pose that the time order of phenomena is determined by characteristics of what is behind phenomena 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 doctrines 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 is 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 are 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. 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 IX. 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 and 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 Liebniz, 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 universal's 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 must 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, the 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 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 and 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 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 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 with 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 into 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 data for example the whole of the page on which I am writing thus the whole page is included in one sense data 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 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 with the 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 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 it is quite 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 formally 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 a 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 and 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 such 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 acquaintance 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 must 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 and 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 chapter 11 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 11 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 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 do you 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 to a 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 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 while arithmetic more over 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 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 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 definet 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 quote 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 where 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 in the case of memory however raises a difficulty for it is notoriously felitious 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-evident 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 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 a 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 to most 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 premise must be true and 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 End of Chapter 11 Recording by Robert Scott mojo-move411.com mojo-move411.com mojo-move411.com mojo-move411.com August the 21st 2007 Chapter 12 of The Problems of Philosophy This is a LibriVox Recording here in the public domain. For more information or to volunteer please visit LibriVox.org The Problems of Philosophy by Bertrand Russell Chapter 12 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 can find 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 belief is true or false. We are asking what is meant by the question whether 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. One, 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. Two, 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 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. Three, but as against what we have just said it is to be observed that the truth or falsehood of a belief always depends 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 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. Thus 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 oppose 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 the most important test of truth after a certain amount of truth has become known. Hence we are given 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 Cassio. We cannot say that this belief consists in a relation to a single object Desdemona's love for Cassio for if there were such an object the belief would be true. There is in fact no subject 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 Cassio. But it is almost as difficult to suppose that there is such an object as this when Desdemona does not love Cassio as it was to suppose that there is Desdemona's love for Cassio. 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 are 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 avoided 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 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 the mominative 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 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 in 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 there 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. 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 object 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 as a certain complex unity of which a mind is a constituent. If the remaining constituents taken in the order which they have in a belief form a complex unity then a 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 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 is allowed 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. End of Chapter 12 Chapter 13 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 13 Knowledge, Error and Probable Opinion The question as to what we mean by truth and falsehood which we considered in the preceding chapter is of much less interest than the question as to how we can know what is true and what is false. This question will occupy us in the present chapter. There can be no doubt that some of our beliefs are erroneous. Thus we are led to inquire what certainty we can ever have that such and such a belief is not erroneous. In other words, can we ever know anything at all? Or do we merely sometimes by good luck believe what is true? Before we can attack this question we must however first decide what we mean by knowing and this question is not so easy as might be supposed. At first sight we might imagine that knowledge could be defined as true belief. When what we believe is true it might be supposed that we had achieved a knowledge of what we believe but this would not accord with the way in which the word is commonly used. To take a very trivial instance if a man believes that the late prime minister's last name began with a B he believes what is true since the late prime minister was Sir Henry Campbell Bannerman but if he believes that Mr. Balfour was the late prime minister he will still believe that the late prime minister's last name began with a B yet this belief, though true would not be thought to constitute knowledge. If a newspaper by an intelligent anticipation announces the result of a battle before any telegram giving the result has been received it may by good fortune announce what afterwards turns out to be the right result and it may produce belief in some of its less experienced readers but in spite of the truth of their belief they cannot be said to have knowledge thus it is clear that a true belief is not knowledge when it is deduced from a false belief. In like manner a true belief cannot be called knowledge when it is deduced by a fallacious process of reasoning even if the premises from which it is deduced are true if I know that all Greeks are men and that Socrates was a man and I infer that Socrates was a Greek I cannot be said to know that Socrates was a Greek because although my premises and my conclusion are true the conclusion does not follow from the premises but are we to say that nothing is knowledge except what is validly deduced from true premises? Obviously we cannot say this such a definition is at once too wide and too narrow in the first place it is too wide because it is not enough that our premises should be true they must also be known the man who believes that Mr. Balfour was the late prime minister may proceed to draw valid deductions from the true premise that the late prime minister's name began with a B but he cannot be said to know the conclusions reached by these deductions thus we shall have to amend our definition by saying that knowledge is what is validly deduced from known premises this however is a circular definition it assumes that we already know what is met by known premises it can therefore at best define one sort of knowledge the sort we call derivative as opposed to intuitive knowledge we may say derivative knowledge is what is validly deduced from premises known intuitively in this statement there is no formal defect but it leaves the definition of intuitive knowledge still to seek leaving on one side for the moment the question of intuitive knowledge let us consider the above suggested definition of derivative knowledge the chief objection to it is that it unduly limits knowledge it constantly happens that people entertain a true belief which has grown up in them because of some piece of intuitive knowledge from which it is capable of being validly inferred but from which it has not as a matter of fact been inferred by any logical process take for example the beliefs produced by reading if the newspapers announce the death of the king we are fairly well justified in believing that the king is dead since this sort of announcement which would not be made if it were false and we are quite amply justified in believing that the newspaper asserts that the king is dead but here the intuitive knowledge upon which our belief is based is knowledge of the existence of sense data derived from looking at the print which gives the news this knowledge scarcely rises into consciousness except in a person who cannot read easily a child may be aware of the shapes of the letters and pass gradually and painfully to a realization of their meaning but anybody accustomed to reading passes it once to what the letters mean and is not aware that he has derived this knowledge from the sense data called seeing the printed letters thus although a valid inference from the letters to their meaning is possible and could be performed by the reader it is not in fact performed since he does not in fact perform any operation which can be called logical inference yet it would be absurd to say that the reader does not know that the newspaper announces the king's death we must therefore admit his derivative knowledge whatever is the result of intuitive knowledge even if by mere association provided there is a valid logical connection and the person in question could become aware of this connection by reflection there are in fact many ways besides logical inference by which we pass from one belief to another the passage from the print to its meaning illustrates these ways these ways may be called psychological inference we shall then admit such psychological inference as a means of obtaining derivative knowledge provided there is a discoverable logical inference which runs parallel to the psychological inference this renders our definition of derivative knowledge less precise than we could wish since the word discoverable is vague it does not tell us how much reflection is needed in order to make the discovery but in fact knowledge is not a precise conception it merges into probable opinion as we shall see more fully in the course of the present chapter a very precise definition therefore should not be sought since any such definition must be more or less misleading the chief difficulty in regard to knowledge however does not arise over derivative knowledge but over intuitive knowledge so long as we are dealing with derivative knowledge we have the test of intuitive knowledge to fall back upon but in regard to intuitive beliefs it is by no means easy to discover any criterion by which to distinguish some is true and others is erroneous in this question it is scarcely possible to reach any very precise result all our knowledge of truths is infected with some degree of doubt and a theory which ignored this fact would be plainly wrong something may be done however to mitigate the difficulties of the question our theory of truth to begin with supplies the possibility of distinguishing certain truths as self-evident in a sense which ensures infallibility when a belief is true we said there is a corresponding fact in which the several objects of the belief form a single complex the belief is said to constitute knowledge of this fact provided it fulfills those further somewhat vague conditions which we have been considering in the present chapter but in regard to any fact besides the knowledge constituted by belief we may also have the kind of knowledge constituted by perception taking this word in its widest possible sense for example if you know the hour of the sunset you can at that hour know the fact that the sun is setting this is knowledge of the fact by way of knowledge of truths but you can also if the weather is fine look to the west and actually see the setting sun you then know the same fact by the way of knowledge of things thus in regard to any complex fact there are theoretically which it may be known 1. by means of a judgment in which its several parts are judged to be related as they are in fact related 2. by means of acquaintance with the complex fact itself which may in a large sense be called perception though it is by no means confined to objects of the senses now we'll be observed that the second way of knowing a complex fact the way of acquaintance is only possible when there really is such a fact while the first way, like all judgment is liable to error the second way gives us the complex whole and is therefore only possible when its parts do actually have that relation which makes them combine to form such a complex the first way on the contrary gives us the parts and the relation and demands only the reality of the parts and the relation the relation may not relate those parts in that way and yet the judgment may occur it will be remembered that at the end of chapter 11 we suggested that there might be two kinds of self-evidence one giving an absolute guarantee of truth the other only a partial guarantee these two kinds can now be distinguished we may say that a truth is self-evident in the first and most absolute sense when we have acquaintance with the fact which corresponds to the truth when Othello believes that Desdemona loves Casio the corresponding fact if his belief were true would be Desdemona's love for Casio this would be a fact with which no one could have acquaintance except Desdemona hence in the sense of self-evidence that we are considering the truth that Desdemona loves Casio if it were a truth could only be self-evident to Desdemona all mental facts and all facts concerning sense data have the same privacy if there is only one person to whom they can be self-evident in our present sense since there is only one person who can be acquainted with the mental things or the sense data concerned thus no fact about any particular existing thing can be self-evident to more than one person on the other hand facts about universals do not have this privacy many minds may be acquainted with the same universals hence a relation between universals may be known by acquaintance to many different people in all cases where we know by acquaintance a complex fact consisting of certain terms in a certain relation we say that the truth that these terms are so related has the first or absolute kind of self-evidence and in these cases the judgment that the terms are so related must be true thus this sort of self-evidence is an absolute guarantee of truth but although this sort of self-evidence is an absolute guarantee of truth it does not enable us to be absolutely certain in the case of any given judgment that the judgment in question is true suppose we first perceive the sun shining which is a complex fact and then proceed to make the judgment the sun is shining in passing from the perception to the judgment it is necessary to analyze the given complex fact we have to separate out the sun and shining as constituents of the fact in this process it is possible to commit an error hence even where a fact has the first or absolute kind of self-evidence a judgment believed to correspond to the fact is not absolutely infallible because it may not really correspond to the fact but if it does correspond in the sense explained in the preceding chapter then it must be true the second sort of self-evidence will be that which belongs to judgments in the first instance and is not derived from direct perception of a fact as a single complex whole this second kind of self-evidence will have degrees from the very highest degree down to a bare inclination in favor of the belief take for example the case of a horse trotting away from us along a hard road at first our certainty that we hear the hooves is complete gradually if we listen intently there comes a moment when we think perhaps it was imagination or the blind upstairs or our own heartbeats at last we become doubtful whether there was any noise at all then we think we no longer hear anything and at last we know we no longer hear anything in this process there is a continual gradation of self-evidence from three to the least not in the sense dated themselves but in the judgments based on them or again suppose we are comparing two shades of color one blue and one green we can be quite sure they are different shades of color but if the green color is gradually altered to be more and more like the blue becoming first a blue green then a greeny blue then blue but when we are doubtful whether we can see any difference and then a moment when we know that we cannot see any difference the same thing happens in tuning a musical instrument or in any other case where there is a continuous gradation thus self-evidence of this sort is a matter of degree and it seems plain that the higher degrees are more to be trusted than the lower degrees in derivative knowledge our ultimate premises must have some degree of self-evidence and so must their connection with the conclusions deduced from them take for example a piece of reasoning in geometry it is not enough that the axioms from which we start should be self-evident it is necessary also that at each step in the reasoning the connection of the premise and conclusion should be self-evident in difficult reasoning this connection has often only a small degree of self-evidence hence errors of reasoning are not improbable where the difficulty is great from what has been said it is evident that both as regards intuitive knowledge and as regards derivative knowledge if we assume that intuitive knowledge is trustworthy in proportion to the degree of self-evidence there will be a gradation in trustworthiness from the existence of noteworthy sense data and the simpler truths of logic and arithmetic which may be taken as quite certain down to judgments which seem only just more probable than their opposites what we firmly believe if it is true is called knowledge provided it is either intuitive or inferred logically or psychologically from intuitive knowledge from which it follows logically what we firmly believe if it is not true is called error what we firmly believe if it is neither knowledge nor error and also what we believe hesitatingly because it is or is derived from something which is not the highest degree of self-evidence may be called probable opinion thus the greater part of what would commonly pass as knowledge is more or less probable opinion in regard to probable opinion we derive great assistance from coherence which we rejected as the definition of truth but may often use as a criterion a body of individually probable opinions if they are mutually coherent become more probable than any one of them would be individually it is in this way that many scientific hypotheses acquire their probability they fit into a coherent system of probable opinions and thus become more probable than they would be in isolation the same thing applies to general philosophical hypotheses often in a single case such hypotheses may seem highly doubtful while yet when we consider the order and coherence which they introduce into a massive probable opinion they become pretty nearly certain this applies in particular to such matters as the distinction between dreams and waking life if our dreams night after night were as coherent one with another as our days we should hardly know whether to believe the dreams or the waking life as it is the test of coherence condemns the dreams and confirms the waking life but this test though it increases probability where it is successful never gives absolute certainty unless there is certainty already at some point in the coherent system thus the mere organization of probable opinion will never by itself transform it into indubitable knowledge end of chapter 13 this recording is in the public domain 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 14 the limits of philosophical knowledge read by Jacob Miller and all that we have said hitherto concerning philosophy was scarcely touched on many matters that occupy great space in the writings of most philosophers most philosophers, or at any rate very many, profess to be able to prove by a priori metaphysical reasoning such things as the fundamental dogmas of religion the essential rationality of the universe the illusoriness of matter the unreality of all evil and so on there can be no doubt that the hope of finding reason to believe such theses as these has been the chief inspiration of many lifelong students of philosophy this hope I believe is vain it would seem that knowledge concerning the universe as a whole is not to be obtained by metaphysics and that the proposed proves that in virtue of the laws of logic such and such things must exist and such and such others cannot are not capable of surviving a critical scrutiny in this chapter we shall briefly consider the kind of way in which such reasoning is attempted with a view to discovering whether we can hope that it may be valid the great representative in modern times of this kind of view which we wish to examine was Hegel 1770-1831 Hegel's philosophy is very difficult and commentators differ as to the true interpretation of it according to the interpretation I shall adopt which is that of many if not most of the commentators and has the merit of giving an interesting and important type of philosophy his main thesis is that everything short of the whole is obviously fragmentary and obviously incapable of existing without the compliment supplied by the rest of the world just as a comparative anatomist from a single bone sees what kind of animal the whole must have been so the metaphysician according to Hegel sees from any one piece of reality what the whole of reality must be at least in its large outlines every apparently separate piece of reality has as it were hooks which grapple it to the next piece the next piece in turn has fresh hooks and so on until the whole universe is reconstructed this essential incompleteness appears according to Hegel equally in the world of thought and in the world of things in the world of thought if we take any idea which is abstract or incomplete we find on examination that if we forget its incompleteness we become involved in contradictions these contradictions turn the idea in question into its opposite or antithesis and in order to escape we have to find new less incomplete idea which is the synthesis of our original idea and its antithesis this new idea though less incomplete than the idea we started with will be found nevertheless to be still not wholly complete but to pass into its antithesis with which it must be combined in a new synthesis in this way Hegel advances until he reaches the absolute idea which according to him has no incompleteness no opposite and no need for the development the absolute idea therefore is adequate to describe absolute reality but all lower ideas only describe absolute reality as it appears to a partial view not as it is to one who simultaneously surveys the whole thus Hegel reaches the conclusion that absolute reality forms one single harmonious system not in space or time not in any degree evil wholly rational and wholly spiritual any appearance to the contrary in the world we know can be proved logically so he believes to be entirely due to our fragmentary piecemeal view of the universe if we saw the universe whole as we may suppose God sees it space and time and matter and evil and all striving and struggling would disappear and we would see instead an eternal perfect unchanging spiritual unity in this conception there is undeniably something sublime something to which we could wish to yield ascent nevertheless when the arguments and support of it are carefully examined there is confusion and many unwarrantable assumptions the fundamental tenet upon which the system is built up is that what is incomplete must be not self-subsistent but must need the support of other things before it can exist it is held that whatever has relations to things outside itself must contain some reference to those outside things in its own nature and could not therefore be what it is if those outside things did not exist a man's nature for example was created by his memories and the rest of his knowledge by his loves and hatred so on thus, but for the objects which he knows or loves or hates he could not be what he is he is essentially and obviously a fragment taken as the sum total of reality he would be self-contradictory this whole point of view however turns upon the notion of the nature of a thing which seems to mean all the truth about the thing it is of course the case that a truth which connects one thing with another thing could not subsist if the other thing did not subsist but a truth about a thing is not part of the thing itself although it must according to the above usage be part of the nature of the thing if we mean by a thing's nature all the truth about the thing then plainly we cannot know a thing's nature unless we know all the things relations to all other things in the universe but if the word nature is used in this sense we shall have to hold that the thing may be known when its nature is not known or at any rate is not known completely there is a confusion when this use of the word nature is employed between knowledge of things and knowledge of truths we may have knowledge of a thing by acquaintance even if we know very few propositions about it theoretically we need not know any propositions about it thus, acquaintance with a thing does not involve knowledge of its nature in the above sense and although acquaintance with a thing is involved in our knowing any one proposition about a thing knowledge of its nature in the above sense is not involved hence one acquaintance with a thing does not logically involve a knowledge of its relations and two a knowledge of some of its relations does not involve a knowledge of all of its relations nor a knowledge of its nature in the above sense I may be acquainted for example my toothache, and this knowledge may be as complete as knowledge by acquaintance ever can be, without knowing all that the dentist, who is not acquainted with it, can tell me about its cause, and without, therefore, knowing its nature in the above sense. Thus the fact that a thing has relations does not prove that its relations are logically necessary. That is to say, from the mere fact that it is the thing it is, we cannot deduce that it must have the various relations which in fact it has. This only seems to follow, because we know it already. It follows that we cannot prove that the universe as a whole forms a single, harmonious system, such as Hegel believes that it forms. And if we cannot prove this, we also cannot prove the unreality of space and time, and matter, and evil. For this is deduced by Hegel from the fragmentary and relational character of these things. Thus we are left to the piecemeal investigation of the world, and are unable to know the characters of those parts of the universe that are remote from our experience. This result, disappointing as it is to those whose hopes have been raised by the systems of philosophers, is in harmony with the inductive and scientific temper of our age, and is borne out by the whole examination of human knowledge which has occupied our previous chapters. Most of the great ambitious attempts of metaphysicians have preceded by the attempts to prove that such and such apparent features of the actual world were self-contradictory, and therefore could not be real. The whole tendency of modern thought, however, is more and more in the direction of showing that the supposed contradictions were illusory, and that very little can be proved a priori from considerations of what must be. A good illustration of this is afforded by space and time. Space and time appear to be infinite in extent, and infinitely divisible. If we travel along a straight line in either direction, it is difficult to believe that we shall finally reach a last point, beyond which there is nothing not even empty space. Similarly, if in imagination we travel backwards or forwards in time, it is difficult to believe that we shall reach a first or last time, with not even empty time beyond it. Thus space and time appear to be infinite in extent. Again, if we take any two points on a line, it seems evident that there must be other points between them, however small the distance between them may be. Every distance can be halved, and the halves can be halved again, and so on, at infinitum. In time, similarly, however little time may elapse between two moments, it seems evident that there will be other moments between them. Thus, space and time appear to be infinitely divisible. But as against these apparent facts, infinite extent and infinite divisibility, philosophers have advanced arguments tending to show that there could be no infinite collections of things, and that therefore the number of points in space, or of instants in time, must be finite. Thus a contradiction emerged between the apparent nature of space and time, and the supposed impossibility of infinite collections. Kant, who first emphasized this contradiction, deduced the impossibility of space and time, which he declared to be merely subjective. But since his time, very many philosophers have believed that space and time are mere appearance, not characteristic of the world as it really is. Now, however, owing to the labors of the mathematicians, notably Georg Kantor, it has appeared that the impossibility of infinite collections was a mistake. They are not, in fact, self-contradictory, but only contradictory of certain rather obstinate mental prejudices. Hence the reason for regarding space and time as unreal have become inoperative, and one of the great sources of metaphysical constructions is dried up. The mathematicians, however, have not been content with showing that space, as it is commonly supposed to be, is possible. They have shown also that many other forms of space are equally possible, so far as logic can show. Some of Euclid's axioms, which appear to common sense to be necessary, and were formally supposed to be necessary by philosophers, are now known to derive their appearance of necessity from our mere familiarity with the actual space, and not from any a priori logical foundation. By imagining worlds in which these axioms are false, the mathematicians have used logic to loosen the prejudices of common sense, and to show the possibility of spaces differing, some more, some less, from that in which we live. And some of these spaces differ so little from Euclidean space, or distances such as we can measure are concerned, that it is impossible to discover by observation whether our actual space is strictly Euclidean, or one of these other kinds. Thus the position is completely reversed. Formally it appeared that experience left only one kind of space to logic, and logic showed this one kind to be impossible. Now logic presents many kinds of space as possible apart from experience, and experience only partially decides between them. Thus, while our knowledge of what is has become less than it was formally supposed to be, our knowledge of what may be is enormously increased. Instead of being shot in within narrow walls of which every nook and cranny could be explored, we find ourselves in an open world of free possibilities, where much remains unknown because there is so much to know. What has happened in the case of space and time has happened to some extent in other directions as well. The attempt to prescribe to the universe by means of a priori principles has broken down. Logic instead of being as formally, the bar to possibilities, has become the great liberator of the imagination, presenting innumerable alternatives which are closed to unreflective common sense, and leaving to experience the task of deciding where decision is possible between the many worlds which logic offers for our choice. Thus knowledge as to what exists becomes limited to what we can learn from experience, not to what we can actually experience. For as we have seen there is much knowledge by description concerning things of which we have no direct experience. But in all cases of knowledge by description we need some connection of universals enabling us from such and such a datum to infer an object of a certain sort as implied by our datum. Thus in regard to physical objects, for example, the principle that since data are signs of physical objects is itself a connection of universals, and it is only in virtue of this principle that experience enables us to acquire knowledge concerning physical objects. The same applies to the law of causality, or to descend to what is less general to such principles as the law of gravitation. Principles such as the law of gravitation are proved, or rather are rendered highly probable, by a combination of experience with some wholly a priori principle, such as the principle of induction. Thus our intuitive knowledge, which is the source of all our other knowledge of truth, is of two sorts. Pure empirical knowledge, which tells us of the existence of some of the properties of particular things with which we are acquainted, and pure a priori knowledge, which gives us connections between universals and enables us to draw inferences from the particular facts given in empirical knowledge. Our derivative knowledge always depends upon some pure a priori knowledge, and usually also depends upon some pure empirical knowledge. Philosophical knowledge, if what has been said above is true, does not differ essentially from scientific knowledge. There's no special source of wisdom, which is open to philosophy, but not to science, and the results obtained by philosophy are not radically different from those obtained from science. The essential characteristic of philosophy, which makes it a study distinct from science, is criticism. It examines critically the principles employed in science and in daily life, and searches out any inconsistencies there may be in these principles, and it only accepts them when, as a result of a critical inquiry, no reason for rejecting them has appeared. If, as many philosophers have believed the principles underlying the sciences were capable, when disengaged from irrelevant detail, of giving us knowledge concerning the universe as a whole, such knowledge would have the same claim on our belief as scientific knowledge has. But our inquiry has not revealed any such knowledge, and therefore, as regards the special doctrines of the bolder metaphysicians, has had a mainly negative result. But as regards what would be commonly accepted as knowledge, our result is in the main positive. We have seldom found reason to reject such knowledge as the result of our criticism, and we have seen no reason to suppose men incapable of the kind of knowledge which he is generally believed to possess. When, however, we speak of philosophy as a criticism of knowledge, it is necessary to impose a certain limitation. If we adopt the attitude of the complete skeptic, placing ourselves wholly outside all knowledge, and asking from this outside position to be compelled to return within the circle of knowledge, we are demanding what is impossible, and our skepticism can never be refuted. For all refutation must begin with some piece of knowledge which the disputants share. From blank doubt no argument can begin. Hence the criticism of knowledge, which philosophy employs, must not be of this destructive kind, if any result has to be achieved. Against this absolute skepticism no logical argument can be advanced. But it is not difficult to see that skepticism of this kind is unreasonable. Descartes' methodical doubt, with which modern philosophy began, is not of this kind, but is rather the kind of criticism which we are asserting to be the essence of philosophy. His methodical doubt consisted in end doubting whatever seemed doubtful, in pausing with each apparent piece of knowledge to ask himself whether, on reflection, he could feel certain that he really knew it. This is the kind of criticism which constitutes philosophy. Some knowledge, such as the knowledge of the existence of our sense data, appears quite indubitable, however calmly and thoroughly we reflect upon it. In regard to such knowledge, philosophical criticism does not require that we should abstain from belief. But there are beliefs, such for example, as the belief that physical objects exactly resemble our sense data, which are entertained until we begin to reflect, but are found to melt away when subjected to a close inquiry. Such beliefs philosophy will bid us reject, unless a new line of argument is found to support them. But to reject the beliefs which do not appear open to any objections, however closely we examine them, is not reasonable, and is not what philosophy advocates. The criticism aimed at, in a word, is not that which, without reason, determines to reject, but that which considers each piece of apparent knowledge on its merits and retains whatever still appears to be knowledge when this consideration is completed. That some risk of error remains must be admitted, since human beings are fallible. Philosophy may claim justly that it diminishes the risk of error, and that in some cases it renders the risk so small as to be practically negligible. To do more than this is not possible in a world where mistakes must occur. And more than this, no prudent advocate of philosophy would claim to have performed. End of Chapter 14 of The Problems of Philosophy by Bertrand Russell. Chapter 15 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. Recording by Leon Meyer. The Problems of Philosophy by Bertrand Russell. Chapter 15. The Value of Philosophy. Having now come to the end of our brief and very incomplete review of The Problems of Philosophy, it will be well to consider, in conclusion, what is the value of philosophy and why it ought to be studied. It is the more necessary to consider this question in view of the fact that many men, under the influence of science or of practical affairs, are inclined to doubt whether philosophy is anything better than innocent but useless trifling, hair splitting distinctions, and controversies on matters concerning which knowledge is impossible. This view of philosophy appears to result partly from a wrong conception of the ends of life, partly from a wrong conception of the kinds of goods which philosophy strives to achieve. Physical science, through the medium of inventions, is useful to innumerable people who are wholly ignorant of it. Thus, the study of physical science is to be recommended not only or primarily because of the effect on the student, but rather because of the effect on mankind in general. Thus, utility does not belong to philosophy. If the study of philosophy has any value at all for others, then students of philosophy, it must be only indirectly, through its effects upon the lives of those who study it. It is in these effects, therefore, if anywhere, that the value of philosophy must be primarily sought. But further, if we are not to fail in our endeavor to determine the value of philosophy, we must first free our minds from the prejudices of what are wrongly called practical men. The practical men, as this word is often used, is one who recognizes only material needs, who realizes that men must have food for the body but is oblivious of the necessity of providing food for the mind. If all men were well off, if poverty and disease had been reduced to the lowest possible point, there would still remain much to be done to produce a valuable society. And even in the existing world, the goods of the mind are at least as important as the goods of the body. It is exclusively among the goods of the mind that the value of philosophy is to be found. And only those who are not indifferent to these goods can be persuaded that the study of philosophy is not a waste of time. Philosophy, like all other studies, aims primarily at knowledge. The knowledge it aims at is the kind of knowledge which gives unity and system to the body of the sciences, and the kind which results from a critical examination of the grounds of our convictions, prejudices, and beliefs. But it cannot be maintained that philosophy has had any very great measure of success in its attempts to provide definite answers to its questions. If you ask a mathematician, a mineralogist, a historian, or any other man of learning, what definite body of truth has been ascertained by his science, his answer will last as long as you're willing to listen. But if you put the same question to a philosopher, he will, if he is candid, have to confess that his study has not achieved positive results such as have been achieved by other sciences. It is true that this is partly accounted for by the fact that, as soon as definite knowledge concerning any subject becomes possible, this subject ceases to be called philosophy, and becomes a separate science. The whole study of the heavens, which now belongs to astronomy, was once included in philosophy. Newton's great work was called the mathematical principles of natural philosophy. Similarly, the study of the human mind, which was a part of philosophy, has now become separated from philosophy and has become the science of psychology. Thus, to a great extent, the uncertainty of philosophy is more apparent than real. Those questions which are already capable of definite answers are placed in the sciences. While those only to which, at present, no definite answer can be given, remain to form the residue which is called philosophy. This is, however, only a part of the truth concerning the uncertainty of philosophy. There are many questions, and among them, those that are the profoundest interest to our spiritual life, which, so far as we can see, must remain insoluble to the human intellect unless its powers become of a quite different order from what they are now. Has the universe any unity of plan or purpose, or is it a fortuitous concourse of atoms? Is consciousness a permanent part of the universe, giving hope of indefinite growth and wisdom? Or is it a transitory accident on a small planet on which life must ultimately become impossible? Are good and evil of importance to the universe or only to man? Such questions are asked by philosophy and variously answered by various philosophers. But it would seem that, whether answers be otherwise discoverable or not, the answers suggested by philosophy are none of them demonstrably true. Yet, however slight may be the hope of discovering an answer, it is part of the business of philosophy to continue the consideration of such questions, to make us aware of their importance, to examine all the approaches to them, and to keep alive that speculative interest in the universe which is apt to be killed by confiding ourselves to definitely ascertainable knowledge. Many philosophers, it is true, have held that philosophy could establish the truth of certain answers to such fundamental questions. They have supposed that what is of most importance in religious beliefs could be proved by strict demonstration to be true. In order to judge of such attempts, it is necessary to take a survey of human knowledge and to form an opinion as to its methods and its limitations. On such a subject it would be unwise to pronounce dogmatically, but if the investigations of our previous chapters have not led us astray, we shall be compelled to renounce the hope of finding philosophical proofs of religious beliefs. We cannot, therefore, include as part of the value of philosophy any definite set of answers to such questions. Hence, once more, the value of philosophy must not depend upon any supposed body of definitely ascertainable knowledge to be acquired by those who study it. The value of philosophy is, in fact, to be sought largely in its very uncertainty. The man who has no tincture of philosophy goes through life imprisoned in the prejudices derived from common sins, from the habitual beliefs of his age or his nation, and from convictions which have grown up in his mind without the cooperation or consent of his deliberate reason. To such a man, the world tends to become definite, finite, obvious. Common objects rouse no questions, and unfamiliar possibilities are contemptuously rejected. As soon as we begin to philosophize, on the contrary, we find, as we saw in our opening chapters, that even the most everyday things lead to problems to which only very incomplete answers can be given. Philosophy, though unable to tell us with certainty what is the true answer to the doubts which it raises, is able to suggest many possibilities which enlarge in our thoughts and free them from the tyranny of custom. Thus, while diminishing our feeling of certainty as to what things are, it greatly increases our knowledge as to what they may be. It removes the somewhat arrogant dogmatism of those who have never traveled into the region of liberating doubt, and it keeps alive our sense of wonder by showing familiar things in an unfamiliar aspect. Apart from its utility in showing unsuspected possibilities, philosophy has a value, perhaps its chief value, through the greatness of the objects which it contemplates, and the freedom from narrow and personal aims resulting from this contemplation.  Family and friends may be included, but the outer world is not regarded, except as it may help or hinder what comes within the circle of instinctive wishes. In such a life there is something feverish and confined, in comparison with which the philosophic life is calm and free. The private world of instinctive interests is a small one, set in the midst of a great and powerful world which must, sooner or later, lay our private world in ruins. Unless we can so enlarge our interests, as to include the whole outer world, we remain like a garrison and a beleaguered fortress, knowing that the enemy prevents escape and that ultimate surrender is inevitable. In such a life there is no peace, but a constant strife between the insistence of desire and the powerlessness of will. In one way or another, if our life is to be great and free, we must escape this prison and this strife. One way of escape is by philosophic contemplation. Philosophic contemplation does not, in its widest survey, divide the universe into two hostile camps, friends and foes, helpful and hostile, good and bad. It views the whole impartially. Philosophic contemplation, when it is unalloyed, does not aim at proving that the rest of the universe is akin to man. All acquisition of knowledge is an enlargement of the self, but this enlargement is best attained when it is not directly sought. It is obtained when the desire for knowledge is a lone operative, by a study which does not wish in advance that its objects should have this or that character, but adapts the self to the characters which it finds in its objects. This enlargement of self is not obtained when, taking the self as it is, we try to show that the world is so similar to the self that knowledge of it is possible without any admission of what seems alien. The desire to prove this is a form of self-assertion and, like all self-assertion, it is an obstacle to the growth of self which it desires, and of which the self knows that it is capable. Views the world as a means to its own ends. Thus it makes the world of less account than self, and the self sets boundaries to the greatness of its goods. In contemplation, on the contrary, we start from the not-self, and through its greatness the boundaries of self are enlarged, through the infinity of the universe the mind which contemplates it achieves some share in infinity. For this reason, greatness of soul is not fostered by those philosophies which assimilate the universe to man. Knowledge is a form of union of self and not self. Like all union, it is impaired by dominion, and therefore by any attempt to force the universe into conformity with what we find in ourselves. There is a widespread philosophical tendency towards the view which tells us that man is the measure of all things, that truth is man-made, that space and time and the world of universals are properties of the mind, and that if there be anything not created by the mind it is unknowable and of no account for us. This view, if our previous discussions are correct, is untrue, but in addition to being untrue it has the effect of robbing philosophical contemplation of all that gives it value, since it fetters contemplation to self. What it calls knowledge is not a union with the not-self, but a set of prejudices, habits and desires, making an impenetrable veil between us and the world beyond. The man who finds pleasure in such a theory of knowledge is like the man who never leaves the domestic circle for fear his word might not be law. The true philosophical contemplation, on the contrary, finds its satisfaction in every enlargement of the not-self, in everything that magnifies the objects contemplated, and thereby in the subject contemplating. Everything and contemplation that is personal or private, everything that depends upon habit, self-interest or desire, distorts the object, and hence impairs the union which the intellect seeks. By thus making a barrier between subject and object, such personal and private things become a prison to the intellect. The free intellect will see as God might see, without a here and now, without hopes and fears, without the trammels of customary beliefs and traditional prejudices, commonly, dispassionately, and a soul and exclusive desire of knowledge, knowledge as impersonal, as purely contemplated, as it is possible for man to attain. Hence, also, the free intellect will value more the abstract and universal knowledge into which the accidents of private history do not enter, than the knowledge brought by the senses, and dependent, as such knowledge must be, upon an exclusive and personal point of view, and a body whose sense organs distort as much as they reveal. The mind which has become accustomed to the freedom and impartiality of philosophical contemplation will preserve something of the same freedom and impartiality in the world of action and emotion. It will view its purposes and desires as parts of the whole, with the absence of insistence that results from seeing them as infinitesimal fragments, and a world of which all the rest is unaffected by anyone man's deeds. The impartiality which, in contemplation, is the unalloyed desire for truth, is the very same quality of mind which, in action, is justice, and in emotion is that universal love which can be given to all, and not only to those who are judged useful or admirable. The contemplation enlarges not only the objects of our thoughts, but also the objects of our actions and our affections. It makes us citizens of the universe, not only of one walled city at war with all the rest. In this citizenship of the universe consists man's true freedom, and his liberation from the thralldom of narrow hopes and fears. Thus, to some upper discussion, the value of philosophy. Philosophy is to be studied, not for the sake of any definite answers to its questions, since no definite answers can as a rule be known to be true, but rather for the sake of the questions themselves, because these questions enlarge our conception of what is possible, enrich our intellectual imagination, and diminish the dogmatic assurance which closes the mind against speculation. But above all because, through the greatness of the universe which philosophy contemplates, the mind also is rendered great, and becomes capable of that union with the universe which constitutes its highest good. Bibliographical note. The student who wishes to acquire an elementary knowledge of philosophy will find it both easier and more profitable to read some of the works of the great philosophers than to attempt to derive an all-round view from handbooks. The following are specially recommended. Plato. The Republic, especially books 6 and 7. Descartes. Meditations. Spinoza. Ethics. Leitnitz. The monadology. Berkeley. Three dialogues between Hylis and Philanoas. Hume. Inquiry concerning human understanding. Kant. Hologamina to any future metaphysic. End of chapter 15. This concludes the reading of The Problems of Philosophy by Bertrand Russell.