Part 2 (1/2)

These latter professed a theory of the structure of knowledge which the philosophers could easily show to be grotesque, but the retort was always ready to hand that at any rate Science seemed somehow to be getting somewhere while Philosophy appeared to lead nowhere in particular.

The conditions for mutual understanding have now greatly improved, thanks mainly to the labour of mathematicians with philosophical minds on the principles of their own science. If we admit that mathematics is true--and it seems quite impossible to avoid the admission--we can now see that neither the traditional Kant-Hegel doctrine nor the traditional sensationalistic empiricism can be sound. Not to speak of inquiries which have been actually created within our own life-time, it may fairly be said that the whole of pure mathematics has been shown, or is on the verge of being shown, to form a body of conclusions rigidly deduced from a few unproved postulates which are of a purely logical character.

Descartes has proved to be right in his view that the exceptional certainty men have always ascribed to mathematical knowledge is not due to the supposed restriction of the science to relation of number and magnitude--there is a good deal of pure mathematics which deals with neither--but to the simplicity of its undefined notions and the high plausibility of its unproved postulates. Bit by bit the bad logic has been purged out of the Calculus and the Theory of Functions and these branches of study have been made into patterns of accurate reasoning on exactly stated premisses. It has appeared in the process that the alleged contradictions in mathematics upon which the followers of Kant and Hegel laid stress do not really exist at all, and only seemed to exist because mathematicians in the past expressed their meaning so awkwardly. Further, it has been established that the most fundamental idea of all in mathematics is not that of number or magnitude but that of _order_ in a series and that the whole doctrine of series is only a branch of the logic of Relations. From the logical doctrine of serial order we seem to be able to deduce the whole arithmetic of integers, and from this it is easy to deduce further the arithmetic of fractions and the arithmetic or algebra of the 'real' and 'complex' numbers. As the logical principles of serial order enable us to deal with infinite as well as with finite series, it further follows that the Calculus and the Theory of Functions can now be built up without a single contradiction or breach of logic. The puzzles about the infinitely great and infinitely small, which used to throw a cloud of mystery over the 'higher' branches of Mathematics, have been finally dissipated by the discovery that the 'infinite' is readily definable in purely ordinal terms and that the 'infinitesimal' does not really enter into the misnamed 'Infinitesimal Calculus' at all. Arithmetic and the theory of serial order have been shown to be the sufficient basis of the whole science which, as Plato long ago remarked, is 'very inappropriately called geometry'. A resume of the work which has been thus done may be found in the stately volumes of the _Principia Mathematica_ of Whitehead and Russell, or--to a large extent--in the _Formulario Matematico_ of Professor Peano. Of other works dealing with the subject, the finest from the strictly philosophical point of view is probably that of Professor G. Frege on _The Fundamental Laws of Arithmetic_. The general result of the whole development is that we are now at last definitely freed from the haunting fear that there is some hidden contradiction in the principles of the exact sciences which would vitiate all our knowledge of universal truths. This removes the chief, if not the only ground for the view that all the truths of Science are only 'partial'.

At the same time, the proof that pure mathematics is a strictly logical development and that all its conclusions are of the hypothetical form, 'if _a b c_ ..., then _x_' definitely disproves the popular Kantian doctrine that _sense_-data are a necessary const.i.tuent of scientific knowledge. And with this dogma falls the _main_ ground for the denial that knowledge about the soul and G.o.d is attainable. The recovery of a sounder philosophical method has, as Mr. Russell himself says, disposed of what was yesterday the accepted view that the function of Philosophy is to narrow down the range of possible interpretations of facts until only one is left. Philosophy rather opens doors than shuts them. It multiplies the number of logically possible sets of premisses from which consequences agreeing with empirical facts may be inferred. Mr.

Russell's unreasoned anti-theism seems to me to make him curiously blind to an obvious application of this principle. On the other side, the revived attention to the logical methods of the sciences is killing the crude sensationalism of the days which saw the first publication of Mach's _Science of Mechanics_ and Pearson's _Grammar of Science_. The claims of 'induction' to be a method of establis.h.i.+ng truths may be fairly said to have been completely exposed. It is clearer now than it was when Kant made the observation that each of the 'sciences' contains just so much science as it contains mathematics, and that the Critical Philosophy was fully justified in insisting that all science implies universal _a priori_ postulates, though it went wrong in thinking that these postulates are laws of the working of the human mind or are 'put into' things by the human mind. How far Science has moved away from crude sensationalistic empiricism may be estimated by a comparison of the successive editions of the _Grammar of Science_. It must always have been apparent to an attentive reader that the chapters of that fascinating book which deal directly with the leading principles of Physics and Biology are of very different quality from the earlier chapters which expound, with many self-contradictions and much wrath against metaphysicians and theologians whom the writer seems never to have tried to understand, the fantastic 'metaphysics of the telephone-exchange'. But the difference of quality is more marked in the second edition than in the first, and in the (alas!) unfinished third edition than in the second. So far, then, as the problem of the unification of the sciences is concerned, the old prejudices which divided the rationalist philosopher from the sensationalist scientific man seem to have been, in the main, dissipated. We can see now that what used to be called Philosophy and what used to be called Science are both parts of one task, that they have a common method and presuppose a common body of principles.

So far it may be said with truth that Philosophy is becoming more faithful than Kant was himself to the leading ideas of 'Criticism', and again that it is reverting once more, as it reverted in the days of Galileo, to the positions of Plato. I do not mean that the whole programme has been completely executed and that there is nothing for a successor of Frege or Russell to do. It is instructive to observe that at the very end of the great work on arithmetic to which I have referred Frege found himself compelled by difficulties which had been overlooked until Russell called attention to them to add an appendix confessing that there was a single important flaw in his elaborate logical construction of the principles of arithmetic. He had shown that if there are certain things called 'integers', defined as he had defined them, the whole of arithmetic follows. But he had not shown that there _is_ any object answering to his definition of an integer, and the logical researches of Russell had thrown some doubt on the point. This proved that some restatement of the initial a.s.sumptions of the theory was needed. Since the date of Frege's appendix (1903), Mr. Russell and others have done something towards the necessary rectification, and the resulting 'Theory of Types' is pretty certainly one of the most important contributions ever made to logical doctrine, but it may still be reasonably doubted whether the 'Theory of Types', as expounded by Whitehead and Russell in their _Principia Mathematica_, is the last word required. At any rate, it seems clear that it is a great step on the right road to the solution of a most difficult problem.

There still remains the greatest problem of all, the harmonization of Science and Life. I cannot believe that this problem is an illegitimate one, or that we must sit down content to accept the severance of 'fact'

and 'value' as final for our thought. Even the unification of the sciences itself remains imperfect so long as we treat it as merely something which 'happens to be the case' that there are many things and many kinds of things in the universe and also a number of relations in which they 'happen' to stand. It is significant that in his later writings Mr. Russell has been driven to abandon the concept of personal ident.i.ty, which is so fundamental for practical life, and to a.s.sert that each of us is not one man but an infinite series of men of whom each only exists for a mathematical instant. I am sure that such a theory requires the abandonment of the whole notion of value as an illusion, and even more sure that it is ruinous to any practical rule of living, and I cannot believe in the 'philosophy' of any man who is satisfied to base his practice on what he regards as detected illusion. Hence I find myself strongly in sympathy with my eminent Italian colleague Professor Varisco, who has devoted his two chief works (_I Ma.s.simi Problemi_ and _Conosci Te Stesso_) to an exceedingly subtle attempt to show that 'what ought to be', in Platonic phrase 'the Good', is in the end the single principle from which all things derive their existence as well as their value. Mr. Russell's philosophy saves us half Plato, and that is much, but I am convinced that it is whole and entire Plato whom a profounder philosophy would preserve for us. I believe personally that such a philosophy will be led, as Plato was in the end led, to a theistic interpretation of life, that it is in the living G.o.d Who is over all, blessed for ever, that it will find the common source of fact and value.

And again I believe that it will be led to its result very largely by what is, after all, perhaps the profoundest thought of Kant, the conviction that the most illuminating fact of all is the _fact_ of the absolute and unconditional obligatoriness of the law of right. It is precisely here that fact and value most obviously meet. For when we ask ourselves what in fact we are, we shall a.s.suredly find no true answer to this question about what _is_ if we forget that we are first and foremost beings who _ought_ to follow a certain way of life, and to follow it for no other reason than that it is good. But I cannot, of course, offer reasons here for this conviction, though I am sure that adequate reasons can be given. Here I must be content to state this ultimate conviction as a 'theological superst.i.tion', or, as I should prefer to put it with a little more certainty, as a matter of faith. The alternative is to treat the world as a stupid, and possibly malicious, bad joke.

_Note_.--It may be thought that something should have been said about the revolt against authority and tradition which has styled itself variously 'Pragmatism' and 'Humanism', and also about the recent vogue of Bergsonianism. I may in part excuse my silence by the plea that both movements are, in my judgement, already spent forces. If I must say more than this, I would only remark about Pragmatism that I could speak of it with more confidence if its representatives themselves were more agreed as to its precise principles. At present I can discern little agreement among them about anything except that they all show a great impatience with the business of thinking things quietly and steadily out, and that none of them seems to appreciate the importance of the 'critical'

problem. 'Pragmatism' thus seems to me less a definite way of thinking than a collective name for a series of 'guesses at truth'. Some of the guesses may be very lucky ones, but I, at least, can hardly take the claims of unmethodic guessing to be a philosophy very seriously. To 'give and receive argument' appears to me to be of the very essence of Philosophy. As for M. Bergson, I yield to no one in admiration for his brilliancy as a stylist and the happiness of many of his ill.u.s.trations.

But I have always found it difficult to grasp his central idea--if he really has one--because his whole doctrine has always seemed to me to be based upon a couple of elementary blunders which will be found in the opening chapter of his _Donnees Immediates de la Conscience_. We are there called on to reject the intellect in Philosophy on the grounds (1) that, being originally developed in the services of practical needs, it can at best tell us how to find our way about among the bodies around us, and is thus debarred from knowing more than the _outsides_ of things; (2) that its typical achievement is therefore geometry, and geometry, _because it can measure only straight lines_, necessarily misconceives the true character of 'real duration'. Now, as to the first point, I should have thought it obvious that the establishment of a _modus vivendi_ with one's fellows has always been as much of a practical need as the avoidance of stones and pit-falls, and the alleged conclusion about the defects of the intellect does not therefore seem to me to follow from M. Bergson's premisses, even if we had any reason, as I do not see that we have, to accept the premisses. And as to the second point, I would ask whether M. Bergson possesses a clock or a watch, and if he has, how he supposes time is measured on them? He seems to me to have forgotten the elementary fact that angles can be measured as well as straight lines. (I might add that he makes the further curious a.s.sumption that all geometry is metrical.) It may be that something would be left of the Bergsonian philosophy if one eliminated the consequences of these initial blunders, but I do not know what the remainder would be. At any rate, the anti-intellectualism which M.

Bergson and his disciple, Professor Carr, seem to regard as fundamental will have to go, unless different and better grounds can be found for it. I must leave it to others to judge of the adequacy of this apology.

FOR REFERENCE

Varisco, _The Great Problem_ (Macmillan).

Varisco, _Know Thyself_ (Macmillan).

Aliotta, _The Idealistic Reaction against Science_ (Macmillan).

Bertrand Russell, _Our Knowledge of the External World_ (Open Court Publis.h.i.+ng Co.).

Bertrand Russell, _The Problems of Philosophy_ (Home University Library).

A.N. Whitehead, _The Principles of Natural Knowledge_ (Cambridge Press).

G.E. Moore, _Ethics_ (H.U.L.).

W. McDougall, _Philosophy_ (H.U.L.).

A.N. Whitehead, _Introduction to Mathematics_ (H.U.L.).

III

RECENT DEVELOPMENTS IN EUROPEAN THOUGHT ON THE EVOLUTION OF RELIGION

F.B. JEVONS

The living beings that exist or have existed upon the earth are of kinds innumerable; and, in the opinion of man, the chief of them all is mankind. Man, for the simple reason that he is man, is anthropomorphic in all his judgements and not merely in his religious conceptions; he holds himself to be the standard and measure in all things. If his right so to regard himself were challenged, if he were called upon to justify himself for having taken his foot as a unit of measurement, or his fingers as the basis of his system of numbers, he might reply that anything will serve as a standard for weights and measures, provided that it never varies, but is always the same whenever referred to. But the reply, valid though it is, does not do full justice to man: it leaves room for the suspicion that a standard is something chosen by man in a purely arbitrary manner and without reference to the facts of nature. If that were really the case, then man's conception of himself as superior to the other animals on earth might be but a prejudice of an arbitrary kind. When, however, we consider, from the point of view of evolution, the place of man among the other animals that occupy or have occupied the earth, it is indubitable that the human organism is in point of time the latest evolved and the human brain is in point of complexity and efficiency the most highly developed. Further, the evidence of embryology goes to show that the organism which has eventually become human became so only by pa.s.sing through successive stages, each of which has its a.n.a.logue in some of the existing forms of animal life. Those forms of animal life exist side by side; and if we conceive them to be represented diagrammatically by vertical lines, differing in height according to their degree of evolution, the line representing the human organism will be the tallest, and may be considered to have become the tallest by successive increments or stages corresponding to the height of the various other parallel vertical lines.

When the conception of evolution, which had been employed to explain the origin of species and the descent of man, and which had been gained by a consideration of material organisms, came to be applied to the world of man's thoughts, to the non-material and spiritual domain, and to be used for the purpose of explaining the growth and the development of religion, it was natural that the conception which had proved so valuable in the one case should be applied without modification to the other--as natural as that the first railway coach should be built on the model of the stagecoach. The possibility that the theory of evolution might itself evolve, and in evolving change, was one that was not, and at that time could hardly be, present to the minds of those who were extending the theory and in the process of extending it were developing it. Yet the possibility was there, implicit in the very conception of evolution, which involves continuous change--change in continuity and continuity in change.