Mathematical logic, even in its most modern form, is not directly of philosophical importance except in its beginnings. After the beginnings, it belongs rather to mathematics than to philosophy. Of its beginnings, which are the only part of it that can properly be called philosophical logic, I shall speak shortly. But even the later developments, though not directly philosophical, will be found of great indirect use in philosophising. They enable us to deal easily with more abstract conceptions than merely verbal reasoning can enumerate; they suggest fruitful hypotheses which otherwise could hardly be thought of; and they enable us to see quickly what is the smallest store of materials with which a given logical or scientific edifice can be constructed. Not only Frege's theory of number, which we shall deal with in Lecture VII., but the whole theory of physical concepts which will be outlined in our next two lectures, is inspired by mathematical logic, and could never have been imagined without it.
In both these cases, and in many others, we shall appeal to a certain principle called “the principle of abstraction.” This principle, which might equally well be called “the principle which dispenses with abstraction,” and is one which clears away incredible accumulations of metaphysical lumber, was directly suggested by mathematical logic, and could hardly have been proved or practically used without its help. The principle will be explained in our fourth lecture, but its use may be briefly indicated in advance. When a group of objects have that kind of similarity which we are inclined to attribute to possession of a common quality, the principle in question shows that membership of the group will serve all the purposes of the supposed common quality, and that therefore, unless some common quality is actually known, the group or class of similar objects may be used to replace the common quality, which need not be assumed to exist. In this and other ways, the indirect uses of even the later parts of mathematical logic are very great; but it is now time to turn our attention to its philosophical foundations.
In every proposition and in every inference there is, besides the particular subject-matter concerned, a certain form, a way in which the constituents of the proposition or inference are put together. If I say, “Socrates is mortal,” “Jones is angry,” “The sun is hot,” there is something in common in these three cases, something indicated by the word “is.” What is in common is the form of the proposition, not an actual constituent. If I say a number of things about Socrates—that he was an Athenian, that he married Xantippe, that he drank the hemlock—there is a common constituent, namely Socrates, in all the propositions I enunciate, but they have diverse forms. If, on the other hand, I take any one of these propositions and replace its constituents, one at a time, by other constituents, the form remains constant, but no constituent remains. Take (say) the series of propositions, “Socrates drank the hemlock,” “Coleridge drank the hemlock,” “Coleridge drank opium,” “Coleridge ate opium.” The form remains unchanged throughout this series, but all the constituents are altered. Thus form is not another constituent, but is the way the constituents are put together. It is forms, in this sense, that are the proper object of philosophical logic.
It is obvious that the knowledge of logical forms is something quite different from knowledge of existing things. The form of “Socrates drank the hemlock” is not an existing thing like Socrates or the hemlock, nor does it even have that close relation to existing things that drinking has. It is something altogether more abstract and remote. We might understand all the separate words of a sentence without understanding the sentence: if a sentence is long and complicated, this is apt to happen. In such a case we have knowledge of the constituents, but not of the form. We may also have knowledge of the form without having knowledge of the constituents. If I say, “Rorarius drank the hemlock,” those among you who have never heard of Rorarius (supposing there are any) will understand the form, without having knowledge of all the constituents. In order to understand a sentence, it is necessary to have knowledge both of the constituents and of the particular instance of the form. It is in this way that a sentence conveys information, since it tells us that certain known objects are related according to a certain known form. Thus some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse. It is the business of philosophical logic to extract this knowledge from its concrete integuments, and to render it explicit and pure.
In all inference, form alone is essential: the particular subject-matter is irrelevant except as securing the truth of the premisses. This is one reason for the great importance of logical form. When I say, “Socrates was a man, all men are mortal, therefore Socrates was mortal,” the connection of premisses and conclusion does not in any way depend upon its being Socrates and man and mortality that I am mentioning. The general form of the inference may be expressed in some such words as, “If a thing has a certain property, and whatever has this property has a certain other property, then the thing in question also has that other property.” Here no particular things or properties are mentioned: the proposition is absolutely general. All inferences, when stated fully, are instances of propositions having this kind of generality. If they seem to depend upon the subject-matter otherwise than as regards the truth of the premisses, that is because the premisses have not been all explicitly stated. In logic, it is a waste of time to deal with inferences concerning particular cases: we deal throughout with completely general and purely formal implications, leaving it to other sciences to discover when the hypotheses are verified and when they are not.
But the forms of propositions giving rise to inferences are not the simplest forms: they are always hypothetical, stating that if one proposition is true, then so is another. Before considering inference, therefore, logic must consider those simpler forms which inference presupposes. Here the traditional logic failed completely: it believed that there was only one form of simple proposition (i.e. of proposition not stating a relation between two or more other propositions), namely, the form which ascribes a predicate to a subject. This is the appropriate form in assigning the qualities of a given thing—we may say “this thing is round, and red, and so on.” Grammar favours this form, but philosophically it is so far from universal that it is not even very common. If we say “this thing is bigger than that,” we are not assigning a mere quality of “this,” but a relation of “this” and “that.” We might express the same fact by saying “that thing is smaller than this,” where grammatically the subject is changed. Thus propositions stating that two things have a certain relation have a different form from subject-predicate propositions, and the failure to perceive this difference or to allow for it has been the source of many errors in traditional metaphysics.
The belief or unconscious conviction that all propositions are of the subject-predicate form—in other words, that every fact consists in some thing having some quality—has rendered most philosophers incapable of giving any account of the world of science and daily life. If they had been honestly anxious to give such an account, they would probably have discovered their error very quickly; but most of them were less anxious to understand the world of science and daily life, than to convict it of unreality in the interests of a super-sensible “real” world. Belief in the unreality of the world of sense arises with irresistible force in certain moods—moods which, I imagine, have some simple physiological basis, but are none the less powerfully persuasive. The conviction born of these moods is the source of most mysticism and of most metaphysics. When the emotional intensity of such a mood subsides, a man who is in the habit of reasoning will search for logical reasons in favour of the belief which he finds in himself. But since the belief already exists, he will be very hospitable to any reason that suggests itself. The paradoxes apparently proved by his logic are really the paradoxes of mysticism, and are the goal which he feels his logic must reach if it is to be in accordance with insight. It is in this way that logic has been pursued by those of the great philosophers who were mystics—notably Plato, Spinoza, and Hegel. But since they usually took for granted the supposed insight of the mystic emotion, their logical doctrines were presented with a certain dryness, and were believed by their disciples to be quite independent of the sudden illumination from which they sprang. Nevertheless their origin clung to them, and they remained—to borrow a useful word from Mr Santayana—“malicious” in regard to the world of science and common sense. It is only so that we can account for the complacency with which philosophers have accepted the inconsistency of their doctrines with all the common and scientific facts which seem best established and most worthy of belief.
The logic of mysticism shows, as is natural, the defects which are inherent in anything malicious. While the mystic mood is dominant, the need of logic is not felt; as the mood fades, the impulse to logic reasserts itself, but with a desire to retain the vanishing insight, or at least to prove that it was insight, and that what seems to contradict it is illusion. The logic which thus arises is not quite disinterested or candid, and is inspired by a certain hatred of the daily world to which it is to be applied. Such an attitude naturally does not tend to the best results. Everyone knows that to read an author simply in order to refute him is not the way to understand him; and to read the book of Nature with a conviction that it is all illusion is just as unlikely to lead to understanding. If our logic is to find the common world intelligible, it must not be hostile, but must be inspired by a genuine acceptance such as is not usually to be found among metaphysicians.
Traditional logic, since it holds that all propositions have the subject-predicate form, is unable to admit the reality of relations: all relations, it maintains, must be reduced to properties of the apparently related terms. There are many ways of refuting this opinion; one of the easiest is derived from the consideration of what are called “asymmetrical” relations. In order to explain this, I will first explain two independent ways of classifying relations.
Some relations, when they hold between A and B, also hold between B and A. Such, for example, is the relation “brother or sister.” If A is a brother or sister of B, then B is a brother or sister of A. Such again is any kind of similarity, say similarity of colour. Any kind of dissimilarity is also of this kind: if the colour of A is unlike the colour of B, then the colour of B is unlike the colour of A. Relations of this sort are called symmetrical. Thus a relation is symmetrical if, whenever it holds between A and B, it also holds between B and A.
All relations that are not symmetrical are called non-symmetrical. Thus “brother” is non-symmetrical, because, if A is a brother of B, it may happen that B is a sister of A.
A relation is called asymmetrical when, if it holds between A and B, it never holds between B and A. Thus husband, father, grandfather, etc., are asymmetrical relations. So are before, after, greater, above, to the right of, etc. All the relations that give rise to series are of this kind.
Classification into symmetrical, asymmetrical, and merely non-symmetrical relations is the first of the two classifications we had to consider. The second is into transitive, intransitive, and merely non-transitive relations, which are defined as follows.
A relation is said to be transitive, if, whenever it holds between A and B and also between B and C, it holds between A and C. Thus before, after, greater, above are transitive. All relations giving rise to series are transitive, but so are many others. The transitive relations just mentioned were asymmetrical, but many transitive relations are symmetrical—for instance, equality in any respect, exact identity of colour, being equally numerous (as applied to collections), and so on.
A relation is said to be non-transitive whenever it is not transitive. Thus “brother” is non-transitive, because a brother of one's brother may be oneself. All kinds of dissimilarity are non-transitive.
A relation is said to be intransitive when, if A has the relation to B, and B to C, A never has it to C. Thus “father” is intransitive. So is such a relation as “one inch taller” or “one year later.”
Let us now, in the light of this classification, return to the question whether all relations can be reduced to predications.
In the case of symmetrical relations—i.e. relations which, if they hold between A and B, also hold between B and A—some kind of plausibility can be given to this doctrine. A symmetrical relation which is transitive, such as equality, can be regarded as expressing possession of some common property, while one which is not transitive, such as inequality, can be regarded as expressing possession of different properties. But when we come to asymmetrical relations, such as before and after, greater and less, etc., the attempt to reduce them to properties becomes obviously impossible. When, for example, two things are merely known to be unequal, without our knowing which is greater, we may say that the inequality results from their having different magnitudes, because inequality is a symmetrical relation; but to say that when one thing is greater than another, and not merely unequal to it, that means that they have different magnitudes, is formally incapable of explaining the facts. For if the other thing had been greater than the one, the magnitudes would also have been different, though the fact to be explained would not have been the same. Thus mere difference of magnitude is not all that is involved, since, if it were, there would be no difference between one thing being greater than another, and the other being greater than the one. We shall have to say that the one magnitude is greater than the other, and thus we shall have failed to get rid of the relation “greater.” In short, both possession of the same property and possession of different properties are symmetrical relations, and therefore cannot account for the existence of asymmetrical relations.
Asymmetrical relations are involved in all series—in space and time, greater and less, whole and part, and many others of the most important characteristics of the actual world. All these aspects, therefore, the logic which reduces everything to subjects and predicates is compelled to condemn as error and mere appearance. To those whose logic is not malicious, such a wholesale condemnation appears impossible. And in fact there is no reason except prejudice, so far as I can discover, for denying the reality of relations. When once their reality is admitted, all logical grounds for supposing the world of sense to be illusory disappear. If this is to be supposed, it must be frankly and simply on the ground of mystic insight unsupported by argument. It is impossible to argue against what professes to be insight, so long as it does not argue in its own favour. As logicians, therefore, we may admit the possibility of the mystic's world, while yet, so long as we do not have his insight, we must continue to study the everyday world with which we are familiar. But when he contends that our world is impossible, then our logic is ready to repel his attack. And the first step in creating the logic which is to perform this service is the recognition of the reality of relations.
Relations which have two terms are only one kind of relations. A relation may have three terms, or four, or any number. Relations of two terms, being the simplest, have received more attention than the others, and have generally been alone considered by philosophers, both those who accepted and those who denied the reality of relations. But other relations have their importance, and are indispensable in the solution of certain problems. Jealousy, for example, is a relation between three people. Professor Royce mentions the relation “giving”: when A gives B to C, that is a relation of three terms.[15] When a man says to his wife: “My dear, I wish you could induce Angelina to accept Edwin,” his wish constitutes a relation between four people, himself, his wife, Angelina, and Edwin. Thus such relations are by no means recondite or rare. But in order to explain exactly how they differ from relations of two terms, we must embark upon a classification of the logical forms of facts, which is the first business of logic, and the business in which the traditional logic has been most deficient.
The existing world consists of many things with many qualities and relations. A complete description of the existing world would require not only a catalogue of the things, but also a mention of all their qualities and relations. We should have to know not only this, that, and the other thing, but also which was red, which yellow, which was earlier than which, which was between which two others, and so on. When I speak of a “fact,” I do not mean one of the simple things in the world; I mean that a certain thing has a certain quality, or that certain things have a certain relation. Thus, for example, I should not call Napoleon a fact, but I should call it a fact that he was ambitious, or that he married Josephine. Now a fact, in this sense, is never simple, but always has two or more constituents. When it simply assigns a quality to a thing, it has only two constituents, the thing and the quality. When it consists of a relation between two things, it has three constituents, the things and the relation. When it consists of a relation between three things, it has four constituents, and so on. The constituents of facts, in the sense in which we are using the word “fact,” are not other facts, but are things and qualities or relations. When we say that there are relations of more than two terms, we mean that there are single facts consisting of a single relation and more than two things. I do not mean that one relation of two terms may hold between A and B, and also between A and C, as, for example, a man is the son of his father and also the son of his mother. This constitutes two distinct facts: if we choose to treat it as one fact, it is a fact which has facts for its constituents. But the facts I am speaking of have no facts among their constituents, but only things and relations. For example, when A is jealous of B on account of C, there is only one fact, involving three people; there are not two instances of jealousy, but only one. It is in such cases that I speak of a relation of three terms, where the simplest possible fact in which the relation occurs is one involving three things in addition to the relation. And the same applies to relations of four terms or five or any other number. All such relations must be admitted in our inventory of the logical forms of facts: two facts involving the same number of things have the same form, and two which involve different numbers of things have different forms.
Given any fact, there is an assertion which expresses the fact. The fact itself is objective, and independent of our thought or opinion about it; but the assertion is something which involves thought, and may be either true or false. An assertion may be positive or negative: we may assert that Charles I. was executed, or that he did not die in his bed. A negative assertion may be said to be a denial. Given a form of words which must be either true or false, such as “Charles I. died in his bed,” we may either assert or deny this form of words: in the one case we have a positive assertion, in the other a negative one. A form of words which must be either true or false I shall call a proposition. Thus a proposition is the same as what may be significantly asserted or denied. A proposition which expresses what we have called a fact, i.e. which, when asserted, asserts that a certain thing has a certain quality, or that certain things have a certain relation, will be called an atomic proposition, because, as we shall see immediately, there are other propositions into which atomic propositions enter in a way analogous to that in which atoms enter into molecules. Atomic propositions, although, like facts, they may have any one of an infinite number of forms, are only one kind of propositions. All other kinds are more complicated. In order to preserve the parallelism in language as regards facts and propositions, we shall give the name “atomic facts” to the facts we have hitherto been considering. Thus atomic facts are what determine whether atomic propositions are to be asserted or denied.
Whether an atomic proposition, such as “this is red,” or “this is before that,” is to be asserted or denied can only be known empirically. Perhaps one atomic fact may sometimes be capable of being inferred from another, though this seems very doubtful; but in any case it cannot be inferred from premisses no one of which is an atomic fact. It follows that, if atomic facts are to be known at all, some at least must be known without inference. The atomic facts which we come to know in this way are the facts of sense-perception; at any rate, the facts of sense-perception are those which we most obviously and certainly come to know in this way. If we knew all atomic facts, and also knew that there were none except those we knew, we should, theoretically, be able to infer all truths of whatever form.[16] Thus logic would then supply us with the whole of the apparatus required. But in the first acquisition of knowledge concerning atomic facts, logic is useless. In pure logic, no atomic fact is ever mentioned: we confine ourselves wholly to forms, without asking ourselves what objects can fill the forms. Thus pure logic is independent of atomic facts; but conversely, they are, in a sense, independent of logic. Pure logic and atomic facts are the two poles, the wholly a priori and the wholly empirical. But between the two lies a vast intermediate region, which we must now briefly explore.
“Molecular” propositions are such as contain conjunctions—if, or, and, unless, etc.—and such words are the marks of a molecular proposition. Consider such an assertion as, “If it rains, I shall bring my umbrella.” This assertion is just as capable of truth or falsehood as the assertion of an atomic proposition, but it is obvious that either the corresponding fact, or the nature of the correspondence with fact, must be quite different from what it is in the case of an atomic proposition. Whether it rains, and whether I bring my umbrella, are each severally matters of atomic fact, ascertainable by observation. But the connection of the two involved in saying that if the one happens, then the other will happen, is something radically different from either of the two separately. It does not require for its truth that it should actually rain, or that I should actually bring my umbrella; even if the weather is cloudless, it may still be true that I should have brought my umbrella if the weather had been different. Thus we have here a connection of two propositions, which does not depend upon whether they are to be asserted or denied, but only upon the second being inferable from the first. Such propositions, therefore, have a form which is different from that of any atomic proposition.
Such propositions are important to logic, because all inference depends upon them. If I have told you that if it rains I shall bring my umbrella, and if you see that there is a steady downpour, you can infer that I shall bring my umbrella. There can be no inference except where propositions are connected in some such way, so that from the truth or falsehood of the one something follows as to the truth or falsehood of the other. It seems to be the case that we can sometimes know molecular propositions, as in the above instance of the umbrella, when we do not know whether the component atomic propositions are true or false. The practical utility of inference rests upon this fact.
The next kind of propositions we have to consider are general propositions, such as “all men are mortal,” “all equilateral triangles are equiangular.” And with these belong propositions in which the word “some” occurs, such as “some men are philosophers” or “some philosophers are not wise.” These are the denials of general propositions, namely (in the above instances), of “all men are non-philosophers” and “all philosophers are wise.” We will call propositions containing the word “some” negative general propositions, and those containing the word “all” positive general propositions. These propositions, it will be seen, begin to have the appearance of the propositions in logical text-books. But their peculiarity and complexity are not known to the text-books, and the problems which they raise are only discussed in the most superficial manner.
When we were discussing atomic facts, we saw that we should be able, theoretically, to infer all other truths by logic if we knew all atomic facts and also knew that there were no other atomic facts besides those we knew. The knowledge that there are no other atomic facts is positive general knowledge; it is the knowledge that “all atomic facts are known to me,” or at least “all atomic facts are in this collection”—however the collection may be given. It is easy to see that general propositions, such as “all men are mortal,” cannot be known by inference from atomic facts alone. If we could know each individual man, and know that he was mortal, that would not enable us to know that all men are mortal, unless we knew that those were all the men there are, which is a general proposition. If we knew every other existing thing throughout the universe, and knew that each separate thing was not an immortal man, that would not give us our result unless we knew that we had explored the whole universe, i.e. unless we knew “all things belong to this collection of things I have examined.” Thus general truths cannot be inferred from particular truths alone, but must, if they are to be known, be either self-evident, or inferred from premisses of which at least one is a general truth. But all empirical evidence is of particular truths. Hence, if there is any knowledge of general truths at all, there must be some knowledge of general truths which is independent of empirical evidence, i.e. does not depend upon the data of sense.
The above conclusion, of which we had an instance in the case of the inductive principle, is important, since it affords a refutation of the older empiricists. They believed that all our knowledge is derived from the senses and dependent upon them. We see that, if this view is to be maintained, we must refuse to admit that we know any general propositions. It is perfectly possible logically that this should be the case, but it does not appear to be so in fact, and indeed no one would dream of maintaining such a view except a theorist at the last extremity. We must therefore admit that there is general knowledge not derived from sense, and that some of this knowledge is not obtained by inference but is primitive.
Such general knowledge is to be found in logic. Whether there is any such knowledge not derived from logic, I do not know; but in logic, at any rate, we have such knowledge. It will be remembered that we excluded from pure logic such propositions as, “Socrates is a man, all men are mortal, therefore Socrates is mortal,” because Socrates and man and mortal are empirical terms, only to be understood through particular experience. The corresponding proposition in pure logic is: “If anything has a certain property, and whatever has this property has a certain other property, then the thing in question has the other property.” This proposition is absolutely general: it applies to all things and all properties. And it is quite self-evident. Thus in such propositions of pure logic we have the self-evident general propositions of which we were in search.
A proposition such as, “If Socrates is a man, and all men are mortal, then Socrates is mortal,” is true in virtue of its form alone. Its truth, in this hypothetical form, does not depend upon whether Socrates actually is a man, nor upon whether in fact all men are mortal; thus it is equally true when we substitute other terms for Socrates and man and mortal. The general truth of which it is an instance is purely formal, and belongs to logic. Since it does not mention any particular thing, or even any particular quality or relation, it is wholly independent of the accidental facts of the existent world, and can be known, theoretically, without any experience of particular things or their qualities and relations.
Logic, we may say, consists of two parts. The first part investigates what propositions are and what forms they may have; this part enumerates the different kinds of atomic propositions, of molecular propositions, of general propositions, and so on. The second part consists of certain supremely general propositions, which assert the truth of all propositions of certain forms. This second part merges into pure mathematics, whose propositions all turn out, on analysis, to be such general formal truths. The first part, which merely enumerates forms, is the more difficult, and philosophically the more important; and it is the recent progress in this first part, more than anything else, that has rendered a truly scientific discussion of many philosophical problems possible.
The problem of the nature of judgment or belief may be taken as an example of a problem whose solution depends upon an adequate inventory of logical forms. We have already seen how the supposed universality of the subject-predicate form made it impossible to give a right analysis of serial order, and therefore made space and time unintelligible. But in this case it was only necessary to admit relations of two terms. The case of judgment demands the admission of more complicated forms. If all judgments were true, we might suppose that a judgment consisted in apprehension of a fact, and that the apprehension was a relation of a mind to the fact. From poverty in the logical inventory, this view has often been held. But it leads to absolutely insoluble difficulties in the case of error. Suppose I believe that Charles I. died in his bed. There is no objective fact “Charles I.'s death in his bed” to which I can have a relation of apprehension. Charles I. and death and his bed are objective, but they are not, except in my thought, put together as my false belief supposes. It is therefore necessary, in analysing a belief, to look for some other logical form than a two-term relation. Failure to realise this necessity has, in my opinion, vitiated almost everything that has hitherto been written on the theory of knowledge, making the problem of error insoluble and the difference between belief and perception inexplicable.
Modern logic, as I hope is now evident, has the effect of enlarging our abstract imagination, and providing an infinite number of possible hypotheses to be applied in the analysis of any complex fact. In this respect it is the exact opposite of the logic practised by the classical tradition. In that logic, hypotheses which seem primâ facie possible are professedly proved impossible, and it is decreed in advance that reality must have a certain special character. In modern logic, on the contrary, while the primâ facie hypotheses as a rule remain admissible, others, which only logic would have suggested, are added to our stock, and are very often found to be indispensable if a right analysis of the facts is to be obtained. The old logic put thought in fetters, while the new logic gives it wings. It has, in my opinion, introduced the same kind of advance into philosophy as Galileo introduced into physics, making it possible at last to see what kinds of problems may be capable of solution, and what kinds must be abandoned as beyond human powers. And where a solution appears possible, the new logic provides a method which enables us to obtain results that do not merely embody personal idiosyncrasies, but must command the assent of all who are competent to form an opinion.
LECTURE III
ON OUR KNOWLEDGE OF THE
EXTERNAL WORLD
Philosophy may be approached by many roads, but one of the oldest and most travelled is the road which leads through doubt as to the reality of the world of sense. In Indian mysticism, in Greek and modern monistic philosophy from Parmenides onward, in Berkeley, in modern physics, we find sensible appearance criticised and condemned for a bewildering variety of motives. The mystic condemns it on the ground of immediate knowledge of a more real and significant world behind the veil; Parmenides and Plato condemn it because its continual flux is thought inconsistent with the unchanging nature of the abstract entities revealed by logical analysis; Berkeley brings several weapons, but his chief is the subjectivity of sense-data, their dependence upon the organisation and point of view of the spectator; while modern physics, on the basis of sensible evidence itself, maintains a mad dance of electrons which has, superficially at least, very little resemblance to the immediate objects of sight or touch.
Every one of these lines of attack raises vital and interesting problems.
The mystic, so long as he merely reports a positive revelation, cannot be refuted; but when he denies reality to objects of sense, he may be questioned as to what he means by “reality,” and may be asked how their unreality follows from the supposed reality of his super-sensible world. In answering these questions, he is led to a logic which merges into that of Parmenides and Plato and the idealist tradition.
The logic of the idealist tradition has gradually grown very complex and very abstruse, as may be seen from the Bradleian sample considered in our first lecture. If we attempted to deal fully with this logic, we should not have time to reach any other aspect of our subject; we will therefore, while acknowledging that it deserves a long discussion, pass by its central doctrines with only such occasional criticism as may serve to exemplify other topics, and concentrate our attention on such matters as its objections to the continuity of motion and the infinity of space and time—objections which have been fully answered by modern mathematicians in a manner constituting an abiding triumph for the method of logical analysis in philosophy. These objections and the modern answers to them will occupy our fifth, sixth, and seventh lectures.
Berkeley's attack, as reinforced by the physiology of the sense-organs and nerves and brain, is very powerful. I think it must be admitted as probable that the immediate objects of sense depend for their existence upon physiological conditions in ourselves, and that, for example, the coloured surfaces which we see cease to exist when we shut our eyes. But it would be a mistake to infer that they are dependent upon mind, not real while we see them, or not the sole basis for our knowledge of the external world. This line of argument will be developed in the present lecture.
The discrepancy between the world of physics and the world of sense, which we shall consider in our fourth lecture, will be found to be more apparent than real, and it will be shown that whatever there is reason to believe in physics can probably be interpreted in terms of sense.
The instrument of discovery throughout is modern logic, a very different science from the logic of the text-books and also from the logic of idealism. Our second lecture has given a short account of modern logic and of its points of divergence from the various traditional kinds of logic.
In our last lecture, after a discussion of causality and free will, we shall try to reach a general account of the logical-analytic method of scientific philosophy, and a tentative estimate of the hopes of philosophical progress which it allows us to entertain.
In this lecture, I wish to apply the logical-analytic method to one of the oldest problems of philosophy, namely, the problem of our knowledge of the external world. What I have to say on this problem does not amount to an answer of a definite and dogmatic kind; it amounts only to an analysis and statement of the questions involved, with an indication of the directions in which evidence may be sought. But although not yet a definite solution, what can be said at present seems to me to throw a completely new light on the problem, and to be indispensable, not only in seeking the answer, but also in the preliminary question as to what parts of our problem may possibly have an ascertainable answer.
In every philosophical problem, our investigation starts from what may be called “data,” by which I mean matters of common knowledge, vague, complex, inexact, as common knowledge always is, but yet somehow commanding our assent as on the whole and in some interpretation pretty certainly true. In the case of our present problem, the common knowledge involved is of various kinds. There is first our acquaintance with particular objects of daily life—furniture, houses, towns, other people, and so on. Then there is the extension of such particular knowledge to particular things outside our personal experience, through history and geography, newspapers, etc. And lastly, there is the systematisation of all this knowledge of particulars by means of physical science, which derives immense persuasive force from its astonishing power of foretelling the future. We are quite willing to admit that there may be errors of detail in this knowledge, but we believe them to be discoverable and corrigible by the methods which have given rise to our beliefs, and we do not, as practical men, entertain for a moment the hypothesis that the whole edifice may be built on insecure foundations. In the main, therefore, and without absolute dogmatism as to this or that special portion, we may accept this mass of common knowledge as affording data for our philosophical analysis.
It may be said—and this is an objection which must be met at the outset—that it is the duty of the philosopher to call in question the admittedly fallible beliefs of daily life, and to replace them by something more solid and irrefragable. In a sense this is true, and in a sense it is effected in the course of analysis. But in another sense, and a very important one, it is quite impossible. While admitting that doubt is possible with regard to all our common knowledge, we must nevertheless accept that knowledge in the main if philosophy is to be possible at all. There is not any superfine brand of knowledge, obtainable by the philosopher, which can give us a standpoint from which to criticise the whole of the knowledge of daily life. The most that can be done is to examine and purify our common knowledge by an internal scrutiny, assuming the canons by which it has been obtained, and applying them with more care and with more precision. Philosophy cannot boast of having achieved such a degree of certainty that it can have authority to condemn the facts of experience and the laws of science. The philosophic scrutiny, therefore, though sceptical in regard to every detail, is not sceptical as regards the whole. That is to say, its criticism of details will only be based upon their relation to other details, not upon some external criterion which can be applied to all the details equally. The reason for this abstention from a universal criticism is not any dogmatic confidence, but its exact opposite; it is not that common knowledge must be true, but that we possess no radically different kind of knowledge derived from some other source. Universal scepticism, though logically irrefutable, is practically barren; it can only, therefore, give a certain flavour of hesitancy to our beliefs, and cannot be used to substitute other beliefs for them.
Although data can only be criticised by other data, not by an outside standard, yet we may distinguish different grades of certainty in the different kinds of common knowledge which we enumerated just now. What does not go beyond our own personal sensible acquaintance must be for us the most certain: the “evidence of the senses” is proverbially the least open to question. What depends on testimony, like the facts of history and geography which are learnt from books, has varying degrees of certainty according to the nature and extent of the testimony. Doubts as to the existence of Napoleon can only be maintained for a joke, whereas the historicity of Agamemnon is a legitimate subject of debate. In science, again, we find all grades of certainty short of the highest. The law of gravitation, at least as an approximate truth, has acquired by this time the same kind of certainty as the existence of Napoleon, whereas the latest speculations concerning the constitution of matter would be universally acknowledged to have as yet only a rather slight probability in their favour. These varying degrees of certainty attaching to different data may be regarded as themselves forming part of our data; they, along with the other data, lie within the vague, complex, inexact body of knowledge which it is the business of the philosopher to analyse.
The first thing that appears when we begin to analyse our common knowledge is that some of it is derivative, while some is primitive; that is to say, there is some that we only believe because of something else from which it has been inferred in some sense, though not necessarily in a strict logical sense, while other parts are believed on their own account, without the support of any outside evidence. It is obvious that the senses give knowledge of the latter kind: the immediate facts perceived by sight or touch or hearing do not need to be proved by argument, but are completely self-evident. Psychologists, however, have made us aware that what is actually given in sense is much less than most people would naturally suppose, and that much of what at first sight seems to be given is really inferred. This applies especially in regard to our space-perceptions. For instance, we instinctively infer the “real” size and shape of a visible object from its apparent size and shape, according to its distance and our point of view. When we hear a person speaking, our actual sensations usually miss a great deal of what he says, and we supply its place by unconscious inference; in a foreign language, where this process is more difficult, we find ourselves apparently grown deaf, requiring, for example, to be much nearer the stage at a theatre than would be necessary in our own country. Thus the first step in the analysis of data, namely, the discovery of what is really given in sense, is full of difficulty. We will, however, not linger on this point; so long as its existence is realised, the exact outcome does not make any very great difference in our main problem.
The next step in our analysis must be the consideration of how the derivative parts of our common knowledge arise. Here we become involved in a somewhat puzzling entanglement of logic and psychology. Psychologically, a belief may be called derivative whenever it is caused by one or more other beliefs, or by some fact of sense which is not simply what the belief asserts. Derivative beliefs in this sense constantly arise without any process of logical inference, merely by association of ideas or some equally extra-logical process. From the expression of a man's face we judge as to what he is feeling: we say we see that he is angry, when in fact we only see a frown. We do not judge as to his state of mind by any logical process: the judgment grows up, often without our being able to say what physical mark of emotion we actually saw. In such a case, the knowledge is derivative psychologically; but logically it is in a sense primitive, since it is not the result of any logical deduction. There may or may not be a possible deduction leading to the same result, but whether there is or not, we certainly do not employ it. If we call a belief “logically primitive” when it is not actually arrived at by a logical inference, then innumerable beliefs are logically primitive which psychologically are derivative. The separation of these two kinds of primitiveness is vitally important to our present discussion.
When we reflect upon the beliefs which are logically but not psychologically primitive, we find that, unless they can on reflection be deduced by a logical process from beliefs which are also psychologically primitive, our confidence in their truth tends to diminish the more we think about them. We naturally believe, for example, that tables and chairs, trees and mountains, are still there when we turn our backs upon them. I do not wish for a moment to maintain that this is certainly not the case, but I do maintain that the question whether it is the case is not to be settled off-hand on any supposed ground of obviousness. The belief that they persist is, in all men except a few philosophers, logically primitive, but it is not psychologically primitive; psychologically, it arises only through our having seen those tables and chairs, trees and mountains. As soon as the question is seriously raised whether, because we have seen them, we have a right to suppose that they are there still, we feel that some kind of argument must be produced, and that if none is forthcoming, our belief can be no more than a pious opinion. We do not feel this as regards the immediate objects of sense: there they are, and as far as their momentary existence is concerned, no further argument is required. There is accordingly more need of justifying our psychologically derivative beliefs than of justifying those that are primitive.
We are thus led to a somewhat vague distinction between what we may call “hard” data and “soft” data. This distinction is a matter of degree, and must not be pressed; but if not taken too seriously it may help to make the situation clear. I mean by “hard” data those which resist the solvent influence of critical reflection, and by “soft” data those which, under the operation of this process, become to our minds more or less doubtful. The hardest of hard data are of two sorts: the particular facts of sense, and the general truths of logic. The more we reflect upon these, the more we realise exactly what they are, and exactly what a doubt concerning them really means, the more luminously certain do they become. Verbal doubt concerning even these is possible, but verbal doubt may occur when what is nominally being doubted is not really in our thoughts, and only words are actually present to our minds. Real doubt, in these two cases, would, I think, be pathological. At any rate, to me they seem quite certain, and I shall assume that you agree with me in this. Without this assumption, we are in danger of falling into that universal scepticism which, as we saw, is as barren as it is irrefutable. If we are to continue philosophising, we must make our bow to the sceptical hypothesis, and, while admitting the elegant terseness of its philosophy, proceed to the consideration of other hypotheses which, though perhaps not certain, have at least as good a right to our respect as the hypothesis of the sceptic.
Applying our distinction of “hard” and “soft” data to psychologically derivative but logically primitive beliefs, we shall find that most, if not all, are to be classed as soft data. They may be found, on reflection, to be capable of logical proof, and they then again become believed, but no longer as data. As data, though entitled to a certain limited respect, they cannot be placed on a level with the facts of sense or the laws of logic. The kind of respect which they deserve seems to me such as to warrant us in hoping, though not too confidently, that the hard data may prove them to be at least probable. Also, if the hard data are found to throw no light whatever upon their truth or falsehood, we are justified, I think, in giving rather more weight to the hypothesis of their truth than to the hypothesis of their falsehood. For the present, however, let us confine ourselves to the hard data, with a view to discovering what sort of world can be constructed by their means alone.
Our data now are primarily the facts of sense (i.e. of our own sense-data) and the laws of logic. But even the severest scrutiny will allow some additions to this slender stock. Some facts of memory—especially of recent memory—seem to have the highest degree of certainty. Some introspective facts are as certain as any facts of sense. And facts of sense themselves must, for our present purposes, be interpreted with a certain latitude. Spatial and temporal relations must sometimes be included, for example in the case of a swift motion falling wholly within the specious present. And some facts of comparison, such as the likeness or unlikeness of two shades of colour, are certainly to be included among hard data. Also we must remember that the distinction of hard and soft data is psychological and subjective, so that, if there are other minds than our own—which at our present stage must be held doubtful—the catalogue of hard data may be different for them from what it is for us.
Certain common beliefs are undoubtedly excluded from hard data. Such is the belief which led us to introduce the distinction, namely, that sensible objects in general persist when we are not perceiving them. Such also is the belief in other people's minds: this belief is obviously derivative from our perception of their bodies, and is felt to demand logical justification as soon as we become aware of its derivativeness. Belief in what is reported by the testimony of others, including all that we learn from books, is of course involved in the doubt as to whether other people have minds at all. Thus the world from which our reconstruction is to begin is very fragmentary. The best we can say for it is that it is slightly more extensive than the world at which Descartes arrived by a similar process, since that world contained nothing except himself and his thoughts.
We are now in a position to understand and state the problem of our knowledge of the external world, and to remove various misunderstandings which have obscured the meaning of the problem. The problem really is: Can the existence of anything other than our own hard data be inferred from the existence of those data? But before considering this problem, let us briefly consider what the problem is not.
When we speak of the “external” world in this discussion, we must not mean “spatially external,” unless “space” is interpreted in a peculiar and recondite manner. The immediate objects of sight, the coloured surfaces which make up the visible world, are spatially external in the natural meaning of this phrase. We feel them to be “there” as opposed to “here”; without making any assumption of an existence other than hard data, we can more or less estimate the distance of a coloured surface. It seems probable that distances, provided they are not too great, are actually given more or less roughly in sight; but whether this is the case or not, ordinary distances can certainly be estimated approximately by means of the data of sense alone. The immediately given world is spatial, and is further not wholly contained within our own bodies. Thus our knowledge of what is external in this sense is not open to doubt.
Another form in which the question is often put is: “Can we know of the existence of any reality which is independent of ourselves?” This form of the question suffers from the ambiguity of the two words “independent” and “self.” To take the Self first: the question as to what is to be reckoned part of the Self and what is not, is a very difficult one. Among many other things which we may mean by the Self, two may be selected as specially important, namely, (1) the bare subject which thinks and is aware of objects, (2) the whole assemblage of things that would necessarily cease to exist if our lives came to an end. The bare subject, if it exists at all, is an inference, and is not part of the data; therefore this meaning of Self may be ignored in our present inquiry. The second meaning is difficult to make precise, since we hardly know what things depend upon our lives for their existence. And in this form, the definition of Self introduces the word “depend,” which raises the same questions as are raised by the word “independent.” Let us therefore take up the word “independent,” and return to the Self later.
When we say that one thing is “independent” of another, we may mean either that it is logically possible for the one to exist without the other, or that there is no causal relation between the two such that the one only occurs as the effect of the other. The only way, so far as I know, in which one thing can be logically dependent upon another is when the other is part of the one. The existence of a book, for example, is logically dependent upon that of its pages: without the pages there would be no book. Thus in this sense the question, “Can we know of the existence of any reality which is independent of ourselves?” reduces to the question, “Can we know of the existence of any reality of which our Self is not part?” In this form, the question brings us back to the problem of defining the Self; but I think, however the Self may be defined, even when it is taken as the bare subject, it cannot be supposed to be part of the immediate object of sense; thus in this form of the question we must admit that we can know of the existence of realities independent of ourselves.
The question of causal dependence is much more difficult. To know that one kind of thing is causally independent of another, we must know that it actually occurs without the other. Now it is fairly obvious that, whatever legitimate meaning we give to the Self, our thoughts and feelings are causally dependent upon ourselves, i.e. do not occur when there is no Self for them to belong to. But in the case of objects of sense this is not obvious; indeed, as we saw, the common-sense view is that such objects persist in the absence of any percipient. If this is the case, then they are causally independent of ourselves; if not, not. Thus in this form the question reduces to the question whether we can know that objects of sense, or any other objects not our own thoughts and feelings, exist at times when we are not perceiving them. This form, in which the difficult word “independent” no longer occurs, is the form in which we stated the problem a minute ago.
Our question in the above form raises two distinct problems, which it is important to keep separate. First, can we know that objects of sense, or very similar objects, exist at times when we are not perceiving them? Secondly, if this cannot be known, can we know that other objects, inferable from objects of sense but not necessarily resembling them, exist either when we are perceiving the objects of sense or at any other time? This latter problem arises in philosophy as the problem of the “thing in itself,” and in science as the problem of matter as assumed in physics. We will consider this latter problem first.
Owing to the fact that we feel passive in sensation, we naturally suppose that our sensations have outside causes. Now it is necessary here first of all to distinguish between (1) our sensation, which is a mental event consisting in our being aware of a sensible object, and (2) the sensible object of which we are aware in sensation. When I speak of the sensible object, it must be understood that I do not mean such a thing as a table, which is both visible and tangible, can be seen by many people at once, and is more or less permanent. What I mean is just that patch of colour which is momentarily seen when we look at the table, or just that particular hardness which is felt when we press it, or just that particular sound which is heard when we rap it. Each of these I call a sensible object, and our awareness of it I call a sensation. Now our sense of passivity, if it really afforded any argument, would only tend to show that the sensation has an outside cause; this cause we should naturally seek in the sensible object. Thus there is no good reason, so far, for supposing that sensible objects must have outside causes. But both the thing-in-itself of philosophy and the matter of physics present themselves as outside causes of the sensible object as much as of the sensation. What are the grounds for this common opinion?
In each case, I think, the opinion has resulted from the combination of a belief that something which can persist independently of our consciousness makes itself known in sensation, with the fact that our sensations often change in ways which seem to depend upon us rather than upon anything which would be supposed to persist independently of us. At first, we believe unreflectingly that everything is as it seems to be, and that, if we shut our eyes, the objects we had been seeing remain as they were though we no longer see them. But there are arguments against this view, which have generally been thought conclusive. It is extraordinarily difficult to see just what the arguments prove; but if we are to make any progress with the problem of the external world, we must try to make up our minds as to these arguments.
A table viewed from one place presents a different appearance from that which it presents from another place. This is the language of common sense, but this language already assumes that there is a real table of which we see the appearances. Let us try to state what is known in terms of sensible objects alone, without any element of hypothesis. We find that as we walk round the table, we perceive a series of gradually changing visible objects. But in speaking of “walking round the table,” we have still retained the hypothesis that there is a single table connected with all the appearances. What we ought to say is that, while we have those muscular and other sensations which make us say we are walking, our visual sensations change in a continuous way, so that, for example, a striking patch of colour is not suddenly replaced by something wholly different, but is replaced by an insensible gradation of slightly different colours with slightly different shapes. This is what we really know by experience, when we have freed our minds from the assumption of permanent “things” with changing appearances. What is really known is a correlation of muscular and other bodily sensations with changes in visual sensations.
But walking round the table is not the only way of altering its appearance. We can shut one eye, or put on blue spectacles, or look through a microscope. All these operations, in various ways, alter the visual appearance which we call that of the table. More distant objects will also alter their appearance if (as we say) the state of the atmosphere changes—if there is fog or rain or sunshine. Physiological changes also alter the appearances of things. If we assume the world of common sense, all these changes, including those attributed to physiological causes, are changes in the intervening medium. It is not quite so easy as in the former case to reduce this set of facts to a form in which nothing is assumed beyond sensible objects. Anything intervening between ourselves and what we see must be invisible: our view in every direction is bounded by the nearest visible object. It might be objected that a dirty pane of glass, for example, is visible although we can see things through it. But in this case we really see a spotted patchwork: the dirtier specks in the glass are visible, while the cleaner parts are invisible and allow us to see what is beyond. Thus the discovery that the intervening medium affects the appearances of things cannot be made by means of the sense of sight alone.
Let us take the case of the blue spectacles, which is the simplest, but may serve as a type for the others. The frame of the spectacles is of course visible, but the blue glass, if it is clean, is not visible. The blueness, which we say is in the glass, appears as being in the objects seen through the glass. The glass itself is known by means of the sense of touch. In order to know that it is between us and the objects seen through it, we must know how to correlate the space of touch with the space of sight. This correlation itself, when stated in terms of the data of sense alone, is by no means a simple matter. But it presents no difficulties of principle, and may therefore be supposed accomplished. When it has been accomplished, it becomes possible to attach a meaning to the statement that the blue glass, which we can touch, is between us and the object seen, as we say, “through” it.
But we have still not reduced our statement completely to what is actually given in sense. We have fallen into the assumption that the object of which we are conscious when we touch the blue spectacles still exists after we have ceased to touch them. So long as we are touching them, nothing except our finger can be seen through the part touched, which is the only part where we immediately know that there is something. If we are to account for the blue appearance of objects other than the spectacles, when seen through them, it might seem as if we must assume that the spectacles still exist when we are not touching them; and if this assumption really is necessary, our main problem is answered: we have means of knowing of the present existence of objects not given in sense, though of the same kind as objects formerly given in sense.
It may be questioned, however, whether this assumption is actually unavoidable, though it is unquestionably the most natural one to make. We may say that the object of which we become aware when we touch the spectacles continues to have effects afterwards, though perhaps it no longer exists. In this view, the supposed continued existence of sensible objects after they have ceased to be sensible will be a fallacious inference from the fact that they still have effects. It is often supposed that nothing which has ceased to exist can continue to have effects, but this is a mere prejudice, due to a wrong conception of causality. We cannot, therefore, dismiss our present hypothesis on the ground of a priori impossibility, but must examine further whether it can really account for the facts.
It may be said that our hypothesis is useless in the case when the blue glass is never touched at all. How, in that case, are we to account for the blue appearance of objects? And more generally, what are we to make of the hypothetical sensations of touch which we associate with untouched visible objects, which we know would be verified if we chose, though in fact we do not verify them? Must not these be attributed to permanent possession, by the objects, of the properties which touch would reveal?
Let us consider the more general question first. Experience has taught us that where we see certain kinds of coloured surfaces we can, by touch, obtain certain expected sensations of hardness or softness, tactile shape, and so on. This leads us to believe that what is seen is usually tangible, and that it has, whether we touch it or not, the hardness or softness which we should expect to feel if we touched it. But the mere fact that we are able to infer what our tactile sensations would be shows that it is not logically necessary to assume tactile qualities before they are felt. All that is really known is that the visual appearance in question, together with touch, will lead to certain sensations, which can necessarily be determined in terms of the visual appearance, since otherwise they could not be inferred from it.
We can now give a statement of the experienced facts concerning the blue spectacles, which will supply an interpretation of common-sense beliefs without assuming anything beyond the existence of sensible objects at the times when they are sensible. By experience of the correlation of touch and sight sensations, we become able to associate a certain place in touch-space with a certain corresponding place in sight-space. Sometimes, namely in the case of transparent things, we find that there is a tangible object in a touch-place without there being any visible object in the corresponding sight-place. But in such a case as that of the blue spectacles, we find that whatever object is visible beyond the empty sight-place in the same line of sight has a different colour from what it has when there is no tangible object in the intervening touch-place; and as we move the tangible object in touch-space, the blue patch moves in sight-space. If now we find a blue patch moving in this way in sight-space, when we have no sensible experience of an intervening tangible object, we nevertheless infer that, if we put our hand at a certain place in touch-space, we should experience a certain touch-sensation. If we are to avoid non-sensible objects, this must be taken as the whole of our meaning when we say that the blue spectacles are in a certain place, though we have not touched them, and have only seen other things rendered blue by their interposition.
I think it may be laid down quite generally that, in so far as physics or common sense is verifiable, it must be capable of interpretation in terms of actual sense-data alone. The reason for this is simple. Verification consists always in the occurrence of an expected sense-datum. Astronomers tell us there will be an eclipse of the moon: we look at the moon, and find the earth's shadow biting into it, that is to say, we see an appearance quite different from that of the usual full moon. Now if an expected sense-datum constitutes a verification, what was asserted must have been about sense-data; or, at any rate, if part of what was asserted was not about sense-data, then only the other part has been verified. There is in fact a certain regularity or conformity to law about the occurrence of sense-data, but the sense-data that occur at one time are often causally connected with those that occur at quite other times, and not, or at least not very closely, with those that occur at neighbouring times. If I look at the moon and immediately afterwards hear a train coming, there is no very close causal connection between my two sense-data; but if I look at the moon on two nights a week apart, there is a very close causal connection between the two sense-data. The simplest, or at least the easiest, statement of the connection is obtained by imagining a “real” moon which goes on whether I look at it or not, providing a series of possible sense-data of which only those are actual which belong to moments when I choose to look at the moon.
But the degree of verification obtainable in this way is very small. It must be remembered that, at our present level of doubt, we are not at liberty to accept testimony. When we hear certain noises, which are those we should utter if we wished to express a certain thought, we assume that that thought, or one very like it, has been in another mind, and has given rise to the expression which we hear. If at the same time we see a body resembling our own, moving its lips as we move ours when we speak, we cannot resist the belief that it is alive, and that the feelings inside it continue when we are not looking at it. When we see our friend drop a weight upon his toe, and hear him say—what we should say in similar circumstances, the phenomena can no doubt be explained without assuming that he is anything but a series of shapes and noises seen and heard by us, but practically no man is so infected with philosophy as not to be quite certain that his friend has felt the same kind of pain as he himself would feel. We will consider the legitimacy of this belief presently; for the moment, I only wish to point out that it needs the same kind of justification as our belief that the moon exists when we do not see it, and that, without it, testimony heard or read is reduced to noises and shapes, and cannot be regarded as evidence of the facts which it reports. The verification of physics which is possible at our present level is, therefore, only that degree of verification which is possible by one man's unaided observations, which will not carry us very far towards the establishment of a whole science.
Before proceeding further, let us summarise the argument so far as it has gone. The problem is: “Can the existence of anything other than our own hard data be inferred from these data?” It is a mistake to state the problem in the form: “Can we know of the existence of anything other than ourselves and our states?” or: “Can we know of the existence of anything independent of ourselves?” because of the extreme difficulty of defining “self” and “independent” precisely. The felt passivity of sensation is irrelevant, since, even if it proved anything, it could only prove that sensations are caused by sensible objects. The natural naïve belief is that things seen persist, when unseen, exactly or approximately as they appeared when seen; but this belief tends to be dispelled by the fact that what common sense regards as the appearance of one object changes with what common sense regards as changes in the point of view and in the intervening medium, including in the latter our own sense-organs and nerves and brain. This fact, as just stated, assumes, however, the common-sense world of stable objects which it professes to call in question; hence, before we can discover its precise bearing on our problem, we must find a way of stating it which does not involve any of the assumptions which it is designed to render doubtful. What we then find, as the bare outcome of experience, is that gradual changes in certain sense-data are correlated with gradual changes in certain others, or (in the case of bodily motions) with the other sense-data themselves.
The assumption that sensible objects persist after they have ceased to be sensible—for example, that the hardness of a visible body, which has been discovered by touch, continues when the body is no longer touched—may be replaced by the statement that the effects of sensible objects persist, i.e. that what happens now can only be accounted for, in many cases, by taking account of what happened at an earlier time. Everything that one man, by his own personal experience, can verify in the account of the world given by common sense and physics, will be explicable by some such means, since verification consists merely in the occurrence of an expected sense-datum. But what depends upon testimony, whether heard or read, cannot be explained in this way, since testimony depends upon the existence of minds other than our own, and thus requires a knowledge of something not given in sense. But before examining the question of our knowledge of other minds, let us return to the question of the thing-in-itself, namely, to the theory that what exists at times when we are not perceiving a given sensible object is something quite unlike that object, something which, together with us and our sense-organs, causes our sensations, but is never itself given in sensation.
The thing-in-itself, when we start from common-sense assumptions, is a fairly natural outcome of the difficulties due to the changing appearances of what is supposed to be one object. It is supposed that the table (for example) causes our sense-data of sight and touch, but must, since these are altered by the point of view and the intervening medium, be quite different from the sense-data to which it gives rise. There is, in this theory, a tendency to a confusion from which it derives some of its plausibility, namely, the confusion between a sensation as a psychical occurrence and its object. A patch of colour, even if it only exists when it is seen, is still something quite different from the seeing of it: the seeing of it is mental, but the patch of colour is not. This confusion, however, can be avoided without our necessarily abandoning the theory we are examining. The objection to it, I think, lies in its failure to realise the radical nature of the reconstruction demanded by the difficulties to which it points. We cannot speak legitimately of changes in the point of view and the intervening medium until we have already constructed some world more stable than that of momentary sensation. Our discussion of the blue spectacles and the walk round the table has, I hope, made this clear. But what remains far from clear is the nature of the reconstruction required.