Part 4

All this, put into so many words, may seem too simple to call for statement, but it makes nonsense of a great deal that has been written about ethics of late years. It disposes once for all of the theory that moral and aesthetic verdicts are 'subjective', that is, that they mean no more than that the persons who make them have certain personal likes and dislikes of which these verdicts are a record. Of course, it might be urged that all of us do indeed mean to express truths which are independent of our personal likings when we make moral and aesthetic judgements, but that we never succeed in doing so. A man might conceivably hold that there is no real distinction between right and wrong or between beautiful and ugly, but that it is a universal illusion of mankind to suppose that there are such distinctions. Or he might hold that the distinctions are real, but that we do not know where to draw them. He might suggest that some ways of acting are really right and others really wrong, but that we do not know which are the right acts and so regularly confuse what we like doing with what is 'really' right. Mr. Russell, in some of his later writings, seems to incline to views of this sort. But the suggestion is really unmotived. It would be just as reasonable to suggest that all geometrical or astronomical propositions are only expressions of the personal and private feelings of geometers and astronomers, and that either there is no distinction between truths and falsehoods in geometry and astronomy, or that, at any rate, we do not know which the true propositions are. That there is a real distinction between true and false propositions and that, with pains and care, we can discover some truths are assumptions we must make if we are to recognize the possibility of pursuing knowledge at all, and there is no reason to suppose that these assumptions do not hold as good in matters of art and morals as elsewhere. No doubt, in practice men are prone to mistake what they like for what is right or beautiful, but this danger, such as it is, is not confined to art and morals. Men do often call acts right merely because they like doing them or pictures beautiful merely because they get pleasure from them. But it is also notorious that many men are prone to believe that a thing is likely to happen merely because they wish it to happen, or that it is unlikely to happen merely because they wish it not to happen. Yet no one seriously makes the reality of these tendencies a ground for denying the possibility of 'inferring the future from the past'. We must then, I hold, regard it as an integral part of the whole story of everything to find an answer to the questions What is good? and What is beautiful? as well as to the question What is fact? By the side of the so-called 'positive sciences', which deal with the third question, we must recognize as having an equal right to exist the so-called 'sciences of value', which deal with the first and the second.

I want now to take a further step in which disciples of Mr. Russell would perhaps decline to follow me. We have already seen what is meant by the co-ordination of the sciences into a single body of deductions from definite ultimate postulates, though in what we have said about the task we were content to speak provisionally as if the sciences of 'what is' were all the sciences to be co-ordinated. We talked, in fact, as if the work of Philosophy were merely to work into a coherent story all that can be known of 'objects that present themselves to the contemplation' of a knower. But, of course, if Philosophy is ever to attack its final problem, we must take into account two things which we have so far ignored. The 'whole story of everything' includes the knowing intelligence itself as well as the 'objects' which present themselves to its gaze. Indeed, it is not even accurate to speak as if 'objects' 'presented themselves' to a merely passive intelligence; to be apprehended, they have to be actively attended to. If we would see them, we have to be on the look-out for them. And the knowing intelligence is not aware merely of these objects. It is also aware of itself, though it is certainly never a 'presented object'. Also, it is not only a knower but a doer and a maker. Intelligence is shown as much in the ordering of life by a rule based on a right valuation of goods and in the making of things of beauty as in the discovery of propositions about what is. Hence, we can hardly be content to leave the 'positive' sciences and the 'sciences of values' simply standing over against one another. There is that which 'is', and there is that which 'ought to be', and, at first sight at any rate, the two seem very different. Much that is--ignorance, sin, misery, ugliness--ought not to be, and much that ought to be is very far from being fact. We are accustomed to regard this as a matter of course, but, closely considered, it is perhaps the supreme wonder of all the wonders. We creatures of circumstance, as we call ourselves, can take stock of the sum of things to which we belong, and judge it. It is not simply that we can, and often do, wish that it were different in various ways; we can judge that it ought to be different, and you may find a man of science like Huxley, after a life spent in trying to understand the laws which prevail in the world, deliberately making it his last word to his fellows that their duty is to set themselves to reverse the 'cosmic process', to select for preservation just the human types which, if the much-abused metaphor may be tolerated, Nature, left to herself, selects for destruction.

We might, of course, regard this apparently unreconcilable conflict between the arrangements which do prevail; as is commonly supposed, in the world, and those which ought to prevail, as a mystery which we must despair of ever understanding. But, to say the least of it, it is hardly consistent with the philosophic temper to treat any question as an insoluble riddle until one has tried all ways of solution and found them culs-de-sac. If we are to be thoroughly loyal to the spirit which prompts all intelligent inquiry, we are bound at least to ask whether it is, after all, beyond the power of human intelligence to think of the world as a system in which somehow, in the end, what ought to be prescribes what is. It is true that, for reasons already mentioned, we cannot, like Spinoza or the Sufis, reconcile facts and values by the simple assumption that what is is shown, by the fact that it is, to be what ought to be, and that our common conviction that sin and ugliness are painfully real is only an illusion due to spiritual short sight. We have just as much reason to believe that some pleasures are good, that pain which is not a means to good is evil, that justice and purity are good, lewdness and cruelty bad, that some colours are lovely and others odious, as we have to believe that between any two points there is always a third, or that, if B and C are two points there is always a point D on the straight line BC such that C is between B and D, and a point A on CB such that B is between C and A. Indeed, the most fanatical champion of what Mr. Russell in his anti-ethical mood calls 'ethical neutrality' cannot well avoid recognizing the truth of at least one proposition in ethics, the proposition that knowledge of scientific truth is better than ignorance of it. The admission of this single truth of value is enough to raise all the time-honoured problems of ethics and theodicy. If knowledge of truth is better than ignorance of it, the actual present state of the world, in which so much truth is yet to seek, is by no means wholly good, and there really is at least one way in which it is our duty to make it more like what it ought to be.

If then we cannot get rid of the apparent conflict between Is and Ought by saying that Ought is an illusion, can we get rid of it, in the only other possible way, by holding that what ought to be is the lasting and primary reality and that the 'facts' which are so far from being what they ought to be are by comparison only half-real, much what shadows are to the solid things which throw them? This was the doctrine of Plato, who makes Socrates say in the Phaedo that it is the 'Good' which holds the Universe together, and that in the end the true reason for each particular arrangement in the world, whether we can see it or not, is that it is 'best' that this arrangement, and no other, should exist. It is also the foundation of Kant's well-known contention that, however barren speculative theology and psychology may be, the reality of the moral order and the unconditionality of moral obligation compel us to make the existence of God, the immortality of our souls, and the moral government of the world postulates of practical philosophy. More generally, it is just this conviction that 'what is' has its source and explanation in what 'ought to be', which is the central thought of all philosophical Theism. If we can accept such a faith, we shall not, of course, be enabled to eliminate mystery from things. We shall, for instance, be still quite in the dark about the way in which evil comes to be in a world of God's making. We shall neither be able to say how any particular thing comes to be other than it ought to be, nor how in the end good is 'brought out of evil'. But if we are to have a right to hold a view of the Platonic or Theistic type, we must be able, not indeed to say how evil comes about or how it is to be finally got rid of, but to say, in a general way, what it is 'good for'. Thus, if there are certain goods of the highest value which could not exist at all except on the condition of the existence of less important evils, this consideration will remove, so far as those goods and evils are concerned, the time-honoured puzzle how evil can exist at all if God is. To take a specific example. To many of us it appears directly certain that such qualities of character as fortitude, patience, superiority to carnal lusts, magnanimity, are goods of the highest value. We think also that we see that these qualities are not primitive psychological endowments but require for their development the experience of struggle and discipline in a world where there is real suffering, real disappointment, real temptation. To us, therefore, there seems to be no contradiction between the existence of God and the presence in a world made by God of the evils needed for the development of these virtues. And this will include some of the worst of all the evils we know of. Few things are more ghastly than some of the cruelties which have been practised in the late War and are still being practised in the distracted country of Russia. Yet we know how revulsion from these horrors has made many a man who seemed to be sunk in sloth or greed or carnality into a Bayard or a Galahad. It may well be that this moral re-birth would never have been effected if the evils which provoked it had been less monstrous. Here, then, we seem to discern a principle which may be adequate to explain what all the ills of human life are 'good for'.

I must not deny that all such explanation, in my judgement, involves the postulate that the ennoblement of character and deepening of insight brought about by suffering are permanent--in fact, that it requires the postulates of the existence of God and the reality of everlasting life. Mr. Russell, I imagine, would regard this as a confession that I am sunk in what he airily dismisses as 'theological superstitions'. I should reply that the 'superstition' is on his side; to dismiss God and the eternal soul, without serious inquiry, as 'superstitions' is just the most superficial of all the superstitions. It is, of course, incumbent on anyone who holds the Platonic view to show that its postulates are not inconsistent with any known truth, and I would add that he ought also to show that there are at any rate known facts which seem to demand just this kind of explanation. Both these points, as I hold, can be established, but I do not in the least wish to suggest that any philosopher will ever find it an easy task to 'justify the ways of God to man'. As Timaeus says in Plato, 'to find the father and fashioner of the Universe is not easy', and I want rather to lay stress on the magnitude of the task than to extenuate it. But I am concerned to urge that the doctrine which accounts for what is by what ought to be is the only philosophical theory on which it ceases to be an unintelligible mystery that we should have--as I maintain we certainly have--the same kind of assurance about values that we have about facts. The chief complaint I have to make about the mental attitude of Mr. Russell and some of his friends is that, in their zeal for the unification of science, they seem inclined to assume that the larger problem of the co-ordination of Science with Life does not exist, or, at any rate, need not occupy our minds. This is what I should call mere atheistic superstition. On this point they might, I believe, learn much which it imports them to know from the works of some of the notable living philosophers of Italy, in particular from Professor Varisco of Rome and Professor Aliotta of Padua, whose labours have been specially directed to the co-ordination in a consistent system of the principles of the sciences of fact with those of the sciences of value. Though, after all, those who have refused to learn the lesson from the noble philosophical work of Professor James Ward, the illustrious champion of sober thought in their own University of Cambridge, are perhaps unlikely to master it in the schools of Rome or Padua.

You will readily see that I am suggesting in effect that if Philosophy is ever to execute her supreme task, she will need to take into much more serious account than it has been the fashion to do, not only the work of the exact sciences but the teachings of the great masters of life who have founded the religions of the world, and the theologies which give reasoned expression to what in the great masters is immediate intuition. For us this means more particularly that it is high time philosophers ceased to treat the great Christian theologians as credulous persons whose convictions need not be taken seriously and the Gospel history as a fable to which the 'enlightened' can no longer pay any respect. They must be prepared to reckon with the possibility that the facts recorded in the Gospel happened and that Catholic theology is, in substance, true. If we are to be philosophers in earnest we cannot afford to have any path which may lead to the heart of life's mystery blocked for us by placards bearing the labels 'reactionary', 'unmodern,' and their likes. That what is most modern must be best is a superstition which it is strange to find in a really educated man--especially after the events of the last five years. A philosopher, at any rate, should be able to endure the charge of being 'unmodern' with fortitude. It is at least a tenable thesis that many of the qualities which we Western men have been losing in our craze for industrialism and commercialistic 'Imperialism' are just those which are most necessary to the seeker after speculative truth. Abelard and St. Thomas would very likely have failed as advertising agents, company promoters, or editors of sensational daily papers. But it may well be that both of them were much better fitted than Lord Northcliffe, Mr. Bottomley, or Mr. A.G. Gardiner to tell us whether God is and what God is. In fact, one would hardly suppose habitual and successful composition of effective 'posters' or alluring prospectuses to be wholly compatible with that candour and scrupulous veracity which are required of the philosopher. As for 'reaction', no one but a writer in a 'revolutionary' journal would be fool enough to use the word as, in itself, an epithet of reproach. Most persons who have a bowing acquaintance with Mechanics know that you cannot have an engine in which there is all action and no reaction, and most sane men can see that before you pronounce a given 'reaction' good or bad you need to know what it is reacting against. If a man who wants to go east discovers that he is walking west, he is usually reactionary enough to go back on his steps.

In short, if we mean to be philosophical, our main concern will be that our beliefs should be true; we shall care very little whether they happen to be popular or unpopular with the intellectual 'proletarians' of the moment, and if we can get at a truth, we shall not mind having to go back a long way for it. Indeed, when one wants to get on the track of the most ultimate and important truths of all, there is usually a great positive advantage in going back a very long way for them. The questions which deal with first principles, being the simplest--though the hardest--of all, are mostly raised very simply and directly by Plato and Aristotle, who were the very first writers to raise them. In the discussions of later times, the great simple questions about principles have so often been overlaid by mainly irrelevant accretions of secondary details that it is usually very hard indeed 'to see the wood for the trees'. This is the chief reason why one who, like myself, finds it his main business in life to introduce younger men and women to the study of Philosophy must think indifference to Greek literature about the worst misfortune which could happen to our intellectual civilization.

I have tried in what I have said so far to explain what I understand by the philosophical spirit and what I regard as the primary problems with which Philosophy has to wrestle. If what I have said is not wholly wide of the mark, it should be clear what is the deadliest enemy of the true spirit of Philosophy. It is the temper which is too indolent to think out a question for itself and consequently prefers to accept traditional ready-made answers to the problems of Science and Life. Traditionalism, wherever it is found, is the enemy, because Traditionalism is only another name for indolence. Observe that I say Traditionalism, not Tradition. Nowhere in life, and least of all in Philosophy, is the solitary likely to work to much purpose unless he has behind him that body of organized sound sense which we call Tradition. And I do not mean that true philosophers are necessarily 'heretics', or that 'orthodoxy' is less philosophical than 'heterodoxy'. I mean that however true an 'orthodox' proposition may be, it is no living truth for me unless I have made it my own, as its first discoverer did, by personal labour of the spirit. The truth is something which each generation must rediscover for itself. True traditions may be quite as injurious, if they have become mere traditions, as false ones. It was not so much because the Aristotelian doctrines were false that the unquestioning acceptance of Aristotelian formulae all but strangled human thought in the later days of Scholasticism. Some of these doctrines were false, but many of them were much truer than anything the seventeenth and eighteenth centuries had to put in their place, and the rediscovery of their real meaning is perhaps the chief service of the Hegelian school to Philosophy. The trouble was that mechanical repetition of Aristotle's formulae as matters of course inevitably led to loss of real insight into the meaning the formulae had borne for Aristotle.

We may say, generally, that because Traditionalism is the death of sound thinking, the ages in which the prospects of advance in Philosophy are brightest are just those in which a powerful historical tradition has broken down and men feel themselves compelled to go back on their steps and raise once more the fundamental questions which their fathers had supposed to be disposed of once for all by a formula. This has happened twice since the downfall of the degenerate Scholasticism, Protestant and Roman, of the sixteenth century. In the seventeenth century the result was the great movement in Philosophy, Mathematics, and Physics, of which Descartes and Galileo are the principal figures. Towards the end of the eighteenth century, when the doctrines of Descartes had themselves been traditionalized, the same thing happened again, the leading actors in the drama being David Hume and Immanuel Kant; the result was first the revival of the 'critical' problem by Kant, and then the great, if over-hasty, attempt at a positive interpretation of the Universe which culminated in the philosophical system of Hegel. In our own age, it is mainly Kant and Hegel who have been traditionalized, and we seem to be living through the last stages of the discrediting of this third tradition with every prospect of a great advance if our own time can only find its Descartes. In what I am going on to say I must naturally speak of the disintegrating influences chiefly as we have seen them at work in our own country; but I should like, before I do so, to remark that on the Continent splendid work has been done in the requickening of genuine philosophical thought by an influence which has, so far, not made itself widely felt among ourselves. I mean the revival of Thomism so earnestly promoted in the academies of the Roman Church by Pope Leo XIII. Neo-Thomism, I am convinced, if its representatives will only maintain it at the high level characteristic, for example, of the Italian Rivista Neo-Scolastica, has a very great contribution to make to the Philosophy of the future, and is much more deserving of the serious attention of students in our own country than the much-advertised 'impressionism' of Pragmatists and Bergsonians. Indeed, I hardly know how much we may not hope from the movement if it should please Providence to send into the world a Neo-Thomist who is also a really qualified mathematician.

Of the state of thought in our own country we may fairly say that a generation ago opinion on the ultimate questions was, in the main, fairly divided into two camps. There were the professional metaphysicians, mainly living on a tradition derived from Kant and Hegel, and there were the men of science whose 'philosophy', such as it was, is perhaps best represented by two well-known and most instructive books, Mach's Science of Mechanics and Karl Pearson's Grammar of Science. The men of the Kant-Hegel tradition, whatever their family dissensions, were generally united by the common view that--as William James accused them of teaching--the function of sensation in contributing to knowledge, whatever it is, is something 'contemptible'. Kant himself, as we have seen, had thought very differently, but he was supposed to have been 'corrected' on this, as on so many points, by Hegel. The most distinguished of my own Oxford teachers seemed agreed to believe that our thought builds up the fabric of knowledge entirely from within by what Hegel called an 'immanent dialectic'. A rough idea of what this means may be given in the following way. You take any experience you please and try to put what you experience into a proposition. The proposition may, to begin with, be as vague as, e.g. 'I am now feeling something,' 'I am now aware of something.' On reflection you find that the statement does not do justice to the experience. You feel the need to say more precisely what you are feeling or are aware of, how it is related to what you experience on other occasions, and what the 'I' is which is said to 'have' the experience. Until you have done this your thought is a miserable reproduction of your experience, and if you could ever do it completely, it would turn out that a really adequate account of the most trivial experience would involve complete knowledge of the structure and working of everything. Thus, if you once begin to think about your experience at all, you are irresistibly driven on to endless further reflection. If you try to stop short anywhere in the process, the results of your reflection are found to contain unexplained contradictions, just because you have not yet fitted on the fact on which you are reflecting to everything else there is to know. All the assumptions of every-day 'common sense' and all the more recondite assumptions of the sciences are saturated with these contradictions, because both 'common sense' and the sciences leave so much of the whole 'story of everything' untouched. If the whole story were told, all things would be found to be just one thing, which these philosophers call the 'Absolute', and the only perfectly true statement we can make would be a statement about this Absolute in which we asserted of it all that it is. Since no science ever attempts to say anything at all about this one sole thing, far less to get all there might be to be said about it into a single statement, no scientific proposition can be more than 'partially' true, and unhappily we do not know what alterations would be required to make our 'partial' truths quite true. Naturally enough Kant's allegation that mathematical first principles are so self-contradictory that you can rigidly demonstrate mathematical propositions which contradict each other was grist to the Hegelian mill. That our notions of space, time, the infinitely great, the infinitely little, are all a jumble of contradictions was steadily repeated by the Hegelian philosophers, and indeed the mathematicians were accustomed to state their own principles so loosely and confusedly that there was a great deal of excuse for the suspicion that the fault lay with Mathematics and not with the mathematicians.

It is clear that such a philosophy ought to end in unqualified Agnosticism. The Hegelians, to be sure, made merry over the Unknowable of Mr. Spencer, but their own Absolute is really just the Unknowable in its 'Sunday best'. Nothing that we can say about anything which is not the Absolute is really true, because there really is nothing but the Absolute to speak about, and nothing that we can say about the Absolute is quite true either, because we can never succeed in saying itself of it. Mr. Bradley, far the most eminent of the philosophers of the Absolute, has made persistent and brilliant attempts to show that, in spite of this, we do know enough to be sure that our own mind is more like the Absolute than a cray-fish, and a cray-fish more like it than a crystal. But when all is said, though I owe more to Mr. Bradley than I can ever acknowledge adequately, I cannot help feeling that there are two men in Mr. Bradley, a great constructive thinker and a subtle destructive critic, and that the destructive Hyde is perpetually pulling to pieces all that the constructive Jekyll has built up. Of course it is obvious that the truth of mathematics, if mathematics are true, is a fatal stone of stumbling for this type of philosophy. Mathematics never attempts to say anything about the 'Absolute'--the only 'Absolute' of which it knows is only a 'degraded conic'--yet it claims that its statements, if once they have been correctly expressed, are not 'partial' but complete.

Over against the Hegelianizing philosophers, we had, of course, the men of science. No one could wish to speak of the scientific men of the days of Huxley without deep respect for their success in adding to our positive knowledge of facts. But it may perhaps be said at this distance of time that it was not precisely the greatest among them who were most prominent as mystagogues of Science with the big S, and it may certainly be said that when the mystagogues, the Cliffords, Huxleys, and the rest, undertook to improvise a theory of first principles, their achievement was little better than infantile. They took it on trust from Hume that the whole of knowledge is built up of sensations, actual or 'revived', and quite missed Kant's point that their empiricism left the formal constituent in knowledge, the type of order by which data are organized into an intelligible pattern, wholly out of account. Even when they deigned to read Kant, they read him without any inkling of the character of the 'critical' problem. Hence they taught dogmatically as true a theory of scientific method which Hume himself had elaborately proved impossible. It was just because Hume had seen so clearly that no universal scientific truths can be derived from premisses which merely record particular facts that he professed himself a follower of the 'academic' or 'sceptical' philosophy. He recognized the impossibility of constructing scientific knowledge out of its material constituent alone, but did not see where the formal constituent could come from, and so resigned himself to regarding the actual successes of science as a kind of standing miracle.

The men of the 'seventies were, after all, in many cases more anxious to damage theology than to build up Philosophy. They read Hume without any delicate sense for his urbane ironies, and believed in good faith that he and John Stuart Mill between them had shown that by a mysterious process called 'induction' it is possible to prove rigorously universal conclusions in science without universal premisses. A scientific law, according to them, is only a convenient short-hand notation in which to register the 'routine of our perceptions'. Thus we have known of a great many men who have died, and have never known of any man who lived to much over a hundred without dying. The universal proposition 'all men are mortal' is a short expression for this information, and it is nothing more. It ought to have been obvious that, if this is a true account of science, all scientific 'generalizations' are infinitely improbable. The number of men of whom we know that they have died is insignificant by comparison with the multitude of those who have lived, are living, or will live, and we have no guarantee that this insignificant number is a fair average sample. So again, unless there are true universal propositions which are not 'short-hand' for any plurality of observed facts whatever, we cannot with any confidence, however faint, infer that a 'regular sequence' or 'routine' which has been observed from the dawn of recorded time up to, say, midnight, August 4, 1919, will continue to be observed on August 5, 1919. How, except by relying on the truth of some principle which does not depend itself on the validity of 'generalization', can we tell that it is even slightly probable that the nature of things will not change suddenly at the moment of midnight between August 4 and August 5, 1919? What is called 'inductive' science certainly has 'pulled off' remarkable successes in the past, but we can have no confidence that these successes will be repeated unless there are much better reasons for believing in its methods and initial assumptions than any which the scientific man who is an amateur 'empiricist' in his philosophy can offer us. We may note, in particular, that this empiricism, which has been expounded most carefully by Pearson and Mach, coincides with Hegelian Absolutism in leading to the denial of the truth of mathematics. It would be a superfluous task to argue at length that, e.g., De Moivre's theorem or Taylor's theorem is not a short-hand formula for recording the 'routine of our perceptions'.

The general state of things at the time of which I am speaking was thus that relations were decidedly strained between a body of philosophers and a body of scientific men who ought at least to have met on the common ground of a complete Agnosticism. The philosophers were, in general, shy of Science, mainly, no doubt, because they were modest men who knew their own limitations, but they had a way of being condescending to Science, which naturally annoyed the scientific men. 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 résumé 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 constituent of scientific knowledge. And with this dogma falls the main ground for the denial that knowledge about the soul and God 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 establishing 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 à 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 assumptions 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 identity, which is so fundamental for practical life, and to assert 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 Massimi 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 God 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 assuredly 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 superstition', 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 illustrations. 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 Données Immédiates 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 assumption 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 Publishing 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.).