!. APPEARANCE AND REALITY
It has appeared that, if we take any common object of the sort that is supposed to be known by the senses, what the senses immediately tell us is not the truth about the object as it is apart from us, but only the truth about certain sense-data which depend upon the relations between us and the object. Thus what we directly see and feel is merely “appearance’, which we believe to be a sign of some ‘reality’ behind. But if the reality is not what appears, have we any means of knowing whether there is any reality at all? And if so, have we any means of finding out what it is like? (p16)

II. THE EXISTENCE OF MATTER
Is there such a thing as matter. Is there a table which has a certain intrinsic nature, and continues to exist when I am not looking?
Although we may doubt the physical existence of the table, we do not doubt the existence of the sense-data which made us think there was a table. (p17)
Some of our immediate experiences seem absolutely certain. (p18)

The problem we have to consider is this: Granted that we are certain of our own sense-data, have we any reason for regarding them as signs of the existence of something else, which we can call the physical object? … Common sense unhesitatingly answers that there is.
One great reason why it is felt that we must secure a physical object in addition to the sense-data, is that we want the same object for different people. ,,, But the sense-data are private to each separate person; what is immediately present to the sight of one is not immediately present to the sight of another: they all see things from slightly different points of view, and therefore see them slightly differently. Thus, if there are to be public neutral objects, which can be in some sense known to many different people, there must be something over and above the private and particular sense-data which appear to various people. What reason, then, have we for believing that there are such public neutral objects?
The answer is that, although different people may see the table slightly differently, still they all see more or less similar things when they look at the table, and the variations in what they see follow the laws of perspective and reflection of light, so that it is easy to arrive at a permanent object underlying all the different people’s sense-data. (pp19-21)

In dreams a very complicated world may seem to be present, and yet on waking we find it was a delusion; that is to say, we find that the sense-data in the dream do not appear to have corresponded with such physical objects as we should naturally infer from our sense-data. (p22)

The way in which simplicity comes in from supposing that there really are physical objects is easily seen. (p23)
Also, the every principle of simplicity urges us to adopt the natural view, that there really are objects other than ourselves and our sense-data which have an existence not dependent upon our perceiving them. (p24)

We originally come by our belief in an independent external world as soon as we begin to reflect. … It is also our instinctive belief that there are objects corresponding to our sense-data. Since this belief does not lead to any difficulties, but on the contrary tends to simplify and systematize our account of our experiences, there seems no good reason for rejecting it. We may therefore admit that the external world does really exist, and is not wholly dependent for its existence upon our continuing tp perceive it. (pp24=25)

All knowledge must be built up upon our instinctive beliefs, and if these are rejected, nothing is left. But among our instinctive beliefs some are much stronger than others, while many have, by habit and association, become entangled with other beliefs, not really instinctive, but falsely supposed to be part of what is believed instinctively.
Philosophy should show us the hierarchy of our instinctive beliefs, beginning with those we hold most strongly, and presenting each as much isolated and as free from irrelevant additions as possible. It should take care to show that, in the form in which they are finally set forth, our instinctive beliefs do not clash, but form a harmonious system. There can never be any reason for rejecting one instinctive belief except that it clashes with others; thus, if they are found to harmonize, the whole system becomes worthy of acceptance. (p25)

It is of course possible that all or any of our beliefs may be mistaken, and therefore all ought to be held with at least some slight element of doubt. But we cannot have reason to reject a belief except on the ground of some other belief. Hence, by organizing our instinctive beliefs and their consequences, by considering which among them is most possible, we can arrive at an orderly systematic organization of our knowledge, in which, though the possibility of error remains, its likelihood is diminished by the interrelation of the parts and by the critical scrutiny which has preceded acquiescence. (pp25-26)

III. THE NATURE OF MATTER
It is rational to believe that our sense-data – for example, those which we regard as associated with my table – are really signs of the existence of something independent of us and our perceptions. … The question we have to consider is: What is the nature of this real table.
To this question physical science gives an answer, somewhat incomplete it is true, and in part still very hypothetical, but yet deserving of respect so far as it goes. (p27)

We agreed provisionally that physical objects cannot be quite like our sense-data, but may be regarded as causing our sensations. (p30)

However, although the relations of physical objects have all sorts of knowable properties, derived from their correspondence with the relations of sense-data, the physical objects themselves remain unknown in their intrinsic nature, so far at least as can be discovered by means of the senses. The question remains whether there is any other method of discovering the intrinsic nature of physical objects. (p34)

IV. IDEALISM
The word ‘idealism’ is used by different philosophers in some different senses. We shall understand by it the doctrine that whatever exists, or at any rate whatever can be known to exist must be in some sense mental.
We have seen that, even if physical objects do have an independent existence, they must differ very widely from sense-data, and can only have a correspondence with sense-data, in the same sort of way in which a catalogue has a correspondence with the things catalogued. Hence common sense leaves us completely in the dark as to the true intrinsic nature of physical objects, and if there were good reason to regard them as mental, we could not legitimately reject this opinion merely because it strikes us strange. (pp37-38)

The grounds on which idealism is advocated are generally grounds derived from the theory of knowledge, that is to say, from a discussion of the conditions which things must satisfy in order that we may be able to know them. The first serious attempt to establish idealism on such grounds was that of Bishop Berkeley. He proved first, by arguments which were largely valid, that our sense-data cannot be supposed to have an existence independent of us, but must be, in part at least, ‘in’ the mind, in the sense that their existence would not continue if there were no seeing or hearing or touching or smelling or tasting. So far, his contention was almost certainly valid, even if some of his arguments were not so. But he went on to argue that sense-data were the only things of whose existence our perceptions would assure us, and that to be known is to be ‘in’ a mind, and therefore to be mental. Hence he concluded that nothing can ever be known except what is in some mind, and that whatever is known without being in my mind must be in some other mind. (p38)

Berkeley then proceeds to consider common objects, such a a tree, for instance. He shows that all we know immediately when we ‘perceive’ the tree consists of ideas in his sense of the word, and he argues that there is not the slightest ground for supposing that there is anything real about the tree except what is perceived. He fully admits that the tree must continue to exist even when we shut our eyes or when no human being is near it. But this continued existence, he says, is due to the fact that God continues to perceive it. (p39)

There are in this argument a good many fallacies. In the first place, there is a confusion engendered by the use of the word ‘idea’. We think of an idea as essentially something in somebody’s mind, and thus when we are told that a tree consists entirely of ideas, it is natural to suppose that, if so, the tree must be entirely in minds. But the notion of being “in” the mind is ambiguous. We speak of bearing a person in mind, not meaning that the person is in our mind, but that a thought of him is in our minds. And so when Berkeley says that the tree must be in our minds if we can know it, all that he really fas a right to say is that a thought of the tree must be in our minds. To argue that the tree itself must be in our minds is like arguing that a person whom we bear in mind is himself in our minds. (p40)

Taking the word ‘idea’ in Berkeley’s sense, there are two quite distinct things to be considered whenever an idea is before the mind. There is on the one hand the thing of which we are aware – say the color of my table – and on the other hand the actual awareness itself, the mental act of apprehending the thing. The mental act is undoubtedly mental, but is there any reason to suppose that the thing apprehended is in any sense mental?
Berkeley’s view, that the color must be in the mind, seems to depend for its plausibility upon confusing the thing apprehended with the act of apprehension.
This question of the distinction between act and object in our apprehending of things is vitally important, since our whole power of acquiring knowledge is bound up with it. The faculty of being acquainted with things other than itself is the main characteristic of a mind. Acquaintance with objects essentially consists in a relation between the mind and something other than the mind; it is this that constitutes the mind’s power of knowing things. … Thus when we realize the nature of knowledge, Berkeley’s argument is seen to be wrong in substance as well as in form, and his grounds for supposing that ‘idea’ – i.e. the objects apprehended – must be mental, are found to have no validity whatever. Hence his grounds in favor of idealism may be dismissed. (pp 41-43)

V. KNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY DESCRIPTION
There are two sorts of knowledge: knowledge of things, and knowledge of truths.
Knowledge of things by acquaintance is essentially simpler than any knowledge of truths, and logically independent of knowledge of truths.
Knowledge of things by description, on the contrary, always involves some knowledge of truths as its source and ground. (p46)

We shall say that we have acquaintance with anything of which we are directly aware, without the intermediary of any process of inference or any knowledge of truths. Thus in the presence of my table I am acquainted with the sense-data that make up the appearance of my table. (p46)

My knowledge of the table as a physical object, on the contrary, is not direct knowledge. My knowledge of the table is of the kind which we shall call ’knowledge by description’. The table is ‘the physical object which causes such-and-such sense-data’. In order to know anything at all about the table, we must know truths connecting it with things with which we have acquaintance” we must know that ‘such-and-such sense-data are caused by a physical object’. There is no state of mind in which we are directly aware of the table: all our knowledge of the table is really knowledge of truths, and the actual thing which is the table is not, strictly speaking, known to us at all. We know a description, and we know that there is just one object to which this description applies, though the object itself is not directly known to us. In such a case, we say that our knowledge of the object is knowledge by description. (pp 47-48)

All our knowledge, both knowledge of things and knowledge of truths, rests upon acquaintance as its foundation. It is therefore important to consider what kinds of things there are with which we have acquaintance.
Sense-data are among the things with which we are acquainted.
The first extension beyond sense-data to be considered is acquaintance by memory. The next extension to be considered is acquaintance by introspection. We are not only aware of things, but we are often aware of being aware of them. This kind of acquaintance, which we may be called self-consciousness, is the source of all our knowledge of mental things.
The acquaintance with the contents of our minds as self-consciousness is not consciousness of our self: it is consciousness of particular thoughts and feelings. The question is whether we are also acquainted with our bare selves? When we try to look into ourselves we always seem to come upon some particular thought or feeling, and not upon ‘I’ which has the thought or feeling. Nevertheless there are some reasons for thinking that we are acquainted with the ‘I’, though the acquaintance is hard to disentangle from other things. (pp 48-50)

We may therefore sum up what has been said as follows concerning acquaintance with things that exist. We have acquaintance in sensation with the data of the outer senses, and in introspection with the data of what may be called the inner sense – thoughts, feelings, desires, etc.; we have acquaintance in memory with things which have been data either of the outer senses or the inner sense, Further, it is probable, though not certain, that we have acquaintance with Self, as that which is aware of things or has desires towards things.
In addition to our acquaintance with particular existing things, we also have acquaintance with what we shall call universals, that is to say, general ideas, such as whiteness, diversity, brotherhood, and so on. Every complete sentence must contain at least one word which stands for a universal, since all verbs have a meaning which is universal. Awareness of universals is called conceiving, and a universal of which we are aware is called a concept. (pp 51-52)

Among the objects with which we are acquainted do not include physical objects (as opposed to sense-data), nor other people’s minds. These things are known to us by what is called ‘knowledge by description’. (p52)
We shall say that an object is ‘known by description’ when we know that there is one object, and no more, having a certain property; and it will generally be implied that we do not have knowledge of the same object by acquaintance. (p53)
Thus when, for example, we make a statement about Julius Caesar, it is plain that Julius Caesar himself is not before our minds, since we are acquainted with him. We have in mind some description of Julius Caesar: ‘the man who was assassinated on the Ides of March’, ‘the founder of the Roman Empire’, or, perhaps, merely ‘the man whose name was Julius Caesar’. (In this last description, Julius Caesar is a noise or shape with which we are acquainted.) Thus our statement means something involving some description of Julius Caesar which is composed wholly of particulars and universals with which we are acquainted. (pp 58-59)

The chief importance of knowledge by description is that it enables us to pass beyond the limits of our private experience. In spite of the fact that we can only know truths which are wholly composed of terms which we have experienced in acquainted, we can yet have knowledge by description of things which we have never experienced, (p59)

VI. ON INDUCTION
If we able to draw inferences from past experience – if we are to know of the existence of matter, of other people, of the past before our individual memory begins, or of the future, we must know general principles of some kind by means of which such inferences can be drawn. It must be known to us that the existence of some one sort of thing, A, is a sign of the existence of some other sort of thing, B, either at the same time as A or at some earlier or later time, as, for example, thunder is a sign of the earlier existence of lightning. If this were not known to us, we could never extend our knowledge beyond the sphere of our private experience; and this sphere, as we have seen, is exceedingly limited. The question we have to consider is whether such an extension is possible, and if so, how it is effected. (p60)

Let us take as an illustration a matter about which none of us, in fact, feel the slightest doubt. We are all convinced that the sun will rise to-morrow. … If we are asked why we believe that the sun will rise to-morrow, we shall naturally answer, ‘Because it always has risen every day’. We have a firm belief that it will rose in the future, because it has risen in the past. If we are challenged as to why we believe that it will continue to rise as heretofore, we may appeal to the laws of motion: the earth is a freely rotating body and there is nothing outside to interfere with the earth’s rotation between now and to-morrow. (p61)
Experience has shown us that, hitherto, the frequent repetition of some uniform succession or coexistence has been a cause of our expecting the same succession or coexistence on the next occasion. (p62)
And this kind of association is not confined to men; in animals also it is very strong. A horse which has been often driven along a certain road resists the attempt to drive him in a different direction. Domestic animals expect food when they see the person who usually feeds them. We know that all these rather crude expectations of uniformity are liable to be misleading. The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the ubiformity of nature would have been useful to the chicken. .. But in spite of the misleadingness of such expectations, they nevertheless exist. We have therefore the need to know whether there is any reasonable ground for giving weight to such expectations after the question of their validity has been raised. (p63)

The problem we have to discuss is whether there is whether there is any reason for believing in what is called ‘the uniformity of nature’. The belief in the uniformity of nature is the belief that everything that has happened or will happen is an instance of some general law to which there are no exceptions. The crude expectations which we have been considering are all subject to exceptions, and therefore liable to disappoint those who entertain them. But science habitually assumes, at least as a working hypothesis, that general rules which have exceptions can be replaced by general rules which have no exceptions. ‘Unsupported bodies in air fall’ is a general rule to which balloons and aeroplanes are exceptions. But the laws of motion and the law of gravitation, which account for the fact that most bodies fall, also account for the fact that balloons and aeroplanes can rise; thus the laws of motion and the law of gravitations are not subject to these exceptions. (pp63-64)

The belief that the sun will rise tomorrow might be falsified if the earth came suddenly into contact with a large body which destroyed its rotation; but the laws of motion and the law of gravitation would not be infringed by such an event. The business of science is to find uniformities, such as the laws of motion and the law of gravitation, to which, so far as our experience extends, there are no exceptions. In this search science has been remarkably successful, and it may be conceded that such uniformities have held hitherto. (p64)

It must be conceded that the fact that two things have been found often together and never apart does not, by itself, suffice to prove demonstratively that they will be found together in the next case we examine. The most we can hope is that the oftener things are found together, the more probable it becomes that they will be found together another time, and that, if they have been found together often enough, the probability will amount almost to certainty. It can never quite reach certainty, because we know that in spite of frequent repetitions there sometimes is a failure at the last, as in the case of the chicken whose neck is wrung. Thus probability is all we ought to seek. (pp65-66)

The principle we are examining may be called the principle of induction, and its two parts may be stated as follows:
(a) The greater the number of cases in which a thing of the sort A has been found associated with a thing of the sort B, the more probable it is (if no cases of failure of association are known) that A is always associated with B;
(b) Under the same circumstances, a sufficient number of cases of the association of A with B will make it nearly certain that A is always associated with B, and will make this general law approach certainty without limit. (pp66-67)

It should be noted that probability is always relative to certain data. In our case, the data are merely the known cases of coexistence of A and B, There may be other data, which might be taken into account, which would gravely alter the probability. For example, a man who had seen a great many white swans might argue, by our principle, that on the data it was probable that all swans were white, and this might be a perfectly sound argument . The argument is not disproved by the fact that some swans are black, because a thing may very well happen in spite of the fact that some data render it improbable. In the case of the swans, a man might know that color is a very variable characteristic in many species of animals, and that, therefore, an induction as to color is peculiarly liable to error. But this knowledge would be a fresh datum, by no means proving that the probability relatively to our previous data had been wrongly estimated. The fact, therefore, that things often fail to fulfill our expectations is no evidence that our expectations will not probably be fulfilled in a given case or a given class of cases. Thus our inductive principle is at any rate not capable of being disproved by an appeal to experience. (pp67-68)

The inductive principle, however, is equally incapable of being proved by an appeal to experience. Experience might conceivably confirm the inductive principle as regards the cases that have been already examined; but as regards unexamined cases, it is the inductive principle alone that can justify any inference from what has been examined to what has not been examined. … Thus we must either accept the inductive principle on the ground of its intrinsic evidence, or forgo all justification of our expectations about the future. If the principle is unsound, we have no reason to expect the sun to rise t0-morrow, or to expect that we throw ourselves off the roof we shall fall. All our conduct is based upon associations which have worked in the past, and which we therefore regard as likely to work in the future; and this likelihood is dependent for its validity upon the inductive principle.

The general principles of science, such as the belief in the reign of law, and the belief that every event must have a cause, are as completely dependent upon the inductive principle as are the beliefs of daily life. All such general principles are believed because mankind have found innumerable instances of their truth and no instances of their falsehood. But this affords no evidence for their truth in the future, unless the inductive principle is assumed. (pp68-69)

The principle of induction, while necessary to the validity of all arguments based on experience, is itself not capable of being proved by experience, and yet is unhesitatingly believed by every one, at least in all its concrete application. (p70)

VII. ON OUR KNOWLEDGE OF GENERAL PRINCIPLES
The principle of induction does not stand alone, there are a number of other principles which cannot be proved or disproved by experience, but are used in arguments which start from what is experienced.
Some of these principles have even greater evidence than the principle of induction, and the knowledge of them has the same degree of certainty as the knowledge of the existence of sense-data. They constitute the means of drawing inferences from what is given in sensation; and if what we infer is to be true, it is just as necessary that our principles of inference should be true as it is that our data should be true. The principles of inference are apt to be overlooked because of their obviousness. But it is very important to realize the use of principles of inference, if a correct theory of knowledge is to be obtained. (p70)

In all our knowledge of general principles, what actually happens is that first of all we realize some particular application of the principle, and then we realize that the particularity is irrelevant, and that there is a generality which may equally truly be affirmed. This is of course familiar in such matters as teaching arithmetic; the same thing happens with logical principles.
The logical principle is as follow” ‘Suppose it known that if this is true, then that is true. Suppose it also known that this is true, then it follows that that is true’. … In other words, ‘anything implied by a true proposition is true’, or ‘whatever follows from a true proposition is true’. (pp70-71)

If any one asked: ‘why should I accept the results of valid arguments based on true premises?’ we can only answer by appealing to our principle (of inference). In fact, the truth of the principle is impossible to doubt, and its obviousness is so great that at first sight it seems almost trivial. Such principles, however, are not trivial to the philosopher, for they show that we may have indubitable knowledge which is in no way derived from objects of sense. (p72)

The above principle is merely one of a certain number of self-evident logical principles, Some at least of these principles must be granted before any arguments or proof becomes possible. Three of these principles have been singled out by tradition under the name of ‘Law of Thought’. They are as follows:
1) The law of identity: ‘Whatever is, is.’
2) The law of contradiction: ‘Nothing can both be and not be.”
3) The law of excluded middle: ‘Everything must either be or not be.’
These three laws are samples of self-evident logical principles, but are not really more fundamental or more self-evident than various other similar principles: for instance, the one we consider just now, which states that what follows from a true premiss is true.
There are other logical principles which enable us to prove, from a given premiss, that there is a greater or less probability that something is true. An example of such principles is the inductive principle. (pp72-73)

Empiricism vs Rationalism (pp73-81)

Logical principles are known to us, and cannot be themselves proved by experience, since all proof presupposes them. In this, therefore, the rationalists were in the right.
On the other hand, even that part of our knowledge which is logical independent of experience (in the sense that experience cannot prove it) is yet elicited and caused by experience. It is on occasion of particular experiences that we become aware of the general laws which their connexions exemplify. Thus, while admitting that all knowledge is elicited and caused by experience, we shall nevertheless hold that some knowledge is a priori. in the sense that we see its truth without requiring any proof from experience. (p74)

There is another point of important, in which the empiricists were in the right as against the rationalists. Nothing can be known to exist except by the help of experience. That is to say, if we wish to prove that something of which we have no direct experience exists, we must have among our premises the existence of one or more things of which we have direct experience. Our belief that the Emperor of China exists, for example, rests upon testimony, and testimony consists, in the last analysis, of sense-data seen or heard in reading or being spoken to. Rationalists believed that, from general consideration as to what must be, they could deduce the existence of this or that in the actual world. In this belief they seem to have mistaken. … Thus the scope and power of a priori principles is strictly limited. All knowledge that something exists must be in part dependent on experience. knowledge is called empirical when it rests wholly or partly upon experience. (pp74-75)

A priori knowledge is not all of the logical kind we have been hitherto considering. Perhaps the most important example of non-logical a priori knowledge is knowledge as to ethical value. I am not speaking of judgments as to what is useful or as to what is virtuous, for such judgments do require empirical premisses; I am speaking of judgments as to the intrinsic desirability of things. If something is useful, it must be useful because it secures some end; the end must, if we have gone far enough, be valuable on its own account, and not merely because it is useful for some further end. Thus all judgments as to what is useful depend upon judgments as to what has value on its own account. (pp75-76)

We judge, for example, that happiness is more desirable than misery, knowledge than ignorance, goodwill than hatred, and so on. Such judgments must, in part at least, be immediate and a priori. Like our previous a priori judgments, they may be elicited by experience, and indeed they must be; for it seems not possible to judge whether anything is intrinsically valuable unless we have experienced something of the same kind. But it is fairly obvious that they cannot be proved by experience; for the fact that a thing exists or does not exist cannot prove either that is good that it should exist or that is bad. In the present connexion, it is only important to realize that knowledge as to what is intrinsically of value is a priori in the sense in which logic is a priori, namely in the sense that the truth of such knowledge can be neither proved nor disproved by experience. (p76)

The process of deduction goes from the general to the general, or from the general to the particular; the process of induction goes from the particular to the particular, or from the particular to the general. (p79)

We have seen that there are propositions known a priori, and that among them are the propositions of logic and pure mathematics, as well as the fundamental propositions of ethics. The question which must next occupy us is this: How is it possible that there should be such knowledge? And more particularly, how can there be knowledge of general propositions in cases where we have not examined all the instances, and indeed never can examine them all, because their number is infinite? These questions were first brought forward by Immanuel Kant. (pp 80-81)

VIII. HOW A PRIORI KNOWLEDGE IS POSSIBLE
Before the time of Kant, it was generally held that whatever knowledge was must be ‘analytic’. … Hume, who accepting the usual view as to what makes knowledge a priori, discovered that, in many cases which had previously been supposed analytic, and notably in the case of cause and effect, the connexion was really synthetic. Before Hume, rationalists had supposed that effect could be logically deduced from the cause, if only we had sufficient knowledge. Hume argued, correctly, that this could not be done. Hence he inferred the proposition that nothing could be known a priori about the connexion of cause and effect.
Kant endeavored to find an answer to it. He perceived that not only the connexion of cause and effect, but all the propositions of arithmetic and geometry, are ‘synthetic’, i.e. not analytic: in all these propositions, no analysis of the subject will reveal the predicate. His stock instance was the proposition 7 + 5 = 12. He pointed out that 7 and 5 have to be put together to give 12: the idea of 12 is not contained in them, nor even in the idea of adding them together. Thus he was led to the conclusion that all pure mathematics, though a priori, is synthetic. (pp 82-84)

The question which Kant put at the beginning of his philosophy, namely ‘How is pure mathematics possible?’ is an interesting and difficult one. The answer of the pure empiricists, that our mathematical knowledge is derived by induction from particular instances, seems to be inadequate. … The general propositions of mathematics, such as ‘two and two always make four’, can obviously be known with certainty by consideration of a single instance. Thus our knowledge of the general propositions of mathematics (and the same applies to logic) must be accounted for otherwise than our (merely probable) knowledge of empirical generalizations such as ‘all men are mortal’. (p84)

The problem arises through the fact that such knowledge is general, whereas all experience is particular. It seems strange that we should apparently be able to know some truths in advance about particular things of which we have as yet no experience; but it cannot easily be doubt that logic and arithmetic will apply to such things. This apparent power of anticipating facts about things of which we have no experience is certainly surprising. Kant’s solution of the problem, though not valid in my opinion, is interesting. It is, however, very difficult, and is differently understood by different philosophers. (pp84-85)

What Kant maintained was that in all our experience there are two elements to be distinguished, the one due to the object (i.e. to what we have called the ‘physical object’), the other due to our own nature. We saw that the physical is different from the associated sense-data, and that the sense-data are to be regarded as resulting from the interaction between the physical object and ourselves. So far, we are in agreement with Kant. But what is distinctive of Kant is the way in which he apportions the shares of ourselves and the physical object respectively. He considers that the crude material given in sensation – the color, hardness, etc. – is due to the object, and that what we supply is the arrangement in space and time, and all the relations between sense-data which result from comparison or from considering one as the cause of the other or in any other way. His chief reason in favor of this view is that we seem to have a priori knowledge as to space and time and causality and comparison, but not as to the actual crude material of sensation, We can be sure, he says, that anything we shall ever experience must show the characteristics affirmed of it in our a priori knowledge, because these characteristics are due to our own nature, and therefore nothing can ever come into our experience without acquiring these characteristics. (pp85-86)

The physical object, which Kant calls the ‘thing in itself’, he regards as essentially unknowable; what can be known is the objects as we have it in experience, which he calls the ‘phenomenon’. The phenomenon, being a joint product of us (our mind) and the thing in itself, is sure to have those characteristics which are due to us, and is therefore sure to conform to our a priori knowledge. Hence this knowledge, though true of all actual and possible experience, must not be supposed to apply outside experience. Thus in spite of the existence of priori knowledge, we cannot know anything about the thing in itself or about what is not an actual or possible object of experience. In this way he tries to reconcile and harmonize the contentions of the rationalists with the arguments of the empiricists. (p86)

(Russell argues) that Kant’s method fails to deal with the problem of a priori knowledge. The thing to be accounted for is our certainty that the facts must always conform to logic and arithmetic. To say that logic and arithmetic are attributed by us does not account for this. (Our mind is the product of nature) and there can be no certainty that it will remain constant. It might happen that tomorrow our nature would so change as to make two and two become five. This possibility would destroy the certainty and universality which Kant used to vindicate for arithmetical propositions. (p87)

The fact seems to be that all our a priori knowledge is concerned with entities which do not exist either in the mental or in the physical world. (p89)

Apart from the special doctrines advocated 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. (p88)
We noted in the preceding chapter the three self-evident logical principles commonly called ‘laws of thought’. … Let us take as an illustration the law of contradiction. This is commonly stated in the form ‘Nothing can be both be and not be’, 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 beech it cannot also be not a beech; if my table is rectangular it cannot also be not rectangular, and so on. (p88)
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 beech, we do not need to look again in order to ascertain whether it is also not a beech; thought alone makes us know that this is impossible. But, [according to Russell], 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. (Note: This appears to be an argument for pragmatism.) The belief in the law of contradiction is a belief about things, not only about thoughts. It is not, e.g., the belief that if we think a certain tree is a beech, we cannot at the same time think that it is not a beech; it is the belief that if the tree a beech, it cannot at the same time be not a beech. Thus the law of contradiction is about things, not merely about thought; 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. (pp88-89)
A similar argument 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 non-mental. These entities are such as can be named by parts of speech which are not substantives; 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 the 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. (pp89-90)

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 ‘I am in my room’. It may be true that an earwig is in my room, even if neither I nor the earwig nor any one else is aware of this truth; for this truth concerns only the earwig and the room, and does not depend upon anything else. Thus relation, 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 in particular to the problem of a priori knowledge. (p90)

IX. THE WORLD OF UNIVERSALS
At the end of the preceding chapter we saw that such entities as relations appears 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 this 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. (p91)

The problem with which we are now concerned is a very old one, since it was brought into philosophy by Plato. Plato’s ‘theory of ideas’ is an attempt to solve this very problem, and in my opinion it is one of the most successful attempts hitherto made. The theory to be advocated in what follows is largely Plato’s, with merely such modifications as time has shown to be necessary. (p91)

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 of 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. (pp91-92)

Thus Plato is led to a supra-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. (p92)

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. (pp92-93)

When we examine common words, we find that, broadly speaking , proper names stand for particulars, while other substantives, adjectives, propositions, 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. (p93)

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. (p93)

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. (pp93-94)

Even among philosophers, we may say, broadly, that only those universals which are named by adjectives or substantives have been much or often recognized, while those named by verbs and prepositions have been usually overlooked. … 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 proposition 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, there cannot possibly interact in any way, since any interaction would be a relation, and relations are impossible. (pp94-95)

As a matter of fact, if any one 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. Let us take in illustration the universal whiteness If we believe that there is such a universal, we shall say 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 universals 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. (pp95-96)

Berkeley and Hume failed to perceive this refutation of their rejection of ‘abstract ideas’, because, like their adversaries (i.e. the rationalists), 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, owing to the neglect or denial of relations, the deductions made by rationalists were more apt to be mistaken than those made by empiricists. (p97)

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. (p97)

Consider such a proposition as ‘Edinburgh is north of London’. Here we have a relation between two places, and it seems plain that the relation subsists independently of our knowledge of it. When we come to know that Edinburgh is north of London, we come to know something which has to do only with Edinburgh and London: we do not cause the truth of the proposition by coming to know it, on the contrary we merely apprehend a fact which was there before we knew it. The part of the earth’s surface where Edinburgh stands would be north of the part where London stands, even if there were no human being to know about north and south, and even if there were no minds at all in the universe. This is, of course, denied by many philosophers, either for Berkeley’s reasons or for Kant’s. But we have already considered these reasons, and decided that they are inadequate. We may therefore now assume it to be true that nothing mental is presupposed in the fact that Edinburgh is north of London. But this fact involves the relation ‘north of’, which is a universal; and it would be impossible for the whole fact to involve nothing mental if the relation ‘north of’, which is a constituent part of the fact, did involve anything mental. Hence we must admit that the relation, like the terms it relates, is not dependent upon thought, but belongs to the independent world which thought apprehends but does not create. (pp97=98)

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 nowhen’. 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. (p98)

It is largely the very peculiar kind of being that belongs to universals which has led many people to suppose that they are really mental. We can think of a universal, and our thinking then exists in a perfectly ordinary sense, like any other mental act. Suppose, for example, that we are thinking of whiteness, Then in one sense it may be said that whiteness is ‘in our mind’. We have here the same ambiguity as we noted in discussing Berkeley in Ch. IV. In the strict sense, it is not whiteness that is in our mind, but the act of thinking of whiteness. … 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 man could think of it, and no one man could think of it twice. That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts. (p99)

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 time). Thus thoughts and feelings, minds and physical objects exist. But universals do not exist in this sense; we shall say that they subsist or have being, where ‘being’ is opposed to ‘existence’ as being timeless. The world of universals, therefore, may also be described as the world of being. The world of being is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life. The world of existence is fleeting, vague, without sharp boundaries, without any clear plan or arrangement, but it contains all thoughts and feelings, all the data of sense, and all physical objects, everything that makes any difference to the value of life and the world, According to our temperaments, we shall prefer the contemplation of the one or the other. … The truth is that 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 afl 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. (pp99=100)

X. ON OUR KNOWLEDGE OF UNIVERSALS
Our knowledge of 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. (p101)

THE KNOWLEDGE OF UNIVERSALS BY ACQUAINTANCE
It is obvious that we are acquainted with such universals as white, red, black, sweet, sour, loud, hard, etc,. i.e. with qualities which are exemplified in the sense-data. When we see a white patch, we are acquainted, in the first instance, with the 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 universals 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 that other universals are. (p101)

We come next to relations. The easiest relations to apprehend are those which hold between the different parts of a single complex sense-datum. For example, I can see at a glance the whole of the page on which I am writing; thus the whole page is included in one sense-datum. But I perceive that some parts of the page are to the left of other parts, and some parts are above other parts. The process of abstraction in this case seems to proceed somewhat as follows: I see successively a number of sense-data in which one part is to the left of another; I perceive, as in the case of different white patches, that all these sense-data have something in common, and by abstraction I find that what they have in common is a certain relation between the parts, namely the relation which I call ‘being to the left of’. In this way I become acquainted with the universal relation. (pp101-102)

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. Thus time-relations, like space-relations, are among those with which we are acquainted. (p102)

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 greens have more resemblance to each other than either has to the red. In this way I become acquainted with the universal resemblance or similarity. (p102)

Between universals, as between particulars, there are relations of which we may be immediately aware. We have just seen that we can perceive that the resemblance between two shades of green is greater than the resemblance between a shade of red and a shade of green. Here we are dealing with a relation, namely ‘greater than’, between two relations. Our knowledge of such relations, though it require more power of abstraction than is required for perceiving the 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. (pp102-103)

THE PROBLEM OF A PRIORI KNOWLEDGE
We have left this problem 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, in view of what has been said, that this proposition states a relation between the universal ‘two’ and the universal ‘four’. This suggests a proposition which we shall now endeavour 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. (p103)

Thus the statement ‘two and two are 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. (p105)

The thing that seemed mysterious, when we formerly considered such knowledge, was that it seemed to anticipate and control experience. This, however, we can see to have been an error. No fact concerning anything capable of being experienced can be known independently of experience. (p105)

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 as 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 all innumerable instances of men dying, and no instances of their living beyond a certain age. .. The ultimate ground [in the empirical case] remains inductive, i.e. derived from instances, and not an a priori connexion of universals such as we have in logic and arithmetic. (pp106-107)

KNOWLEDGE OF THINGS AND KNOWLEDGE OF TRUTHS
We may now take a survey of the sources of our knowledge, as they have appeared in the course of our analysis. We have first to distinguish knowledge of things and knowledge of truths. In each there are two kinds, one immediate and one derivative. Our immediate knowledge of things, which we called acquaintance, consists of two sorts, according as the things known are particulars or universals. Among particulars, we have acquaintance with sense-data and (probably) with ourselves. Among universals, there seems to be no principle by which we can decide which can be known by acquaintance, but it is clear that among those that can be so known are sensible qualities, relations of space and time, similarity, and certain abstract logical universals.
Our derivative knowledge of things, which we call knowledge by description, always involves both acquaintance with something and knowledge of truths. Our immediate knowledge of truths may be called intuitive knowledge, and the truths so known may be called self-evident truths. Among such truths are included those which merely state what is given in sense, and also certain abstract logical and arithmetical principles, and (though with less certainty) some ethical propositions. Our derivative knowledge of truths consists of everything that we can deduce from self-evident truths by the use of self-evident principles and deduction. (p109)

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 considered 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, 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. (p109-110)

XI. ON INTUITIVE KNOWLEDGE
There is a common impression that everything that we believe ought to be capable of proof, or at least of being shown to be highly probable. It is felt by many that a belief for which no reason can be given is an unreasonable belief. In the main, this view is just. Almost all our common beliefs are either inferred, or capable of being inferred, from other beliefs which may be regarded as giving the reason for them. As a rule, the reason has been forgotten, or has even never been consciously present to our minds. Yet we feel, when challenged, that a perfectly good reason could be found. And in this belief we are usually justified. (p111)

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 be driven to a point where we cannot find any further reason. Starting with the common beliefs of daily life, we can be driven back from point to point, until we come to some general principle which is not itself capable of being deduced from some simpler self-evident principle.
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. (pp111-112)

Self-evidence, however, is not confined to those among general principles which are incapable of proof. When a certain number of logical principles have been admitted, the rest can be deduced from them; but the propositions deduced are often just as self-evident as those that were assumed without proof. All arithmetic, moreover, can be deduced from the general principle of logic, yet the simple propositions of arithmetic, such as ‘two and two are four’, are just as self-evident as the principles of logic. (p112)

It would seem, also, though this is more disputable, that there are some self-evident ethical principles, such as ‘we ought to pursue what is good’. (p112)

In addition to general principles, the other kind of self-evident truths are those immediately derived from sensation. We will call such truths 'truths of perception', and the judgments expressing them we will call '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 be 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. (pp113-114)

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 'there is such-and-such a patch of red', or more strictly 'there is that'; this is one kind of intuitive judgment of perception. The other kind arises when the object of sense is complex, and we subject it to some degree of analysis. If, for instance, we see a round patch of red, we may judge 'that patch of red is round'. 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 analyses 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 'this is to the right of that', where 'this' and '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. (p114)

Another class of intuitive judgments, analogous to those of sense and yet quite distinct from them, are judgments of memory. There is some danger of confusion as to the nature of memory, owing to the fact that memory of an object is apt to be accompanied by an image of the object, and yet the image cannot be what constitutes memory. This is easily seen by merely noticing that the image is in the present, whereas what is remembered is known to be in the past. Moreover, we are certainly able to some extent to compare our image with the object remembered, so that we often know, within somewhat wide limits, how far our image is accurate; but this would be impossible, unless the object, as opposed to the image, were in some way before the mind. Thus the essence of memory is not constituted by the image, but by having immediately before the mind an object which is recognized as past. But for the fact of memory in this sense, we should not know that there ever was a past at all, nor should we be able to understand the word 'past', any more than a man born blind can understand the word 'light'. Thus there must be intuitive judgments of memory, and it is upon them, ultimately, that all our knowledge of the past depends. (pp114-115)

The case of memory, however, raises a difficulty, for it is notoriously fallacious, and thus throws doubt on the trustworthiness of intuitive judgments in general. This 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. (p115)

Thus the first answer to the difficulty of fallacious memory is to say that memory has degrees of self-evidence, and that these correspond to the degrees of its trustworthiness, reaching a limit of perfect self-evidence and perfect trustworthiness in our memory of events which are recent and vivid. (p116)

It would seem, however, that there are cases of very firm belief in a memory which is wholly false. (p116)

One important point about self-evidence is made clear by the case of memory, and that is, that self-evidence has degrees: it is not a quality which is simply present or absent, but a quality which may be more or less present, in gradations ranging from absolute certainty down to an almost imperceptible faintness.
Truths of perception and some of the principles of logic have the very highest degree of self-evidence; truths of immediate memory have an almost equally high degree. The inductive principle has less self-evidence than some of the other principles of logic, such as 'what follows from a true premiss must be true'. Memories have a diminishing self-evidence as they become remoter 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. (p117)

Degrees of self-evidence are important in the theory of knowledge, since, if propositions may (as seems likely) have some degree of self-evidence without being true, it will not be necessary to abandon all connexion 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. (p117)

It seems, however, highly probable that two different notions are combined in '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 connexion with the distinction between knowledge and error. (pp117-118)

XII. TRUTH AND FALSEHOOD
Our knowledge of truths, unlike our knowledge of things, has an opposite, namely error. So far as things are concerned, we may know them or not know them, but there is no positive state of mind which can be described as erroneous knowledge of things, so long, at any rate, as we confine ourselves to knowledge by acquaintance. Whatever we are acquainted with must be something; we may draw wrong inferences from our acquaintance, but the acquaintance itself cannot be deceptive. Thus there is no dualism as regards acquaintance. But as regards knowledge of truths, there is a dualism. We may believe what is false as well as what is true. We know that on very many subjects different people hold different and incompatible opinions: hence some beliefs must be erroneous. Since erroneous beliefs are often held just as strongly as true beliefs, it becomes a difficult question how they are to be distinguished from true beliefs. How are we to know, in a given case, that our belief is not erroneous? This is a question of the very greatest difficulty, to which no completely satisfactory answer is possible. There is, however, a preliminary question which is rather less difficult, and that is: What do we mean by truth and falsehood? It is this preliminary question which is to be considered in this chapter. (p119)

In this chapter we are not asking how we can know whether a belief is true or false: we are asking what is meant by the question whether a belief is true or false. It is to be hoped that a clear answer to this question may help us to obtain an answer to the question what beliefs are true, but for the present we ask only 'What is truth?' and 'What is falsehood?' not 'What beliefs are true?' and 'What beliefs are false?' It is very important to keep these different questions entirely separate, since any confusion between them is sure to produce an answer which is not really applicable to either. (pp119-120)

There are three points to observe in the attempt to discover the nature of truth, three requisites which any theory must fulfill.
(1) Our theory of truth must be such as to admit of its opposite, falsehood. In this respect our theory of belief must differ from our theory of acquaintance, since in the case of acquaintance it was not necessary to take account of any opposite.
(2) It seems fairly evident that if there were no beliefs there could be no falsehood, and no truth either, in the sense in which truth is correlative to falsehood. If we imagine a world of mere matter, there would be no room for falsehood in such a world, and although it would contain what may be called 'facts', it would not contain any truths. (Note: A world of mere matter is a world of no mind.)
(3) The truth or falsehood of a belief always depends upon something which lies outside the belief itself. 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. (pp120-121)

The third of the above requisites leads us to adopt the view—which has on the whole been commonest among philosophers—that truth consists in some form of correspondence between belief and fact. It is, however, by no means an easy matter to discover a form of correspondence to which there are no irrefutable objections. By this partly—and partly by the feeling that, if truth consists in a correspondence of thought with something outside thought, thought can never know when truth has been attained—many philosophers have been led to try to find some definition of truth which shall not consist in relation to something wholly outside belief. The most important attempt at a definition of this sort is the theory that truth consists in coherence. It is said that the mark of falsehood is failure to cohere in the body of our beliefs, and that it is the essence of a truth to form part of the completely rounded system which is The Truth. (pp121-122)

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. 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. (p122)

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. (p122)

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 beech' and 'this tree is not a beech', are not coherent, because of the law of contradiction. But if the law of contradiction itself were subjected to the test of coherence, we should find that, if we choose to suppose it false, nothing will any longer be incoherent with anything else. Thus the laws of logic supply the skeleton or framework within which the test of coherence applies, and they themselves cannot be established by this test. (pp122-123)

For the above two reasons, coherence cannot be accepted as giving the meaning of truth, though it is often a most important test of truth after a certain amount of truth has become known. (p123)

Hence we are driven back to correspondence with fact as constituting the nature of truth. It remains to define precisely what we mean by 'fact', and what is the nature of the correspondence which must subsist between belief and fact, in order that belief may be true. (p123)

In accordance with our three requisites, we have to seek a theory of truth which (1) allows truth to have an opposite, namely falsehood, (2) makes truth a property of beliefs, but (3) makes it a property wholly dependent upon the relation of the beliefs to outside things. (p123)

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. (p126)

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. (p126)

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. (p127)

Thus a belief is true when it corresponds to a certain associated complex, and false when it does not. (p128)

. Thus although truth and falsehood are properties of beliefs, yet they are in a sense extrinsic properties, for the condition of the truth of a belief is something not involving beliefs, or (in general) any mind at all, but only the objects of the belief. A mind, which believes, believes truly when there is a corresponding complex not involving the mind, but only its objects. This correspondence ensures truth, and its absence entails falsehood. Hence we account simultaneously for the two facts that beliefs (a) depend on minds for their existence, (b) do not depend on minds for their truth. (p129)

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 (except in exceptional cases) in any way involve the mind of the person who has the belief. (pp129-130)

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. (p130)

XIII. 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. (p131)

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. (pp131-132)

In like manner, a true belief cannot be called knowledge when it is deduced by a fallacious process of reasoning, even if the premisses from which it is deduced are true. If I know that all Greeks are men and that Socrates was a man, and I infer that Socrates was a Greek, I cannot be said to know that Socrates was a Greek, because, although my premisses and my conclusion are true, the conclusion does not follow from the premisses. . (p132)

But are we to say that nothing is knowledge except what is validly deduced from true premisses? Obviously we cannot say this. Such a definition is at once too wide and too narrow. In the first place, it is too wide, because it is not enough that our premisses should be true, they must also be known. The man who believes that Mr. Balfour was the late Prime Minister may proceed to draw valid deductions from the true premiss that the late Prime Minister's name began with a B, but he cannot be said to know the conclusions reached by these deductions. Thus we shall have to amend our definition by saying that knowledge is what is validly deduced from known premisses. This, however, is a circular definition: it assumes that we already know what is meant by 'known premisses'. It can, therefore, at best define one sort of knowledge, the sort we call derivative, as opposed to intuitive knowledge. We may say: 'Derivative knowledge is what is validly deduced from premisses known intuitively'. In this statement there is no formal defect, but it leaves the definition of intuitive knowledge still to seek. . (pp132-133)

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. (p133)

Take, for example, the beliefs produced by reading. If the newspapers announce the death of the King, we are fairly well justified in believing that the King is dead, since this is the sort of announcement which would not be made if it were false. And we are quite amply justified in believing that the newspaper asserts that the King is dead. But here the intuitive knowledge upon which our belief is based is knowledge of the existence of sense-data derived from looking at the print which gives the news. This knowledge scarcely rises into consciousness, except in a person who cannot read easily. A child may be aware of the shapes of the letters, and pass gradually and painfully to a realization of their meaning. But anybody accustomed to reading passes at once to what the letters mean, and is not aware, except on reflection, that he has derived this knowledge from the sense-data called seeing the printed letters. Thus although a valid inference from the-letters to their meaning is possible, and could be performed by the reader, it is not in fact performed, since he does not in fact perform any operation which can be called logical inference. Yet it would be absurd to say that the reader does not know that the newspaper announces the King's death. (pp133-134)

We must, therefore, admit as derivative knowledge whatever is the result of intuitive knowledge even if by mere association, provided there is a valid logical connexion, and the person in question could become aware of this connexion by reflection. There are in fact many ways, besides logical inference, by which we pass from one belief to another: the passage from the print to its meaning illustrates these ways. These ways may be called 'psychological inference'. We shall, then, admit such psychological inference as a means of obtaining derivative knowledge, provided there is a discoverable logical inference which runs parallel to the psychological inference. This renders our definition of derivative knowledge less precise than we could wish, since the word 'discoverable' is vague: it does not tell us how much reflection may be needed in order to make the discovery. But in fact 'knowledge' is not a precise conception: it merges into 'probable opinion', as we shall see more fully in the course of the present chapter. A very precise definition, therefore, should not be sought, since any such definition must be more or less misleading. (p134)

The chief difficulty in regard to knowledge, however, does not arise over derivative knowledge, but over intuitive knowledge. So long as we are dealing with derivative knowledge, we have the test of intuitive knowledge to fall back upon. But in regard to intuitive beliefs, it is by no means easy to discover any criterion by which to distinguish some as true and others as erroneous. In this question it is scarcely possible to reach any very precise result: all our knowledge of truths is infected with some degree of doubt, and a theory which ignored this fact would be plainly wrong. Something may be done, however, to mitigate the difficulties of the question. (pp134-135)

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. (p135)

Thus in regard to any complex fact, there are, theoretically, two ways in 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 it will be observed that the second way of knowing a complex fact, the way of acquaintance, is only possible when there really is such a fact, while the first way, like all 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 severally, and demands only the reality of the parts and the relation: the relation may not relate those parts in that way, and yet the judgment may occur. (pp135-136)

It will be remembered that at the end of Chapter XI we suggested that there might be two kinds of self-evidence, one giving an absolute guarantee of truth, the other only a partial guarantee. These two kinds can now be distinguished. (p136)

We may say that a truth is self-evident, in the first and most absolute sense, when we have acquaintance with the fact which corresponds to the truth. When Othello believes that Desdemona loves Cassio, the corresponding fact, if his belief were true, would be 'Desdemona's love for Cassio'. This would be a fact with which no one could have acquaintance except Desdemona; hence in the sense of self-evidence that we are considering, the truth that Desdemona loves Cassio (if it were a truth) could only be self-evident to Desdemona. All mental facts, and all facts concerning sense-data, have this same privacy: there is only one person to whom they can be self-evident in our present sense, since there is only one person who can be acquainted with the mental things or the sense-data concerned. Thus no fact about any particular existing thing can be self-evident to more than one person.
On the other hand, facts about universals do not have this privacy. Many minds may be acquainted with the same universals; hence a relation between universals may be known by acquaintance to many different people. In all cases where we know by acquaintance a complex fact consisting of certain terms in a certain relation, we say that the truth that these terms are so related has the first or absolute kind of self-evidence, and in these cases the judgment that the terms are so related must be true. Thus this sort of self-evidence is an absolute guarantee of truth. (pp136-137)

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 thence proceed to make the judgment 'the sun is shining'. In passing from the perception to the judgment, it is necessary to analyse the given complex fact: we have to separate out 'the sun' and 'shining' as constituents of the fact. In this process it is possible to commit an error; hence even where a fact has the first or absolute kind of self-evidence, a 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. (pp137-138)

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 hoofs is complete; gradually, if we listen intently, there comes a moment when we think perhaps it was imagination or the blind upstairs or our own heartbeats; at last we become doubtful whether there was any noise at all; then we think we no longer hear anything, and at last we know we no longer hear anything. In this process, there is a continual gradation of self-evidence, from the highest degree to the least, not in the sense-data themselves, but in the judgments based on them. (p138)

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, there will come a moment when we are doubtful whether we can see any difference, and then a moment when we know that we cannot see any difference. The same thing happens in tuning a musical instrument, or in any other case where there is a continuous gradation. Thus self-evidence of this sort is a matter of degree; and it seems plain that the higher degrees are more to be trusted than the lower degrees. (pp138-139)

In derivative knowledge our ultimate premisses must have some degree of self-evidence, and so must their connexion with the conclusions deduced from them. Take for example a piece of reasoning in geometry. It is not enough that the axioms from which we start should be self-evident: it is necessary also that, at each step in the reasoning, the connexion of premiss and conclusion should be self-evident. In difficult reasoning, this connexion has often only a very small degree of self-evidence; hence errors of reasoning are not improbable where the difficulty is great. (p139)

From what has been said it is evident that, both as regards intuitive knowledge and as regards derivative knowledge, if we assume that intuitive knowledge is trustworthy in proportion to the degree of its self-evidence, there will be a gradation in trustworthiness, from the existence of noteworthy sense-data and the simpler truths of logic and arithmetic, which may be taken as quite certain, down to 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 has not the highest degree of self-evidence, may be called probable opinion. Thus the greater part of what would commonly pass as knowledge is more or less probable opinion. (pp139-140)

In regard to probable opinion, we can derive great assistance from coherence, which we rejected as the definition of truth, but may often use as a criterion. A body of individually probable opinions, if they are mutually coherent, become more probable than any one of them would be individually. It is in this way that many scientific hypotheses acquire their probability. They fit into a coherent system of probable opinions, and thus become more probable than they would be in isolation. The same thing applies to general philosophical hypotheses. Often in a single case such hypotheses may seem highly doubtful, while yet, when we consider the order and coherence which they introduce into a mass of probable opinion, they become pretty nearly certain. This applies, in particular, to such matters as the distinction between dreams and waking life. If our dreams, night after night, were as coherent one with another as our days, we should hardly know whether to believe the dreams or the waking life. As it is, the test of coherence condemns the dreams and confirms the waking life. But this test, though it increases probability where it is successful, never gives absolute certainty, unless there is certainty already at some point in the coherent system. Thus the mere organization of probable opinion will never, by itself, transform it into indubitable knowledge. (p140)

XIV. THE LIMITS OF PHILOSOPHICAL KNOWLEDGE
In all that we have said hitherto concerning philosophy, we have scarcely touched on many matters that occupy a 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 life-long 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 proofs 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. (p141)

The great representative, in modern times, of the 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 complement 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 a 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 of further development. The Absolute Idea, therefore, is adequate to describe Absolute Reality; but all lower ideas only describe 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 should see instead an eternal perfect unchanging spiritual unity. (pp141-143)

In this conception, there is undeniably something sublime, something to which we could wish to yield assent. Nevertheless, when the arguments in support of it are carefully examined, they appear to involve much 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, is constituted by his memories and the rest of his knowledge, by his loves and hatreds, and 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. (p143)

This whole point of view, however, turns upon the notion of the 'nature' of a thing, which seems to mean 'all the truths 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 truths about the thing, then plainly we cannot know a thing's 'nature' unless we know all the thing's relations to all the 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, (1) acquaintance with a thing does not logically involve a knowledge of its relations, and (2) 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, with 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. (pp144-145)

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. (p145)

Most of the great ambitious attempts of metaphysicians have proceeded by the attempt 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. (pp145-146)

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 ad 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. (p146)

Kant, who first emphasized this contradiction, deduced the impossibility of space and time, which he declared to be merely subjective; and 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 Cantor, 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 reasons for regarding space and time as unreal have become inoperative, and one of the great sources of metaphysical constructions is dried up. (pp146-147)

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 formerly supposed to be necessary by philosophers, are now known to derive their appearance of necessity from our mere familiarity with 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, where distances such as we can measure are concerned, that it is impossible to discover by observation whether our actual space is strictly Euclidean or of one of these other kinds. Thus the position is completely reversed. Formerly 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 formerly supposed to be, our knowledge of what may be is enormously increased. Instead of being shut 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. (pp147-148)

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 formerly, 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 connexion 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 sense-data are signs of physical objects is itself a connexion 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. (pp148-149)

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 truths, is of two sorts: pure empirical knowledge, which tells us of the existence and some of the properties of particular things with which we are acquainted, and pure a priori knowledge, which gives us connexions 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. (p149)

Philosophical knowledge, if what has been said above is true, does not differ essentially from scientific knowledge; there is 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; it searches out any inconsistencies there may be in these principles, and it only accepts them when, as the 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 man incapable of the kind of knowledge which he is generally believed to possess. (pp149-150)

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 is 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 doubting whatever seemed doubtful; in pausing, with each apparent piece of knowledge, to ask himself whether, on reflection, he could feel certain that he really knew it. This is the kind of criticism which constitutes philosophy. Some knowledge, such as knowledge of the existence of our sense-data, appears quite indubitable, however calmly and thoroughly we reflect upon it. In regard to such knowledge, philosophical criticism does not require that we should abstain from belief. But there are beliefs—such, for example, as the belief that physical objects exactly resemble our sense-data—which are entertained until we begin to reflect, but are found to melt away when subjected to a close inquiry. Such beliefs philosophy will bid us reject, unless some new line of argument is found to support them. But to reject the beliefs which do not appear open to any objections, however closely we examine them, is not reasonable, and is not what philosophy advocates. (pp150-151)

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. (pp151-152)

XV. 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. (p153)

This view of philosophy appears to result, partly from a wrong conception of the ends of life, partly from a wrong conception of the kind 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 than 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. (p153)

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' man, 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 their 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. (p154)

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 truths has been ascertained by his science, his answer will last as long as you are 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 been 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. (pp154-155)

This is, however, only a part of the truth concerning the uncertainty of philosophy. There are many questions—and among them those that are of 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 quite a 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 in 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 confining ourselves to definitely ascertainable knowledge. (pp155-156)

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. (p156)

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 sense, from the habitual beliefs of his age or his nation, and from convictions which have grown up in his mind without the co-operation 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 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 travelled into the region of liberating doubt, and it keeps alive our sense of wonder by showing familiar things in an unfamiliar aspect. (pp156-157)

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. The life of the instinctive man is shut up within the circle of his private interests: 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 in 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. (pp157-158)

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 alone 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 this 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. Self-assertion, in philosophic speculation as elsewhere, views the world as a means to its own ends; thus it makes the world of less account than Self, and the Self sets bounds 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. (pp158-159)

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 were correct, is untrue; but in addition to being untrue, it has the effect of robbing philosophic 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. (pp159-160)

The true philosophic contemplation, on the contrary, finds its satisfaction in every enlargement of the not-Self, in everything that magnifies the objects contemplated, and thereby the subject contemplating. Everything, in 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, calmly, dispassionately, in the sole and exclusive desire of knowledge—knowledge as impersonal, as purely contemplative, 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. (p160)

The mind which has become accustomed to the freedom and impartiality of philosophic 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 in a world of which all the rest is unaffected by any one 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. Thus 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. (pp160-161)

Thus, to sum up our discussion of 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. (p161)