Part 6 (1/2)

'But then,' added he, speaking from his own point of view, 'to enjoy honour when alive one would readily die on a war-s.h.i.+eld or in the headsman's basket.'

So he rejected the pigs' point of view and adopted his own point of view. In what sense, then, was he different from the pigs?”

I much fear that the evolutionists too often resemble the Grand Augur and the pigs.

The ethical element which has been prominent in many of the most famous systems of philosophy is, in my opinion, one of the most serious obstacles to the victory of scientific method in the investigation of philosophical questions. Human ethical notions, as Chuang Tzu perceived, are essentially anthropocentric, and involve, when used in metaphysics, an attempt, however veiled, to legislate for the universe on the basis of the present desires of men. In this way they interfere with that receptivity to fact which is the essence of the scientific att.i.tude towards the world. To regard ethical notions as a key to the understanding of the world is essentially pre-Copernican. It is to make man, with the hopes and ideals which he happens to have at the present moment, the centre of the universe and the interpreter of its supposed aims and purposes. Ethical metaphysics is fundamentally an attempt, however disguised, to give legislative force to our own wishes. This may, of course, be questioned, but I think that it is confirmed by a consideration of the way in which ethical notions arise. Ethics is essentially a product of the gregarious instinct, that is to say, of the instinct to co-operate with those who are to form our own group against those who belong to other groups. Those who belong to our own group are good; those who belong to hostile groups are wicked. The ends which are pursued by our own group are desirable ends, the ends pursued by hostile groups are nefarious. The subjectivity of this situation is not apparent to the gregarious animal, which feels that the general principles of justice are on the side of its own herd. When the animal has arrived at the dignity of the metaphysician, it invents ethics as the embodiment of its belief in the justice of its own herd. So the Grand Augur invokes ethics as the justification of Augurs in their conflicts with pigs.

But, it may be said, this view of ethics takes no account of such truly ethical notions as that of self-sacrifice. This, however, would be a mistake. The success of gregarious animals in the struggle for existence depends upon co-operation within the herd, and co-operation requires sacrifice, to some extent, of what would otherwise be the interest of the individual. Hence arises a conflict of desires and instincts, since both self-preservation and the preservation of the herd are biological ends to the individual. Ethics is in origin the art of recommending to others the sacrifices required for co-operation with oneself. Hence, by reflexion, it comes, through the operation of social justice, to recommend sacrifices by oneself, but all ethics, however refined, remains more or less subjective. Even vegetarians do not hesitate, for example, to save the life of a man in a fever, although in doing so they destroy the lives of many millions of microbes. The view of the world taken by the philosophy derived from ethical notions is thus never impartial and therefore never fully scientific. As compared with science, it fails to achieve the imaginative liberation from self which is necessary to such understanding of the world as man can hope to achieve, and the philosophy which it inspires is always more or less parochial, more or less infected with the prejudices of a time and a place.

I do not deny the importance or value, within its own sphere, of the kind of philosophy which is inspired by ethical notions. The ethical work of Spinoza, for example, appears to me of the very highest significance, but what is valuable in such work is not any metaphysical theory as to the nature of the world to which it may give rise, nor indeed anything which can be proved or disproved by argument. What is valuable is the indication of some new way of feeling towards life and the world, some way of feeling by which our own existence can acquire more of the characteristics which we must deeply desire. The value of such work, however immeasurable it is, belongs with practice and not with theory. Such theoretic importance as it may possess is only in relation to human nature, not in relation to the world at large. The scientific philosophy, therefore, which aims only at understanding the world and not directly at any other improvement of human life, cannot take account of ethical notions without being turned aside from that submission to fact which is the essence of the scientific temper.

II

If the notion of the universe and the notion of good and evil are extruded from scientific philosophy, it may be asked what specific problems remain for the philosopher as opposed to the man of science?

It would be difficult to give a precise answer to this question, but certain characteristics may be noted as distinguis.h.i.+ng the province of philosophy from that of the special sciences.

In the first place a philosophical proposition must be general. It must not deal specially with things on the surface of the earth, or with the solar system, or with any other portion of s.p.a.ce and time. It is this need of generality which has led to the belief that philosophy deals with the universe as a whole. I do not believe that this belief is justified, but I do believe that a philosophical proposition must be applicable to everything that exists or may exist. It might be supposed that this admission would be scarcely distinguishable from the view which I wish to reject. This, however, would be an error, and an important one. The traditional view would make the universe itself the subject of various predicates which could not be applied to any particular thing in the universe, and the ascription of such peculiar predicates to the universe would be the special business of philosophy. I maintain, on the contrary, that there are no propositions of which the ”universe” is the subject; in other words, that there is no such thing as the ”universe.” What I do maintain is that there are general propositions which may be a.s.serted of each individual thing, such as the propositions of logic. This does not involve that all the things there are form a whole which could be regarded as another thing and be made the subject of predicates. It involves only the a.s.sertion that there are properties which belong to each separate thing, not that there are properties belonging to the whole of things collectively. The philosophy which I wish to advocate may be called logical atomism or absolute pluralism, because, while maintaining that there are many things, it denies that there is a whole composed of those things. We shall see, therefore, that philosophical propositions, instead of being concerned with the whole of things collectively, are concerned with all things distributively; and not only must they be concerned with all things, but they must be concerned with such properties of all things as do not depend upon the accidental nature of the things that there happen to be, but are true of any possible world, independently of such facts as can only be discovered by our senses.

This brings us to a second characteristic of philosophical propositions, namely, that they must be _a priori_. A philosophical proposition must be such as can be neither proved nor disproved by empirical evidence. Too often we find in philosophical books arguments based upon the course of history, or the convolutions of the brain, or the eyes of sh.e.l.l-fish. Special and accidental facts of this kind are irrelevant to philosophy, which must make only such a.s.sertions as would be equally true however the actual world were const.i.tuted.

We may sum up these two characteristics of philosophical propositions by saying that _philosophy is the science of the possible_. But this statement unexplained is liable to be misleading, since it may be thought that the possible is something other than the general, whereas in fact the two are indistinguishable.

Philosophy, if what has been said is correct, becomes indistinguishable from logic as that word has now come to be used. The study of logic consists, broadly speaking, of two not very sharply distinguished portions. On the one hand it is concerned with those general statements which can be made concerning everything without mentioning any one thing or predicate or relation, such for example as ”if _x_ is a member of the cla.s.s a and every member of a is a member of , then _x_ is a member of the cla.s.s , whatever _x_, a, and may be.” On the other hand, it is concerned with the a.n.a.lysis and enumeration of logical _forms_, i.e. with the kinds of propositions that may occur, with the various types of facts, and with the cla.s.sification of the const.i.tuents of facts. In this way logic provides an inventory of possibilities, a repertory of abstractly tenable hypotheses.

It might be thought that such a study would be too vague and too general to be of any very great importance, and that, if its problems became at any point sufficiently definite, they would be merged in the problems of some special science. It appears, however, that this is not the case. In some problems, for example, the a.n.a.lysis of s.p.a.ce and time, the nature of perception, or the theory of judgment, the discovery of the logical form of the facts involved is the hardest part of the work and the part whose performance has been most lacking hitherto. It is chiefly for want of the right logical hypothesis that such problems have hitherto been treated in such an unsatisfactory manner, and have given rise to those contradictions or antinomies in which the enemies of reason among philosophers have at all times delighted.

By concentrating attention upon the investigation of logical forms, it becomes possible at last for philosophy to deal with its problems piecemeal, and to obtain, as the sciences do, such partial and probably not wholly correct results as subsequent investigation can utilise even while it supplements and improves them. Most philosophies. .h.i.therto have been constructed all in one block, in such a way that, if they were not wholly correct, they were wholly incorrect, and could not be used as a basis for further investigations. It is chiefly owing to this fact that philosophy, unlike science, has. .h.i.therto been unprogressive, because each original philosopher has had to begin the work again from the beginning, without being able to accept anything definite from the work of his predecessors. A scientific philosophy such as I wish to recommend will be piecemeal and tentative like other sciences; above all, it will be able to invent hypotheses which, even if they are not wholly true, will yet remain fruitful after the necessary corrections have been made. This possibility of successive approximations to the truth is, more than anything else, the source of the triumphs of science, and to transfer this possibility to philosophy is to ensure a progress in method whose importance it would be almost impossible to exaggerate.

The essence of philosophy as thus conceived is a.n.a.lysis, not synthesis. To build up systems of the world, like Heine's German professor who knit together fragments of life and made an intelligible system out of them, is not, I believe, any more feasible than the discovery of the philosopher's stone. What is feasible is the understanding of general forms, and the division of traditional problems into a number of separate and less baffling questions.

”Divide and conquer” is the maxim of success here as elsewhere.

Let us ill.u.s.trate these somewhat general maxims by examining their application to the philosophy of s.p.a.ce, for it is only in application that the meaning or importance of a method can be understood. Suppose we are confronted with the problem of s.p.a.ce as presented in Kant's Transcendental aesthetic, and suppose we wish to discover what are the elements of the problem and what hope there is of obtaining a solution of them. It will soon appear that three entirely distinct problems, belonging to different studies, and requiring different methods for their solution, have been confusedly combined in the supposed single problem with which Kant is concerned. There is a problem of logic, a problem of physics, and a problem of theory of knowledge. Of these three, the problem of logic can be solved exactly and perfectly; the problem of physics can probably be solved with as great a degree of certainty and as great an approach to exactness as can be hoped in an empirical region; the problem of theory of knowledge, however, remains very obscure and very difficult to deal with. Let us see how these three problems arise.

(1) The logical problem has arisen through the suggestions of non-Euclidean geometry. Given a body of geometrical propositions, it is not difficult to find a minimum statement of the axioms from which this body of propositions can be deduced. It is also not difficult, by dropping or altering some of these axioms, to obtain a more general or a different geometry, having, from the point of view of pure mathematics, the same logical coherence and the same t.i.tle to respect as the more familiar Euclidean geometry. The Euclidean geometry itself is true perhaps of actual s.p.a.ce (though this is doubtful), but certainly of an infinite number of purely arithmetical systems, each of which, from the point of view of abstract logic, has an equal and indefeasible right to be called a Euclidean s.p.a.ce. Thus s.p.a.ce as an object of logical or mathematical study loses its uniqueness; not only are there many kinds of s.p.a.ces, but there are an infinity of examples of each kind, though it is difficult to find any kind of which the s.p.a.ce of physics may be an example, and it is impossible to find any kind of which the s.p.a.ce of physics is certainly an example. As an ill.u.s.tration of one possible logical system of geometry we may consider all relations of three terms which are a.n.a.logous in certain formal respects to the relation ”between” as it appears to be in actual s.p.a.ce. A s.p.a.ce is then defined by means of one such three-term relation. The points of the s.p.a.ce are all the terms which have this relation to something or other, and their order in the s.p.a.ce in question is determined by this relation. The points of one s.p.a.ce are necessarily also points of other s.p.a.ces, since there are necessarily other three-term relations having those same points for their field.

The s.p.a.ce in fact is not determined by the cla.s.s of its points, but by the ordering three-term relation. When enough abstract logical properties of such relations have been enumerated to determine the resulting kind of geometry, say, for example, Euclidean geometry, it becomes unnecessary for the pure geometer in his abstract capacity to distinguish between the various relations which have all these properties. He considers the whole cla.s.s of such relations, not any single one among them. Thus in studying a given kind of geometry the pure mathematician is studying a certain cla.s.s of relations defined by means of certain abstract logical properties which take the place of what used to be called axioms. The nature of geometrical _reasoning_ therefore is purely deductive and purely logical; if any special epistemological peculiarities are to be found in geometry, it must not be in the reasoning, but in our knowledge concerning the axioms in some given s.p.a.ce.

(2) The physical problem of s.p.a.ce is both more interesting and more difficult than the logical problem. The physical problem may be stated as follows: to find in the physical world, or to construct from physical materials, a s.p.a.ce of one of the kinds enumerated by the logical treatment of geometry. This problem derives its difficulty from the attempt to accommodate to the roughness and vagueness of the real world some system possessing the logical clearness and exact.i.tude of pure mathematics. That this can be done with a certain degree of approximation is fairly evident If I see three people _A_, _B_, and _C_ sitting in a row, I become aware of the fact which may be expressed by saying that _B_ is between _A_ and _C_ rather than that _A_ is between _B_ and _C_, or _C_ is between _A_ and _B_. This relation of ”between” which is thus perceived to hold has some of the abstract logical properties of those three-term relations which, we saw, give rise to a geometry, but its properties fail to be exact, and are not, as empirically given, amenable to the kind of treatment at which geometry aims. In abstract geometry we deal with points, straight lines, and planes; but the three people _A_, _B_, and _C_ whom I see sitting in a row are not exactly points, nor is the row exactly a straight line. Nevertheless physics, which formally a.s.sumes a s.p.a.ce containing points, straight lines, and planes, is found empirically to give results applicable to the sensible world. It must therefore be possible to find an interpretation of the points, straight lines, and planes of physics in terms of physical data, or at any rate in terms of data together with such hypothetical additions as seem least open to question. Since all data suffer from a lack of mathematical precision through being of a certain size and somewhat vague in outline, it is plain that if such a notion as that of a point is to find any application to empirical material, the point must be neither a datum nor a hypothetical addition to data, but a _construction_ by means of data with their hypothetical additions. It is obvious that any hypothetical filling out of data is less dubious and unsatisfactory when the additions are closely a.n.a.logous to data than when they are of a radically different sort. To a.s.sume, for example, that objects which we see continue, after we have turned away our eyes, to be more or less a.n.a.logous to what they were while we were looking, is a less violent a.s.sumption than to a.s.sume that such objects are composed of an infinite number of mathematical points. Hence in the physical study of the geometry of physical s.p.a.ce, points must not be a.s.sumed _ab initio_ as they are in the logical treatment of geometry, but must be constructed as systems composed of data and hypothetical a.n.a.logues of data. We are thus led naturally to define a physical point as a certain cla.s.s of those objects which are the ultimate const.i.tuents of the physical world. It will be the cla.s.s of all those objects which, as one would naturally say, _contain_ the point. To secure a definition giving this result, without previously a.s.suming that physical objects are composed of points, is an agreeable problem in mathematical logic. The solution of this problem and the perception of its importance are due to my friend Dr. Whitehead. The oddity of regarding a point as a cla.s.s of physical ent.i.ties wears off with familiarity, and ought in any case not to be felt by those who maintain, as practically every one does, that points are mathematical fictions. The word ”fiction” is used glibly in such connexions by many men who seem not to feel the necessity of explaining how it can come about that a fiction can be so useful in the study of the actual world as the points of mathematical physics have been found to be. By our definition, which regards a point as a cla.s.s of physical objects, it is explained both how the use of points can lead to important physical results, and how we can nevertheless avoid the a.s.sumption that points are themselves ent.i.ties in the physical world.

Many of the mathematically convenient properties of abstract logical s.p.a.ces cannot be either known to belong or known not to belong to the s.p.a.ce of physics. Such are all the properties connected with continuity.

For to know that actual s.p.a.ce has these properties would require an infinite exactness of sense-perception. If actual s.p.a.ce is continuous, there are nevertheless many possible non-continuous s.p.a.ces which will be empirically indistinguishable from it; and, conversely, actual s.p.a.ce may be non-continuous and yet empirically indistinguishable from a possible continuous s.p.a.ce. Continuity, therefore, though obtainable in the _a priori_ region of arithmetic, is not with certainty obtainable in the s.p.a.ce or time of the physical world: whether these are continuous or not would seem to be a question not only unanswered but for ever unanswerable. From the point of view of philosophy, however, the discovery that a question is unanswerable is as complete an answer as any that could possibly be obtained. And from the point of view of physics, where no empirical means of distinction can be found, there can be no empirical objection to the mathematically simplest a.s.sumption, which is that of continuity.

The subject of the physical theory of s.p.a.ce is a very large one, hitherto little explored. It is a.s.sociated with a similar theory of time, and both have been forced upon the attention of philosophically minded physicists by the discussions which have raged concerning the theory of relativity.

(3) The problem with which Kant is concerned in the Transcendental aesthetic is primarily the epistemological problem: ”How do we come to have knowledge of geometry _a priori_?” By the distinction between the logical and physical problems of geometry, the bearing and scope of this question are greatly altered. Our knowledge of pure geometry is _a priori_ but is wholly logical. Our knowledge of physical geometry is synthetic, but is not _a priori_. Our knowledge of pure geometry is hypothetical, and does not enable us to a.s.sert, for example, that the axiom of parallels is true in the physical world. Our knowledge of physical geometry, while it does enable us to a.s.sert that this axiom is approximately verified, does not, owing to the inevitable inexact.i.tude of observation, enable us to a.s.sert that it is verified _exactly_. Thus, with the separation which we have made between pure geometry and the geometry of physics, the Kantian problem collapses.

To the question, ”How is synthetic _a priori_ knowledge possible?” we can now reply, at any rate so far as geometry is concerned, ”It is not possible,” if ”synthetic” means ”not deducible from logic alone.” Our knowledge of geometry, like the rest of our knowledge, is derived partly from logic, partly from sense, and the peculiar position which in Kant's day geometry appeared to occupy is seen now to be a delusion. There are still some philosophers, it is true, who maintain that our knowledge that the axiom of parallels, for example, is true of actual s.p.a.ce, is not to be accounted for empirically, but is as Kant maintained derived from an _a priori_ intuition. This position is not logically refutable, but I think it loses all plausibility as soon as we realise how complicated and derivative is the notion of physical s.p.a.ce. As we have seen, the application of geometry to the physical world in no way demands that there should really be points and straight lines among physical ent.i.ties. The principle of economy, therefore, demands that we should abstain from a.s.suming the existence of points and straight lines. As soon, however, as we accept the view that points and straight lines are complicated constructions by means of cla.s.ses of physical ent.i.ties, the hypothesis that we have an _a priori_ intuition enabling us to know what happens to straight lines when they are produced indefinitely becomes extremely strained and harsh; nor do I think that such an hypothesis would ever have arisen in the mind of a philosopher who had grasped the nature of physical s.p.a.ce. Kant, under the influence of Newton, adopted, though with some vacillation, the hypothesis of absolute s.p.a.ce, and this hypothesis, though logically un.o.bjectionable, is removed by Occam's razor, since absolute s.p.a.ce is an unnecessary ent.i.ty in the explanation of the physical world. Although, therefore, we cannot refute the Kantian theory of an _a priori_ intuition, we can remove its grounds one by one through an a.n.a.lysis of the problem. Thus, here as in many other philosophical questions, the a.n.a.lytic method, while not capable of arriving at a demonstrative result, is nevertheless capable of showing that all the positive grounds in favour of a certain theory are fallacious and that a less unnatural theory is capable of accounting for the facts.

Another question by which the capacity of the a.n.a.lytic method can be shown is the question of realism. Both those who advocate and those who combat realism seem to me to be far from clear as to the nature of the problem which they are discussing. If we ask: ”Are our objects of perception _real_ and are they _independent_ of the percipient?” it must be supposed that we attach some meaning to the words ”real” and ”independent,” and yet, if either side in the controversy of realism is asked to define these two words, their answer is pretty sure to embody confusions such as logical a.n.a.lysis will reveal.

Let us begin with the word ”real.” There certainly are objects of perception, and therefore, if the question whether these objects are real is to be a substantial question, there must be in the world two sorts of objects, namely, the real and the unreal, and yet the unreal is supposed to be essentially what there is not. The question what properties must belong to an object in order to make it real is one to which an adequate answer is seldom if ever forthcoming. There is of course the Hegelian answer, that the real is the self-consistent and that nothing is self-consistent except the Whole; but this answer, true or false, is not relevant in our present discussion, which moves on a lower plane and is concerned with the status of objects of perception among other objects of equal fragmentariness. Objects of perception are contrasted, in the discussions concerning realism, rather with psychical states on the one hand and matter on the other hand than with the all-inclusive whole of things. The question we have therefore to consider is the question as to what can be meant by a.s.signing ”reality” to some but not all of the ent.i.ties that make up the world. Two elements, I think, make up what is felt rather than thought when the word ”reality” is used in this sense. A thing is real if it persists at times when it is not perceived; or again, a thing is real when it is correlated with other things in a way which experience has led us to expect. It will be seen that reality in either of these senses is by no means necessary to a thing, and that in fact there might be a whole world in which nothing was real in either of these senses. It might turn out that the objects of perception failed of reality in one or both of these respects, without its being in any way deducible that they are not parts of the external world with which physics deals. Similar remarks will apply to the word ”independent.”

Most of the a.s.sociations of this word are bound up with ideas as to causation which it is not now possible to maintain. _A_ is independent of _B_ when _B_ is not an indispensable part of the _cause_ of _A_.