cannot at the same time think that it is not a beach. It is the belief that if the tree is a beach, it cannot at the same time be not a beach. Thus the law of contradiction is about things, and not merely about thoughts, and although belief in the law of contradiction is a thought, the law of contradiction itself is not a thought, but a fact concerning the things in the world. If this, which we believe when we believe the law of contradiction, we're not true of all the things in the world. The fact that we were compelled to think it's true would not save the law of contradiction from being false, and this shows that the law is not a law of thought. A similar judgment applies to any other a priori judgment. When we judge that two and two or four, we are not making a judgment about our thoughts, but about all actual or possible couples. The fact that our minds are so constituted as to believe that two and two are four, though it is true, is emphatically not what we assert when we assert that two and two are four, and no fact about the constitution of our minds could make it true that two and two are four. Thus our a priori knowledge, if it is not erroneous, is not merely knowledge about the constitution of our minds, but is applicable to whatever the world may contain, both what is mental and what is not mental. The fact seems to be that all our a priori knowledge is concerned with entities which do not, properly speaking, exist, either in the mental or in the physical world. These entities are such as can be named by parts of speech which are not substantive. They are such entities as qualities and relations. Suppose, for instance, that I am in my room. I exist and my room exists. But does in exist? Yet obviously the word in has a meaning. It denotes a relation which holds between me and my room. This relation is something, although we cannot say that it exists in the same sense in which I and my room exist. The relation in is something which we can think about and understand, for if we could not understand it, we could not understand a sentence, I am in my room. Many philosophers following Kant have maintained that relations are the work of the mind, that things in themselves have no relations, but that the mind brings them together in one act of thought and thus produces the relations which it judges them to have. This view, however, seems open to objections similar to those which we urged before against Kant. It seems plain that it is not thought which produces the truth of the proposition, quote, I am in my room. It may be true that an earwig is my room, even if neither I nor the earwig nor anyone else is aware of this truth. For this truth concerns only the earwig and the room. It does not depend upon anything else. Thus relations, as we shall see more fully in the next chapter, must be placed in a world which is neither mental nor physical. This world is of great importance to philosophy and particularly to the problems of a priori knowledge. In the next chapter, we shall proceed to develop its nature and its bearing upon the questions with which we have been dealing. Chapter 9 The World of Universals At the end of the preceding chapter, we saw that such entities as relations appear to have a being which is in some way different from that of physical objects, and also different from that of minds and from that of sense data. In the present chapter, we have to consider what is the nature of this kind of being, and also what objects there are that have this kind of being. We will begin with the latter question. The problem with which we are now concerned is a very old one, since it was brought into philosophy by Plato. Plato's theory of ideas is an attempt to solve this very problem, and in my opinion it is one of the most successful attempts hitherto made. The theory to be advocated in what follows is largely Plato's, with merely such modifications as time is shown to be necessary. The way the problem arose for Plato was more or less as follows. Let us consider, say, such a notion as justice. If we ask ourselves what justice is, it is natural to proceed by considering this, that, and the other just act, with a view to discovering what they have in common. They must all, in some sense, partake of a common nature, which will be found in whatever is just and in nothing else. This common nature, in virtue of which they are all just, will be justice itself, the pure essence, the admixture of which, with facts of ordinary life, produces the multiplicity of just acts. Similarly, with any other word which may be applicable to common facts, such as whiteness, for example. The word will be applicable to a number of particular things because they all participate in a common nature or essence. This pure essence is what Plato calls an idea, or form. It must not be supposed that ideas, in his sense, exist in minds, though they may be apprehended by minds. The idea justice is not identical with anything that is just. It is something other than particular things, which particular things partake of. Not being particular, it cannot itself exist in the world of sense. Moreover, it is not fleeting or changeable like the things of sense. It is eternally itself, immutable, and indestructible. Thus, Plato has led to a super-sensible world, more real than the common world of sense. The unchangeable world of ideas, which alone gives to the world of sense whatever pale reflection of reality may belong to it. The truly real world, for Plato, is the world of ideas. For, whatever we may attempt to say about things in the world of sense, we can only succeed in saying that they participate in such and such ideas, which, therefore, constitute all their character. Hence, it is easy to pass on into amisticism. We may hope, in a mystical illumination, to see the ideas as we see objects of sense, and we may imagine that the ideas exist in heaven. These mystical developments are very natural, but the basis of the theory is in logic, and it is as based in logic that we have to consider it. The word idea has acquired, in the course of time, many associations which are quite misleading when applied to Plato's ideas. We shall therefore use the word universal instead of the word idea to describe what Plato meant. The essence of the sort of entity that Plato meant is that it is opposed to the particular things that are given in sensation. We speak of whatever is given in sensation, or is of the same nature as things given in sensation, as a particular. By opposition to this, a universal will be anything which may be shared by many particulars, and has those characteristics which, as we saw, distinguish justice and whiteness from just acts and white things. When we examine common words, we find that, broadly speaking, proper names stand for particulars, while other substantives, adjectives, prepositions, and verbs stand for universals. Pronouns stand for particulars, but are ambiguous. It is only by the context or the circumstances that we know what particulars they stand for. The word now stands for a particular, namely the present moment. But like pronouns, it stands for an ambiguous particular, because the present is always changing. It will be seen that no sentence can be made up without at least one word which denotes a universal. The nearest approach would be some such statement as, I like this, but even here the word like denotes a universal, for I may like other things, and other people may like things. Thus, all truths involve universals, and all knowledge of truths involves acquaintance with universals. Seeing that nearly all the words to be found in the dictionary stand for universals, it is strange that hardly anybody, except students of philosophy, ever realizes that there are such entities as universals. We do not naturally dwell upon these words in a sentence which do not stand for particulars. And if we are forced to dwell upon a word which stands for a universal, we naturally think of it as standing for some one of the particulars that come under the universal. When, for example, we hear the sentence, Charles the first's head was cut off, we may naturally enough think of Charles the first, of Charles the first's head, and of the operation of cutting off his head, which are all particulars, but we do not naturally dwell upon what is meant by the word head or the word cut, which is a universal. We feel such words to be incomplete and insubstantial, they seem to demand a context before anything can be done with them. Hence, we succeed in avoiding all notice of universals as such, until the study of philosophy forces them upon our attention. Even among philosophers, we may say, broadly, that only those universals which are named by adjectives or substandives have been much or often recognized, while those named by verbs and prepositions have been usually overlooked. This omission has had a very great effect upon philosophy. It is hardly too much to say that most metaphysics, since Spinoza, has been largely determined by it. The way this has occurred is, in outline, as follows. Speaking generally, adjectives and common nouns express qualities or properties of single things, whereas prepositions and verbs tend to express relations between two or more things. Thus the neglect of prepositions and verbs led to the belief that every preposition can be regarded as attributing a property to a single thing, rather than as expressing a relation between two or more things. Hence it was supposed that, ultimately, there can be no such entities as relations between things. Hence, either there can be only one thing in the universe, or, if there are many things, they cannot possibly interact in any way, since any interaction would be a relation, and relations are impossible. The first of these views, advocated by Spinoza, and held in our own day by Bradley and many other philosophers, is called monism. The second, advocated by Liebnis, but not very common nowadays, is called monadism, because each of the isolated things is called a monad. Both these opposing philosophies, interesting as they are, result, in my opinion, from an undue attention to one sort of universals, namely the sort represented by adjectives and substantives, rather than by verbs and preposition. As a matter of fact, if anyone were anxious to deny altogether that there are such things as universals, we should find that we cannot strictly prove that there are such entities as qualities, i.e., the universals represented by adjectives and substantives, whereas we can prove that there must be relations, i.e., the sort of universals generally represented by verbs and prepositions. Let us take, in illustration, the universal whiteness. If we believe that there is such a universal, we shall find that things are white because they have the quality of whiteness. This view, however, was strenuously denied by Berkeley and Hume, who have been followed in this by later empiricists. The form which their denial took was to deny that there are such things as abstract ideas. When we want to think of whiteness, they said, we form an image of some particular white thing and reason concerning this particular, taking care not to deduce anything concerning it which we cannot see to be equally true of any other white thing. As an account of our actual mental processes, this is no doubt largely true. In geometry, for example, when we wish to prove something about all triangles, we draw a particular triangle and reason about it, taking care not to use any characteristic which it does not share with other triangles. The beginner, in order to avoid error, often finds it useful to draw several triangles, as unlike each other as possible, in order to make sure that his reasoning is equally applicable to all of them. But a difficulty emerges as soon as we ask ourselves how we know that a thing is white or a triangle. If we wish to avoid the universal's whiteness and triangularity, we shall choose some particular patch of white or some particular triangle, and say that anything is white or a triangle if it has the right sort of resemblance to our chosen particular. But then the resemblance required will have to be a universal. Since there are many white things, the resemblance must hold between many pairs of particular white things, and this is the characteristic of a universal. It will be useless to say that there is a different resemblance for each pair, for then we shall have to say that these resemblances resemble each other. And thus, at last we shall be forced to admit resemblance as a universal. The relation of resemblance, therefore, must be a true universal. And having been forced to admit this universal, we find that it is no longer worthwhile to invent difficult and unplausible theories to avoid the emission of such universals as whiteness and triangularity. Berkeley and Hume failed to perceive this refutation of their rejection of abstract ideas, because, like their adversaries, they only thought of qualities, and altogether ignored relations as universals. We have therefore here another respect in which the rationalists appear to have been in the right as against the empiricists. Although, owing to the neglect or denial of relations, the deductions made by rationalists were, if anything, more apt to be mistaken than those made by empiricists. Having now seen that there must be such entities as universals, the next point to be proved is that their being is not merely mental. By this is meant that whatever being belongs to them is independent of their being thought of, or in any way apprehended by minds. We have already touched on this subject at the end of the preceding chapter, but we must now consider more fully what sort of being it is that belongs to universals. Consider such a proposition as, Edinburgh is north of London. Here we have a relation between two places, and it seems plain that the relation subsists independently of our knowledge of it. When we come to know that Edinburgh is north of London, we come to know something which has to do only with Edinburgh in London. We do not cause the truth of the proposition by coming to know it. On the contrary, we merely apprehend a fact which was there before we knew it. The part of the earth's surface where Edinburgh stands would be north of the part where London stands, even if there were no human being to know about north and south, and even if there were no minds at all in the universe. This is, of course, denied by many philosophers, either for Berkeley's reasons or for Kant's. But we have already considered these reasons, and decided that they are inadequate. We may therefore now assume it to be true that nothing mental is presupposed in the fact that Edinburgh is north of London, but this fact involves the relation north of, which is a universal, and it would be impossible for the whole fact to involve nothing mental if the relation north of, which is a constituent part of the fact, did involve anything mental. Hence, we must admit that the relation, like the terms it relates, is not dependent upon thought, but belongs to the independent world which thought apprehends, but does not create. This conclusion, however, is met by the difficulty that the relation north of does not seem to exist in the same sense in which Edinburgh and London exist. If we ask, where and when does this relation exist, the answer must be nowhere and no when. There is no place or time where we can find the relation north of. It does not exist in Edinburgh any more than in London, for it relates the two and is neutral as between them. Nor can we say that it exists at any particular time. Now, everything that can be apprehended by the senses or by introspection exists at some particular time. Hence, the relation north of is radically different from such things. It is neither in space nor in time, neither material nor mental, yet it is something. It is largely the very peculiar kind of being that belongs to universals which has led many people to suppose that they are really mental. We can think of a universal and our thinking then exists in a perfectly ordinary sense, like any other mental act. Suppose, for example, that we are thinking of whiteness, then in one sense it may be said that whiteness is in our mind. We have here the same ambiguity as we noted in discussing Berkeley in Chapter 4. In the strict sense, it is not whiteness that is in our mind, but the act of thinking of whiteness. The connected ambiguity in the word idea, which we noted at the same time, also causes confusion here. In one sense of this word, namely the sense in which it denotes the object of an act of thought, whiteness is an idea. Hence, if the ambiguity is not guarded against, we may come to think that whiteness is an idea in the other sense, i.e., an act of thought, and thus we come to think that whiteness is mental. But in so thinking, we rob it of its essential quality of universality. One man's act of thought is necessarily a different thing from another man's. One man's act of thought at one time is necessarily a different thing from the same man's act of thought at another time. Hence, if whiteness were the thought, as opposed to its object, no two different men could think of it, and no one man could think of it twice. That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus, universals are not thoughts, though when known they are the objects of thoughts. We shall find it convenient only to speak of things existing when they are in time. That is to say, when we can point to some time at which they exist, not excluding the possibility of their existing at all times. Thus, thoughts and feelings, minds and physical objects exist. But universals do not exist in this sense. We shall say that they subsist, or have being, where being is opposed to existence as being timeless. The world of universals, therefore, may also be described as the world of being. The world of being is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life. The world of existence is fleeting, vague, without sharp boundaries, without any clear plan or arrangement, but it contains all thoughts and feelings, all the data of sense, and all physical objects, everything that can do either good or harm, everything that makes any difference to the value of life and the world. According to our temperaments, we shall prefer the contemplation of the one or of the other. The one we do not prefer will probably seem to us a pale shadow of the one we prefer, and hardly worthy to be regarded as, in any sense, real. But the truth is that both have the same claim on our impartial attention. Both are real, and both are important to the metaphysician. Indeed, no sooner have we distinguished the two worlds than it becomes necessary to consider their relations. But first of all, we must examine our knowledge of universals. This consideration will occupy us in the following chapter, where we shall find that it solves the problem of a priori knowledge, from which we were first led to consider universals. End of Chapter 9 The Problems of Philosophy This recording is in the public domain. Chapter 10 of The Problems of Philosophy This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to find out how to volunteer, please contact LibriVox.org. The Problems of Philosophy by Bertrand Russell Chapter 10 On Our Knowledge of Universals In regard to one man's knowledge at a given time, universals, like particulars, may be divided in those known by acquaintance, those known only by description, and those not known either by acquaintance or by description. Let us consider first the knowledge of universals by acquaintance. It is obvious, to begin with, that we are acquainted with such universals as white, red, black, sweet, sour, loud, hard, etc., i.e., with qualities which are exemplified and sense data. When we see a white patch, we are acquainted, in the first instance, with a particular patch. But by seeing many white patches, we easily learn to abstract the whiteness, which they all have in common. And in learning to do this, we are learning to be acquainted with whiteness. A similar process will make us acquainted with any other universal of the same sort. Universals of this sort may be called sensible qualities. They can be apprehended with less effort of abstraction than any others, and they seem less removed from particulars than other universals are. The easiest relations to apprehend are those which hold between the different parts of a single complex sense datum. For example, the whole of the page on which I am writing, thus the whole page is included in one sense datum. But I perceive that some parts of the page are to the left of other parts, and some parts are above other parts. The process of abstraction in this case seems to proceed somewhat as follows. I see successively a number of sense data in which one part is to the left of another. I perceive, as in the case of different white patches, that all these sense data have something in common. And by abstraction I find that what they have in common is a certain relation between their parts, namely the relation which I call being to the left of. In this way, I become acquainted with the universal relation. In like manner, I become aware of the relation of before and after in time. Suppose I hear a chime of bells. When the last bell of the chime sounds, I can retain the whole chime before my mind, and I can perceive that the earlier bells came before the later ones. Also in memory, I perceive that what I am remembering came before the present time. From either of these sources I can abstract the universal relation of before and after, just as I abstracted the universal relation being to the left of. Thus time relations, like space relations, are among those with which we are acquainted. Another relation with which we become acquainted in much the same way is resemblance. If I see simultaneously two shades of green, I can see that they resemble each other. If I also see a shade of red, at the same time, I can see that the two shades of green have more resemblances to each other than either has to the red. In this way, I become acquainted with the universal resemblance or similarity. Between universals, as between particulars, there are relations of which we may be immediately aware. We have just seen that we can perceive that the resemblance between two shades of green is greater than the resemblance between a shade of red and a shade of green. Here we are dealing with a relation, namely, greater than, between two relations. Our knowledge of such relations, though it requires more power of abstraction than is required for perceiving qualities of sense data, appears to be equally immediate and, at least in some cases, equally indubitable. Thus there is immediate knowledge concerning universals as well as concerning sense data. Returning now to the problem of a priori knowledge, which we left unsolved when we began the consideration of universals, we find ourselves in a position to deal with it in a much more satisfactory manner than was possible before. Let us revert to the proposition two and two are four. It is fairly obvious, and view of what has been said, that this proposition states a relation between the universal two and the universal four. This suggests a proposition with which we shall now endeavor to establish, namely, all a priori knowledge deals exclusively with the relations of universals. This proposition is of great importance and goes a long way towards solving our previous difficulties concerning a priori knowledge. The only case in which it might seem, at first sight, as if our proposition were untrue, is the case in which an a priori proposition states that all of one class of particulars belong to some other class, or what comes to the same thing, that all particulars having some one property also have some other. In this case, it might seem as though we were dealing with the particulars that have the property rather than with the property. The proposition two and two are four is really a case in point, for this may be stated in the form, any two and any other two are four, or any collection formed of two twos is a collection of four. If we can show that such statements as this really deal only with universals, our proposition may be regarded as proved. One way of discovering what a proposition deals with is to ask ourselves what words we must understand. In other words, what objects we must be acquainted with in order to see what the proposition means. As soon as we see what the proposition means, even if we do not yet know whether it is true or false, it is evident that we must have acquaintance with whatever is really dealt with by the proposition. By applying this test, it appears that many propositions which might seem to be concerned with particulars are really concerned only with universals. In the special case of two and two or four, even when we interpret it as meaning, any collection formed of two twos is a collection of four. It is plain that we can understand the proposition, i.e., we can see what it is that it asserts as soon as we know what is meant by a collection, and two and four. It is quite unnecessary to know all the couples in the world. If it were necessary, obviously we could never understand the proposition, since the couples are infinitely numerous and therefore cannot all be known to us. Thus, although our general statement implies statements about particular couples, as soon as we know that there are such particular couples, yet it does not itself assert or imply that there are such particular couples, and thus fails to make any statement whatever about any actual particular couple. The statement made is about couple, the universal, and not about this or that couple. Thus the statement, two and two or four, deals exclusively with universals, and therefore may be known by anybody who is acquainted with the universals concerned and can perceive the relation between them which the statement asserts. It must be taken as a fact, discovered by reflecting upon our knowledge, that we have the power of sometimes perceiving such relations between universals, and therefore of sometimes knowing general a priori propositions, such as those of arithmetic and logic. The thing that seemed mysterious, when we formerly considered such knowledge, was that it seemed to anticipate and control experience. This however, we can now see to have been an error. No fact concerning anything capable of being experienced can be known independently of experience. We know a priori that two things and two other things together make four things, but we do not know a priori that if Brown and Jones are two, and Robinson and Smith are two, then Brown and Jones and Robinson and Smith are four. The reason is that this proposition cannot be understood at all, unless we know that there are such people as Brown and Jones and Robinson and Smith, and this we can only know by experience. Hence, although our general proposition is a priori, all its applications to actual particulars involve experience and therefore contain an empirical element. In this way, what seemed mysterious in our a priori knowledge is seen to have been based upon an error. It will serve to make the point clearer if we contrast our genuine a priori judgment with an empirical generalization, such as all men are mortals. Here is before we can understand what the proposition means as soon as we understand the universals involved, namely, man and mortal. It is obviously unnecessary to have an individual acquaintance with the whole human race in order to understand what our proposition means. Thus, the difference between an a priori general proposition and an empirical generalization does not come in the meaning of the proposition. It comes in the nature of the evidence for it. In the empirical case, the evidence consists in the particular instances. We believe that all men are mortal because we know that there are innumerable instances of men dying, and no instances of their living beyond a certain age. We do not believe it because we see a connection between the universal man and the universal mortal. It is true that if physiology can prove, assuming the general laws that govern living bodies, that no living organism can last forever, that gives a connection between man and mortality, which would enable us to assert our proposition without appealing to the special evidence of men dying. But that only means that our generalization has been subsumed under a wider generalization, for which the evidence is still of the same kind, though more extensive. The progress of science is constantly producing such subsumptions, and therefore giving a constantly wider inductive basis for scientific generalizations. But although this gives a greater degree of certainty, it does not give a different kind. The ultimate ground remains inductive, i.e., derived from instances, and not from a priori connection of universals, such as we have in a logic and arithmetic. Two opposite points are to be observed concerning a priori general propositions. The first is that, if many particular instances are known, our general proposition may be arrived at in the first instance by induction, and the connection of universals may be only subsequently perceived. For example, it is known that if we draw perpendicular to the sides of a triangle from the opposite angles, all three perpendiculars meet in a point. This experience might lead us to look for the general proof and find it. Such cases are common in the experience of every mathematician. The other point is more interesting, and of more philosophical importance. It is that we may sometimes know a general proposition in cases where we do not know a single instance of it. Take such a case as the following. We know that any two numbers can be multiplied together, and will give a third called their product. We know that all pairs of integers, the product of which is less than a hundred, have been actually multiplied together, and the value of the product recorded in the multiplication table. But we also know that the number of integers is infinite, and that only a finite number of the pairs of integers have ever been or ever will be thought of by human beings. Hence it follows that there are pairs of integers which never have been and never will be thought of by human beings, and that all of them deal with integers the product of which is over a hundred. Hence we arrive at the proposition. All products of two integers, which never have been and never will be thought of by any human being, are over a hundred. Here is a general proposition of which the truth is undeniable, and yet from the very nature of the case we can never give an instance, because any two numbers we may think of are excluded by the terms of the proposition. This possibility of knowledge of general propositions of which no instance can be given is often denied, because it is not perceived that the knowledge of such propositions only requires a knowledge of the relations of universals, and does not require any knowledge of instances of the universals in question. Yet the knowledge of such general propositions is quite vital to a great deal of what is generally admitted to be known. For example, we saw in our early chapters that knowledge of physical objects, as opposed to sense data, is only obtained by inference, and that they are not things with which we are acquainted. Hence we can never know any proposition of the form, this is a physical object, where this is something immediately known. It follows that all our knowledge concerning physical objects is such that no actual instance can be given. We can give instances of the associated sense data, but we cannot give instances of the actual physical objects. Hence our knowledge as to physical objects depends throughout upon this possibility of general knowledge where no instance can be given. And the same applies to our knowledge of other people's minds, or of any other class of things of which no instance is known to us by acquaintance. We may now take a survey of the sources of our knowledge as they have appeared in the course of our analysis. We have first to distinguish knowledge of things and knowledge of truths. In each there are two kinds, one immediate and one derivative. Our immediate knowledge of things, which we called acquaintance, consists of two sorts. According, as the things are known, are particulars or universals. Among particulars we have acquaintance with sense data, and probably with ourselves. Among universals, there seems to be no principle by which we can decide which can be known by acquaintance, but it is clear that among those that can be so known are sensible qualities, relations of space and time, similarity, and certain abstract logical universals. Our derivative knowledge of things, which we call knowledge by description, always involves both acquaintance with something and knowledge of truths. Our immediate knowledge of truths may be called intuitive knowledge, and the truths so known may be called self-evident truths. Among such truths are included those which merely state what is given in sense, and also certain abstract logical and arithmetical principles, and, though with less certainty, some ethical propositions. Our derivative knowledge of truths consists of everything that we can deduce from self-evident truths by the use of self-evident principles of deduction. If the above account is correct, all our knowledge of truths depends upon our intuitive knowledge. It therefore becomes important to consider the nature and scope of intuitive knowledge. In much the same way, as at an earlier stage, we consider the nature and scope of knowledge by acquaintance. But knowledge of truths raises a further problem, which does not arise in regard to knowledge of things, namely the problem of error. Some of our beliefs turn out to be erroneous, and therefore it becomes necessary to consider how, if at all, we can distinguish knowledge from error. This problem does not arise with regard to knowledge by acquaintance, for, whatever may be the object of acquaintance, even in dreams and hallucinations, there is no error involved so long as we do not go beyond the immediate object. Error can only arise when we regard the immediate object, i.e., the sense-datum as the mark of some physical object. Thus the problems connected with knowledge of truths are more difficult than those connected with knowledge of things. As the first of the problems connected with knowledge of truths, let us examine the nature and scope of our intuitive judgments. End of Chapter 10 on our knowledge of universals. This recording is in the public domain. The Problems of Philosophy by Bertrand Russell Chapter 11 On Intuitive Knowledge There is a common impression that everything that we believe ought to be capable of proof, or at least of being shown to be highly probable. 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. Almost all our common beliefs are either inferred or capable of being inferred from other beliefs which may be regarded as giving the reason for them. As a rule, the reason has been forgotten or has even never been consciously present to our minds. Few of us ever ask ourselves, for example, what reason there is to suppose the food we are just going to eat will not turn out to be poison. Yet we feel when challenged that a perfectly good reason could be found, even if we are not ready with it at the moment. And in this belief we are usually justified. 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 or some instance of general principle which seems luminously evident and is not itself capable of being deduced from anything more evident. In most questions of daily life, such as whether our food is likely to be nourishing and not poisonous, we shall be driven back to the inductive principle, which we discussed in Chapter 6. But beyond that there seems to be no further regress. The principle itself is constantly used in our reasoning, sometimes consciously, sometimes unconsciously. But there is no reasoning which starting from some simpler self-evident principle leads us to the principle of induction as its conclusion, and the same holds for other logical principles. Their truth is evident to us, and we employ them in constructing demonstrations, but they themselves, or at least some of them, are incapable of demonstration. Self-evidence, however, is not confined to those among general principles which are incapable of proof. When a certain number of logical principles have been admitted, the rest can be deduced from them. But the propositions deduced are often just as self-evident as those that were assumed without proof. All arithmetic, moreover, can be deduced from the general principles of logic. Yet the simple propositions of arithmetic, such as 2 and 2 are 4, are just as self-evident as the principles of logic. It would seem also, though this is more disputable, that there are some self-evident ethical principles such as, quote, we ought to pursue what is good, end quote. It should be observed that in all cases of general principles, particular instances dealing with familiar things are more evident than the general principle. For example, the law of contradiction states that nothing can both have a certain property and not have it. This is evident as soon as it is understood, but it is not so evident as that a particular rose which we see cannot be both red and not red. It is, of course, possible that parts of the rose may be red and parts not red, or that the rose may be of a shade of pink, which we hardly know whether to call red or not. But in the former case, it is plain that the rose as a whole is not red. While in the latter case, the answer is theoretically definite, as soon as we have decided on a precise definition of, quote, red. It is usually through particular instances that we can be able to see the general principle. Only those who are practiced in dealing with abstractions can readily grasp a general principle without the help of instances. In addition to general principles, the other kind of self-evident truths are those immediately derivable from sensation. We will call such truths, quote, truths of perception, and the judgments expressing them, we will call, quote, judgments of perception. But here a certain amount of care is required in getting at the precise nature of the truths that are self-evident. The actual sense data are neither true nor false. A particular patch of color which I see, for example, simply exists. It is not the sort of thing that is true or false. It is true that there is such a patch. True that it has a certain shape and degree of brightness. True that it is surrounded by certain other colors. But the patch itself, like everything else in the world of sense, is of a radically different kind from the things that are true or false, and therefore cannot properly said to be true. Thus whatever self-evident truths may be obtained from our senses must be different from the sense data from which they are obtained. It would seem that there are two kinds of self-evident truths of perception, though perhaps in the last analysis the two kinds may coalesce. First, there is the kind which simply asserts the existence of the sense datum, without in any way analyzing it. We see a patch of red and we judge, quote, there is such and such a patch of red, end quote, or more strictly, there is that. This is one kind of intuitive judgment of perception. The other kind arises when the object of sense is complex and we subject it to some degree of analysis. If, for instance, we see a round patch of red, we may judge, quote, that patch of red is round, end quote. This is again a judgment of perception, but it differs from our previous kind. In our present kind, we have a single sense datum which has both color and shape. The color is red and the shape is round. Our judgment analyzes the datum into color and shape and then recombines them by stating that the red color is round in shape. Another example of this kind of judgment is, quote, this is to the right of that, where quote this and quote that are seen simultaneously. In this kind of judgment, the sense datum contains constituents which have some relation to each other and the judgment asserts that these constituents have this relation. Another class of intuitive judgments, analogous to those of sense and yet quite distinct from them, are judgments of memory. There is some danger of confusion as to the nature of memory, owing to the fact that memory of an object is apt to be accompanied by an image of the object, and yet the image cannot be what constitutes memory. This is easily seen by merely noticing that the image is in the present, whereas what is remembered is known to be in the past. Moreover, we are certainly able to some extent to compare our image with the object remembered so that we often know within somewhat wide limits how far our image is accurate, but this would be impossible unless the object, as opposed to the image, were in some way before the mind. Thus, the essence of memory is not constituted by the image, but by having immediately before the mind an object which is recognized as past. But for the fact of memory in this sense, we should not know that there ever was a past at all, or should we be able to understand the word quote past any more than a man born blind can understand the word quote light. Thus there must be intuitive judgments of memory, and it is upon them ultimately that all our knowledge of the past depends. The case of memory, however, raises a difficulty for it is notoriously fallacious, and thus throws doubt on the trustworthiness of intuitive judgments in general. The difficulty is no light one, but let us first narrow its scope as far as possible. Broadly speaking, memory is trustworthy in proportion to the vividness of the experience and to its nearness in time. If the house next door was struck by lightning half a minute ago, my memory of what I saw and heard will be so reliable that it would be preposterous to doubt whether there had been a flash at all. And the same applies to less vivid experiences, so long as they are recent. 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 upon attendant circumstances, and some things of which I am by no means certain. I am quite certain that I ate my breakfast this morning, but if I were as indifferent to my breakfast as a philosopher should be, I should be doubtful. As to the conversation at breakfast, I can recall some of it easily, some with an effort, some only with a large element of doubt, and some not at all. Thus there is a continual gradation in the degree of self-evidence of what I remember and a corresponding gradation of the trustworthiness of my memory. Thus the first answer to the difficulty of the fallacious memory is to say that the memory has degrees of self-evidence, and that these correspond to the degrees of its trustworthiness, reaching a limit of perfect self-evidence and perfect trustworthiness in our memory of events which are recent and vivid. It would seem, however, that there are cases of very firm belief in a memory which is wholly false. It is probable that in these cases what is really remembered in the sense of being immediately before the mind is something other than what is falsely believed in, though something generally associated with it. George IV is said to have at last believed that he was at the Battle of Waterloo, because he had so often said that he was. In this case what was immediately remembered was his repeated assertion, the belief in what he was asserting, if it existed, would be produced by association with the remembered assertion, and would therefore not be a genuine case of memory. It would seem that cases of fallacious memory can probably all be dealt with in this way, i.e. they can be shown to be not cases of memory in the strict sense at all. 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. Truths of perception and some of the principles of logic have the very highest degree of self-evidence. Truths of immediate memory have an almost equally high degree. The inductive principle has less self-evidence than some of the other principles of logic, such as, quote, what follows from a true premise must be true, end quote. Memories have a diminishing self-evidence as they become remotor and fainter. The truths of logic and mathematics have, broadly speaking, less self-evidence as they become more complicated. Judgments of intrinsic ethical or aesthetic value are apt to have some self-evidence, but not much. Degrees of self-evidence are important to the theory of knowledge, since, if propositions may, as seems likely, have some degree of self-evidence without being true, it will be necessary to abandon all connection between self-evidence and truth. But merely to say that where there is a conflict, the more self-evident proposition is to be retained and the less self-evident rejected. It seems, however, highly probable that two different notions are combined in, quote, self-evidence, as above explained, that one of them, which corresponds to the highest degree of self-evidence, is really an infallible guarantee of truth, while the other, which corresponds to all the other degrees, does not give an infallible guarantee, but only a greater or less presumption. This, however, is only a suggestion which we cannot as yet develop further. After we have dealt with the nature of truth, we shall return to the subject of self-evidence, in connection with the distinction between knowledge and error. CHAPTER XII of The Problems of Philosophy This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. The Problems of Philosophy by Bertrand Russell Chapter XII Truth and Falsehood Our knowledge of truths, unlike our knowledge of things, has an opposite, namely error. So far as things are concerned, we may know them or not know them, but there is no positive state of mind which can be described as erroneous knowledge of things, so long at any rate as we confine ourselves to knowledge by acquaintance. Whatever we are acquainted with must be something. We may draw wrong inferences from our acquaintance, but the acquaintance itself cannot be deceptive. Thus there is no dualism as regards acquaintance. But as regards knowledge of truths, there is a dualism. We may believe what is false as well as what is true. We know that on very many subjects different people hold different and incompatible opinions, hence some beliefs must be erroneous. Since erroneous beliefs are often held just as strongly as true beliefs, it becomes a difficult question how they are to be distinguished from true beliefs. How are we to know, in a given case, that our belief is not erroneous? This is a question of the very greatest difficulty to which no completely satisfactory answer is possible. There is, however, a preliminary question which is rather less difficult, and that is, what do we mean by truth and falsehood? It is this preliminary question which is to be considered in this chapter. In this chapter we are not asking how we can know whether a belief is true or false. We are asking what is meant by the question whether a belief is true or false. It is to be hoped that a clear answer to this question may help us to obtain an answer to the question what beliefs are true, but for the present we ask only what is truth and what is falsehood, not what beliefs are true and what beliefs are false. It is very important to keep these different questions entirely separate, since any confusion between them is sure to produce an answer which is not really applicable to either. There are three points to observe in the attempt to discover the nature of truth, three requisites which any theory must fulfill. 1. Our theory of truth must be such as to admit of its opposite, falsehood. A good many philosophers have failed adequately to satisfy this condition. They have constructed theories according to which all our thinking ought to have been true, and have then had the greatest difficulty in finding a place for falsehood. In this respect our theory of belief must differ from our theory of acquaintance, since in the case of acquaintance it was not necessary to take account of any opposite. 2. It seems fairly evident that if there were no beliefs there could be no falsehood and no truth either, in the sense in which truth is correlated to falsehood. If we imagine a world of mere matter there would be no room for falsehood in such a world, and although it would contain what may be called facts, it would not contain any truths, in the sense in which truths are things of the same kind as falsehoods. In fact 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. 3. But as against what we have just said, it is to be observed that the truth or falsehood of a belief always depends upon something which lies outside the belief itself. If I believe that Charles I died on the scaffold, I believe truly not because of any intrinsic quality of my belief, which could be discovered by merely examining the belief, but because of an historical event which happened two-and-a-half centuries ago. If I believe that Charles I died in his bed, I believe falsely. No degree of vividness in my belief, or of care and arriving at it, prevents it from being false, again because of what happened long ago, and not because of any intrinsic property of my belief. Hence although truth and falsehood are properties of beliefs, they are properties dependent upon the relations of the beliefs to other things, not upon any internal quality of the beliefs. The third of the above requisites leads us to adopt the view, which has on the whole been commonest among philosophers, that 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. By this partly, and partly by the feeling that if truth consists in a correspondence of thought with something outside thought, thought can never know when truth has been attained, many philosophers have been led to try to find some definition of truth which shall not consist in relation to something wholly outside belief. The most important attempt at a definition of this sort is the theory that truth consists in coherence. It is said that the mark of falsehood is failure to cohere in the body of our beliefs, and that it is the essence of a truth to form part of the completely rounded system which is the truth. There is however a great difficulty in this view, or rather two great difficulties. The first is that there is no reason to suppose that only one coherent body of beliefs is possible. It may be that with sufficient imagination a novelist might invent a past for the world that would perfectly fit onto what we know, and yet be quite different from the real past. In more scientific matters it is certain that there are often two or more hypotheses which account for all the known facts on some subject, and although in such cases men of science endeavor to find facts which will rule out all the hypotheses except one, there is no reason why they should always succeed. In philosophy again it seems not uncommon for two rival hypotheses to be both able to account for all the facts. Thus for example it is possible that life is one long dream, and that the outer world has only that degree of reality that the objects of dreams have, but although such a view does not seem inconsistent with known facts, there is no reason to prefer it to the common sense view according to which other people and things do really exist. Those coherence as the definition of truth fails because there is no proof that there can be only one coherent system. The other objection to this definition of truth is that it assumes the meaning of coherence known whereas in fact coherence presupposes the truth of the laws of logic. Two propositions are coherent when both may be true and are incoherent when one at least must be false. Now in order to know whether two propositions can both be true we must know such truths as the law of contradiction. For example the two propositions this tree is a beach and this tree is not a beach are not coherent because of the law of contradiction. But if the law of contradiction itself were subjected to the test of coherence we should find that if we choose to suppose it false nothing will any longer be incoherent with anything else. Thus the laws of logic supply the skeleton or framework within which the test of coherence applies and they themselves cannot be established by this test. For the above two reasons coherence cannot be accepted as giving the meaning of truth though it is often a most important test of truth after a certain amount of truth has become known. Hence we are driven back to correspondence with fact as constituting the nature of truth. It remains to define precisely what we mean by fact and what is the nature of the correspondence which must subsist between belief and fact in order that belief may be true. In accordance with our three requisites we have to seek a theory of truth which one allows truth to have an opposite namely falsehood. Two makes truth a property of beliefs but three makes it a property wholly dependent upon the relation of the beliefs to outside things. The necessity of allowing for falsehood makes it impossible to regard belief as a relation of the mind to a single object which could be said to be what is believed. If belief were so regarded we should find that like acquaintance it would not admit of the opposition of truth and falsehood but would have to be always true. This may be made clear by examples. Othello believes falsely that Desdemona loves Casio. We cannot say that this belief consists in a relation to a single object Desdemona's love for Casio for if there were such an object the belief would be true. There is in fact no sub-object and therefore Othello cannot have any relation to such an object hence his belief cannot possibly consist in a relation to this object. It might be said that his belief is a relation to a different object namely that Desdemona loves Casio. But it is almost as difficult to suppose that there is such an object as this when Desdemona does not love Casio as it was to suppose that there is Desdemona's love for Casio. Hence it will be better to seek for a theory of belief which does not make it consist in a relation of the mind to a single object. It is common to think of relations as though they always held between two terms but in fact this is not always the case. Some relations demand three terms some four and so on. Take for instance the relation between. So long as only two terms come in the relation between is impossible. Three terms are the smallest number that render it possible. York is between London and Edinburgh. But if London and Edinburgh were the only places in the world there could be nothing which was between one place and another. Similarly jealousy requires three people. There can be no such relation that does not involve three at least. Such a proposition as A wishes B to promote C's marriage with D involves a relation of four terms. That is to say A and B and C and D all come in and the relation involved cannot be expressed otherwise than in a form involving all four. Incidences might be multiplied indefinitely but enough has been said to show that there are relations which require more than two terms before they can occur. The relation involved in judging or believing must if falsehood is to be duly allowed for be taken to be a relation between several terms not between two. When Othello believes that Desdemona loves Cassio he must not have before his mind a single object Desdemona's love for Cassio or that Desdemona loves Cassio for that would require that there should be objective falsehoods which subsist independently of any minds and this though not logically refutable is a theory to be avoidant if possible. Thus it is easier to account for falsehood if we take judgment to be a relation in which the mind and the various objects concerned all occur severally. That is to say Desdemona and loving and Cassio must all be terms in the relation which subsists when Othello believes that Desdemona loves Cassio. This relation therefore is a relation of four terms since Othello also is one of the terms of the relation. When we say that it is a relation of four terms we do not mean that Othello has a certain relation to Desdemona and has the same relation to loving and also to Cassio. This may be true of some other relation than believing but believing plainly is not a relation which Othello has to each of the three terms concerned but to all of them together. There is only one example of the relation of believing involved but this one example knits together four terms. Thus the actual occurrence at the moment when Othello is entertaining his belief is that the relation called believing is knitting together into one complex whole the four terms Othello, Desdemona, loving and Cassio. What is called belief or judgment is nothing but this relation of believing or judging which relates a mind to several things other than itself. An act of belief or of judgment is the occurrence between certain terms at some particular time of the relation of believing or judging. We are now in a position to understand what it is that distinguishes a true judgment from a false one. For this purpose we will adopt certain definitions. In every act of judgment there is a mind which judges and there are terms concerning which it judges. We will call the mind the subject in the judgment and the remaining terms the objects. Thus when Othello judges that Desdemona loves Cassio Othello is the subject while the objects are Desdemona and loving and Cassio. The subject and the objects together are called the constituents of the judgment. It will be observed that the relation of judging has what is called a sense or direction. We may say metaphorically that it puts its objects in a certain order which we may indicate by means of the order of the words in the sentence. In an inflected language the same thing will be indicated by inflections, e.g. by the difference between nominative and accusative. Othello's judgment that Cassio loves Desdemona differs from his judgment that Desdemona loves Cassio in spite of the fact that it consists of the same constituents because the relation of judging places the constituents in a different order in the two cases. Similarly if Cassio judges that Desdemona loves Othello the constituents of the judgment are still the same but their order is different. This property of having a sense or direction is one which the relation of judging shares with all other relations. The sense of relations is the ultimate source of order and series and a host of mathematical concepts but we need not concern ourselves further with this aspect. We spoke of the relation called judging or believing as knitting together into one complex whole the subject and the objects. In this respect judging is exactly like every other relation. Whenever a relation holds between two or more terms it unites the terms into a complex whole. If Othello loves Desdemona there is such a complex whole as Othello's love for Desdemona. The terms united by the relation may be themselves complex or may be simple but the whole which results from their being united must be complex. Wherever there is a relation which relates certain terms there is a complex object formed of the union of those terms and conversely wherever there is a complex object there is a relation which relates its constituents. When an act of believing occurs there is a complex in which believing is the uniting relation and subject and objects are arranged in a certain order by the sense of the relation of believing. Among the objects as we saw in considering Othello believes that Desdemona loves Casio one must be in a relation in this instance the relation loving. But this relation as it occurs in the act of believing is not the relation which creates the unity of the complex whole consisting of the subject and the objects. The relation loving as it occurs in the act of believing is one of the objects. It is a brick in the structure not the cement. The cement is the relation believing. When the belief is true there is another complex unity in which the relation which was one of the objects of the belief relates the other objects. Thus e.g. if Othello believes truly that Desdemona loves Casio then there is a complex unity Desdemona's love for Casio which is composed exclusively of the objects of the belief in the same order as they had in the belief with the relation which was one of the objects occurring now as the cement that binds together the other objects of the belief. On the other hand when a belief is false there is no such complex unity composed only of the objects of the belief. If Othello believes falsely that Desdemona loves Casio then there is no such complex unity as Desdemona's love for Casio. Thus a belief is true when it corresponds to a certain associated complex and false when it does not. Assuming for the sake of definiteness that the objects of the belief are two terms and a relation the terms being put in a certain order by the sense of believing then if the two terms in that order are united by the relation into a complex the belief is true if not it is false. This constitutes the definition of truth and falsehood that we were in search of. Judging or believing is a certain complex unity of which a mind is a constituent. If the remaining constituents taken in the order which they have in the belief form a complex unity then the belief is true if not it is false. Thus although truth and falsehood are properties of beliefs yet they are in a sense extrinsic properties for the condition of the truth of a belief is something not involving beliefs or in general any mind at all but only the objects of the belief. A mind which believes believes truly when there is a corresponding complex not involving the mind but only its objects. This correspondence ensures truth and its absence entails falsehood. Hence we account simultaneously for the two facts that believes a depend on their minds for their existence b do not depend on minds for their truth. We may restate our theory as follows. If we take such a belief as Othello believes that Desdemona loves Casio we will call Desdemona and Casio the object terms and loving the object relation. If there is a complex unity Desdemona's love for Casio consisting of the object terms related by the object relation in the same order as they have in the belief then this complex unity is called the fact corresponding to the belief. Thus a belief is true when there is a corresponding fact and is false when there is no corresponding fact. It will be seen that minds do not create truth or falsehood they create beliefs but when once the beliefs are created the mind cannot make them true or false except in the special case where they concern future things which are within the power of the person believing such as catching trains. What makes a belief true is a fact and this fact does not accept in exceptional cases in any way involve the mind of the person who has the belief. Having now decided what we mean by truth and falsehood we have next to consider what ways there are of knowing whether this or that belief is true or false. This consideration will occupy the next chapter.