THE PHILOSOPHY OF HUMANISM
 
 BY VISCOUNT HALDANE 
 
 THE REIGN OF RELATIVITY 
 
 THE PATHWAY TO REALITY 
 
 The Gifford Lectures delivered in the 
 University of St. Andrews. First Series, 
 1902-3. Second Series, 1903-4. 
 
 THE CONDUCT OF LIFE 
 
 AND OTHER. ADDRESSES 
 
 UNIVERSITIES AND 
 NATIONAL LIFE 
 
 Three Addresses to Students. 
 
 HIGHER NATIONALITY 
 
 A Study in Law and Ethics. An Address 
 delivered before the American Bar Asso- 
 ciation at Montreal on September i, 1913. 
 
 LONDON : JOHN MURRAY
 
 THE PHILOSOPHY 
 OF HUMANISM 
 
 AND OF OTHER SUBJECTS 
 
 BY VISCOUNT HALDANE 
 
 LONDON 
 
 JOHN MURRAY, ALBEMARLE STREET, W. 
 
 1922
 
 ALL RIGHTS BBSBRTKD
 
 821 
 
 PREFACE 
 
 IF I had called this book The Philosophy of Humanism 
 without more, that title would virtually have covered 
 its scope. But the reader would not have had his 
 attention drawn to the significance which the word 
 ' Humanism ' imports for myself. 
 
 To avoid misinterpretation I have therefore added 
 in the title the words and of Other Subjects. Part I, 
 which is concerned with Humanism in its restricted 
 sense, contains the substance of three Donnellan 
 lectures delivered this summer at Trinity College, 
 Dublin. 
 
 In a volume published last year, The Reign of 
 Relativity, I sought to lay the foundations of a view 
 of the uniqueness distinctive of individuality which 
 would show the relation of its principle to that of 
 the general relativity of reality to knowledge. This 
 view is carried further in the present volume, which 
 is a companion one to that of a year ago. 
 
 As regards two of the scientific subjects discussed, 
 I am under much indebtedness for counsel and assist- 
 ance while working out the principle. Professor 
 A. N. Whitehead, F.R.S., has gone over the proofs 
 of the three chapters devoted to mathematical 
 physics. My brother, Professor J. S. Haldane, F.R.S., 
 has done the same for the chapter on biology. Neither
 
 ri PREFACE 
 
 of them is thereby to be looked on as responsible for 
 sharing my point of view in philosophy, or for modes 
 of expression which are my own. But none the less 
 my debt to them is great for having permitted me the 
 advantage of their criticism in what I have written 
 on their respective subjects. 
 
 LONDON, 
 June 1922.
 
 TABLE OF CONTENTS 
 
 INTRODUCTION 
 
 Aristotle and Goethe on the character of the object world. The 
 actual is always concrete. The real nature of our experience. The re- 
 lation to it of thinking. W. K. Clifford on this subject. The character 
 of the object in mathematics. The character of our knowledge 
 generally. What is 'mind' ? The continuity in the history of 
 philosophy. Philosophy must not hope for finality. The meaning 
 of this. The Italian Idealists and Professor Gentile. His teaching 
 about space and time. New Realism. The purpose of this book 
 is to examine the characters of the standpoints assumed in various 
 branches of knowledge to be adequate for explaining the aspects of 
 reality with which these branches of knowledge are concerned. The 
 relation of reality, as appearing in the various orders of knowledge, 
 to knowledge itself. Primarily the object of knowledge appears to 
 be always individual and unique. It implies universals as well as 
 particulars in its aspect, and it is the former that reflection isolates in 
 its abstractions. The plan of the book . .. . pp. 1-32 
 
 PART I 
 
 THE PHILOSOPHICAL SIGNIFICANCE OF 
 HUMANISM 
 
 CHAPTER I 
 
 THE PHILOSOPHICAL SIGNIFICANCE OF HUMANISM 
 
 Humanism means what conforms to the standards of value in 
 domains such as those of Literature, of Music, of Art, and of Religion. 
 The standards there employed are different from those by which we 
 test values in Science and Metaphysics. There is a kind of value 
 recognised in what we call direct apprehension which is other than 
 that which we set on correctness in inference from general principles. 
 Still, there must be a common standard of some kind which will bring 
 into congruence knowledge of the most different sorts. The purpose of 
 
 vii
 
 viii CONTENTS 
 
 these three chapters is to endeavour to bring this question under 
 the light cast by the principle of the Relativity of Knowledge. 
 What lies at the foundation of this principle is, that when we say 
 we know it is not sufficient merely to regard the self as a thing that 
 establishes an external and accidental relation between something 
 that knows and an object outside the relation of knowledge. Our 
 personal thoughts do not make things, and yet things have no 
 meaning, and therefore no reality, apart from knowledge. We are 
 ourselves objects in knowledge, but knowledge not the less must come 
 first in logical order in our interpretation of ourselves as actual. For, 
 outside of actual or possible knowledge, existence has no significance. 
 It was reserved for Kant to point out, as against the British 
 School of thinkers, that when we know we are always more than we 
 take ourselves to be, and that meaning is the essential foundation 
 of existence. The question of the genesis of knowledge is thus an 
 inherently irrational one. All scepticism assumes that it possesses 
 the instrument for which it sets out to account. We must, therefore, 
 inquire what knowledge in the fuller sense imports. The problem is 
 as old as the Greeks. In the relation of the Active to the Passive 
 Reason there seemed to them to lie a solution. When we talk of 
 thought as making things we conceive it inadequately, and represent 
 it under the form of a set of abstract conceptions which we present to 
 our minds as if objects. The ultimately real appears to be, on the 
 contrary, neither mere subject nor mere object, but the significance of an 
 activity within which both are distinguished in reflection. By his applica- 
 tion of the principle of relativity in knowledge to mathematical physics 
 Einstein has awakened a vivid interest in this subject. His application 
 is, however, only a particular and limited one. Explanation of the 
 fashion into which he has cast it. The basic four-dimensional world 
 and the tensor principle. A wider application to the case of the 
 living organism. Life and mind. Levels in experience and degrees 
 in knowledge. The form of the concrete universal is that assumed 
 by all reality. It contains, not as separate entities but as logical 
 moments, the universal and particular, which are actual only in what 
 is individual and unique, and it is resolved into its logical moments by 
 our abstractions. It is only in reflection that these are dissociated. 
 The particular is essential for reality not less than the universal. The 
 dangers of the uncritical use of metaphors about knowledge. With 
 this view of its true character we come in sight of the interpretation 
 of its Humanistic phases ...... pp. 35-57 
 
 CHAPTER II 
 
 THE PHILOSOPHICAL SIGNIFICANCE OF HUMANISM 
 
 (continued) 
 
 Recapitulation. The implications of ' uniqueness.' The pure 
 particular an asymptotic limit and unattainable in description. But
 
 CONTENTS ix 
 
 none the less an essential moment in actual individuality. In its 
 attempts to find in the particular a basis scepticism has always defeated 
 itself. The dialectical character of reflection. The character of mind. 
 Its abstractions and the symbols it employs in the activity of thinking. 
 These symbols are individual facts, even in mathematics. We begin 
 from what is concrete and work downwards in the process of reflection. 
 The necessity of being critical in our selection of the conceptions that 
 are appropriate to the aspects of reality we are concerned with. The 
 nature of character in individual men. A certain particularism implied. 
 Abstract principles not enough. The instinct for individuality of 
 the man in the street. Leadership. The meaning of ' Humanism. ' 
 Illustrations of this meaning. Values. The testimony of Browning. 
 Two descriptions of Humanistic value given by great writers. The 
 Oxford Movement as characterised by Cardinal Newman, and the 
 reflections of educated bystanders on the execution of a murderer as 
 described by Hegel. Matthew Arnold on the inseparability from the 
 finest forms of Humanism of high knowledge. The importance in 
 poetry of moral ideas. But Arnold is emphatic in holding that in the 
 case of Wordsworth, for example, his philosophy is of secondary value 
 as compared with his poetical gift. He seems to mean that general 
 principles taken by themselves are inadequate to reality, and are actual 
 only in living and individual form, and that in poetry in particular 
 genius in style is what is determining. For it is this which, at least 
 as much as reflection, is essential in art. The quality of ' inevitable- 
 ness.' Still, the beauty of Wordsworth's poetry, like all beauty 
 of its kind, is a beauty born of the mind. The difficulties in the 
 relation of the Irish to the English mind are partly due to that tendency 
 to insist on particular aspects which imparts to the outlook on life a 
 dynamic character. Still, in literature and philosophy alike, this has 
 on the whole proved a source of strength. Sainte-Beuve on Greek 
 literature, and on Shakespeare and Goethe. He declares that criticism 
 cannot be static in its standards. In the very relativity of all criticism 
 in literature to the standpoint of its time, its truth and reality appear 
 to lie +,_. ...... . . . . pp. 58-83 
 
 CHAPTER III 
 
 THE PHILOSOPHICAL SIGNIFICANCE OF HUMANISM 
 
 (continued) 
 
 Humanism in literature is that form of knowledge in which the 
 stress is laid on the individuality and uniqueness found in direct 
 perception and emotion. It is as values that the universals of know- 
 ledge enter into such Humanism. Such imaginative constructions 
 thus owe their beauty to their being born of the mind. The standards 
 by which their value is estimated may be relative to periods and 
 altering modes of expression, but they imply continuity in principle.
 
 x CONTENTS 
 
 In Humanism it is in the main only on certain aspects falling 
 within the entirety of knowledge that we dwell. The recognition of 
 marked personality, as in leadership, is of this kind. There is an 
 inexhaustible and indefinable particularism in this sort of personality 
 which compels the imagination of others and confers transforming 
 power. We fall in love with persons, not qualities. So, too, in 
 religion. The significance of its symbolism. Fanaticism lays exces- 
 sive stress on a merely abstract principle. Even science has to avoid 
 such one-sidedness strenuously. But Humanism is capable of excesses 
 as great as those of the abstract mind. Neither the particular nor 
 the general moment in knowledge can safely be taken in isolation 
 from the other. Humanism, not less than science and philosophy, 
 has to recognise that knowledge is an entirety. The merit of the 
 Upanishads. The attempt at present being made to introduce into 
 the organisation of the German universities what is called a Hu- 
 manistic Faculty. Our own effort to spread the true university 
 spirit extra-murally through our democracy. The necessity of pre- 
 serving the balance in the higher knowledge between its two sides. 
 Goethe on the value in this regard of the Scottish School in philosophy. 
 His own attitude to philosophy. Summing up of the three chapters. 
 Reality is indissolubly one with knowledge, but is neither a construc- 
 tion by merely abstract thinking, on the one hand, nor, on the other 
 hand, has it meaning or existence apart from the setting which thought 
 gives to the particularism implied in all knowledge. Humanism is an 
 interpretation which owes its nature to the standpoint from which the 
 entirety is surveyed . . . . . . . pp. 84-99 
 
 PART II 
 
 THE PHILOSOPHICAL SIGNIFICANCE OF OTHER 
 SUBJECTS: MATHEMATICAL PHYSICS, BIO- 
 LOGY, AND PSYCHOLOGY 
 
 CHAPTER IV 
 
 MATHEMATICAL PHYSICS 
 
 The fresh ideas recently introduced into mathematical physics. 
 Their relation to philosophy. The universal and the particular actual 
 only as logical moments in a form that is individual. This is the 
 character of all experience. The quantum theory. Max Planck on 
 the true point of departure for the physicist. His justification of the 
 concept of Force. The J5ther. The deductive tendency in geometry.
 
 CONTENTS ari 
 
 Newton and Euclid. The axiom of parallels. Lobatschefsky and 
 Bolyai. Riemann's geometry. Kant. The introduction of the 
 notion of the ' Field ' by Faraday and Clerk-Maxwell, and the further 
 conception of time and space as separable only by abstraction. 
 The new view of geometry which has been gradually developed. 
 The character of the doubts about Euclidean space. Riemann's 
 search for a wider foundation for geometry. The analogy between 
 his new principle and that of physical action in the field at indefinitely 
 close range. The infinitesimal treatment is for Riemann what enables 
 him to reach the continuity of which Euclid cannot assure us. For 
 Riemann the world can only be interpreted through its relations in 
 the infinitely small, and the supposed three-dimensional space of per- 
 ception may turn out to be curved space of yet more dimensions. 
 Gauss had already thought of this point. The character of space may 
 therefore be multiform. But Riemann's method brings him to 
 principles inherent in that character which are identical through all 
 change of form and are invariant. These principles are descriptive of 
 the field of activity of point events reached by the method of limits. 
 Comparison with Gaussian co-ordinates. The Tensor doctrine 
 
 pp. 103-126 
 
 CHAPTER V 
 
 MATHEMATICAL PHYSICS (continued) 
 
 The presence of the discrete character in experience as well as of 
 continuity. Position essentially transitory The ' now ' and the ' here ' 
 merely limiting notions. Time and space imply each other, and the 
 actual is not static. The resolution into relations of time and space by 
 the observer of change in his awareness. Coincidence. The notional 
 construction of objects out of changing events in awareness. Time 
 and space as relations constructed not between events, but between 
 objects. The transformation in the standpoint of the observer signified 
 in Gravitation. The velocity of light and the meaning of its con- 
 stancy for congruence. It is the limited conception we form of mind 
 that has given rise to the difficulty in explaining the general congruence 
 which we assume to exist. Einstein's analysis of the relations of 
 objects in the external world. The Special Theory of Relativity, and 
 the necessity for its development into the General Theory. What are 
 dealt with primarily are relations of shape and measurement, but not 
 the actual facts out of which they are differentiated. The Minkowski 
 ' world ' as such a fact. Its character. Minkowski himself. His 
 discourse in 1908 at Cologne. His description of his ' world ' and of 
 three-dimensional geometry as no more than a branch of four-dimen- 
 sional physics. His view of the velocity of light as necessarily the 
 dominating constant in mathematical physics. He sought to restrict 
 closely the deduotiva function of geometry . . pp. 126-154
 
 xii CONTENTS 
 
 ,( i- 
 
 CHAPTER VI 
 
 MATHEMATICAL PHYSICS (continued) 
 
 The four- dimensional world of Minkowski is the bridge for Einstein 
 between the domain of geometrical abstractions and that of concrete 
 actuality. The introduction of the new relation between time and 
 space has enabled the work done by Gauss and Riemann to be 
 carried further. The meaning of Relativity. The metaphors in 
 Minkowski's mathematical expressions and the difficulties they cause. 
 The explanations given by Professor Born. Inertia and the velocity 
 of light. The quantum theory. Space cannot be looked on as a 
 cause, or the aether as a substance. The possibility that Einstein's 
 theory of interval relations may have to be widened. Weyl's doubts 
 as to whether invariance can be attributed in the characters of the 
 intervals between sets of point events at a finite distance from each 
 other. There may, he thinks, be a chain of intervals, with ' gauges ' 
 which vary, so that the metric varies. The metric will thus have 
 an objective nature, not explicable by the mere creation of a gravita- 
 tional field through relativity of observation. Variation of relativity 
 in magnitude in co-ordinate systems must be taken account of as well 
 as relativity in motion. If so, the intervals dealt with will not neces- 
 sarily be integrable. Weyl believes that we are forced to recognise 
 the identity of certain co-efficients with electro-magnetic potentials, 
 just as we have identified others with the potentials of the gravita- 
 tional field. Weyl may be right in his criticism, but the conclusion 
 that seems to follow as regards curvature and metric is not that the 
 Einstein principle must be thrown over but that it should be developed 
 in a yet wider form. Cassirer seems to think this possible, and Hans 
 Reichenbach has recently discussed the way in which it may be done. 
 The question of this conceivable development is one largely, though 
 not wholly, for mathematicians .... pp. 165195 
 
 CHAPTER VII 
 
 BIOLOGY 
 
 Essays in Philosophical Criticism. The view suggested by Professor 
 Haldane and myself thirty-eight years ago. Comparison with that of 
 Cassirer. The task of philosophy in relation to science. The character 
 of Life. The contrast between the logical significances of ' Cause ' and 
 ' End.' Our anthropomorphism in biological investigation. Lavoisier's 
 ideas. The practical physician's idea. What is distinctive in the 
 character of the organism. Reproduction. Contrast with the crystal. 
 The old-fashioned ' vitalism.' What we observe when we study the
 
 CONTENTS xiii 
 
 living organism. Structure and activity are both distinctive mani- 
 festations of what lives. The circulation of the blood. Claude Bernard. 
 The arrangements by which the blood is kept supplied with oxygen 
 and carbonic acid. Breathing. Hydrogen-ion concentration. The 
 action of the kidneys. The responsiveness of their epithelial cells. 
 The secretion of sugar and water. Temperature. Microzoa. Life 
 contending with life. Diabetes and diabetic coma. Biot and the 
 Arcella. The swim-bladder in fishes. Conclusions about the nature 
 of life. Contrast with the principles in mathematical physics 
 
 pp. 196-231 
 
 CHAPTER VIII 
 
 PSYCHOLOGY 
 
 The meaning of the expression ' psychology.' The contrast between 
 the standpoint of Aristotle in his investigations on the subject with the 
 usual standpoint of to-day. The three modern methods of approach. 
 The criticism of the ' Behaviourists.' Professor Lloyd Morgan on 
 Instinct. The value of the study of the biological organism in which 
 mind expresses itself. The difficulty of taking the mere form of external 
 succession in series as the final form of the phenomena observed. The 
 category even of End, while sufficient in the study of life, appears to be 
 insufficient for that of mind. The great necessity for caution in assum- 
 ing conceptions introduced from other sciences to be adequate. Not 
 the less these other sciences assist and are required, but for purposes 
 that do not appear to be exhaustive of the truth. The danger of un- 
 conscious metaphysics. What the soul really appears to mean. The 
 relation of physiological to introspective psychology. What physio- 
 logical psychology can reach. ' Cause ' and ' stimulus.' Reflex 
 action. Professor McDougall's view of the relation of body to mind. 
 The cerebral hemispheres. Neural action. Neurones and synapses. 
 Our sensations are not related like self-contained atoms. The varieties 
 in nervous processes. How their results come together in the soul. 
 Volition seems to lie beyond any biological interpretation. Psycho- 
 analysis. The teaching of Freud. Its distinctive nature. What is 
 meant by the ' unconscious.' The employment by Freud of language 
 that is only metaphorical. The criticisms that have been made of 
 his results. The ' all or none ' theory. Can instinct be marked off 
 sharply from other mental content ? The distinction made between 
 ' mental structure ' and ' mental functioning.' Is there an actual line of 
 demarcation between the conscious and the unconscious ? Can we 
 study mind adequately if we confine ourselves to the conceptions of one 
 or two special sciences ? The difficulty which introspective psychology 
 encounters. The phenomena of double personality. The real value 
 of psychological methods. Professor John B. Watson's book on 
 Behaviourism. Can any such method guide us to the whole truth ? 
 
 pp. 232-278
 
 xir CONTENTS 
 
 CHAPTER IX 
 
 CONCLUDING REMARKS 
 
 The true character of the actual. The ideal of knowledge. It has to 
 deal with what is essentially concrete and individual, and to ascertain its 
 variety in significance as it presents itself. Goethe on the other and more 
 abstract procedure. The reality of the world in the f ulness of its aspects. 
 Truth in science. The fallacy of trying to break up and get behind the 
 basic fact that we know. The dangers of a metaphysical slough. The 
 contrast of the view taken here with that adopted in Mr. Bertrand 
 Russell's Analysis of Mind. Observations on his book and on its 
 qualities. The real contributions to science which he has made, and 
 the difficulties in the way of his method. His views on ' continuity,' 
 and on other subjects. The ultimate criterion of truth in knowledge. 
 Philosophy as criticism of categories . . . pp. 281-300
 
 THE 
 
 PHILOSOPHY OF HUMANISM 
 
 INTRODUCTION 
 
 IN an early passage in his Metaphysics Aristotle pro- 
 nounces the views of his predecessors to be tainted 
 with an artificial character. Of this he sets himself 
 to get rid in his own view of the object world. 
 " Surely/' he says, " it is not likely either that fire 
 or earth or any such element should be the reason 
 why things manifest goodness and beauty both in 
 their being and their coming to be, or that those 
 thinkers should have supposed it was ; nor again could 
 it be right to ascribe so great a matter to spontaneity 
 and luck. When one man declared, then, that reason 
 was present as in animals so throughout nature 
 being the cause of the world and of all its order, he 
 seemed like a sober man in contrast with the random 
 talk of his predecessors. . . . Those who thought thus 
 stated that there is a principle of things which is at 
 the same time the cause of beauty, and that sort of 
 cause from which things acquire movement/' 
 
 It is more than two thousand years since Aristotle 
 said this. In the interval there has been enormous 
 progress in knowledge of certain orders. Turning to 
 facts and applying methods for exact observation 
 and measurement the science of to-day has grown,
 
 2 INTRODUCTION 
 
 and is still growing. But the progress has been in 
 the main progress in knowledge of quantitative 
 relations. In literature and art we have not added 
 to the store in the same fashion. We have indeed 
 added much, but in point of quality and sense of 
 form it is not clear that we have made any ad- 
 vance beyond the level reached by Ancient Greece. 
 Glancing at philosophy, this appears to be something 
 different from science and from literature and art. 
 It is concerned with the significance of the universe 
 regarded as a whole, with the same problem as that 
 to which Aristotle devoted much of his genius. 
 
 Have we got beyond Aristotle in our philosophical 
 outlook ? If it is a question which concerns quality 
 in knowledge the answer is not a plain one. Like 
 Plato and Plotinus, perhaps more so than either of 
 these, Aristotle had freed himself from certain obses- 
 sions that seem to hamper philosophical thinking 
 with us moderns. His metaphysics and his psy- 
 chology are largely critical. They consist in an effort 
 to drag to light and eliminate unconsciously made 
 assumptions in these subjects. It is in truth of 
 assumptions of this type that he is complaining in the 
 words quoted. 
 
 It is significant that Goethe, the range of whose 
 intelligence has among moderns rivalled that of 
 Aristotle, makes the same sort of criticism. He is 
 not content to tell us in merely general terms that we 
 do not know how anthropomorphic we are. He 
 devotes many pages to the expansion of this theme, 
 insisting that experience in every form is moulded by 
 the intrusion of the personality of the observer, and 
 that it is accordingly only when men work together 
 and compare their results that anything reliable
 
 ARISTOTLE AND GOETHE 3 
 
 emerges. 1 Science requires more than the work of 
 one individual for its creation. It is the child of 
 time sufficient to eliminate the intrusion of the sub- 
 jectivity of observers, both in facts supposed to have 
 been observed and in theories about them. 
 
 It was for this reason that Goethe took little interest 
 in the metaphysical systems of his day, although 
 he had given them more attention than is generally 
 supposed. He thought them all too abstract, and he 
 would not set out in quest of an Absolute, any more 
 than he was tolerant towards attempts to reduce mind 
 and matter to constructions from atomic particulars, 
 basic to both. Like Aristotle his starting-point was 
 the world as it seems to present itself in the fulness 
 of everyday life. He was not troubled by the fact 
 that this is the experience of a particular individual, 
 for he seems to have held that the individual 
 himself has meaning only in and through it. 
 It is this experience, as interpreted by mankind 
 generally through the course of time, that was his 
 problem. He did not look for finality in such an 
 interpretation. There was no finality for him in 
 the forms of truth. It was, as in art, perfection 
 in the quality of the effort that mattered. His 
 object was not to fashion a theory of final first 
 principles, but to eliminate unconscious prejudices. 
 Aristotle had previously set himself to what was at 
 least in part the same purpose. 
 
 Were these great thinkers right, each in his 
 individual way, in what they appear to have held 
 to a large extent in common ? The question is a 
 
 1 What he said in a number of his prose writings on this subject 
 will be found, conveniently collected, in a volume by Max Heynacher, 
 called Goethe's PhUoaophie aus aeinen Werken (Leipsig, Meiner, 1905). 
 2
 
 4 INTRODUCTION 
 
 serious one. For if it is answered in the affirmative 
 we must be critical about the point of departure in 
 philosophy. They bade us take the world as we find 
 it ; accept its reality, as it seems, and then trace out 
 the relativity of that reality, as it grows or ' becomes,' 
 to our own standpoints. There is much to be said 
 for such an elimination of metaphysical presupposi- 
 tions, provided that it is thrown into the form of 
 scientific principle. It gets rid of the controversy 
 between idealism and realism ; for the distinction 
 between mind and matter, observer and observed, 
 appears now to be one that falls within knowledge 
 itself and assumes it as already there. Any particular 
 activity in knowledge is found to proceed by way 
 of abstraction downwards from what is most con- 
 crete, that is the actual. " Man/' says Goethe, in 
 his Der Versuch als Vermittler von Objekt und Subjekt, 
 11 takes interest in an object just in so far as he 
 fashions an idea of it. It has therefore to pass into 
 his mode of apprehension." And a little later on : 
 " In living nature nothing happens except what 
 stands in relation to the whole, and if phenomena 
 appear to us as if isolated, and we have to look on 
 our investigations into them as isolated facts, this 
 does not really mean that they are isolated ; it only 
 raises the question how are we to ascertain the con- 
 nection of these phenomena and these circumstances." 
 Accordingly, our experience is not static, but is 
 dynamic or self-evolving, its phases passing into each 
 other. For clearness we set them in our knowledge 
 as fixed objects for our reflection, and in so doing 
 have always somewhat transformed them by the 
 process of abstraction in which we do so. If this be 
 the true character of experience, then the different
 
 VARIETY IN KNOWLEDGE 5 
 
 varieties of knowledge about it will differ according 
 to the conceptions which are dominant in the abstrac- 
 tions so made. But all these varieties have their 
 origin in the unique and individual entirety we name 
 * knowledge/ a source that is not broken up in our 
 experience of the individual object in the fashions 
 or degrees that the varieties of abstract reflection 
 are ; as little broken up even in human experience 
 when it is left to itself as the limitations of the mind 
 in which it expresses itself permit. 
 
 If the main thesis of the Greeks and of Goethe is 
 a true one it carries with it far-reaching consequences 
 in the adoption of method in philosophy. For it 
 imports that what we must start with as our basic 
 fact is first of all the world as it seems to us, the 
 concrete many-sided world, with the whole of its 
 riches, that appears present in our every-day experi- 
 ence. We must not begin by trying to find elements 
 out of which this world of actuality is put together 
 and pieced up. As soon as we try to start explana- 
 tions of this kind we fall into the fallacy for which 
 Aristotle criticises his predecessors, the fallacy of the 
 abstract mind. Our experience is no passive aware- 
 ness put together out of isolated elements of sensation 
 that exist as self-subsistent entities in independence 
 of each other. The ideas of such entities are them- 
 selves arrived at only by abstract methods, and give 
 us merely phases within a larger entirety in which 
 they stand in ever- changing relations which are 
 integral for the whole. All such relations are there- 
 fore internal, that is they are inseparable from the 
 reality of the phases into which they enter. What 
 are termed " external " relations, and are treated 
 as severable, are themselves abstractions, without
 
 6 INTRODUCTION 
 
 reality independent of the whole in which they have 
 meaning. Meaning, indeed, enters into reality every- 
 where, and is of its essence. 
 
 Now the character of meaning is that of mind. 
 Meaning imports the presence of mind and has its 
 home there. It is beside the point to say that such 
 mind is always the mind of a particular individual. 
 For such an individual himself has only meaning as 
 an object within the world as it is for mind. Know- 
 ledge as such therefore comes first. Those who try 
 to reduce reality to isolated and self-subsistent sensa- 
 tions encounter the difficulty that the nerves, and the 
 brain itself which receives stimulation from without, 
 and so builds up the external world which has to 
 be accounted for as inclusive of all of these, must be 
 assumed to be present before we can conceive our- 
 selves as having any sensations to build with. Just 
 so the fact of individual experience has to be pre- 
 supposed before we can make any departure at all. 
 But those who thus start with experience as already 
 there are at least free from a fatal obstacle which 
 confronts the subjective idealist and the materialist 
 alike. If I look at the people who are crowded into 
 a room, listening it may be to myself who am 
 speaking, there is a .fact that confronts me. Into the 
 sensations produced in their respective brains, by the 
 electro-magnetic waves of light or the atmospheric 
 waves of sound which stimulate their optic or 
 auditory nerves, I cannot enter. These produce 
 sensations which belong exclusively to the individual 
 in whom they are awakened. I, the speaker, know 
 and can know nothing directly of these sensations. 
 They cannot come within my immediate awareness. 
 Nor can the audience enter into my own sensations.
 
 SENSATION IMPORTS GENERAL KNOWLEDGE 7 
 
 But yet we are certain that we see the same room 
 and hear the same words. How is this possible ? 
 Only in one way. What we know in common cannot 
 consist in immediacy of feeling, which is excluded 
 from everyone excepting the person whose private 
 feeling it is. But there may be knowledge in common 
 of a kind that is logically quite different from mere 
 feeling, the knowledge in common which arises from 
 thinking about our private experiences in identically 
 the same conceptions as others employ, and thus 
 giving to our respective sense experiences an identical 
 meaning. It does appear as though what those 
 present have in common is not sensation but know- 
 ledge about sensation. Apart from interpretation 
 such sensation amounts to nothing at all. Yet 
 without material to set for itself into objective form 
 the thought would be an abstraction which had no 
 objective or individual character in which to make 
 itself real. If it can so set itself in individual form 
 the form becomes symbolic of the conception through 
 which it is fashioned. Neither the lecturer nor his 
 audience in the lecture-room seem to separate the two 
 aspects which their individual experiences present. 
 These vary with the individual. But in the differ- 
 ences there is pervading identity, and it comes from 
 identity of form in thinking. The particularism which 
 is the other aspect has the character of a ' happen- 
 ing ' in space and time. But no conception used in 
 interpretation appears to be any such happening. It 
 belongs to a different order, one which is concerned 
 not with events, but with what is required before 
 events can have the meanings that have to be inherent 
 in them if they are to belong to reality. 
 
 It was something of this kind that Aristotle appears
 
 8 INTRODUCTION 
 
 to have meant when he distinguished the Passive 
 Reason, which operates in human form in the world 
 of which we are denizens, from the Active Reason 
 which that form and the world itself presuppose as 
 foundational to them. I am speaking of his Meta- 
 physics, rather than of his Logic. These two forms 
 of reason were not for him separate entities. The 
 ideal completion or truth of the Passive or human 
 Reason was just itself ' become ' the Active Reason. 
 Such becoming could never be adequately accom- 
 plished in time or under the conditions of the human 
 organism, but it was due to the activity of the supreme 
 form as the end which was determinative, an activity 
 not merely in time but in thinking. Such activity was 
 no happening of events, but was presupposed in the 
 significance of all such happening. 
 
 Modern versions of what is called objective idealism 
 embody principles which are analogous. But just as 
 sensationalism veers over into the idea of thought as 
 a construction by or an activity of things, so there has 
 been a tendency in modern times to speak of things 
 as though constructed by thought. The strength of 
 the Greeks was that they were not prone to these 
 temptations. The reason was that they did not 
 dream of subject and object as different things, or as 
 being more than correlated phases in a single basic 
 activity. Where, as is often the case, they hesitate 
 about the singleness of the process, it is not because 
 they are seeking to distinguish these as things or 
 objects in a world of experience. With all their 
 shortcomings in precision of language they had not 
 to bear the burden of our modern obsessions, arising 
 from the hypostatising methods which were almost 
 inevitably consequent on the contracted view of the
 
 EXAMPLE FROM THE LECTURE-ROOM 9 
 
 inwardness of facts observed which followed on 
 Bacon's work for science. 
 
 Those assembled in a lecture-room have thus 
 identities before minds which differ numerically only 
 in that the organisms in which they express them- 
 selves differ numerically as objects in space and time. 
 But these objects are individual, that is to say they 
 are actual objects only in so far as judgment through 
 universals as much as the particularism of feeling 
 enters into their character. As I shall endeavour to 
 point out in the subsequent chapters of this book, 
 that is how these objects are real as well as significant. 
 The particular of sense could have no meaning at all 
 for us, and therefore no existence, but for its setting 
 in universals imported by some mode of reflection, 
 however slight. In this fashion concepts enter into the 
 constitution of reality. Because of the distinctions 
 with which the particularism of the actual is so 
 endowed, mere logical identity becomes identity in 
 difference, or correspondence. It is correspondence 
 in our conceptions thus based, not on ' happenings ' 
 which are necessarily diverse, but on identity of 
 thought, that makes us experience the same lecture - 
 room, the same sun, moon and stars, and, generally, 
 the same world. A single world is before us by 
 reason of an identity in our thinking apart from 
 which it would not be there in common for us. 
 
 It is for such thinking and only for such thinking 
 that space and time themselves are present and are 
 possible. Such reflection appears to be foundational 
 for the very possibility of an object world, and of 
 ourselves as in that world. We are therefore more 
 than we take ourselves to be when we regard ourselves 
 as our own object and hypostatise knowledge into a
 
 10 INTRODUCTION 
 
 property of this object. Something of the kind Kant 
 told us, but not altogether consistently. In another, 
 but I think rather partial aspect, Bergson also has 
 expressed it. And it is interesting to observe the 
 traces of this foundational view of the activity of 
 reflection in what was written, nearly half a century 
 ago, by one of the most acute of modern British 
 thinkers, W. K. Clifford. In his Lectures on the 
 Philosophy of the Pure Sciences, delivered at the 
 Royal Institution in 1873, he says that in all our 
 sense experience there is a part which comes from 
 the external world, and a part supplied by the mind. 
 Not the whole of a sensation is immediate experience, 
 but " this experience is supplemented by something 
 else which is not in it." Motion, for instance, he 
 says, we imagine according to the rule of mathe- 
 matical continuity. Between the distinct pictures 
 which we have on the retina we insert an infinite 
 number of intermediate pictures. The motion is 
 imagined according to the laws of geometry, that is 
 to say, it is so imagined that the relations of distance 
 at any instant obey these laws. The rules according 
 to which we analyse and ascertain its nature are the 
 laws of the pure science of motion, kinematics. 
 Putting the matter more generally, " we supplement 
 our experience in accordance with certain rules, and 
 some of these rules are the foundations of the pure 
 sciences of space and motion." In an approach to 
 an anticipation of what Minkowski was to say more 
 than thirty years later, he goes on to declare that he 
 speaks of space and motion, because he thinks it more 
 correct to hold that " we imagine time by putting 
 together space and motion than that we imagine 
 motion by putting together space and time." He then
 
 W. K. CLIFFORD 11 
 
 proceeds to discuss what is called the continuity of 
 things. ' Things that is to say, combinations of 
 possible experience are not persistent, but they 
 change continuously in the imagination by which we 
 fill up that experience." Number is just as much a 
 conception of reflection as is the relation of continuity 
 with which geometry is primarily concerned. We 
 group things by using language or by signs, such as we 
 get by counting on our fingers. We thus form 
 ' complicated conceptions/ imaginations of series of 
 things and their combinations. ' We carry about 
 with us a certain apparatus of counting, which was 
 primarily our fingers, but is now extended into a 
 series of signs which we can remember in a certain 
 order the names of numbers. Our language is so 
 formed as to make us able to talk to ourselves about 
 the results of counting. The propositions of arith- 
 metic are compounded in general of two parts : a 
 statement about the counting apparatus, and a 
 statement about the different ways of describing its 
 results/' There is an assumption which underlies 
 the foundation of the whole science of number. It is, 
 he says, that when we count, for instance with our 
 fingers, while the order in which we use our fingers is 
 no doubt fixed, we make the assumption that a group 
 of things comes ultimately to the same finger in 
 whatever order they are counted. Of the things 
 taken in the original order the last one touched is, 
 say, that one which my thumb touches. It is assumed, 
 in oblivion that it is a principle that is just 
 assumed by the mind, that if the things are taken in 
 any other order and applied to my fingers the last 
 one touched will be the thumb. This proposition is, 
 he finds, the foundation of the whole science of
 
 12 INTRODUCTION 
 
 number, and he gives credit for its elucidation to 
 Cayley and Sylvester. His theory of mental apparatus 
 of different kinds he applies to the character of space. 
 He points out that the space of Euclid is conditioned 
 by certain assumptions which we have introduced 
 into our knowledge of it, with the result that it is 
 taken to have no curvature, whereas it may equally 
 well, so far as closer analysis of the fact may show, 
 have a negative curvature, like the space of Lobatschef- 
 sky, or a constant positive curvature. In this last 
 view it is clear that he finds himself in the main in 
 accord with the reasoning of Biemann. In the 
 volume of mathematical papers which was published 
 after Clifford's death, there is a rendering into 
 English of Riemann's famous essay on the Hypo- 
 theses which lie at the Foundations of Geometry. 
 In that essay Riemann, as Clifford was to do a little 
 later in a different fashion, had set himself to the 
 task of constructing the notion of a multiply extended 
 magnitude out of general notions of magnitude. It 
 followed for him that a multiply extended magnitude 
 was capable of different measure relations, and conse- 
 quently that the space which we take to be actual 
 was only a particular case of a triply extended 
 magnitude. He therefore concluded that the pro- 
 positions of current geometry could not be derived 
 from general notions of magnitude, but that the 
 properties which distinguish actual space from other 
 conceivable triply extended magnitudes were only to 
 be deduced from experience. 
 
 Put shortly the outcome for both of these mathe- 
 maticians was that, in the object world with which 
 mathematics deals, conceptual thought enters into 
 and is inseparable from the constitution of reality,
 
 RIEMANN 13 
 
 which is in this sense relative to our knowledge of it. 
 Clifford did not think that Kant was right in holding 
 that in knowledge there are genuinely pure a priori 
 forms which are imposed on the substance of the 
 object world as it were ab extra, and apparently he 
 did not realise the methods in which this semblance 
 of a breaking up of the entirety of knowledge on the 
 part of Kant had been sought to be got rid of by 
 later metaphysicians. Believing, however, with Kant 
 that there were forms in knowledge contributed by 
 mind, he appears to have held that there were simple 
 ultimate elements of ' mind stuff ' which constituted 
 the structure out of which thought and feeling were 
 both built up. That principles which dominate and 
 shape thought should have become implanted in 
 knowledge, as the outcome of activity on this basis, 
 he attributed to evolution aided by heredity ; so far 
 in agreement with Herbert Spencer. Subject to this, 
 and as evolved in this fashion, he seems to have 
 considered mind so conceived as the ultimate 
 reality. 
 
 The result of this fundamental conception was 
 potent in his mathematical investigations, and led 
 him to anticipate much that has since emerged in 
 the mathematical physics of Relativity. Riemann's 
 teaching he grasped and appreciated as almost no 
 other did. Those who have read the fragments on 
 philosophy at the end of the volume containing Rie- 
 mann's collected works, will appreciate the bond 
 between the two men. Well may Professor Weyl 
 pay the tribute to Clifford's genius which is quoted 
 later on, at p. 181. 
 
 The thinking in which the world of objects has its 
 foundation is no event to be looked on as a particular
 
 14 INTRODUCTION 
 
 object among others in the world to which it gives 
 the significance of reality. Nor can it be an attri- 
 bute or activity of the self as an object in that 
 world. Such a self is made present to itself as object 
 only in an abstraction which does not yield the whole 
 truth. The entirety appears to be that activity of 
 knowledge within which not only object but subject 
 for which it is object arise. The genuine subject 
 aspect within this entirety remains intact in the 
 abstractive process which segregates the object but 
 cannot reach that for which it is there. It is only 
 by watching thought develop itself in its own self- 
 implications that we can discover its nature. The pro- 
 cess must be in its essence one of mediate inference. 
 For in what we call self- consciousness we are always 
 tending to make the abstraction which identifies the 
 self with the thinghood in which it expresses itself 
 even for the mind that is aware of itself as knowledge. 
 From that knowledge, from what experience implies 
 and reveals, we start. We assume it as our point of 
 departure and behind it we cannot get by any direct 
 inspection. But although we cannot by analysis 
 resolve our experience into further elements out of 
 which it is constructed we can by analysis study its 
 nature conceptually, as we do in logic. Only the 
 logic must be one in which the facts are simply made 
 free, through the exclusion of what is foreign to them, 
 to do justice to themselves by revealing their own 
 implications. Something of this kind we seem to 
 approach whenever we are brought to the sense 
 of the fullest reality, in poetry, in art, in religion. 
 The sense which comes to us in instances of this kind 
 is not developed knowledge, for such knowledge is 
 fully intelligible only when it assumes rational form
 
 EXPERIENCE AND ASSOCIATION 15 
 
 in conceptions that are not fragmentary but belong 
 to an entirety. Such conceptions it may be impossible 
 for our minds, conditioned as they are by the 
 physical organism in practical possibilities of retention 
 and expression, to fashion forth in the completeness 
 of their system and relations. It is always, as I 
 shall point out in the chapter which follows in this 
 book, in individual form, that is, with the moment of 
 the particular implied as present, that we know, even 
 when we appear to reason abstractly. But at least 
 the insight thus gained into the nature of knowledge 
 delivers us from the mistake of supposing that we 
 have exhausted the entirety when we have analysed, 
 be it never so apparently fully, the object aspect which 
 it always presents. For this thesis, and as plainly 
 supporting it, it would be easy to cite witnesses, not 
 only from the domains of poetry, art, religion and 
 philosophy, but from teachers such as Riemann and 
 Clifford and their successors of to-day, as well as 
 from inquirers in fields other than those of mathe- 
 matical physics. 
 
 The doctrine that the origin of knowledge may be 
 found in habitual association in contiguity has to 
 encounter this initial difficulty. How is a series or 
 aggregate of contiguous impressions possible except 
 as presupposing the knowledge within which it is 
 presented ? Assume such knowledge as conceded, 
 then the association principle becomes very useful as 
 showing uniformities in the ways in which ideas 
 treated as external phenomena suggest each other. 
 But it is of no value in throwing light on the genesis 
 of a knowledge which it has already presupposed 
 for its own foundation. Sensations, even if we could 
 conceive bare sensations, would not bring other sen-
 
 16 INTRODUCTION 
 
 sations into being by suggestion. For it is only ideas 
 that are suggested. 
 
 We are thus forced back to the subject, which is 
 itself no event happening in externality, for the 
 explanation of the world as it actually seems to us. 
 By subject we mean here neither a thing in space nor 
 an activity in space. We mean that for which such 
 things and activities are, and apart from which they 
 have no significance and so no reality. Thus inter- 
 preted the presence of the subject aspect of reality, 
 of knowledge as that to which reality is essentially 
 relative, is everywhere apparent, even in what, 
 looked at superficially, we take to be a mere object 
 world. I meet my neighbour in the street. Abstract- 
 ing from other aspects which he expresses for me I 
 can regard him as consisting in only so many pounds' 
 weight of chemical stuffs, atoms and molecules. But 
 this aspect rarely interests me. I come nearer to my 
 habitual point of view when I look on him in another 
 aspect of his factual relativity to knowledge, the fact 
 that he is a living organism. For this concerns his 
 health. I may hold a policy of insurance on his 
 life, or I may be dependent on him, and therefore 
 desire his continuance in existence as any parasite 
 might do. But none of such aspects are adequate to 
 his personality for me. What he expresses above 
 and beyond all these is meaning for me of another 
 kind and level. He is a thinking being, he reflects, 
 he has a store of knowledge and of memories, he is a 
 fellow citizen, he is my friend for whom I have a 
 deep regard, he and I are equals and identical in this, 
 that we both say ' I ' and are the centres of our own 
 conceptual worlds. Physically he occupies a different 
 part of space from myself. Spiritually he does not,
 
 PERSONALITY 17 
 
 for our concepts and our modes of thinking are based 
 on what are logical identities, and are not occur- 
 rences in space and time at all. As a physical object 
 he is indeed numerically different from myself, but 
 if that were all I could not know him as a self standing 
 in relation to me, another self. Identity has in certain 
 aspects superseded difference. In virtue of such 
 identity I attach significance to external activities 
 on his part, such as speech, which are for me symbolic. 
 Meaning enters into the very essence of reality in 
 this connection. That is the foundation for me of 
 my recognition of personality in him. He says 'I/ 
 This gives to the activities which his freedom in 
 volition and self-control fashions a significance which 
 is, throughout divergence in external form, identical 
 with my own. For I, too, say ' I ' and act with 
 self-determination accordingly. I am subject and 
 he is subject. We do not explain this subject nature 
 as a physical object built up out of external happen- 
 ings. For, apart from the common world which we 
 have in virtue of being subjects who know identically, 
 external happenings could have no meaning for us. 
 It is of course true that each of us has been developed 
 from the union of a spermatozoon with an ovum, and 
 that our organisms are the result of a long process of 
 evolution and inheritance. This concerns the aspect 
 which is that of life, just as oxidation concerns the 
 aspect which is that of chemistry, and gravitation 
 that which concerns the material through the meta- 
 bolism of which the organism functions. But the 
 processes of evolution and inheritance belong to the 
 object world, which, with time and space, are there 
 only for knowledge. Even if we think of a cosmos 
 before any living or intelligent being appeared in it
 
 18 INTRODUCTION 
 
 that remains true. Such a cosmos of course would 
 present itself as an object, or idea of an object, within 
 the world as it is for knowledge, and would have no 
 significance excepting as a construction in knowledge. 
 It is a conception got at by an abstraction which is 
 quite legitimate for limited scientific purposes, but has 
 no application in an inquiry into the ultimate nature 
 of reality and of its relativity to knowledge, taken as 
 more than itself an object within its experience of the 
 object world. If my neighbour and I were not more 
 than mere objects for knowledge, and did not express 
 in some aspect the foundation of knowledge itself, 
 we should not only contemplate no such cosmos, nor 
 any past, present or future, but we should be 
 impenetrable to each other. In short, we should not 
 exist. 
 
 We see thus the potent effect of abstractions in 
 fashioning for us our universe. With abstractions we 
 have in the main to be content to dwell. For, as 
 Goethe said, he who would accomplish anything must 
 limit himself, and it is only by limiting our activities 
 and directions in knowledge that we can exercise the 
 degree of concentration that is required to render it 
 distinct and progressive. All scientific method pro- 
 ceeds by way of concentration on methods which are 
 of necessity partial. The part played by philosophy, 
 which has to observe mind as it applies its activity in 
 its freedom for self-development, is to be the observer 
 and recorder of the process in its varying forms. 
 Philosophy dare at no time forget that knowledge 
 belongs to an entirety in the sense of the expression 
 already discussed. It dare no more forget that mind 
 is never static but is continuously active in the 
 changing dispositions it makes. Knowledge is con-
 
 KNOWLEDGE AND MIND 19 
 
 stantly passing beyond the distinctions which it sets 
 up and including them in larger wholes. That is why 
 the Greeks called the activity of knowledge ' dialec- 
 tic/ and why some such term is still required. In 
 looking at mind from the level at which it presents 
 itself as subject in knowledge we ought not to try to 
 distinguish it from knowledge itself. There is no 
 real distinction in meaning between the two names, 
 and to speak of mind with special emphasis on that 
 word suggests, just what we ought to desire to avoid, 
 the idea of mind as a thing. 
 
 These considerations raise the question why the 
 starting-point from which we set out in the inquiry 
 into the character of reality is spoken of as either 
 knowledge or as mind. Now this question appears 
 to be a very legitimate one. As I have already said 
 the word * mind ' is apt to suggest thinghood. On the 
 other hand knowledge conveys the impression that 
 what is merely abstract is intended. Such sugges- 
 tions would be, it is needless to add, quite out of 
 place. What we have to do, if the purpose in hand 
 is to be carried out, is to try to express the actual as 
 starting-point, just as we find it, and without sheering 
 it, by any process whatever of bifurcation, of aspects 
 in its reality. Now the actual is nothing that stands 
 still. Distinctions are always developing themselves 
 within it. Even its limits are always altering both 
 in extent and in content. We may say that the 
 actual is experience, if we are careful not to import 
 into our meaning any delimitation of object from 
 subject as separable from it. In other words, ex- 
 perience in this sense means the entirety within which 
 both fall. Past, present and future fall within it 
 likewise. Those who have read Minkowski may notice 
 3
 
 20 INTRODUCTION 
 
 that the analytical conceptions he employs in his 
 presentation of his idea of the real world for mathe- 
 matical physics appear to be far from out of harmony 
 with the last sentence. Widened in this fashion, and 
 taken as covering all its own implications, experience 
 becomes indistinguishable from knowledge, if know- 
 ledge is given its full meaning. For knowledge as it 
 is expressed in us includes not only what we treat 
 as abstract conceptions, but the feelings which they 
 qualify and set in various orders. We distinguish 
 them. But, as all knowledge of objects is of objects 
 in individual form, general and particular are not 
 separate factors here, but are just logically distin- 
 guished moments, real only in their union in the 
 form of individuality itself and separable only by 
 abstraction. To this topic I shall return in the 
 ensuing chapter. Knowledge completely interpreted 
 appears to be neither general nor particular. If it is 
 always expressed in its objects in a form that is indi- 
 vidual and so unambiguous, it would appear natural 
 that in other aspects, those in which it signifies 
 self-awareness as subject, we should not look for 
 any different aspect. Human knowledge is rendered 
 incomplete in its self-expression by the organic 
 appearance to which it gives significance as intelli- 
 gent. Were it to express itself at a level less partial, 
 in which it could attain completion, it would be 
 God's knowledge, within which the entirety of the 
 universe, the subject as well as the object, fell without 
 distinction, and in which all abstractions and degrees 
 distinguished from each other presented themselves 
 as belonging to an entirety every phase of which was 
 comprehended in its proper relation to the whole. 
 Into speculations on such a possibility we need not
 
 GOD AND MAN 11 
 
 enter. It is enough for us that the distinctions 
 which fall within our human knowledge, although 
 they seem to be imposed on it, are brought about 
 by itself and not ab extra. The influence which 
 brings them about is apparently immanent. There 
 is no reason for assuming any external boundary 
 between God and man. None the less for man his 
 knowledge is never creative, in the sense in which 
 to think and to call into existence are one and the 
 same act. The difference set up between these is 
 however one to be sought within and not without 
 ourselves. It is also not the less on that account 
 real for our practice as human beings. 
 
 Such an interpretation of human knowledge leaves 
 us free to make it a point of departure which is, for 
 us at all events, foundational. It is no new inter- 
 pretation. To imagine that it could be so after 
 many centuries of the striving of thought to reach 
 the basis of reality would be contrary to common 
 probability. It would also be to misread the records. 
 The history of philosophy discloses the constant 
 recurrence of such an interpretation in varying forms. 
 We find it alike in the philosophy of India, and in 
 that of Ancient Greece. We find it in Neoplatonism. 
 We find it striven after by the Schoolmen. We find 
 it again in the renascence of 'speculative activity in 
 Europe, and we see it, both latent and in overt 
 expression, in Kant and the so-called Idealists who 
 have followed after him. But in the interpretation 
 we may give it to-day it is hardly Idealism. It is 
 rather a transformation of Realism. The necessity 
 for it has been brought about by recognition of too 
 contracted views on the part of those who thought 
 that physical and natural science could be made com-
 
 22 INTRODUCTION 
 
 plete without reference to philosophy itself. Science 
 gives us truth which is invariably relative. Philosophy 
 does not seem to give us final truth. It dare not, 
 if it understands its own business, warrant its result 
 as ever being either final or complete. What it can 
 do is to drag relativity to light, and perform the 
 essential function of the critic of knowledge in its 
 various aspects. Its work can never be ended, for 
 it is always being called on to deal with the new 
 material which science is producing. It has not, as 
 is usually the case in science, any possibility of 
 resorting to external standards by which to measure 
 its results. But it can assign the values, possessed in 
 different orders in knowledge, of such measurement. 
 To desire itself to measure in such a fashion would 
 be to misinterpret its own function. It is akin to 
 literature at least as much as to science in this, 
 that it is concerned as is literature with quality, 
 and is not merely concerned with relations of 
 quantity. 
 
 No more, then, than in the case of poetry can 
 philosophy hope for finality. But it may hope for 
 progress in the quality of its interpretation, and in 
 the width of its grasp of the facts presented by the 
 sciences only in special relations. The task, in short, 
 of philosophy is that which Goethe assigned, when he 
 insisted, as was remarked early in this Introduction, on 
 its being essential that men should work at a common 
 task, and compare results attained only after the 
 lapse of a long period of work in common, if anything 
 reliable was to emerge. It is in the quality of the 
 struggle to attain it, and not in any finality we 
 suppose ourselves to have reached and to be entitled 
 to rest on, that truth consists for human beings. It
 
 FINALITY IN TRUTH 23 
 
 is only by striving daily to conquer them anew that 
 we gain and keep our life and freedom. 
 
 But if the historical development of philosophy 
 has not brought us to anything that we are entitled 
 to regard as final truth, it has at least shown us how 
 narrow much of our thinking has been, and how we 
 are prone to lapse into abstractions. Call it mind, 
 call it knowledge, call it experience, the criticism of 
 method in the search after the ultimate foundation 
 of reality has at least brought to us certain lights. 
 It has eliminated merely conventional problems. 
 However we name the basis from which we start, 
 this seems clear ; we cannot dissociate it into con- 
 stituent elements, and what we call nature is itself 
 an abstraction from its more concrete reality. It is 
 only if we have these things always before our minds 
 that we can hope to analyse the character of a basis 
 which is itself foundational for all analysis. 
 
 There are, in particular, two present-day schools 
 of philosophical thought which take up different 
 attitudes to this conclusion. One is that of the 
 modern Italian Idealists ; the other that of New 
 Realism. The first of these claims to be able to 
 carry the conclusion just indicated to still more 
 definite developments. In his book on the Theory of 
 Mind as Pure Act, which we here are under a debt 
 of gratitude to Professor Wildon Carr for having 
 translated into an admirable English version, Pro- 
 fessor Giovanni Gentile, of the University of Rome, 
 has set forth an idealism which is akin to, while yet 
 differing from, that of Croce. In the third chapter 
 of his book Gentile describes the character of mind 
 in terms which exclude all notions of it as substance, 
 and display it as pure spiritual activity. His idealism
 
 24 INTRODUCTION 
 
 is the negation of any reality which can be opposed 
 to thought as independent of it or as presupposed by 
 it. The subject is a purely constructive process in 
 which the object is evolved, and is therefore never 
 itself object nor being nor a state of being. All that 
 is turns out to be the constructive process itself. 
 This is pure activity within which all forms arise, 
 including that of the self when sought to be made 
 object, a form which is thus only derivative and is 
 not a true one. The phenomena which mind produces 
 in its continuous self-development may assume an 
 apparently static form. They do so because of the 
 limitations of the end to realise which mind has 
 made them what they are. A stone is because it is 
 already all it can be, and has realised its essence. 
 The restricted nature of objects is a consequence 
 which follows from the fact that everything is pre- 
 sented in its relation to mind as a reality which 
 presupposes knowledge. But mind itself is not so 
 presented. It is the source of its own laws, and is 
 not restricted to a definite nature in which its process 
 is exhausted and completed. It is no object but is 
 opposed to objects. It is process or act and is 
 limitless. " Just as all which has been understood 
 is nothing in regard to what we want to and are 
 yet unable to understand, so likewise in the moral 
 life all the merits of the noblest deeds hitherto per- 
 formed do not diminish by a hair's breadth the sum 
 of duties there are to fulfil and in the fulfilment of 
 which the whole value of our conduct will lie, so long 
 as we continue to have worth as spiritual beings." 
 Verum est factum quatenus fit. 
 
 The value of this form of Idealism pushed to the 
 extremes which characterise it lies in its insistence
 
 THE ITALIANS AND GENTILE 25 
 
 on rejecting the category of substance in its appli- 
 cation to mind. The method rejects the psycho- 
 logical view wholly in favour of a different method, 
 wherever the purpose is to get at the final nature of 
 the real. In so doing it can hardly render justice 
 to science, or appreciate adequately the respective 
 values of the degrees or varying levels which 
 knowledge discloses. There appears to be little 
 room for any principle of degrees in an idealism 
 which is so determinedly opposed to the claim of 
 the object world to present intelligence as a fact 
 disclosing itself in different levels at which it 
 rises towards mind. There is but little room left 
 for the world in any such system of truth. The 
 strength of Gentile's reasoning lies in its affirmance 
 of unity, and it remains to be seen whether its 
 apparent degradation of multiplicity in aspect leaves 
 philosophy free to fulfil its mission of doing justice 
 to all forms of knowledge as they present themselves. 
 If it fails in this it may have to pay a penalty by 
 being in the end adjudged inadequate as descriptive 
 of reality. 
 
 Not the less Gentile's analysis is a penetrating one. 
 In the chapter on Space and Time in the book referred 
 to he makes some observations which are especially 
 valuable for those who hold both to be unintelligible 
 apart from construction in reflection. For Gentile 
 space and time are the two general systems of the 
 manifold in nature. To affirm such a manifold is to 
 affirm space and time. To imply the reciprocal 
 exclusion of all the terms of the experience of mani- 
 fold objects, we resolve into elements and finally into 
 points, each of which is outside the other, and has 
 all the others outside itself. The points are ideal
 
 26 INTRODUCTION 
 
 constructions ; we do not find or distinguish them in 
 experience, yet we cannot but treat them as inherently 
 distinguishable in the order of experience as conceived 
 in reflection. Each point in space is a centre for all 
 other points, and thus taken by itself would render 
 multiplicity impossible. For the point is a limit of 
 space, and is therefore itself not spatial. But the 
 point which is ' here ' does not remain in uniqueness, 
 or as a centre which excludes from itself multiplicity. 
 It is a-' now ' which, without spatial change, becomes 
 a ' then ' implying by its very character other points 
 which are now or will become so. In this fashion 
 time is the spatialisation of the centre from which 
 arises the unity of the multiple nature of space. It 
 is on this account that space and time can be schemati- 
 cally represented as two intersecting lines having only 
 one point in common. A unique point in space 
 cannot be such unless it is also one among many 
 points in time. The conception of space thus com- 
 pletes itself in time by becoming an absolute multi- 
 plicity, every element of which is itself a multiplicity. 
 The conception of time is different. There we have 
 to arrest the spatial process by fixing a point in space 
 in order to understand the instant which is generated 
 by the multiplication of the spatial point. There is 
 a new spatialisation of the first element of space. 
 If we conceive space as a pure multiplicity immedi- 
 ately given we cannot withdraw from it any of its 
 units without having to conceive this unit in a 
 second pure multiplicity. The reality in the case of 
 space is spatialisation. Co-existence is the con- 
 vergence of all the points of space to a point of time 
 to which all other points are related as outside it, 
 so that it is the negation of their multiplicity. Com-
 
 GENTILE ON SPACE AND TIME 27 
 
 presence is the convergence of all the moments of 
 time (past, present and future, in their distinctions 
 and multiplications) in a present now, which is not 
 in itself something between a past and a future, but 
 is a negation of all such temporal multiplicity and of 
 all succession. It is not duration, for this implies 
 space, but is a negation of what distinguishes time 
 from eternity. Space is the spatiality of such a 
 point, and the point is in itself non-spatial. Time is 
 the temporality of the instant and the instant is in 
 itself non-temporal. That is only possible in so far 
 as they are forms of the activity of thought. Nature 
 is only intelligible as the life of mind. To use W. K. 
 Clifford's phrase we ' nil in ' our experience. 
 
 New Realism stands as the very antithesis to this. 
 It seeks to go behind what is called knowledge, and 
 to find all that is within nature, which it resolves 
 into a complex of self-subsistent entities with relations 
 that are independent of them as they are of the 
 relations. In this sense the relations are called 
 external. The whole of both the entities and the 
 relations can be completely described without refer- 
 ence to mind. The latter may or may not have an 
 existence of its own, but it is an existence which is 
 not required for the explanation of our object world. 
 
 New Realism tends to the resolution of reality into 
 series and groups of atomic sense data, standing in 
 relations to each other which are not only as real as 
 the atomic data they relate, but are of the character 
 of universals. By this recognition of the reality of 
 universals it is distinguished radically from material- 
 ism and from the old-fashioned sensationalism. It 
 will be observed that in this view there is transferred 
 to the object world a great deal that for other
 
 28 INTRODUCTION 
 
 schools has been equally recognised as essential in the 
 constitution of the object world, but as being there 
 inasmuch, but only inasmuch, as that world is what 
 it is as the object of knowledge. One of the diffi- 
 culties with which New Realism appears to be con- 
 fronted is that it seems to stop, in its acceptance of 
 general relations as inherent in the self-subsistent 
 object world, at relations of certain kinds, such as 
 those of mechanism. Some of its most prominent 
 adherents do not even hesitate to suggest that the 
 basic relations in the universe may all be expressed 
 in the form of differential equations. But this 
 suggestion brings the theory to a test. If the rela- 
 tions with which mathematical physics is exclusively 
 concerned are thus to be bifurcated off, what of the 
 infinity of other relations which confront us, for 
 example, in the case of life. These must be either 
 reduced to a mechanistic form or else ignored as not 
 belonging to what is actual. The same difficulty 
 arises when we turn to the domain of ethical pheno- 
 mena, and have to take account of personality, of 
 duty, of freedom, as phenomena apparently con- 
 fronting us. So with the phenomena in the domains 
 of art and religion and of other regions which we 
 think of only as mental or spiritual. These appear, 
 not less than what the standpoint of mechanism 
 discloses, to belong to objectivity. Are they to be 
 transferred to the objective side likewise ? There is 
 no reason why they should not be. But such a con- 
 clusion would entail consequences. One of them is 
 that the difference of the object world from mind 
 disappears and subject and object seem alike to 
 become phases within a larger entirety for which New 
 Realism has no place.
 
 CONTRAST WITH NEW REALISM 29 
 
 On the whole the Italians and the New Realists 
 may be left to fight out this battle of extremes. In 
 the end the controversy may tend to adjust itself. 
 
 I have now said enough to indicate the principle 
 which I have endeavoured to apply in the chapters 
 which follow. It remains to state in what the sub- 
 stance of these chapters consists. 
 
 My purpose is to bring to light the characters of 
 the standpoints assumed in various sciences to be 
 adequate for the explanation of the aspects of reality 
 with which they deal. What the standpoints are 
 depends on the conceptions which define and limit 
 them. In so far as reality is relative to knowledge 
 reality therefore presents itself as belonging to various 
 orders which have to be distinguished. Into an in- 
 dividual phenomenon the categories of more than one 
 of these orders may enter. In The Reign of Relativity 
 I was concerned mainly with the fashion in which 
 knowledge enters into and fashions reality. Want of 
 space prevented me from doing more than deal with 
 the question as one of principle and from following 
 the principle into its application in detail in science. 
 In this volume I have sought to add what is con- 
 cerned with the application in detail. Not the whole 
 of it, for I have restricted myself to mathematical 
 physics, biology, and psychology. But even in these 
 domains alone the ground to be covered is so exten- 
 sive that I am well aware that it is only a few of the 
 main features that I have been able to deal with. 
 These features, however, are indicative of certain root 
 conceptions, and these I have tried to bring to light. 
 The whole task for its completion would require the 
 investigation of other fields, such as those of ethics, 
 the theory of the state, jurisprudence, art and
 
 30 INTRODUCTION 
 
 religion. How a proper inquiry has to be fashioned 
 for these I have indicated, but only indicated, in 
 the chapters of the earlier book in which their 
 treatment is approached. I have not tried in the 
 present volume to revert to these subjects again. 
 The task would be an enormous one. Indeed, the task 
 of the present and limited inquiry is a great one, 
 and requires in reality, a much closer training in the 
 special subjects than I have the privilege of possessing. 
 No one knows this better than I do. But then I am 
 not setting myself to attempt a series of expositions 
 of special sciences. What I am concerned to do is 
 to endeavour to bring out the relations of certain 
 sciences to each other and to knowledge, relations 
 which depend on the principle of relativity in its 
 most general form. Now this is work which lies 
 beyond the limits of any single science. It is a task 
 which is that of philosophy, and in these days philo- 
 sophy fails if it shirks the effort to grapple with it. 
 More and more philosophy is becoming dependent on 
 materials which the sciences alone can provide for its 
 work, and more and more it is becoming plain that 
 immersion in particular sciences is apt to bring with 
 it a tendency to some form of dogmatism, based on 
 the assumption, usually made quite unconsciously, 
 that the method and conceptions employed are 
 adequate for the description of reality in its entirety, 
 and not merely in special aspects. 
 
 Holding this to be the case I have sought, before 
 entering on the treatment of special standpoints in 
 science, to examine in the first place the form of all 
 our knowledge as such. This appears to me to be 
 that the object of knowledge is in all cases individual 
 and unique, that is to say, includes a particular as
 
 PLAN OF THIS BOOK 31 
 
 well as a universal character. These characters, or 
 moments as I have called them, are not, however, as 
 is too often assumed, separate entities in the whole, 
 which is the point of departure. They are neither 
 separate nor separable, otherwise than by abstrac- 
 tions made reflectively. I think that the neglect of 
 this distinction has given rise to much confusion in 
 philosophical thought. Of course the kind of reflection 
 when brought to bear varies and, as it varies, different 
 kinds of emphasis are laid on the aspects of particu- 
 larity or universality, as the case may be. It is this 
 difference in emphasis, carrying with it difference in 
 standpoint, that lies at the foundation of the differ- 
 ence between Humanism and Science. To the treat- 
 ment of this foundation the first three of the chapters 
 which follow are devoted. They were delivered in 
 the summer of this year as the Donnellan Lectures at 
 the University of Dublin, and they serve with the 
 present Introduction as a preliminary study for the 
 remainder of the book. They are printed almost 
 as they were delivered. I fear that those who may 
 have hoped to find them full of matter that is 
 humanistic in the usual sense of the word, and a 
 relief from discussion of dry topics, will be somewhat 
 disappointed. 
 
 The chapters which immediately follow these are 
 directed to the implications of the standpoint of 
 mathematical physics. I am fully conscious that 
 mathematicians and physicists will say with truth 
 that they are on the face of them not written by one 
 of themselves. That is abundantly true. But it is 
 not the details of mathematical physics on which I 
 am venturing to pronounce opinions. It is on certain 
 questions which the mathematical physicists are now
 
 32 INTRODUCTION 
 
 being called on to face in a fashion in which they have 
 not been summoned before. Physics and metaphysics 
 have got into a territory which is a monopoly of 
 neither, and the students in these branches of know- 
 ledge have to try to assist each other to a full con- 
 sciousness of the nature of the knowledge employed 
 and of its methods. If to say this be to make some- 
 thing in the nature of an apology I make it freely. 
 
 As to the later subjects, the chapters dealing with 
 them speak for themselves. In the concluding 
 chapter of the book I have sought to bring together 
 results I seem to myself to have reached.
 
 PART I 
 
 THE PHILOSOPHICAL SIGNIFICANCE OF 
 HUMANISM
 
 THE PHILOSOPHICAL SIGNIFICANCE 
 OF HUMANISM 
 
 CHAPTER I 
 
 SCIENCE AND HUMANISM 
 
 I HAVE chosen, for the subject of these three chapters, 
 the "Philosophical Significance of Humanism." Under 
 " Humanism " I include what conforms to the stan- 
 dards of value in domains such as those of Literature, 
 of Music, of Art, and of Religion. The standards we 
 employ in these domains stand in some contrast with 
 other standards by which we test values in science and 
 in metaphysics. They imply on their faces reference 
 to self-conscious personality, and they are less abstract. 
 None the less my purpose is to find if possible some 
 common denominator for all knowledge, and to bring 
 within the light cast by the principle of its relativity 
 the aspects of human experience which stand in 
 contrast with what we call scientific knowledge. In 
 touching on the general relativity of all reality 
 to knowledge, I will first of all seek briefly to 
 make plain what I mean by knowledge, and the 
 interpretation I place on its relation to reality. 
 This renders inevitable a reference to philosophy. 
 To philosophy I will therefore direct myself in the 
 first place ; I hope although concisely yet not dog- 
 matically or obscurely. Since, however, I devoted 
 a good deal of space to this particular question in 
 a volume published last year, I do not propose now 
 
 4 35
 
 36 THE SIGNIFICANCE OF HUMANISM 
 
 to do more than is essential for bringing out the 
 significance of a general principle. 
 
 What the principle of the relativity of knowledge 
 really imports is that when we say that we know, 
 it is not enough to think of the self as a sort of thing 
 that establishes a merely external and accidental 
 relation between what knows and the object known, 
 as if that object had its existence independently and 
 outside of the relation in which it is known. What we 
 know even most directly seems, when we look more 
 closely than we do in common life, to have neither 
 meaning nor reality apart from being an object for the 
 subject in knowledge. I do not mean that our indi- 
 vidual thoughts make things. For it is plain that we 
 individually are ourselves objects within the general 
 system of experience, just as much as are the other 
 things we know. But I do mean that in logical order 
 the fact of knowledge must come in the first place, and 
 that the nature of what is known is not actually 
 different from that of the knowledge for which it is there. 
 Existence is nothing for us apart from its meaning, 
 and meaning belongs to existence only as known. 
 Outside meaning for knowledge, actual or possible, 
 being has no significance and no reality. What I 
 can in no sense conceive cannot intelligibly be held 
 to exist. Bishop Berkeley saw this so far fully, as 
 his predecessor, John Locke, had seen it partially. 
 But Bishop Berkeley, nevertheless, went on to divorce 
 existence from meaning along another line. Our 
 ideas he declared to be self-contained and inde- 
 pendently subsisting phenomena of our minds, and 
 the orderly relations which made them belong to a 
 system, and so be significant, he held to be something 
 added to what he took to be a self-contained exis-
 
 LOCKE, BERKELEY, HUME AND KANT 37 
 
 tence of these ideas, by the work of a God operating 
 on the mind ab extra. Then came David Hume, who 
 asked what we knew or could know of this orderly 
 arrangement ab extra. No more than Locke knew 
 of the substance, with its primary qualities, in which 
 the latter sought the explanation of reality. But 
 Hume proved to have himself assumed the presence 
 of systematic and reliable knowledge as the foundation 
 of the possibility even of his own scepticism. He 
 could not explain how the self, if resolved into a 
 mere succession of impressions and ideas, could know 
 or be aware of itself as intelligence or as what experience 
 shows. It was reserved for Kant to point out that 
 when we have experience we are always more than 
 we take ourselves in direct experience to be ; that 
 knowledge is the essential condition for any experi- 
 ence at all ; and that the meaning which is intelligible 
 only in so far as that experience is there for know- 
 ledge, is essential as the foundation of the existence 
 of any object world, even of ideas. 
 
 If this be true, then in the universe the knowledge 
 for which that universe is there must be recognised as 
 the primary fact. Behind this fact we cannot get. 
 For every question directed to the genesis of our know- 
 ledge, as of an instrument or dependent relationship, 
 assumes it as already there present in some form from 
 the beginning. We ourselves, conceived and appre- 
 hended as objects which know, fall within the field 
 of objects in knowledge. The question of the genesis 
 of knowledge in general is accordingly an irrational 
 one, and the presence of knowledge in possible if 
 not yet actual perfection is assumed in every form of 
 the scepticism which is thus compelled to start by pre- 
 supposing knowledge as its own reliable instrument.
 
 38 THE SIGNIFICANCE OF HUMANISM 
 
 This is a doctrine as old as the Greeks. Not only 
 did they grasp it fully, but by Aristotle, and by 
 Plotinus after him, it was seen clearly that knowledge 
 can have before it only what is akin to itself. For 
 them full knowledge was the vcfycris vo^'crews, the 
 Active Reason, the unity of thinking with the thought 
 which thinks itself and knows itself alone. Passive 
 Reason was one among the subordinate and deriva- 
 tive forms in which knowledge .presents itself to 
 itself. We find the same principle less perfectly 
 enunciated by Kant, and more definitely by some of 
 the objective Idealists who came after him. Thought 
 does not make things, because when we talk of 
 thought making them we have conceived inadequately, 
 and have ignored the basic character of thought, 
 taking it too narrowly as an activity of abstract con- 
 struction which we present in object form before our 
 individual minds. The ultimate reality is neither sub- 
 ject nor object, but is the fact of the significance which 
 embraces both, and in which they are, as it were, 
 poles which we distinguish only in reflection. 
 
 This principle had of late ceased, in these days of 
 scientific inquiry tested only by measurement, to in- 
 terest the public, until quite suddenly, in the present 
 century, it received a new application in the domain 
 of science itself. In the hands of Einstein the 
 principle of the relativity of knowledge has been 
 applied in a fresh form. Confining himself to the 
 domain of mathematical physics, he has developed a 
 standpoint that appears to be revolutionary, more 
 startling in its scope than even that of Copernicus 
 or of Newton. For he has denied the independent 
 reality of both space and time, and has pronounced 
 them to consist merely in certain relations belong-
 
 NEWTON AND EINSTEIN 30 
 
 ing to knowledge between the observer and what 
 he observes, which vary in shape and measurement 
 with the situation and conditions of the observer 
 himself, depending as they do for their significance 
 and for their reality also on whether the observer is 
 taken to be at rest or in motion. 
 
 Newton held the view that we look out on a world 
 which exists quite independently of our knowledge 
 of it, and that space and time are analogous to forms 
 or frames subsisting in themselves and independently 
 even of the objects in them. For him space and 
 time were under all circumstances uniform every- 
 where. A foot and a second had the same signifi- 
 cance throughout the whole universe notwithstanding 
 differences in the conditions of observation. They 
 never changed their significance. Those who followed 
 him therefore inferred that if there were, as was held 
 until recently, a physical substance called the aether 
 which filled space and time, but in which objects 
 moved freely and without friction or retardation, 
 this independent substance could be used as a 
 medium in which light might be taken to be in 
 motion relative to it, and accordingly as a standard 
 by reference to which its velocity could be estimated 
 as being an absolute velocity. It was, however, 
 discovered thirty or forty years ago that the velocity 
 of light disclosed itself as appearing to be always the 
 same, whether we were moving through the aether 
 towards its source, or whether, when we sought to 
 measure that velocity, we were stationary. How was 
 this apparent constancy to be accounted for ? It 
 seemed impossible to explain if space and time and the 
 aether were independent and unchanging existences, 
 unless indeed the aether perchance contracted our
 
 40 THE SIGNIFICANCE OF HUMANISM 
 
 measuring apparatus in proportion to the rate at 
 which we advanced through it. For this hypothesis 
 there was no particle of evidence, and it could only 
 legitimately be resorted to if the apparent uniformity 
 for observers under all conditions of the velocity 
 of light at 186,000 miles a second could not be 
 explained more simply. It was the simpler 
 alternative explanation which Einstein's principle 
 yielded that has constituted one among a good 
 many other reasons for accepting it as inevitable. 
 By the new principle, as I have said, the inde- 
 pendent reality of space and time was denied, 
 and they were defined to be varying relations, estab- 
 lished as such through interpretation on the part of 
 observers varying in situation. What we actually 
 observe is, for Einstein, not space and time, but at 
 most the basis on which they are erected as construc- 
 tions of reflection. This basis is what he calls the 
 four-dimensional manifold, or the continuum. It is, 
 in point of scientific knowledge, antecedent to space 
 and time, but has some qualities analogous to 
 their qualities. Still, in this manifold the space- 
 like and the time-like characteristics do not exist 
 in independence. They imply each other in the 
 entirety in which alone they are actual. Such 
 an entirety has as its nature to be activity, a passage 
 of mere events, a multiplicity of world-lines of 
 change. What we are primarily aware of is thus only 
 change in events not yet differentiated into objects 
 with shapes and measurements. But it is the founda- 
 tion of physical reality, and it is upon and out of it 
 that there are developed in our minds space and 
 time, and the objects whose relations and whose 
 relations to the observer constitute the meaning
 
 INVARIANTS 41 
 
 and the reality alike of space and time. They thus 
 become actual but only relatively so. 
 
 Mathematical analysis of a highly refined order 
 has furnished principles by which the character of 
 the activity within the manifold, taken by itself, 
 may be defined and described. It cannot be 
 measured, because we have not yet reached the 
 stage where measurement first gets a meaning and 
 is possible. But there are general principles of a 
 nature that is at least as much qualitative as it is 
 quantitative, which ascertain characters in the mani- 
 fold dependent on bare coincidences in the world-lines 
 of the activity of which we are aware as basic, and 
 these are independent of all the particular measure- 
 ments which can only be superinduced after definite 
 spatial and temporal relations have been differentiated 
 in knowledge and set up. Such general characters 
 yield definitions of a new kind for the general nature 
 of change in position of events, such as that ex- 
 pressed in what we call gravitation and energy 
 and matter. They hold good whatever the nature 
 of the superinduced space-time system arising for 
 an observer in a particular situation of motion or 
 rest may be, such as his altering situation in a 
 gravitational field. Obviously his space- time systems 
 will, on Einstein's principle, vary, but here we have 
 what is true in all space-time systems because it 
 expresses relations which obtain in the foundation 
 of every possible relation of the observer to the 
 object, however it may vary with the conditions 
 of observation. It was by reference to this kind of 
 foundational standard that Einstein was able to 
 predict that when the British Astronomical Expedition 
 was, on the 29th of May, 1919, about to observe the
 
 42 THE SIGNIFICANCE OF HUMANISM 
 
 deflection by the sun of the rays from fixed stars 
 coming to us during its eclipse, it would find these 
 rays to be deflected by an exact amount in addi- 
 tion to that predicted by those who calculated on 
 merely Euclidean and Newtonian principles. He 
 said that the situation and motion of the observer 
 on the earth, relative to that in the system of 
 the sun, would give rise to a space-time system 
 different from the uniform system which Newtonians 
 assumed, in which it would be found that the lines 
 of light would be curved and not straight, simply 
 because the space in which they were visible must 
 itself be curved and not straight. The name given 
 to the principle embodied in the mathematical 
 expressions for the foundational characteristics of 
 every form of space and time is the Tensor principle. 
 The employment of tensors enables the astronomer, 
 who has to measure within a remote spatial system 
 in some far-away region of the firmament, to divide 
 his calculation into two parts. One depends on 
 ordinary processes of astronomical measurement 
 in his observatory, which, if Einstein is right, give 
 results that are dependent on his situation, and are 
 therefore varying. The other part is the application 
 to these results of the tensor equations, which 
 define the fundamental character of the space ex- 
 perienced, and finally yield a concrete outcome 
 enabling the phenomena, as they will actually 
 appear to the telescope when directed from afar in 
 a different space and time system, to be predicted 
 and described with exactness. 
 
 The distinction between the space-time manifold 
 itself and the relations which we abstract from it 
 and isolate from each other under the titles of
 
 43 
 
 space and time brings us to a second great con- 
 ception of Einstein which illustrates the general 
 principle of the relativity of all knowledge to mind 
 as its foundation. For Einstein asks what is the 
 meaning, in the light of what has been said by him 
 of the character of the basic manifold or continuum, 
 of the external universe in which we observe the 
 earth, the sun, moon and stars, and all other bodies. 
 His answer is that the law of gravitation as for- 
 mulated by Newton fails, both in generality and in 
 precision, as a description of the general and dominant 
 characteristic of this universe. He specifies what he 
 says must be the only possible view as the principle 
 of equivalence. All motion supposed to take place 
 under the pull of gravitational force can equally 
 well be scientifically described as mere inertial 
 motion, without reference to what was taken to be 
 force or pull. If this can be done we get rid at once, 
 not only of the old puzzle about the possibility of 
 action at a distance, but of a number of other per- 
 plexities. In order to pass to the wider explanation 
 all we have to do is to remember that it is a mere 
 arbitrary assumption that we, the observers, are 
 stationary. This can never be known to be the case, 
 for rest and motion are purely relative ideas. The 
 earth on which west and is taken as moving curvi- 
 linearly round the sun with vast velocity, and as 
 carrying us with it. It is easy to see why the sun 
 seems, as Ptolemy actually thought, to arise in the 
 east and pursue a daily curve over the heads of us 
 who seem to be at rest. It is really we and not the 
 sun that are in motion, though we have assumed 
 ourselves wrongly to be stationary. The result is 
 that the sun appears to be pursuing a path which
 
 44 THE SIGNIFICANCE OF HUMANISM 
 
 is curved and not straight, because of the relationship 
 to the earth's rotation and orbit. The combina- 
 tion, when truly analysed, discloses what is equivalent 
 to velocity in an orbit of the earth itself of a curved 
 form, entailing the consequence that lines of light pass- 
 ing the sun appear in a space that is itself curved. We 
 are constantly, because of our continuous change 
 in position, resolving differently as regards propor- 
 tions the combined spatial and temporal qualities 
 of the basic fact we apprehend. Thus space and 
 time have different interpretations as the situation 
 of the observer on the earth alters. To the units in 
 which we express our measurements of space and 
 time we give the same names, but their meanings are 
 different. So it is also when we observe the more 
 distant heavenly bodies. The lines of light are 
 curved, not straight. The planets do not move in 
 straight lines under Newton's classical law of inertia, 
 but in various orbits depending for their forms not 
 on any supposed pull of gravitation, but on the 
 relative and changing situations and velocities of 
 us, the observers. We have, in short, each of us 
 our own private space-time system gotten by inter- 
 pretation from our individual situations. But as 
 these situations are for most purposes practically 
 indistinguishable, so far as the surface of our earth 
 and the observation of objects on it are concerned, 
 no practical question arises in everyday life. It 
 is, in the main, only when we observe phenomena 
 at vast distances, or are concerned with the relations 
 of objects moving at great intervals from us, or with 
 immense velocities, such as those of electrons, that the 
 differences become of vital importance for science. 
 The magnetic field, which extends beyond our earth
 
 SPACE AND TIME 46 
 
 throughout the observable universe, presents us every- 
 where with analogous questions for consideration. 
 
 We have thus, as I have said, our own private 
 space-time systems within which the phenomena 
 of the universe vary in their relations of shape and 
 measurement for observers differently situated. It 
 is these relations one set of which, as the outcome 
 of our interpretations, constitutes space and another 
 set time. There is no space or time which has any 
 scientific meaning other than that of relations of 
 phenomena inter se to the observer. Space and 
 time derive their everyday reality from them. One of 
 the first hindrances to the grasp of Einstein's doctrine 
 is the idea that he is speaking of only apparent 
 spaces and times that are constructed out of a real 
 space and time existing independently of them. This 
 is wholly wrong. The sole space and the sole time are 
 space and time as they appear to those who observe. 
 
 This conclusion seems at first sight to make them 
 merely sub j ecti ve appearances . But it is not properly 
 so. As I have already pointed out, there is for Einstein 
 a basic reality existing wholly independently of the 
 particular observer, a four-dimensional manifold from 
 which space and time are derived by interpretation. 
 Such an interpretation we are bound to make if 
 we would know as human beings do, and it varies 
 proportionately in relation to the situation and 
 conditions of the observer. But the manifold itself 
 has characteristics which must, just because it is 
 treated as a foundational reality independent of the 
 situation of the observer, be true of every kind of 
 space-time system that is based on it. Motion, 
 whether it is called gravitational or inertial, conforms 
 in quality, as distinguished from measurement and
 
 46 THE SIGNIFICANCE OF HUMANISM 
 
 shape, to the basic laws of activity in the manifold. 
 We get thus a principle which penetrates more 
 deeply into the behaviour of objects in space and 
 time than does Newton's law of gravitation. It is 
 that the action of a particle in the manifold must be 
 the most direct one geodesically that is according 
 to the character of the manifold as it exists indepen- 
 dently of the individual observer. This is obviously 
 what I have called an expression of a tensor nature. 
 For if we pass to the different forms of space and 
 time which at a later stage, when we know the 
 position of the observer, we can estimate by measure- 
 ment, we find that the paths vary in shape and 
 measurement. We can only apply Einstein's basic 
 law to concrete problems if we take into account the 
 measurements obtained first at the later stage when 
 we have found our observer and determined his posi- 
 tion. But in the absence of the basic principle 
 we shall go wrong, because we shall have no means 
 of distinguishing what is only relatively from what 
 is physically absolute. 
 
 Thus the physical universe as Newton conceived 
 it turns out to be what it appears only relatively to 
 the kind of knowledge brought to bear. It is a 
 revolutionary conception, and its consequences are 
 far-reaching. One of them is that we can no longer 
 distinguish matter from energy. All matter is simply 
 a form of energy, active or bound up, and we come 
 back to activity in the manifold as the basic fact. It 
 must be added that the tendencies of modern physics 
 appear to have been already in this direction. From 
 the particle science was increasingly turning atten- 
 tion to the field of action within which the particle 
 behaved. Of Einstein's principle it remains to be
 
 THE WIDER PRINCIPLE 47 
 
 observed that, while it appears to be true as according 
 with the observed facts so far as it goes, it has yet 
 to be seen whether it expresses the whole truth. 
 There are already questions about this. 
 
 Einstein's doctrine of the relativity of our physical 
 knowledge to the observing mind may thus be said to 
 be a scientific and exact illustration of the wider prin- 
 ciple which affirms that in all knowledge the object 
 is determined, in its significance as real, by the 
 conceptions which mind brings to bear in interpreting 
 and giving it meaning. In other departments of 
 the science of nature this is as apparent as it is 
 in mathematical physics. I cannot render my ob- 
 servation of a living organism in terms of causes 
 operating externally to their effects in space or time. 
 The life of the organism consists in the preservation 
 not only of its characteristic form but of its develop- 
 ment amid constant change in material. Minute 
 micro-organisms give birth to millions of similar 
 organisms which all inherit behaviour in the same 
 way. This is scientifically inexplicable as a mere 
 result of fortuitous concourse of atoms, or of action 
 upon each other of molecules accidentally coming 
 together. The reluctance of the older biologists to 
 accept this inference arises from the assumption 
 that all reality is merely mechanical in nature, 
 and that to admit any other view is to interpret 
 life as produced by some external cause of a 
 miraculous character, miraculous in that it cannot 
 be made to harmonise with the only real facts 
 observed in nature. But are the supposed facts the 
 only real facts, or are they the outcome of restricted 
 standpoints which, analogously to the Newtonians, 
 we have imposed on ourselves in such a way as to
 
 48 THE SIGNIFICANCE OF HUMANISM 
 
 limit what observation really discloses ? Have we 
 been, in other words, the creatures of conventional 
 and unconscious assumptions ? There is an alter- 
 native view which would teach us, if accepted, to see 
 in life a set of phenomena at a logically different 
 level in knowledge from that of physical causation, 
 a level at which the interpretation is one, not of the 
 merely mechanical and external relation of cause 
 and effect, but of the fact of behaviour. Now 
 behaviour may be consciously purposive, but we have 
 not necessarily got before us in the bare fact of life 
 conscious purpose. There is apparent on all hands 
 behaviour which is unconscious. Its essence is 
 fulfilment of what I will call an end, and not response 
 as the mere effect of a mechanical cause operating 
 ab extra. Let us look at what confronts us in the 
 domain of animal life. The organism pursues a 
 definite course of self-development from conception 
 through birth to death. This development conforms 
 to a course which is marked out in the interest 
 of an end which is more than merely individual, 
 that of the species. It is only in the light of this 
 standpoint that we can state heredity, with the 
 preservation of individual form and capacity from 
 conception to death. The action which guides 
 this seems to be, not, as mechanicians would have it, 
 action at a distance. It is the operative consequence 
 of an end, continuously present and directly mani- 
 festing itself in the behaviour of the living being, 
 the life of which depends on the continuous main- 
 tenance and development of a definite form due to 
 the self-imposed influence of a particular kind of 
 end. The kind differs in the various forms of animal 
 life. The lower we go the simpler and more uniform
 
 END AND PURPOSE 49 
 
 is the resemblance in the behaviour of the individuals 
 that constitute the species. A germ reproduces 
 itself, it may be by fission, and the resulting myriads 
 of germs are indistinguishable in point of conduct. 
 It is only when the freedom of intelligent self-control 
 comes in, as in the cases of the horse or the dog or 
 the human being, that individual variety is markedly 
 established, and the more the phenomena approach 
 the level of such intelligently self -directing freedom, 
 the greater the variety between individuals. That 
 is what observation teaches us. The operation of 
 ends in producing behaviour is everywhere apparent, 
 but among these ends there is difference in their 
 nature. Conscious purpose belongs to a higher 
 level or degree in experience than that of mere end. 
 At neither level is it a cause acting externally, but 
 it is an immediately present end that determines 
 the behaviour of the organism, though at the lower 
 level we have before us life only and not yet con- 
 sciousness. At the degree in knowledge and reality 
 at which the latter is characteristic the end is the 
 expression of purpose which is largely self-determining 
 and the outcome of freely directed volition. We 
 live as well as know. In merely living we are not 
 free. In knowing and in the execution of purpose 
 directed by knowledge we belong to an order of 
 objects within nature which transcend the ordinary 
 principle of external nature in that they imply a 
 significance which is that of the self-directing and 
 self -recognising subject in knowledge. We find a new 
 set of conceptions here brought into operation in 
 the construction and interpretation of reality at 
 this degree, conceptions which lead us on to per- 
 sonality, and to the larger aspects of our individuali-
 
 ties that take form in society, in the state, in ethics, 
 in art, in religion, in knowledge. But our activi- 
 ties as the expressions of these conceptions are 
 much more than mere happenings or activities in 
 space and time. By an abstraction which he makes 
 for the purpose of getting a sharp picture the psy- 
 chologist conceives them as such objective activities. 
 For limited purposes this is as legitimate as it is 
 for the physicist and the chemist to measure the 
 structure and the energy of the living organism in 
 such a fashion as to get definite knowledge of certain 
 limited kinds. But neither in their case nor in that 
 of the psychologist is the image so fashioned more 
 than an artificial and inadequate one. Its utility 
 is akin to that of the equations in which the mathe- 
 matician, by ignoring all other aspects of reality 
 excepting order in series, can extend his knowledge. 
 But his knowledge is always only of a kind which 
 is true as far as it goes, but is incapable of taking 
 account of the inexhaustible riches of the actual 
 which it shuts out. So it is with the psychologist 
 also. His method is only one by which he strips the 
 actual, and, by confining himself to a limited stand- 
 point, transforms its real aspect. He makes intellect- 
 ual processes into objects in space and time. We can 
 only adequately interpret life and mind in the terms 
 that are appropriate to life and mind, and so it is 
 in ethics, in art, and in religion. They are actual 
 at levels that are their own, and they require for 
 the presentation of these levels their own conceptions 
 and terminologies, and these are implied in their 
 significance and enter into their actuality. 
 
 We thus reach a view of experience in which its 
 reality, as well as our knowledge of that reality,
 
 THE QUALITY OF THOUGHT 61 
 
 appears as of different kinds and at different levels 
 or stages within experience. The entirety of both 
 knowledge and reality we do not take in completely, 
 because of the finiteness of our minds, a finiteness that 
 arises from these minds being conditioned by the char- 
 acter of the physical organisms in which they express 
 themselves. But thought, which is in its own nature 
 no action in space and time, but is that which gives 
 their significance and actuality to the relations 
 of objects to ourselves as physical existences and 
 among themselves, is itself no event in space and 
 time. Such events it reaches over just because it is 
 their foundation. It is identical in all of us, despite 
 its differences. This is why our thoughts corre- 
 spond. They are not merely happenings which 
 resemble. They are logical conceptions identical 
 throughout difference. Into each other's sensations 
 we cannot enter. These depend on our individual 
 organisms and exist only in relation to them. But 
 thought is of a different nature. It is concerned with 
 the universal, that which is the identical for all of 
 us, however the particulars it fashions and gives 
 setting to may vary. This is what is implied when 
 we say that we all see the same sun, moon, and 
 stars. However private and particular the sensations 
 transmitted through our respective optic nerves may 
 be, we place on these sensations a common interpre- 
 tation, and so construct the common experience, 
 identical really only in the universals which are 
 signified in recognition. It is in its universals, the 
 thought in which we think the objects, that the 
 identity of their significance and therefore the same- 
 ness of their reality lie. 
 We may now realise what we mean when we speak
 
 52 THE SIGNIFICANCE OF HUMANISM 
 
 of our individual experience as an entirety which 
 we regard as singular or unique. It concerns our 
 special and private existences as living and intelligent 
 organisms dependent on our senses. To these in- 
 dividual aspects of knowledge, implying as they do 
 private sensations and feelings, experience always 
 refers. But it imports more than this. It arises 
 and is real only in so far as we know as well as feel. 
 It is indeed only by abstraction that we separate the 
 general knowledge implied from the feeling ; the per- 
 manent universals which are ambiguous and of a 
 merely general form, inasmuch as they describe only 
 classes, from what is particular and fleeting. But 
 knowledge is in its full nature more than can be repre- 
 sented by either set of these abstractions. It is a 
 concrete whole within which all that we distiDguish 
 falls as inseverable, a whole in which every aspect is 
 included. Only by abstraction can we take our know- 
 ledge to be an instrument standing by itself, as it is 
 made by the psychologist to do. Subject and object 
 are only relatively distinguishable within it, and then 
 merely for special purposes and from standpoints 
 that are limited. The self in knowledge is no mere 
 object even for itself. It is always more than this. 
 It is a centre to which all reflection refers, the 
 activity .of reflection which alone gives meaning and 
 coherence to its object world and is the basis and 
 condition of its existence. We make ourselves ob- 
 jects only when we think of ourselves as having places 
 in space and time. But we find that space and time 
 themselves, and all the objects that fall within 
 them, including the self when so regarded, are there, 
 present, past, and future, only in relation to the self 
 that holds them together and in unison. The
 
 KNOWLEDGE 53 
 
 essential character of this self is to be subject for 
 which the object, and the present, past, and future, 
 are there and are significant. The self reaches over 
 all objects. It is aware of and establishes its own 
 limitations, for it finds that even these owe their 
 existence to reflection. Subject and object thus 
 disclose themselves as aspects falling within a single 
 entirety, differentiated only by the standpoints from 
 which we approach them. An entirety is implied 
 at the points at which both are transcended and 
 embraced, and that entirety is just the final fact that 
 we know, and that to knowledge no distinction is 
 impenetrable just because every such distinction 
 is itself but the creature of knowledge. 
 
 It is in this sense that knowledge is related to 
 experience as the foundational and ultimate reality 
 within which the whole of the individual experiences 
 of the mind fall. It is for this reason that when 
 we know we are always more than we take ourselves 
 to be. It is to relativity in standpoint that we owe 
 the view that we are no more than individual human 
 beings that walk in the streets and are describable 
 in terms of mere life and private happenings. It is 
 from this degree and sense of relativity that we are 
 delivered by the conceptions belonging to knowledge 
 at higher levels which we meet in duty, in art, and 
 in religion, and these indicate yet higher standpoints 
 at which the finiteness of existence presents itself as 
 such only because of limitations in outlook to which 
 our position and history in nature confine us. Such 
 limitations we pass beyond when we assert the pre- 
 sence of the higher reality that is their foundation, 
 and so illustrate the power of thought to overcome 
 obstacles which are its own creatures.
 
 54 THE SIGNIFICANCE OF HUMANISM 
 
 We thus come to the true character of knowledge. 
 It is in its essence obviously neither merely general 
 nor merely particular, for the distinction between 
 these two aspects is a distinction established by and 
 within knowledge. The true character of knowledge 
 seems to be what has been called the concrete universal. 
 The expression means that, whatever its form, there 
 enter into knowledge moments or factors, particular 
 as well as general, which have nevertheless no in- 
 dependent existence, but express in the concrete 
 unity in which alone they are real the aspects of 
 particularity and generality. Even when I try to 
 proceed to particularity in its extreme suggestion, 
 and point with my finger to what I call ' this/ the 
 general or universal aspect is forced on my con- 
 sciousness. What is ' this ' at the moment becomes 
 * that ' as the moment passes, and the coming 
 moment brings a new ' this/ Such relations, from 
 their very character, cannot be particular objects. 
 They signify in truth references to the subject in 
 knowledge, and they are the expressions, not of self- 
 contained events in space and time, but of concep- 
 tions brought to bear in our thinking, which give 
 reality to particulars with which reflection is con- 
 cerned. They are thus of a nature which is of general 
 application. They are what logicians call universals. 
 But not the less there is no ' this ' which must 
 not combine with its general character some par- 
 ticular aspect or moment in its constitution. If 
 it is a universal it is a concrete universal in the sense 
 that its reality always implies the particular. That 
 reality is thus a significant fact from which, by 
 making abstractions, we can deduce both of the 
 aspects implied in it. But it is only in the integral
 
 PARTICULAR AND GENERAL 55 
 
 form of the actual unique and unambiguous fact 
 that these aspects have reality in an object world. 
 It is in reflection, and reflection alone, that univer- 
 sal and particular are dissociable. That is what we 
 mean when we speak of the concrete universal, and 
 designate it as the form which the object of know- 
 ledge must always assume. Even when we reason 
 most generally, as in mathematics or metaphysics, we 
 always have to fashion for ourselves images and use 
 metaphors. The reason is the necessity of the essen- 
 tial moment in knowledge of the particular. But 
 when even a dog sees a wasp crawling on the ground 
 near his nose, he seems to proceed to study and 
 to classify it through universals as a member of a 
 noxious species which must be treated with caution. 
 
 All knowledge is particular as well as general, and 
 when it is supposed to be dealing with the most 
 abstract universals it is really making use of particular 
 symbols or images in which they are realised. On 
 the other hand, every son of Adam and all animals 
 that rise above merely instinctive action seem to 
 employ universals in some form. When a man pulls 
 on his boots he uses the conceptions of physics ; 
 when a horse feeds he recognises a general coincidence 
 between the satisfaction of the feeling of hunger in his 
 stomach with the consumption of enough corn. 
 
 Put in other words, the actual is of a character 
 neither general nor particular, but singular or indi- 
 vidual. It is this singularity that renders it unam- 
 biguous and what is called unique, significant just 
 of one self-contained existence, different from every 
 other in the universe, and of that alone. But this 
 uniqueness is itself only possible in that the general 
 and the particular both enter into its logical com-
 
 56 THE SIGNIFICANCE OF HUMANISM 
 
 position. It requires the former for its meaning 
 and nature. It requires the latter in order to enter 
 as an individual form of living experience. Every 
 object thus presupposes the fact of knowledge as its 
 foundation, for in knowledge alone do these two 
 aspects come together in unison and as an entirety. 
 All knowledge is, therefore, as much concrete as it 
 is abstract. For the real with which it is concerned, 
 and to which it gives the meaning apart from which 
 no object could be spoken of as existing, implies both 
 aspects. 
 
 In all experience sensations, images, and metaphors 
 are invested with significance. This depends for 
 its reality on interpretation through universals, 
 which give their meaning and not less their actuality 
 to the apparent particulars to which they are applied. 
 For it is only within the entirety that is character- 
 istic of knowledge that this actuality has meaning. 
 It may be the actuality of an erroneous idea. For 
 truth and error, reality and unreality, righteousness 
 and sin, beauty and ugliness, and all else that is 
 distinguished, get meaning only within knowledge. 
 It is only for knowledge that they are existent. Our 
 hesitation about accepting this view arises from our 
 uncritical use of images and metaphors. We think 
 and speak of knowledge as though it were a relation 
 between two independently subsisting objects, a pro- 
 perty of a self conceived as a kind of self-contained 
 thing in space and time. But this cannot be an ade- 
 quate view, for it is only by presupposing what is in its 
 implications the entire system of knowledge that we 
 can come to this conception itself. Knowledge is 
 indeed no activity of anything else. It is the foun- 
 dational reality into which and in terms of which alone
 
 THE FINITE SELF 57 
 
 our universe, without and within, can be resolved. 
 If we may use the dubious word ' absolute/ it is the 
 absolute to which all else is relative. It is because 
 for our own working purposes we have formed a 
 distorted picture of knowledge that we hesitate before 
 accepting this obvious fact. I may and must speak 
 of my knowledge, that of a finite self conceived as 
 falling within the object world. For everyday pur- 
 poses it is inevitable that I should do so. But 
 the expression is no exhaustive one, for the simple 
 reason that the standpoint from which it is employed 
 is not the only conceivable standpoint nor adequate 
 to the full reality. If I would get at the underlying 
 nature of the universe I must therefore subject it 
 to analysis, not wholly dissimilar from the analysis 
 to which Einstein found himself driven when he set 
 himself to determine the meaning of shapes and 
 measurements in space and time, and to discover true 
 invariants. 
 
 I have now completed the examination, so far 
 as is needed for my purpose, of the character of ulti- 
 mate reality, and have to a certain extent made 
 an explanation of the significance of the expression 
 ' concrete universal/ I can accordingly, before 
 very long, pass from the abstract physics and meta- 
 physics that had to be referred to in the first place, 
 towards the extension of their underlying principle to 
 that other and humanistic side of knowledge which 
 is most concerned with the aspects it presents under 
 forms which we call feeling and emotion.
 
 THE PHILOSOPHICAL SIGNIFICANCE OF 
 HUMANISM (continued) 
 
 CHAPTER II 
 
 THE TRANSITION TO HUMANISM 
 
 IN the first of these chapters I stated certain reasons 
 that made me think of the object in every kind of 
 knowledge as being what I called a concrete universal, 
 an unambiguous and unique fact of an individual 
 character. It was suggested that this must be the 
 actual form of every object of knowledge, whether 
 of knowledge which we treat as being of an abstract 
 character or of knowledge which we regard as par- 
 ticular, for example in our barest awareness of feeling. 
 We never really think in purely general abstractions. 
 We always form images which are symbolic of 
 possible particular cases included, but indicate a 
 class determined by general predicates with which 
 our immediate purposes are concerned. The dynamic 
 character of thought causes us to do this. On the 
 other hand into the barest passive awareness there 
 enter characteristics of universal character through 
 which we have to distinguish and classify. Feeling 
 is fraught with thought and thought with feeling, and 
 we discover finally that each, taken in isolation, is 
 an abstraction with no actuality independent of 
 the other. The only reality is what contains both 
 in integral unity, the unambiguous and unique con- 
 crete universal, which is so called because it is felt 
 as well as thought, and is the fusion of these moments, 
 
 8
 
 UNIQUENESS 69 
 
 unreal in independence, in an object which is in our 
 experience just itself. For it is particular as much as 
 it is universal, inasmuch as it is just this and no other 
 object, and as such is self-contained. It is what the 
 Germans name eindeutig. It means only just this one 
 particular fact in the universe, and is unequivocal. 
 Of course we can never exhaustively describe a 
 concrete universal. The process would imply, for 
 the completion of its general aspects, reference to 
 relations to all else in the universe, and would be 
 infinite in its extent. It would, on the other hand, 
 suggest an asymptotic approach to the elusive pure 
 particular, and a denial of the reliability of knowledge 
 itself. But no consistent scepticism has ever been able 
 to reach the pure particular. The inconsistent uncon- 
 scious assumptions involved in the attempt to do so 
 have always ruined pure scepticism, and always must. 
 On the other hand, describe the concrete universal 
 exhaustively in general terms we cannot. It imports 
 more than what is general and therefore ambiguous, 
 as being applicable indifferently to all or any 
 within its scope, in that the universal defines only 
 a class and not the individual member of the class 
 to reach which we always seek. Even when we point 
 with the finger and say ' this ' we have only indicated 
 in terms of a universal what an instant later is 
 true of something else, and therefore indicates what 
 is equivocal and not unique. ' This ' passes into 
 ' that ' ; ' now ' into ' then/ It is in the nature of 
 thinking that it should be so. Much mystery has 
 been made over what the Greeks quite naturally 
 called the dialectical character of thinking. This 
 name is a mere description of what we observe if 
 we let our thought alone and watch it developing itself.
 
 60 THE SIGNIFICANCE OF HUMANISM 
 
 We see, if we do so, that it is dynamic and not static, 
 and presents itself in that form. 
 
 The merely particular, stripped of the universals 
 in which it is set in our experience, neither means 
 nor is anything for us. The merely universal, di- 
 vorced from the particulars to which it gives their 
 setting in experience while leaving the result a unique 
 and individual fact for observation, is a mere unreal 
 abstraction apart from the particulars to which it 
 is thus essentially related. The unique individual 
 fact in experience, just because of the dynamic 
 or dialectical character of the thought that so sets 
 it, is always breaking out into further and new re- 
 lations which give to experience its continuity. Both 
 aspects, that of the universal which is equivocal, 
 and that of the particular which is in itself a mere 
 disappearing point of application, are essential, if 
 the fact of the actual is to be recognised. It is for 
 this reason that generality and uniqueness, con- 
 tinuity and discretion, necessarily imply each other 
 in nature. That is, in effect, saying that the character 
 of the real is to be a concrete universal. 
 
 If this be so consequences follow on which I shall 
 not dwell in detail here, for I have devoted a good 
 deal of space to them elsewhere, in the book already 
 referred to. The ultimate form, the foundational 
 fact in our experience, is the concrete universal, 
 the unique and unambiguous individuality in which 
 the actual is always finally self-presenting. This 
 is so in daily life as much as in abstract science, 
 and it is so because this form of individuality is 
 foundational in all knowledge when freed from the 
 relativity we impose on it. We seem to be here 
 contemplating mind as having for its essence free-
 
 THE CHARACTER OF EXPERIENCE 61 
 
 dom and self-direction. For we are taking it at 
 a level at which it is not confined by the abstractions 
 of physics, and at which the category of a cause and 
 effect external to one another is inadequate. With 
 mind as we are now expressing its nature, driven to 
 do so by the demands of reflection, to think and to 
 create are not in ultimate analysis essentially different 
 activities. For all falls within the whole, the 
 entirety that is mind within which the universe, 
 including all distinctions made within it, falls, its 
 object world existent through the intelligence from 
 which that world is inseparable, an intelligence which 
 is always more than it takes itself to be. 
 
 Should this conception prove well founded it 
 furnishes a new light on the significance for us of 
 the universe itself. We begin with the fact, the ex- 
 pression of which we find in what is nearest to us, 
 our direct experience, the fact of the concrete uni- 
 versal into which both thinking and feeling enter 
 for finite or conditioned reflection, and, starting 
 from this fact, thought proceeds to make ab- 
 stractions. Such abstractions yield only the general 
 notions which ascertain general classes as distinguished 
 from individuals, and in the end are therefore am- 
 biguous in their guidance for ascertaining facts. But, 
 if thus ambiguous, they are potent in eliminating 
 what is irrelevant to the purpose in hand. They 
 enable us to concentrate and even to extend know- 
 ledge, as does the mathematician by developing 
 the implications of his symbols. These symbols 
 are in reality metaphorical. Because they are in 
 a sense ' things ' we can operate with them and form 
 new combinations in space and time, images from 
 which we can make further useful abstractions and
 
 62 THE SIGNIFICANCE OF HUMANISM 
 
 deductions of what is implicit in them. But sym- 
 bols only they are, inadequate as descriptions of 
 the full reality the concrete aspects of which they 
 shut out. 
 
 It is in this fashion that we start from the actual 
 that is the foundational fact of reality. We begin 
 with what is in the highest degree concrete, and the 
 inherent activity of thought is ever establishing 
 distinctions, themselves of the nature of abstractions. 
 Our commencement is with what is most free from 
 the fission between universal and particular, which 
 reflection is ever establishing in an increasing degree. 
 We make abstractions under the guiding concepts 
 which the dialectic of reflection sets up. Starting 
 from mind as free we work downwards to the external 
 world which seems to come to us through our sen- 
 sations, and relatively speaking does so in our history 
 as self -presented objects in space and time. But it 
 is only because the entire system of knowledge is 
 implied as potentially present throughout that we 
 can so interpret. We work in truth from what is 
 above and concrete to what is below and more 
 abstract. We find in our experience what suggests 
 such conceptions as freedom, mind, life, causation. 
 Going further in reflection, we can limit ourselves, 
 as does the pure mathematician, to mere order of 
 series in externality. But we can also employ, 
 as not less suggested for definition by the actual, 
 conceptions like those of value, as in art and in 
 religion. Thus we find that the universe displays 
 its actuality from many standpoints, and that these 
 standpoints give us distinct forms at different levels, 
 not only of knowledge but of reality. The stand- 
 points are moulded by the categories the mind in
 
 SCIENTIFIC EXPERIENCE C3 
 
 its freedom of purpose selects, and they give rise to 
 degrees or levels in knowledge and reality which 
 constitute a hierarchy within the all-embracing fact 
 of mind. That is the ground principle to which 
 the history of thought has pointed since the days 
 of Plato and Aristotle, and which seems to me to 
 be pointed to in our own time not only by philosophy 
 but not less by modern science. The real is what 
 it is because it is in ultimate analysis relative to 
 knowledge, and it has many forms because knowledge 
 has many levels. What is actual fact thus presents 
 many aspects. The living organism is a mechanism 
 from the standpoint of the physicist and the chemist, 
 a useful and essential standpoint. But this is yet 
 only a partial standpoint which yields no more than 
 an aspect in which the real here presents itself. 
 The aspect in which that real is living is a different 
 aspect that cannot be reduced to or rendered in 
 terms of the first. It belongs to a different order 
 in knowledge. But that order is more compre- 
 hensive and adequate in furnishing a level from 
 which we can generalise about what we actually 
 observe and dare not ignore if we would reach full 
 truth. It is the duty of the philosopher to ask the 
 man of science, who claims to be an accurate observer 
 of nature, to remember the need of care in choosing 
 the conceptions under which he brings what he 
 observes, and to bear in mind the possibly distorting 
 effects of these conceptions on the images and 
 metaphors he uses. 
 
 It is the glory of science to establish general 
 principles and to exhibit order in sequence. But 
 this it does at a sacrifice. It is not only the mathe- 
 matician who has to make abstraction from other
 
 64 THE SIGNIFICANCE OF HUMANISM 
 
 phases of the actual. The biologist does so also. 
 What does he tell us of the minute micro-organism ? 
 Only that in living it exhibits the characteristics 
 of its field, the self-conduct of the species. Of its 
 individuality for it may possess individuality our 
 methods enable us to take but little cognisance. We 
 shut this out, as does the statistician in his abstract 
 investigation of human beings. What the difference 
 between individual micro-organisms may be, whether 
 they possess any form of mind or freedom, we are 
 not quite certain. The methods of the future 
 may be able to tell us these things. The methods 
 of to-day do not. They are based on concep- 
 tions which exclude the practicability of such an 
 inquiry. Biology and physiology are, like mathe- 
 matics, abstract sciences, although they make their 
 abstractions in a different fashion and under the 
 guidance of different concepts. 
 
 I turn again to the nature of experience as indi- 
 cated, not only by what in daily life we encounter, 
 but by the considerations I have dwelt on. What 
 we are aware of is always what is individual and 
 self-contained, although we may not always approach 
 it from this point of view. But even its indivi- 
 duality and self-containedness subsist in virtue of 
 relations, general characteristics, which do not them- 
 selves possess the quality of singularity. Yet apart 
 from this quality that of which we are aware would 
 have no meaning and so no reality. The real is 
 always individual, and on that account the logical 
 moment of particularity must enter into it. General 
 and particular are derivatives from concrete actuality 
 through the abstractive tendency of knowledge 
 to define in terms that apply not to one but to
 
 INDIVIDUALITY 65 
 
 any of a class of individuals. But first in order of 
 thought as well as of fact comes the unambiguous 
 singular from which we start, and this is always 
 characterised by the moment of particularity that 
 enters into and is inseparable from its being. It 
 gives it, as I have already observed, what the Germans 
 call its Eindeutigkeit. The quality appears in every 
 form of direct knowledge. We regard our sensations 
 and emotions as individual, although we cannot 
 define them without some recognition of the class 
 to which they belong in other words, by directing 
 reflection to the relations in which they always 
 subsist. So it is with the various objects in a land- 
 scape ; they are always individual in just the same 
 fashion. So with the apparently infinitesimal aspects 
 of nature. They may be ultra-microscopic, but 
 they never appear to be merely of a continuous or 
 general nature. We always have to aim at fixing 
 them as individual in some sense. Our ideas of 
 them as such may be merely limiting ideas, but the 
 character of experience forces them on us. This 
 is because of the fundamental character of all know- 
 ledge. The universality that appears in it is always, 
 for the reasons assigned, concrete that is to say, of 
 individual form. This is why, even when we try 
 to think most abstractly, we find ourselves, like 
 the pure mathematician, unable to do without 
 images and symbols and metaphors. It may be 
 that this is what is fundamental in what seems to 
 force itself on us in accordance with the quantum 
 theory in modern physics. The exclusive stress laid 
 on continuity in Newtonian dynamics appears to 
 have deflected observation from an equally real 
 characteristic of the actual before it, its character
 
 66 THE SIGNIFICANCE OF HUMANISM 
 
 of being discrete not less than it is continuous. The 
 solution of the problems which the facts disclosed 
 by the sciences of light, heat, and electricity in their 
 most modern forms are now pressing on us may turn 
 out to require resort to the ultimate character of 
 our knowledge for their complete interpretation. 
 It may be that it is necessary to penetrate as 
 deeply as only epistemology can in order to reconcile 
 apparently conflicting appearances. 
 
 But, however it may be with physical science, when 
 we get to our observation of mankind we are left 
 in no doubt. What is it that we call character in 
 individual men, and why do we esteem it ? It 
 stands for us as a highly distinctive quality in 
 him who possesses it. It means that he is a man 
 standing out among other men and incapable of 
 being confused with other individuals. A man may 
 be clever, he may be eloquent, he may be good, but 
 none of these attributes mark him out as just 
 this one person who is unmistakable, and who exists 
 for us as being different from all his fellows. For 
 the qualities to which I refer are general qualities 
 in which an indefinite number of others may share. 
 They are not in themselves enough to render the 
 possessor unique. He is this in virtue of his per- 
 sonality, which implies what is peculiar to himself. 
 The elusive and indefinable moment of the particular 
 enters into it. General qualities or particularism 
 may either of them preponderate in the individuality 
 of the man. He may be so dominated by par- 
 ticularism as to be hopelessly ignorant, or unfit 
 for society, or a criminal. But the particularism 
 which marks him off when sufficiently prominent 
 goes to the making of a higher individuality when
 
 CHARACTER IN HUMAN BEINGS 67 
 
 fused with general ability or moral quality. We 
 cannot therefore estimate men by merely abstract 
 standards. These are invaluable and indispensable 
 in the task. But they are not everything. The 
 instinct of the man-in-the-street comes in to play 
 its part. This, again, is not everything. It may 
 clash with abstract estimation from a much wider 
 point of view. It may in itself prove insufficient 
 and misleading. But it belongs to the nature of 
 human knowledge that a so-called instinct, which 
 as it were intuitively lays stress on the moment of 
 the particular in reality, must have account taken 
 of it. That is why, in order to make a leader of 
 men, various and diverse qualifications are requisite. 
 A man may possess one-sided qualities in a degree 
 that entitles him to be distinguished as great by 
 their possession. But he will hardly lead men 
 unless he possesses, in addition, other qualities which 
 can appeal to the direct apprehension of the mass 
 of his fellow-men. A great American statesman 
 once declared to me, as the result of long observation, 
 that he believed the really essential gift of a national 
 leader to be the power to persuade. 
 
 I do not mean to suggest that this capacity for 
 recognition as leader of necessity imports the highest 
 quality. All knowledge and all the higher capacities 
 are essentially of a more remote kind. They require 
 a concentration amounting to passion which may 
 shut out the vision of all to which it is not directed. 
 Browning's ' Grammarian ' was of this type. In 
 mundane affairs he was a weak man, and yet the 
 people saw that, measured by standards of value of 
 a great kind, his quality was of the highest order, 
 and they reverenced him accordingly. They would 
 6
 
 68 THE SIGNIFICANCE OF HUMANISM 
 
 not have chosen him to lead in battle or as Prime 
 Minister, but they saw and said that he was great. 
 That was because they recognised his knowledge, 
 though abstract knowledge, as being of a lofty type. 
 This brings me to what is, I think, really meant 
 when the critic uses the word ' Humanism/ It 
 imports what is more than merely general, individual 
 uniqueness based no doubt on particularism, but on 
 particularism invested with high quality of general 
 human interest which shapes it into a whole. The 
 uniqueness may be of the most divergent kinds. But 
 its freedom from abstractness within the order to 
 which it belongs stamps it with a directness and 
 perfection that gives the full sense of reality. 
 It implies nothing short of conceptions which 
 import human personality. In poetry we look for 
 and find this quality, as we do in Wordsworth and 
 in Goethe's lyrics. We find the same sort of quality 
 in individual form in the ancients, what is suggested 
 in, for example, the well-known description in Virgil : 
 
 " Tendebantque manua, ripse ulterioris amore." 
 
 We find it in the domain of religion in the sayings 
 of Jesus. We find it in public life in the penetrating 
 words of really great orators, and in art in the works 
 of very great painters and sculptors. We meet it 
 in Beethoven's Sonatas, and in the work of musicians 
 who give us the sense of what we cannot even in 
 imagination pass beyond. In all these cases there 
 is ever present as the essential moment an element 
 of quality of a high order in reflection. This is of 
 the character of the universal, and it therefore lifts 
 us above the moment. We feel that we are put to 
 a great test by the question whether we dare say to
 
 VALUE IN HUMANISM 60 
 
 that moment, ' Stay, thou art fair/ The test brings 
 us face to face with the necessity for a decision about 
 value, about the true nature of the eternal, and for 
 the rejection of the appearance of attractive but 
 false finality. 
 
 The standard of the universal that thus enters 
 compels us to recognise that, as knowledge itself 
 is ultimately foundational of reality, so in our daily 
 practice it assumes the form of values that are 
 foundational. They are this because when they are 
 really present we cannot go behind them. We are 
 aware that they are presupposed in every attempt 
 to set up the other standards that are in truth of 
 a derivative nature. That is why the doctrine of 
 Hedonism has been a failure. If pleasure is to be 
 of lasting value it must always in the end be dis- 
 tinguished, even when it possesses uniqueness, by 
 quality. And if the test of quality is once admitted, 
 what we have so admitted may imply a nature going 
 beyond the moment, and belonging to the universals 
 that lie at the foundations of the actual itself. 
 
 Everywhere we experience in what is unique in 
 its concreteness the inseparability of the particular 
 and transitory from the universal that abides through 
 it and gives it meaning. In values, and in the 
 inevitable preferences between orders of quality 
 that disclose themselves at every turn, we are face 
 to face with this in our daily lives. It is more than 
 an abstract preference for a general rule that makes 
 men accept high quality in value, while for want of 
 such a standard the mere animal cannot get beyond 
 the passing feeling : 
 
 " Poor vaunt of life indeed, 
 Were man but formed to feed
 
 70 THE SIGNIFICANCE OF HUMANISM 
 
 On joy, to solely seek and find and feast, 
 Such feasting ended, then 
 As sure an end to men ; 
 
 Irks care the crop-full bird ? Frets doubt the 
 Maw-crammed beast ? " 
 
 On the other hand : 
 
 " Let us not always say, 
 ' Spite of this flesh to-day 
 I strove, made head, gained ground 
 Upon the whole ! ' 
 As the bird wings and sings 
 Let us cry, ' All good things 
 Are ours, nor soul helps flesh more now 
 Than flesh helps soul ! ' " 
 
 In lines such as these we have the reflective poet 
 coming to reinforce a theoretical conclusion. In 
 what Browning says in them we have a feature 
 which is distinctive in Humanism. Even when our 
 intellects reject on general grounds the suggestions 
 of a poem, or of what some particular religious doc- 
 trine seeks to insist on, we may yet be aware of quality 
 high in other aspects, and esteem what is written 
 accordingly. It may be here value of a different 
 kind from what belongs to science or philosophy 
 that we are aware of, and it may belong to a different 
 order in reflection. The standpoint is not the same 
 as it would be for science, but not the less it guides 
 us in an appreciation of the value that is appropriate 
 to its own order of ideas ideas which enter into 
 individuality, its finiteness notwithstanding, and are 
 inseparable from that individuality. I will take 
 two widely divergent descriptions given by great 
 writers as illustrative of this kind of relative truth, 
 truth of a humanistic kind, in which the insepara- 
 bility of the particular from the general is insisted
 
 DEAN CHURCH AND THE OXFORD MOVEMENT 71 
 
 on. The first of these illustrations is concerned 
 with a movement that, in the sense in which I am 
 using the word ' Humanism/ was intensely of this 
 character and was distinguished by its refusal to 
 bow before the merely abstract side of knowledge. 
 
 We are beginning to forget the Oxford Movement 
 in the Church of England between 1833 and 1845. 
 Yet it formed a splendid passage in the history 
 of the national life, notwithstanding its failure, 
 which we now see clearly to have been inevitable. 
 The picture is one which has always deeply moved 
 me as an illustration of Humanism in a very lofty 
 form. We of this generation are fortunate enough 
 to have had that picture presented to us, not merely 
 in contemporary records, but by an historian as 
 gifted as was Dean Church, who combined artistic 
 skill with deeply sympathetic insight. This is what 
 he tells us of the Oxford Movement, at p. 167 
 of his book on it, which I quote to introduce what 
 follows : 
 
 " The Movement was, above all, a moral one ; 
 it was nothing, allowed to be nothing, if it was not 
 this. Seriousness, reverence, the fear of insincere 
 words and unsound professions, were essential in 
 the character, which alone it would tolerate in those 
 who made common cause with it. Its ethical ten- 
 dency was shown in two things, which were charac- 
 teristic of it. One was the increased care for the 
 Gospels, and study of them, compared with other 
 parts of the Bible. Evangelical theology had dwelt 
 upon the work of Christ, and laid comparatively 
 little stress on His example, or the picture left us of 
 His Personality and Life. It regarded the Epistlei 
 of St. Paul as the last word of the Gospel message.
 
 72 THE SIGNIFICANCE OP HUMANISM 
 
 People who can recall the popular teaching, which 
 was spoken of then as ' sound ' and ' faithful/ and 
 ' preaching Christ/ can remember how the Epistles 
 were ransacked for texts to prove the ' sufficiency of 
 Scripture ' or ' the right of private judgment/ or 
 the distinction between justification and sancti- 
 fication, while the Gospel narrative was imperfectly 
 studied and was felt to be much less interesting. 
 The Movement made a great change. The great 
 Name stood no longer for an abstract symbol of 
 doctrine, but for a living Master who could teach 
 as well as save. And, not forgetting whither He had 
 gone and what He was, the readers of Scripture 
 now sought Him eagerly in those sacred records, 
 where we can almost see and hear His going in and 
 out among them. It was a change in the look and 
 use of Scripture, which some can still look back to 
 as an epoch in their religious history." 
 
 From the point of view of literature and philosophy 
 alike the greatest figure in the Movement, of which 
 Dean Church thus characterises the essence, was that 
 of John Henry, Cardinal Newman. He failed to 
 succeed, as he was bound to fail. The Spirit of 
 God and man was too great to be confined within 
 the limits which he assigned. But, none the less, 
 he stands out as one of the great Humanists of 
 English literature, a man with an almost matchless 
 sense both of form and of reality. I will therefore 
 quote from The British Critic of April, 1839, some 
 words from an article of his on the state of religious 
 parties, directed to the question of what the Move- 
 ment of which he was the leader meant. 1 He 
 
 1 This article is reprinted in vol. i of Newman's Essays, Critical 
 and Historical, p. 271.
 
 CARDINAL NEWMAN 73 
 
 would not tolerate the view that the influence of 
 that Movement was merely due to the energetic 
 action of a few individuals. 
 
 " Of course every event in human affairs has a 
 beginning ; and a beginning implies a when, and 
 a where, and a by whom, and how. But, except 
 in these necessary circumstances, the phenomenon 
 in question is in a manner quite independent of 
 things visible and historical. It is not here or 
 there ; it has no progress, no causes, no fortunes ; it 
 is not a movement, it is a spirit ; it is a spirit afloat, 
 neither ' in the secret chambers ' nor ' in the desert/ 
 but everywhere. It is within us, arising up in the 
 heart where it was least expected, and working its 
 way, though not in secret, yet so subtly and impal- 
 pably, as hardly to admit of precaution or encounter 
 on any ordinary human rules of opposition. It is 
 an adversary in the air, a something one and entire, 
 a whole wherever it is, unapproachable and incapable 
 of being grasped, as being the result of causes far 
 deeper than political or other visible agencies, the 
 spiritual awakening of spiritual wants." 
 
 A noble description this of the humanistic spirit, 
 indicative of the compelling character of the in- 
 dividuality and particularism of the concrete uni- 
 versal and of the uniqueness that belongs to it. 
 
 I will pass to a very different illustration, selected 
 for the purpose of bringing out the antithesis between 
 concrete and abstract. The German metaphysician 
 Hegel is often smiled at as an authority on such a 
 matter by people who know about him only at 
 second-hand, and to quote him excites as much 
 repugnance with some as to cite Cardinal Newman 
 does with others. I must not be deterred by prejudice
 
 74 THE SIGNIFICANCE OF HUMANISM 
 
 in either instance. My object is to select illustrations 
 of the most useful kind. 
 
 Among other essays which Hegel left behind, and 
 which are collected in volume xvii of his collected works 
 (the second volume of the Vermischte Schriften), is 
 an essay entitled, " Who is the Man who thinks 
 Abstractly ? " He begins by observing that no 
 one is so great a bore as he who is always trying to 
 explain everything in the beautiful world in which 
 we live. It is because we have a fine sense of what 
 such abstract explanations amount to, and because 
 we do not want them, that we flee before them. But, 
 although in polite society we assume that we avoid 
 what is abstract, we sometimes fail. The question 
 remains, who are the people with really abstract 
 minds ? They are, says Hegel, for the most part, 
 the less educated ; not the most educated. Yet not 
 always. He takes, as an illustration, what happened 
 at an execution in Leipsic, where a man was broken 
 on the wheel and then beheaded, for the crime of 
 murder. In what follows I have used the translation 
 given by the late Professor Wallace, in chapter xx 
 of his Prolegomena, not of the whole essay, but of a 
 passage containing Hegel's description of what took 
 place : 
 
 " In the eyes of the multitude he is a murderer, 
 and nothing more. The ladies, perhaps, may make 
 the remark that he is a strong, handsome, and in- 
 teresting man. At such a remark the populace is 
 horrified. * What ! A murderer handsome ? Can 
 anybody's mind be so low as to call a murderer 
 handsome ? You must be little better yourselves/ 
 And perhaps a priest who sees into the heart, and 
 knows the reasons of things, will point to this remark
 
 HEGEL ON THE ABSTRACT MIND 75 
 
 as evidence of the corruption prevailing among the 
 upper classes. A student of character, again, in- 
 quires into the antecedents of the criminal's up- 
 bringing ; he finds that he owes his existence to ill- 
 assorted parents ; or he discovers that this man has 
 suffered severely for some trifling offence, and cannot 
 support himself otherwise than by crime. No doubt 
 there will be people who, when they hear this explana- 
 tion, will say, ' Does this person, then, mean to excuse 
 the murderer ? ' In my youth I remember hearing 
 a city magistrate complain that book-writers were 
 going too far, and trying to root out Christianity 
 and good morals altogether. Someone, it appeared, 
 had written a defence of suicide. It was horrible ! 
 too horrible ! On further inquiry it turned out that 
 the book in question was the Sorrows of Werther. 
 
 " By abstract thinking, then, is meant that in 
 the murderer we see nothing but the simple fact that 
 he is a murderer, and by this single quality annihilate 
 all the human nature which is in him. The polished 
 and sentimental world of Leipsic thought otherwise. 
 They threw their bouquets, and twined their flowers 
 round the wheel and the criminal who was fastened 
 to it. But this also is the opposite pole of abstrac- 
 tion. It was in a different strain that I heard a poor 
 old woman, an inmate of the workhouse, rise above 
 the abstraction of the murderer. The sun shone, 
 as the severed head was laid upon the scaffold. 
 ' How finely/ said the woman, ' does God's gracious 
 sun lighten up Binder's head ! ' We often say of 
 a poor creature who excites our anger that he is 
 not worth the sun shining on him. That woman saw 
 that the murderer's head was in the sunlight, and 
 that it had not become worthless. She raised
 
 76 THE SIGNIFICANCE OF HUMANISM 
 
 him from the punishment of the scaffold into the 
 sunlit grace of God. It was not by wreaths of 
 violets or by sentimental fancies that she brought 
 about the reconciliation ; she saw him in the sun 
 above received into grace." 
 
 In the preface which he wrote to his edition of 
 Wordsworth's poems Matthew Arnold, who had a 
 firm grasp of the meaning of the humanistic element, 
 dwells on the inseparability from it of high know- 
 ledge : '* The noble and profound application of 
 ideas to life is the most essential part of poetic 
 greatness." It is worth noting, this opinion of a 
 competent critic, because it appears by no means 
 clear that his standard is receiving full recognition 
 in the poetry of the present day. He goes on to 
 observe that a great poet receives his distinctive 
 character of superiority from his application, under 
 the conditions inevitably fixed by the laws of 
 poetic beauty and poetic truth, to the subject, 
 whatever it may be, of the ideas 
 
 " On man, on nature, and on human life," 
 
 which he has acquired for himself. But the treat- 
 ment of large ideas, say moral ideas, in a poem is 
 a very different thing from the composition of a 
 moral and didactic poem, which can bring us ' but 
 a very little way in poetry/ Moral ideas are really 
 a main element in life, and therefore are that with 
 which, in some way or other, we are as human beings 
 perpetually occupied. A large sense belongs to 
 the expression when thus applied to the subject 
 matter of poetry. Whatever bears upon the ques- 
 tion ' how to live ' comes under it. Thus, when 
 Milton says
 
 ARNOLD AND WORDSWORTH 77 
 
 " Nor love thy life, nor hate ; but, what thou liv'st, 
 Live well ; how long or short, permit to Heaven," 
 
 these are noble words of a great artist. But not the 
 less does Keats express a moral idea when he consoles 
 the forward-bending lover on the Grecian Urn, the 
 lover arrested and presented in immortal relief by 
 the sculptor's hand before he can kiss, with the 
 line : 
 
 " For ever wilt thou love and she be fair." 
 
 So when Shakespeare tells us that 
 
 " We are such stuff 
 
 As dreams are made of, and our little life 
 Is rounded with a sleep ." 
 
 All these three examples are, for Arnold, examples 
 of true poetry. For what they present is no abstract or 
 general moral lesson but universal truth, in concrete 
 and individual form, in its union with the unique- 
 ness that is of the essence of our experience of life. 
 And so, whatever else such poetry may be, it is con- 
 spicuously humanistic. Wordsworth's own great 
 power lay in the largeness of his outlook and in his 
 ability to find more in life than other poets. Add 
 this to his artistic faculty, and you have the secret 
 of his superiority to other poets. " He dealt with 
 life," says Arnold, " as a whole more powerfully." 
 He goes on to warn us against the ' Wordsworthians ' 
 who hold up Wordsworth's poetry as precious be- 
 cause of its ' sound philosophy.' An illusion. They 
 praise him for the wrong thing. " His poetry is 
 the reality ; his philosophy in so far at least as 
 it may put on the form and habit of ' a scientific 
 system of thought,' and the more it puts them on
 
 78 THE SIGNIFICANCE OF HUMANISM 
 
 is the illusion." Arnold dismisses the formal philo- 
 sophy which appears as such in Wordsworth, and 
 thinks that " poetry is the reality, philosophy the 
 illusion/' I do not differ from him if he means, 
 as I think he really does, that the universal by 
 itself is wholly inadequate to reality, and is actual 
 only in the individual. But then, for full insight 
 into the individual, we require the mind that can 
 think in universals, and of this there is no more 
 conspicuous proof than the advantage Arnold himself 
 possessed over most contemporary critics of poetry. 
 When he tells us of the power with which Words- 
 worth feels the joy offered to us in nature and in 
 the primary affections and duties, however simple, 
 he couples his comment with one on the extra- 
 ordinary power which Wordsworth displays in show- 
 ing us this joy, and in so rendering it as to make us 
 share it. " Everyone/' he says, referring to other 
 poets, " who has any sense for these things feels 
 the subtle turn, the heightening, which is given to 
 a poet's verse by his genius for style. We can feel 
 it in the 
 
 ' After life's fitful fever he sleeps well.' ' 
 
 And in the case of Milton he declares that it is the 
 " incomparable charm of Milton's power of poetic 
 style which gives such worth to Paradise Regained 
 and makes a great poem of a work in which Milton's 
 imagination did not soar high." If Wordsworth 
 himself did great things with what was often no more 
 than a ' nobly plain manner,' we must notice that 
 Wordsworth's use of that manner has something 
 unique and unmistakable. Nature seems to take 
 the pen out of his hand, and to write for him with
 
 PHILOSOPHY AND LITERATURE 79 
 
 her own bare, sheer, penetrating power. That is 
 due to the profound sincereness with which he feels 
 his subject, and to the prof oundly sincere and natural 
 character of the subject itself. ' The right sort of 
 verse to choose from Wordsworth, if we are to seize 
 his true and most characteristic form of expression, 
 is a line like this from ' Michael ' : 
 
 ' And never lifted up a single stone.' 
 
 There is nothing subtle in it, no heightening, no 
 study of poetic style, strictly so called, at all ; yet 
 it is expression of the highest and most truly ex- 
 pressive kind." There is, for Arnold, in Wordsworth 
 an inevitableness which was often lacking in Goethe, 
 though in him too we sometimes find it, for it comes 
 to Wordsworth from Nature herself. 
 
 None the less I think it must be added that the 
 beauty of Wordsworth's poetry is a beauty born of 
 the mind, and born of the mind not the less because 
 that mind is no factory of abstract universals but 
 produces through the creative imagination of genius 
 descriptions of what is individual and unique. 
 
 Even for the greatest masters of art the combination 
 of the universal with the particular is often too diffi- 
 cult. Excessive stress is laid on one moment or the 
 other in the reality from which they are inseparable. 
 But it is not only in art that we find this difficulty. 
 In these Islands we are perhaps stronger than many 
 on the Continent in our steadfast refusal to dissociate 
 the two moments, and to fall in particular into the sin 
 of the abstract mind. Yet insistence on the aspect 
 of the particular often brings troubles for us. Those 
 in Ireland know that. There is much of the dynamic 
 in their outlook on life. In the Anglo-Saxon portion
 
 80 THE SIGNIFICANCE OF HUMANISM 
 
 of the geographical area there is less, perhaps too 
 little. But, as a group of nations, we have succeeded 
 in producing what the common denominator of the 
 general genius tends to yield. Even in philosophy 
 this is so. Where can we wish for better examples 
 of this than in plain John Locke, whose Humanism 
 is manifest in a style consistently inspired by his 
 declaration that " God has not been so sparing to 
 men as to make them two-legged creatures, and left 
 it to Aristotle to make them rational/' In the 
 Bishop of Cloyne we have the same spirit. With 
 Berkeley philosophy was always literature, and 
 literature not less philosophy. And I must not 
 forget the David Hume whose ashes repose in the 
 Calton burying-ground of Edinburgh. Of all thinkers 
 he had perhaps the greatest gift for putting uni- 
 versals into concrete form. 
 
 Philosophy and literature differ less than is popu- 
 larly imagined in their purposes and methods. Both 
 seek to bring us to awareness of what is most real. 
 The level in each ought therefore to be of high 
 quality. For the philosopher knowledge has to be 
 approached more abstractly than by the artist, 
 just for the same reason as prevails for the mathe- 
 matician. It is a general form that is with the 
 abstract thinker essential if he is to so express himself 
 as to be intelligible. But no more than the artist 
 dare he break away from the particularity of what is 
 actual. If he fails in self-restraint in this he suffers. 
 If he succeeds he may be himself ranked as an artist, 
 as Plato has been. The best critics have seen the 
 point very clearly. I have already cited as a witness 
 Matthew Arnold. 
 
 I will conclude by citing another very highly
 
 SAINTE-BEUVE 81 
 
 endowed critic, Sainte-Beuve, who tells us the same 
 thing in different language. I will quote from the 
 address he delivered in 1858 to the students of the 
 ]cole Normale on " Literary Tradition," with the 
 purpose, as he himself tells us, of illustrating the 
 difference between the duties of a critic and those 
 of a profefcsor. On the authority of Pericles, in his 
 funeral oration over the warriors who had died for 
 Athens, Sainte-Beuve describes it as a city where 
 no chagrins, no jealousies, no rigid austerities 
 offended the eye or mortified a neighbour's pleasure ; 
 where it was a joy merely to live, to breathe, to walk 
 abroad, and where the mere beauty of buildings 
 and public edifices, the beauty of daylight and a 
 certain air of festivity, drove sadness far from the 
 mind ; where it was possible to love beauty with 
 simplicity of life and philosophy without being 
 effeminate ; where wealth was used for a practical 
 purpose, and not for ostentation ; where courage 
 was not blind, like that of the furious Mars, but 
 enlightened and knowing its own reasons, as befitted 
 the city of Minerva. An exaggerated description 
 no doubt of Athens even as Pericles made it, 
 but a description of the place of a people who had 
 come to embody its life in the proportions of the 
 real concrete universal. Of Pericles himself, to 
 whom he attributes the guidance which resulted in 
 this disposition, Sainte-Beuve says that he was the 
 most noble and brilliant type of the popular chief, 
 the man who becomes dictator of a democracy by 
 reason, eloquence, talent, and continual persuasion. 
 Sainte-Beuve goes on to a later epoch when " Bib- 
 lical grandeur and Hellenic beauty met and were 
 fused and mingled, in spirit and in form, with lofty
 
 82 THE SIGNIFICANCE OF HUMANISM 
 
 simplicity." For him it is this fusion which created 
 at all events a tradition. The real product of this 
 tradition he finds in Shakespeare, who had learned 
 it, he thinks, from Montaigne and Plutarch. 
 
 For his general thesis he invokes the witness of 
 Goethe, in whom he says that all tradition united, 
 but that from a literary point of view the classical 
 predominated. Greece taught him to so contemplate 
 the universe that it might appear in its most beautiful 
 light. " As for himself, whenever we wish to form 
 an image of the critical spirit at its highest point 
 of intelligence and of considered understanding, we 
 figure him to ourselves as an attentive and watchful 
 spectator, curious from afar off, on the outlook for 
 every discovery, for all that goes by, for every sail 
 on the horizon but from the heights of his Sunium." 
 
 Yet nobody, goes on the great French critic, has 
 any right to rest quiet, even in the best established 
 admirations. " One thing or another is constantly 
 moving as we watch it, and there open, as in the old 
 cities, long new vistas which change the most familiar 
 views. Instruction is bound, whether it will or 
 not, to take fresh bearings, to reconsider in these 
 things. There are ways also in which it can renew 
 itself, in which it can modify the manner in which it 
 does service to taste and defends tradition." This 
 we may fully recognise while taking care that " the 
 old method, and what has sprung from it, shall 
 remain in honour, an object of worship and of study, 
 present to the memory and to the meditation of 
 those faithful intellects which can still be touched 
 by the idea of beauty." 
 
 A fine description this of what we as Humanists 
 should set before our minds. Our criticism must
 
 THE RELATIVITY OF ITS STANDARDS 83 
 
 be based on reflection if it is not to miss what is 
 greatest, and to fail to recognise that in its very 
 relativity to the standpoint of its time has lain its 
 truth and reality. For such relativity applies in 
 the case of the standards of beauty just as it does 
 in those of science. Knowledge never stands still 
 in any form. Its accuracy depends on its power of 
 adjustment in form and outcome. Its scope is so 
 wide that it reaches not merely what is general and 
 abstract, but not less that in which it is expressed 
 imaginatively in the symbols of feeling and emotion.
 
 THE PHILOSOPHICAL SIGNIFICANCE OF 
 HUMANISM (continued) 
 
 CHAPTER III 
 
 FORMS OF HUMANISM 
 
 I ENDED the last chapter by touching on the distin- 
 guishing feature of Humanism in literature. It is 
 a form of knowledge in its widest sense in which 
 the stress is laid on that individuality and uniqueness 
 which we find in what seems direct perception and 
 in emotion. With this the distinctively humanistic 
 purpose is concerned. The universals of knowledge 
 are always latent. It is these that give their meaning 
 for reflection to the works of art in which they are 
 embodied. But it is not in the abstract form of 
 general rules that they appear, for the end to which 
 we are directing attention is different from the end 
 of the man of science. It is in the main as values 
 that we recognise them here, values which are founda- 
 tional in artistic experience but are never merely 
 abstract concepts. What is before us we recognise 
 as imaginative constructions, born of the spirit. 
 Mere reproductions of nature they cannot be. 
 They require mind for their recognition and develop- 
 ment. Personality is always implied in them. Here 
 again we find the relativity of reality to knowledge. 
 The highest may be the highest only in a particular 
 period and its quality may alter. But the highest 
 of its kind it is always seen or felt to be if it is 
 accepted without reservation. If it is not so 
 
 84
 
 RELATIVITY IN HUMANISM 86 
 
 accepted that is because we are aware of its 
 deficiency in value, a deficiency which imports 
 that the range of mind extends beyond it. There 
 is no standard of universal applicability under 
 all variations of circumstance, such as the mathe- 
 matician discovers by abstraction in his invariants. 
 But there is apparent value in the form which know- 
 ledge presents, a value which is there only for mind 
 at a high level and which remains identical in know- 
 ledge despite differences in the mode in which reality 
 presents itself in respect of periods and fashions of 
 expression. That is the meaning of the doctrine 
 of relativity as applicable to Humanism. 
 
 Knowledge is an entirety, and within that entirety 
 appear many standpoints irreducible to each other 
 which give rise to relativity in orders of appearance. 
 The result is that reality discloses itself as varying 
 in character. Now the reality with which Humanism 
 concerns itself is one in which the form of knowledge 
 is directed neither to general rules nor to abstract con- 
 cepts, as what express its standpoints and standards 
 of excellence, but to a mode of apprehension that 
 presents itself as if more direct. We have seen 
 that it is no passive apprehension, for mind is active 
 there as elsewhere in the construction of the object 
 in which it finds itself and only itself. Aristotle 
 taught us this long ago. But the recognition of 
 value and of standard or quality in value is the 
 evidence that here, as in every other case, we cannot 
 escape from knowledge, and that just because it is 
 only through distinctions made by and within know- 
 ledge that we and our objects arise. Eeality and 
 unreality, truth and error, sin and righteousness, 
 beauty and hideousness, all find their actuality and
 
 86 THE SIGNIFICANCE OF HUMANISM 
 
 the distinctions that are the foundation of such 
 actuality in knowledge itself. But in Humanism 
 it is in the main only on knowledge in certain of its 
 many aspects that we are dwelling. The quality 
 of beauty may be what absorbs our attention. It 
 discloses itself in what is unique but is still an ex- 
 ample of value, and so implies what is in ultimate 
 analysis of a general character as an active moment 
 in its nature. 
 
 What is true of beauty in form as we meet with 
 it is also true of our impressions of what is called 
 personality. There is always some kind of unique- 
 ness in the men whom the world distinguishes as 
 leaders, something that appeals to the imagination. 
 No man is great merely because he preaches a par- 
 ticular doctrine. Whether it be in his deeds or in 
 his words or in his writing, what moves those who 
 follow him is what is beyond his mere doctrine, that 
 in him which fires the imagination and makes others 
 feel that in him there is what cannot be adequately 
 described or forecast. He is for them an individual 
 marked out from the others around him by a quality 
 that cannot be exhausted in any phrases. It suggests 
 what is not capable of being included in any abstract 
 description. The universal is there, but in union 
 with a particularity that gives it dynamic force. 
 Here also we have the concrete universal, and we 
 feel that in his way, if we recognise him as leader, 
 we shall not look on just the like of this man again. 
 Thought and will are not really different in nature. 
 Both are activity, both dynamic in their capacity 
 to transform their object world. It is only in the 
 form of the transformations they bring about that 
 they differ. The great man stands for the trans-
 
 PERSONALITY 87 
 
 forming man. If he be an administrator of genius 
 he will compel those around him to do his will by 
 the inspiring power he brings to bear on them. If 
 he be of the first order in literature or science he will 
 create a school of disciples, inspired by faith, by the 
 sense of what is unseen, and not merely by notional 
 agreement with what he lays down. To exercise 
 such power and to bring its might to fruition may in 
 some cases require time, while in others the result 
 comes quickly. The variety of such personalities 
 is infinite, as the history of action and thought shows. 
 But the lesson we learn is always that leadership 
 depends on personality in some form, on the quality 
 that comes from the grasp of universals that are 
 concrete. A great leader is no mere book to read. 
 It is because the study of him is inexhaustible, and 
 involves the appeal to the imaginative and pictorial, 
 that he lays hold of the mind of the man in the 
 street. The approach to what is purely particular 
 in character is here as elsewhere elusive, for it is 
 asymptotic and incapable of definition. He may 
 be very human, very finite. He may often be 
 wrong. But if his knowledge or his power of action 
 is dynamic and can compel the imaginations of men, 
 his shortcomings, very real perhaps to the few that 
 are sufficiently equipped to estimate them, will not 
 destroy his power over the multitude who are drawn 
 after his banner. Here is yet another form of 
 Humanism, resulting from the fashion in which we 
 all of us have to think in images that, while inadequate 
 to full knowledge, are yet essential in it. For the 
 real is never merely abstract. It is always concrete 
 even in its general principles. This is a plain and 
 obvious truth. We fall in love with persons, not
 
 88 THE SIGNIFICANCE OF HUMANISM 
 
 with qualities. It is just you, here and now, that 
 we turn to, not to any abstract construction out of 
 general principles. The devotion of a dog or a horse 
 to its master is hardly less of this order. 
 
 In religion Humanism exercises a similar influence. 
 It has been said truly that a test of its truth and work 
 in practice is the scope it allows to disciplined imagi- 
 nation. The ' practice of the presence of God ' has 
 been given as the expression for a mode of its exercise. 
 Such practice is made easier for the majority if it 
 takes place when they are assembled together, with 
 common conditions and a sufficient ritual. This 
 means that emotion requires channels in which to 
 flow readily, channels which symbolise universals 
 in reflection. A few, and among them the best, 
 have the faculty of supplying such universals through 
 their own unaided reflection. But for the bulk 
 of mankind co-operation under leadership is required 
 for the stimulation of the reflection in which religious 
 emotion is clothed. Still, apart from such emotion 
 the universals become barren and tend to degenerate 
 into formalism. Religion depends on mastery by 
 emotion, the sense of self-surrender to what is highest. 
 This sense is developed by the methods of its general 
 expression. To some one set of symbols appeals more 
 than does another. . The emotion to be called forth 
 varies with individuals. There are those with whom 
 it must take the form, if it is to be real, of the con- 
 sciously experienced presence of the sublime. There 
 are others with whom it may be of a more personal and 
 transitory form, and for these help from the repeated 
 production of external conditions can count for more. 
 But for religious men of all temperaments the sense 
 of self-surrender, of willingness to die in order to
 
 RELIGION 89 
 
 live, is essential in some shape if the highest is to 
 be attained. In all cases the work of imagina- 
 tion comes in. The moving occasion is always in 
 some sort symbolic. It is through a symbol that 
 imagination gets its strength and practicability, and 
 enables men and women to turn away from the 
 engrossing details of daily life to what they feel to 
 be abiding through the fashion of the day. This, 
 too, is what binds them together, and makes them 
 aware of a brotherhood in humanity which calls 
 even from the very depths for compassion and mutual 
 helpfulness. The reality of the appeal relates religion 
 to ethical conduct, and demands a high ethical level. 
 If the response to this demand is wholly absent we 
 naturally utter the word ' hypocrite/ 
 
 Here, again, we see the stress that is distinctive of 
 Humanism, with its emphasis on concreteness and 
 the necessity for the recognition of that inexhaustible 
 moment of the particular which is the condition of 
 imaginative construction. The churches, the minis- 
 ters, the ritual, are but symbolic of what is wider 
 and deeper, a form which knowledge in its highest 
 and fullest sense assumes, a form in which the general 
 and the particular are inseparable in its reality. 
 For such knowledge an effort of what we call will 
 is indispensable ; it is itself the outcome of a form 
 of knowledge. Mind, in the aspect of disciplined will 
 and emotion, is at the foundation. No animal short 
 of man possesses mind of such a kind as to be capable 
 of religion, and this is one of the proofs of the ne- 
 cessary presence of the universal as a moment in the 
 religious consciousness. Other such proofs are to 
 be found in the possibility of a large number of human 
 beings joining together in the effort to develop that
 
 90 THE SIGNIFICANCE OF HUMANISM 
 
 consciousness and to keep it in a systematic shape 
 alive. What is called fanaticism is due to excessive 
 stress having been laid in such combinations on 
 merely abstract principles, divested of the Humanism 
 which expresses the actual character of the relation 
 of the inolividual to God as immanent in him. 
 
 As in religion, so it is in natural science. Here 
 we come back to observation of actual facts as the 
 basic test. But the observation must be disciplined 
 observation, and no unrestrained means of stimu- 
 lating fancy. As Helmholtz says, Goethe was a 
 very great observer, one of the most gifted on record. 
 But even his acute experiments with the phenomena 
 of light led him wrong. His mind was deflected from 
 the significance of the discoveries of Newton in this 
 domain because he was not adequately trained in 
 mathematical principles. Had it been so he might 
 well have attached to the facts he observed the same 
 significance as they had for Newton. The history 
 and subsequent development of knowledge about 
 light has proved that Goethe got into a wrong path 
 through lack of this sort of training. From want 
 of knowledge of a general character he misconstrued 
 what was particular. 
 
 To-day there are physicists of great eminence 
 who are sceptics about the truth of the claim made 
 by Einstein to have resolved matter into energy, 
 energy into mere change of position, and change of 
 position into relationships that are merely relative, 
 with the result that space and time themselves are 
 reduced by him to mere relations of relativity to 
 the observer and his situation and conditions. 
 Against this it is said that, although force is 
 naturally interpreted through our subjective feelings
 
 RECENT TENDENCIES IN SCIENCE 91 
 
 and muscular sense, it yet means something real, 
 and that the relativity doctrine does not account 
 for enough of what the facts reveal to be able to 
 claim anything like the whole field. A residuary 
 domain called that of the set her is, it is maintained, 
 still required in order to account for facts observed. 
 To this criticism Einstein replies that, so far, no such 
 fact has been described which does not allow itself 
 to be recorded and interpreted in the terms of his 
 system. As to space and time and the aether, he 
 insists not only that the old view of them cannot 
 explain things that are beyond question in our 
 experience, but that the significance which we 
 attribute to them is due to our having taken them 
 to be of a single form. A more adequate geometry, 
 he says, the geometry which has been developed 
 out of the work of Gauss and Biemann by bringing 
 in, in addition, his own interpretation of the gravi- 
 tational field, with the changing shapes and measure- 
 ments of the relations in it, shows that space and time 
 are of a more general character and vary far more 
 as forms of experience than the old classical physi- 
 cists have permitted themselves to think. The basic 
 character that underlies both space and time can 
 for him be expressed merely in definitions of a tensor 
 character. 
 
 Only progress in work by the few whose minds 
 are adequately trained for research in this region 
 can settle which of these two schools of thought is 
 right. It must be remembered that Humanism is 
 itself capable of excesses as great as those of the 
 abstract mind, and that under the stress of emotion 
 we are always prone to humanistic excess. It is a 
 temptation arising out of our natural preference for
 
 2 THE SIGNIFICANCE OF HUMANISM 
 
 what appears to be direct knowledge. But that 
 which is taken to be direct experience constantly 
 discloses itself as having been deflected by uncon- 
 scious assumptions. The history of science, and 
 indeed of philosophy generally, is the history of 
 a slow but steady vindication by the universal of 
 its claim to be equally real with the particular, and 
 we therefore can never be certain how much of that 
 which we have taken ourselves to have had directly 
 revealed to us in passive awareness has really been 
 the outcome of the activity of thought in qualifying 
 particularism. Here we have the same character 
 in knowledge disclosed to us as in art and in religion, 
 only in more elusive form. The concrete is always 
 a concrete universal. We cannot lay exclusive 
 stress on either of the moments implicit in it or on 
 the polar aspects which it presents. If we do, we 
 fall in one case into the sin of the abstract mind, and 
 in the other case into the disorderliness of those 
 who build on shifting sand. The well-balanced intelli- 
 gence takes full account of both aspects, refusing to 
 be plunged into abstractions, on the one hand, or 
 to live from hand to mouth, on the other. The mind 
 of genius reaches a yet higher level, for it does justice 
 to the claims of both by bringing them into larger 
 wholes in which the .two aspects are transcended and 
 so reconciled in a fuller entirety. This is the secret 
 of genius alike in poetry and in science. It is such 
 genius that we see also in the highest triumphs of 
 religion and in the most penetrating insight in 
 science and philosophy. 
 
 The doctrine that every' department of knowledge 
 belongs to a single entirety, and can be adequately 
 interpreted only in its organic relation to the other
 
 ORIENTAL HUMANISM 93 
 
 departments, is of the very essence of Humanism. 
 Between the pure mathematician and the poet and 
 the preacher there are no gulfs fixed. Each deals 
 within his own order of reflection and in its peculiar 
 terms with the same material, the unique reality which 
 belongs to a whole that discloses itself from differing 
 standpoints. The reality, although varying in form, 
 is the same, and it is possible to exhibit all forms of 
 knowledge about it as organic to each other, if our 
 outlook is wide enough. It is interesting to observe 
 how this view is beginning to make itself apparent 
 even in the present period in our own country, and 
 perhaps more on the Continent than among the 
 Anglo-Saxon peoples. It is a view which is essentially 
 humanistic. We find it foreshadowed in the sayings 
 in the Upanishads. There the problems of meta- 
 physics are not discussed in what we of the West 
 would call a sufficiently systematic fashion. But 
 they are discussed nevertheless, and close attention 
 is bestowed on the question of the nature of the self 
 in knowledge. The spirit is that of Humanism, but 
 the underlying principle is the doctrine that know- 
 ledge is an entirety, and that it possesses grades or 
 levels. This is well brought out in the books and 
 articles which have recently appeared from the pen 
 of Professor Radhakrishnan, formerly of the Univer- 
 sity of Mysore and now, I think, of that of Calcutta, 
 who is versed in the metaphysical systems of the West 
 as well as in those of his own East. One phase of 
 value in the study of oriental philosophy seems to 
 me to lie in this, that the gap between thinking in 
 abstract conceptions and thinking in images is reduced 
 to what leaves the concrete nature of the humanistic 
 outlook on life with its proper and full value.
 
 94 THE SIGNIFICANCE OF HUMANISM 
 
 But it is not only in India that we have the spec- 
 tacle presented of an intense desire to grasp and 
 realise the inherent unity of knowledge. A move- 
 ment is on foot in the German universities which has 
 so far attracted here less attention than it should. 
 One of the best accounts of this movement, still 
 in its infancy but being pursued with scientific 
 thoroughness, is contained in a pamphlet entitled, 
 Humanismus, Hochschule, und Student. 1 There 
 was a conference attended by representatives of 
 various German Universities, including representa- 
 tives of the students as well as the professors, which 
 took place at Hanstein, not far from Gottingen, in May 
 1921. The papers read and the addresses delivered 
 are in substance reproduced in this pamphlet. 
 
 The purpose of the movement is nominally the 
 establishment of a Humanistic Faculty. But in 
 this connection ' faculty ' does not mean a separate 
 faculty of humanistic studies. With the existing 
 distribution of subjects in the universities of Germany 
 it is not sought to interfere. The real object is to 
 bring these subjects into organic relation to one 
 another, and exhibit university teaching not as a 
 collection of fragments isolated from one another, but 
 as the outcome of standpoints all of which have 
 their places within the entirety of knowledge. Thus 
 classics and pure science are to become no longer 
 ignorant of each other, or of what each really signifies. 
 This is to be accomplished by systematic work, in 
 which the professors and students are to co-operate. 
 The professors are to lead the students to the wider 
 view of what a university can teach. Philosophy is 
 to be made aware of science and science of philosophy, 
 
 1 Published by ' Die Studentenschaft,' Gottingen.
 
 A HUMANISTIC FACULTY 95 
 
 and the atmosphere of literature Is to be made 
 available for both. This is to be done by lectures 
 and courses of more general scope than that to 
 which the universities have hitherto been limited. 
 It is hoped that the movement will penetrate through 
 university- trained teachers, with their outlook thus 
 enlarged, to the new ' People's High Schools ' 
 which form a fresh feature appearing in German 
 educational life since the war. These schools are 
 being established in various industrial and agri- 
 cultural centres, and their object is to continue the 
 education of the democracy, after the age of eighteen 
 has been attained, throughout the course of life. 
 
 With us in these Islands the plan for bringing 
 the higher knowledge within the reach of democracy 
 has been that the universities should take on new 
 extra-mural functions, and that their fellows and 
 tutors, increased in number for the purpose, should 
 proceed to the industrial centres, and there reproduce 
 as far as possible the system of university teaching 
 in evening courses. In Germany the traditional 
 spirit of the universities and their geographical 
 distribution have made this more difficult. While 
 the aim of the new popular high school movement is 
 to produce what we aim at producing, a democracy 
 with its mind trained partially at least in the atmo- 
 sphere of a university, the main reliance seems 
 to be on the work of the highly trained teachers 
 in the great secondary schools of Germany, who 
 are to do, outside their walls, what the university 
 tutors we possess have assigned to them. It is too 
 soon to be sure of prospects under either system, but 
 in both countries the aim is the same. It is be- 
 lieved by the supporters of the movement in both
 
 96 THE SIGNIFICANCE OF HUMANISM 
 
 forms that the great problem to be solved is to lay 
 foundations on which, not immediately but in the 
 future, a democracy with a more enlightened mind 
 than that of to-day can be produced, a democracy 
 characterised by the stability in purpose and sentiment 
 which only adequate mental training can found. 
 Those who are at the back of this movement in Ger- 
 many are, in the main, the same as those who are at 
 the back of the humanistic movement to which 
 I have just referred, and it remains to be seen 
 how they will progress. Throughout its financial 
 difficulties Germany seems to have no disposition 
 to economise in education. The indications suggest 
 that in this she is wise. 
 
 It is also a part of the policy of the German Govern- 
 ment to insist on the policy of Einheit in the 
 national schools. Before the war the children of the 
 rich were generally educated separately, as has been 
 the case here. This is being rigorously discouraged. 
 Rich and poor are to have the same chances as far as 
 possible, the only difference being that it is neces- 
 sarily easier for the children of the rich to continue 
 longer in educational higher courses than is practi- 
 cable in the case of those who have to earn a living 
 at an early stage in life. 
 
 It was Goethe who proclaimed what was, for a mind 
 of his type, the peculiar value of the Scottish philo- 
 sophy, as we find it in men so different as David 
 Hume, Thomas Reid, and Dugald Stewart. ' The 
 reason," he says, " why foreigners Britons, Ameri- 
 cans, Frenchmen and Italians can gain no profit 
 from our new [German] philosophy, is simply that 
 it does not directly lay hold on life. '^ They can see 
 no practical advantages to be derived from it, and so
 
 GOETHE ON THE SCOTTISH PHILOSOPHY 7 
 
 it is that men turn more or less to the teaching of 
 the Scottish school as it is expounded by Reid and 
 Stewart. This teaching is intelligible to the ordinary 
 understanding, and this it is that wins its favour. It 
 seeks to reconcile sensationalism and what is spiritual, 
 to effect the union of the real and the ideal, and thus 
 to create a more satisfactory foundation for human 
 thought and action. The fact that it undertakes 
 this work, and promises to accomplish it, obtains for 
 it disciples and votaries." 
 
 Goethe was in his own way a King of Humanists. 
 We must not take his words as literal truth. Less 
 than did Schiller he had appreciated what Kant 
 accomplished Kant, who was finally to overthrow 
 the Scottish school of thought. It was not, as Pro- 
 fessor Seeley reminded people, in an article which he 
 wrote in The Contemporary Review in 1884, from any 
 pedantry that Goethe turned his back on German 
 literature. There were no German Mil tons and 
 Shakespeares against whose examples it would have 
 been impiety to rebel. But could he not have gone 
 back to the Minnesingers ? He answered this question 
 himself : " The Minnesingers lay too far from us ; 
 we should have had to begin by learning their lan- 
 guage, and that was not in our way ; we wanted to 
 live, and not to learn/* These, then, were the circum- 
 stances which drove Goethe to seek for foreign 
 models. He could not find at home either poets or 
 philosophers who could teach him how to speak in 
 the great style. He was forced to look abroad. 
 Shakespeare attracted him first ; there he found, even 
 in the heart of the cold north, the vigour, freshness, 
 freedom, natural passion, and natural grace of which 
 he was in search. But later on he thought he saw
 
 98 THE SIGNIFICANCE OF HUMANISM 
 
 that what was to be found in Shakespeare alone among 
 the moderns was to be found everywhere among the 
 ancients, and that the true home of the artist is not 
 where an exceptional genius triumphs over the gloom 
 of nature, but where nature itself is sunny and where 
 men have a religion of joy. So it was with his study 
 of philosophy. This he met with in his stride, and 
 had to take account of it in a sustained effort to 
 survey the whole field of knowledge. But never was 
 he deserted by the conviction that reality assumed in 
 all cases the form of the concrete universal. That 
 was why the Critique of Pure Reason was not sufficient 
 for him. But, as Helmholtz said in the criticism to 
 which I have already made reference, it would have 
 been better for Goethe, as a student of science, if he 
 had borne in mind steadily that the real is not to be 
 fully understood unless the principles which deter- 
 mine its form are disentangled in the light that can 
 be cast by exact knowledge and by exact knowledge 
 only. The general is implied in what is actual as 
 much as is the particular. Apart from mind and the 
 meanings in which it sets its objects, these two 
 moments in our knowledge do not attain reality. 
 
 I will sum up what has been the purport of these 
 three chapters in closing my endeavour. It seems, 
 as the result of the inquiry, that the ultimate reality 
 to which we come back in the end, and in terms of 
 which alone we can express all the distinctions 
 through which our universe is present to us, is just 
 knowledge itself. It is our habit, natural and 
 necessary for the purposes of ordinary life, but in- 
 adequate when we are seeking the foundations of 
 mind and its objects, that leads us to assume that 
 knowledge can be adequately explained as a property
 
 THE SCOPE OF KNOWLEDGE 99 
 
 of certain of these objects. In truth it is that within 
 which subject and object alike fall as its own phases, 
 and it cannot itself be described or interpreted in any 
 terms that go beyond it. But just because of this, 
 its foundational character, its objects are always 
 what are disclosed in the unity which confronts us 
 when we turn reflection on to the nature of our direct 
 and actual experience. The real, from its very nature 
 as belonging to knowledge, is, on the one hand, no 
 construction by merely abstract thought, nor, on the 
 other hand, has it meaning or existence apart from the 
 setting which thought gives to the vanishing parti- 
 culars with which it is concerned. The two phases 
 have reality only in the wholes to which they belong 
 and in which they are interpreted. 
 
 Such a view at least affords a principle through 
 which Humanism can be vindicated and be made 
 intelligible. It bids us to lay exclusive stress on 
 neither of two abstractions, each of which taken in 
 isolation is false, but to direct our attention to the 
 fulness and richness of life, and to interpret these 
 from a really comprehensive outlook.
 
 PART II
 
 THE PHILOSOPHICAL SIGNIFICANCE OP 
 OTHER SUBJECTS 
 
 CHAPTER IV 
 
 MATHEMATICAL PHYSICS 
 
 IN the observations I am about to make on the subject 
 of Mathematical Physics I shall address myself in the 
 main to those who, like myself, are concerned with 
 the theory of knowledge. It is from this point of 
 view, concerned as it is only with logical principles, 
 that I write. In The Reign of Relativity an effort 
 was made to work out such a principle and to apply 
 it in various regions of science in which it seemed to 
 appear. But the amount of ground which had to be 
 covered compelled me to confine attention only to 
 general features in the course of that survey. There 
 are some matters which remain for consideration in 
 connection with the physical interpretations, not 
 always as it seems to me very clear, which the 
 mathematicians offer of their symbols. 
 
 There are thus one or two subjects which I now 
 wish to approach in rather more detail than in the 
 earlier book. The first of these concerns a method 
 adopted in the most modern developments of mathe- 
 matical physics. For the light it is casting on 
 fundamental questions philosophy appears to me 
 to be under a real debt to those who wield this 
 method. Indeed philosophy had got almost as far 
 as it could in the only medium that was available, 
 and its waters were tending to become stagnant. 
 
 103
 
 104 MATHEMATICAL PHYSICS 
 
 To-day it has been furnished with other waters to 
 navigate further. But that is neither all nor the 
 most important thing. The conceptions and methods 
 of the mathematical physicist himself are also being 
 refashioned. Most of the physicists who are eminent 
 as mathematicians have been at one about this, 
 though a few still doubt. At all events, the majority 
 have provided ideas so fresh that philosophy has 
 before it a task such as it has not had for a long time. 
 It can neither shirk the duty to attempt to find 
 systematic expressions into which these fresh ideas 
 may fit, nor can it itself advance without making an 
 effort to interpret them for itself. Interpretation 
 which may bring them into relation with other forms 
 of knowledge they certainly require. Mathematicians 
 are apt too easily to take their own formulas as ade- 
 quately descriptive of the nature of reality. 
 
 I will begin by referring briefly to some points in 
 the argument of the first part of the present volume. 
 
 In order to apply the principle of the form of 
 individuality as basic to which these points were 
 directed, let us ask what is the character of the 
 object world of the physicist. The actual object in 
 knowledge is, as we have seen, always and essentially 
 individual and unique in character. Even when we 
 think in the most general terms, as in tensor expres- 
 sions or even in such as are yet more abstract 
 inasmuch as they are of a purely logical nature, 
 we really form images, with which we operate as 
 symbolic of meanings of general application. When 
 we point or feel it is also in every case with an 
 interpretation through universals, which is essential 
 to significance and so for reality. The logical 
 moment of the purely particular is always present as
 
 THE SYMBOLISM OF SCIENCE 105 
 
 implied, but it is no entity apart from or independent 
 of the universals in which it is set in knowledge. 
 The purely particular is implicit in experience, but 
 its nature is to be the asymptotic limit to the opera- 
 tion of reflection. We cannot even name such a 
 particular as being merely such. If we try to do 
 this we have transformed its character into that of 
 an individual, for the description always implies 
 general terms which are requisite for description of 
 any aspect and which import what is of a universal 
 not less than what is of a particular nature. Such 
 a method as that of Extensive Abstraction, introduced 
 as one of mathematical logic by Professor Whitehead, 
 is akin to the method of the differential calculus. It 
 attains to simplicity in the object it sets up by 
 reducing it to the symbol for a limiting concept which 
 has significance of a general kind only in and through a 
 relation, and not as an independent entity which can 
 confront knowledge as a self-subsistent particular. 
 
 This result becomes more and more apparent the 
 further science is pushed. It brings the ultimate 
 conceptions of science under aspects in which in the 
 end they enter the domain of philosophy, and require 
 the aid of the logician for their final interpretation. 
 Knowledge is an entirety within which all its logical 
 moments fall, but they fall into this entirety only 
 as distinctions within the whole, and they have no 
 meaning excepting as distinctions so made by know- 
 ledge. 
 
 None the less such distinctions belong, just on 
 that account, to the foundations of our actual 
 experience. In that experience they are bound to 
 appear in some form. What seems at first sight 
 particular always turns out to be what it is
 
 106 MATHEMATICAL PHYSICS 
 
 because of generality in its meaning. It may be 
 that certain of the problems which are to-day 
 perplexing mathematicians and physicists will have 
 a further significance when this, the essential char- 
 acteristic of experience, is realised ; possibly the 
 difficulties of the quantum doctrine, for example. 
 It appears that experience, when closely tested by 
 analysis and experiment, shows the ultimate form 
 in which action takes place, for instance in the 
 radiation of light and electrical energy, to be one 
 of discrete quanta of action. The form of action 
 always has characters which point us to continuity, 
 but these also imply discreteness, and the discrete- 
 ness of form seems not less to confront the observer. 
 What is the explanation of this ? As a pure question 
 of physics the reason of the phenomenon is perplexing. 
 But if the double relation is the outcome of the very 
 nature of experience, arising from the necessary 
 union in the actual of general and particular in the 
 uniqueness and individuality which characterise all 
 objects, the form of the antithesis is one which may 
 at least be expected. 
 
 We find the emergence of something like this 
 form of antithesis in the quantum doctrine however 
 abstractly we consider the object world. Geometry 
 itself affords an example of this, and I shall presently 
 turn to it. But before entering on this subject we 
 must make clear to ourselves how much there is 
 for the observer of which his geometry does not take 
 account. About the extent of this there is con- 
 troversy. The tendency, however, appears to be to 
 insist that the actual object world which presents 
 itself to us is of a highly concrete and individual 
 nature, incapable of being broken up into what are
 
 MAX PLANCK ON FORCE 107 
 
 separately subsistent secondary as distinguished from 
 primary qualities. 
 
 In the fourth edition of his book on the Con- 
 servation of Energy (so far available only in 
 German), at page 169, Professor Max Planck, one 
 of the pioneers of the quantum theory, and also a 
 sharp critic of the attempt to exhibit the universe 
 adequately merely in terms of the geometry of 
 Relativity, or indeed of any other geometry, makes 
 some characteristic observations about what he holds 
 to be the true point of departure for the physicist. 
 A humanistic tendency is apparent throughout. 
 He points out that Newton and Kelvin, with whom 
 he is on this point in much agreement, referred 
 the notion of energy to an origin in that of force, 
 actually experienced in the sense of pressure. The 
 muscular sense and the senses of touch and feeling 
 are those where it is expressed. The other way, he 
 says, was, as with Kirchhoff, to define force and 
 acceleration as identical, by doing which the notion 
 of force lost in significance, inasmuch as all reference 
 to sense was excluded. The advantage of the second 
 idea was that the notions of work and energy became 
 deductions from that of force. A third course was 
 that of Huygens, who, Planck says, placed the 
 concept of energy at the head of mechanics and 
 assigned to the other ground-notions, including force, 
 a secondary place. The advantage of this was that 
 the characteristic concept of energy became a de- 
 finable magnitude for all the different branches of 
 physics, so that not only mechanics, but also the 
 theories of heat, electricity, etc., could be grounded 
 on this concept, and a more unified and far-reaching 
 idea of physical phenomena could be obtained. For
 
 108 MATHEMATICAL PHYSICS 
 
 this Planck holds that there is much to be said, pro- 
 vided that we accustom ourselves to the view that 
 there is more in this concept of energy than is usually 
 thought. For it has to be remembered that the 
 notion of force, on which, since Newton's time, 
 mechanics has been built up, has an advantage which 
 that of energy lacks, in the fact that in the muscular 
 sense we possess a sense through which indeed we 
 cannot measure exactly but which gives us a direct 
 experience that is lacking in the case of energy as 
 such. He says that in Newton 's view the idea 
 of force appears as what is primary, as the cause, 
 while motion and work done appear as effects, 
 notwithstanding that force and acceleration are 
 connected in time. The reason is, that when we 
 alter the position of a body by muscular effort the 
 physiological phenomenon in fact precedes in time 
 the motion to which it gives rise. Even when a 
 body which is independent of our muscular activity 
 is set in motion by the attraction of another body, 
 we can always imagine this as taking place through 
 some kind of pull, and so we speak with a definite 
 meaning of a force as producing the motion. That 
 the measurement of the force takes place only 
 through observation of the motion which follows 
 does not affect this conclusion, nor does the fact 
 stand in the way of our recognising, with Kirchhoff, 
 that if we proceed to abstract from the relation of 
 the concept of force to that which muscular feeling 
 yields, we can treat force from a purely kinematical 
 standpoint, as for instance in astronomy and all the 
 sciences which depend only on perception through 
 sight. Still, physics, says Planck, is concerned with 
 the description of every kind of form of external
 
 THE RESIDUARY PHASE IN EXPERIENCE 109 
 
 phenomena, temperature, colour, etc., and accordingly 
 in the end we come back to reference of fundamental 
 physical ideas to the sensations of the various specific 
 senses. These may reveal to us new material which 
 we have to be in a better position to incorporate 
 than we can be if we take a view which, though of 
 great practical use, is not necessarily adequate to 
 the possible fulness of experience. 
 
 Planck's criticism of attempts to resolve the 
 individuality of experience into certain universals 
 is at least an indication that there is always in 
 science a residuary phase, a particularity in what is 
 objective which cannot be so resolved. If the advo- 
 cates of the necessity of recognising the existence of 
 an aether would confine themselves to this, instead 
 of insisting that their aether must have the status 
 of an independent and individual entity, some 
 reconciliation of conflicting standpoints would be 
 possible. Here, as in some other cases, physics 
 has at times laid itself open to the criticism of the 
 logician. 
 
 The same thing seems to be true of the classical 
 conception of empty space as significant in itself 
 apart from the observer. Newton was driven to so 
 conceive it as the foundation for his principle of 
 inertia. In his time such a conception appeared, 
 as it does not so appear to-day, to harmonise with 
 all the results of exact observation. Those who wish 
 to see how for Newton the conception of our space 
 as absolute and uniform was inevitable will find 
 the subject worked out in Professor Max Bern's 
 recent book, Die Relativitdtstheorie Einsteins. De- 
 ductive methods have played an even larger part 
 in our conceptions in physics than we realise. And
 
 110 MATHEMATICAL PHYSICS 
 
 nowhere is this more apparent than in the story 
 of the development of geometry itself. It has been 
 profoundly influenced by the ideas of objectivity 
 to which it has been applied. Our ideas about space 
 appear to have been come at too easily. 
 
 The geometry of Euclid rested on an assumption 
 which appeared very natural. It postulated that in 
 a plane surface on which there were a straight line 
 and also a point outside that line, there was only one 
 other straight line which could be drawn through 
 the point so as not, when prolonged, to cut the 
 first line. This was the axiom of parallels, which 
 implied a fundamental assumption about the freedom 
 from inherent curvature of space. Many attempts 
 were made to prove its truth, even in the days of 
 the Greeks themselves ; but these attempts, even in 
 their time, gave rise to doubt. Mere observation 
 could not exclude the possibility that there might 
 be drawn through the point a pair of straight lines 
 asymptotic with the original straight line and 
 dividing the lines through that point into two 
 bundles, one bundle of lines cutting the given 
 line, and another bundle of lines not cutting it. 
 Alternatively there is Riemann's hypothesis of finite 
 geometry, in which every line returns into itself. In 
 this geometry any two lines in a plane successively 
 intersect. Neither of these hypotheses have any 
 necessary reference to any heterogeneity of space. 
 But Riemann's method allows such an hypothesis to 
 be entertained. It is on this possibility of spatial 
 heterogeneity that Einstein's discoveries are based. 
 Space might have in its own character a curvature 
 such as to involve this. 
 In our own period the doubt has been worked
 
 THE PRINCIPLE OF THE 'FIELD' 111 
 
 into systematic form. Early in the nineteenth 
 century Lobatschefsky, who was Professor of Mathe- 
 matics at the University of Kasan in Russia, and 
 Bolyai, an officer in the Austro-Hungarian Army, 
 produced systems of geometry which did not assume 
 the validity of the axiom of parallels. The question 
 of the general character of space then began to be 
 realised as being an open one, and questions were 
 soon put in searching fashion. 
 
 For our forefathers space and time were fixed and 
 independent forms or frameworks in which things 
 existed. Even Kant really thought of them in this 
 way. For others, if not in the main for him, matter 
 was a substance set in such frameworks. Each particle 
 of matter had its place at a definite point of space 
 and in a definite instant of time. We thus got to 
 a world of supposed invariant primary qualities, and 
 these fitted in admirably with geometry as Euclid 
 conceived it. But criticism of the conceptions pre- 
 supposed in this presently set in. That criticism 
 in its later stages came largely from two ultimate 
 sources. One was the work in physics of Faraday 
 and Clerk-Maxwell, who directed attention to the 
 ' Field ' in which action takes place as requiring to 
 be itself interpreted before any clear light could be 
 got on the character and behaviour of the matter 
 which had to be interpreted with reference to it. 
 Still later on Minkowski and Einstein came to think 
 that this field could not be adequately interpreted 
 unless it were first understood that time and space 
 mutually implied each other, and were indissoluble 
 aspects of reality aspects which only the abstrac- 
 tions of mathematics could treat, even for limited 
 purposes, as independent.
 
 112 MATHEMATICAL PHYSICS 
 
 The stimulus given by the new conception of the 
 importance of the field led to a revision of mathe- 
 matical ideas. In the investigation of such a field 
 we require differential expressions which enable us 
 to make abstraction from what is irrelevant by con- 
 fining ourselves to what is indefinitely small in other 
 words, to limiting conceptions as our guides in calcu- 
 lation, instead of to what are imagined as possible 
 individual objects in sense perception, however 
 minute. This method was extended to the investiga- 
 tion of space taken by itself. Before this was done 
 effectively the notion of space had to be reconsidered. 
 
 Riemann was not satisfied with the conception of 
 space current at his time. He endeavoured to resolve 
 the individuality of the phenomena of the external 
 world. For Riemann the universals into which this 
 individuality of spatial phenomena must be resolved 
 if it is to be made scientifically intelligible, have to be 
 of a wider and more fundamental nature than those 
 characters beyond which Euclidean geometry does not 
 go. It is an epistemological question not less than 
 one which is mathematical, and he says so in his 
 essay on the hypotheses which lie at the basis of 
 geometry. Geometry assumes, he says, as things 
 given, both space and the first principles of construc- 
 tion in it. But " she gives definitions of them which 
 are merely nominal, while the true determinations 
 appear in the form of axioms. The relation of these 
 assumptions remains consequently in darkness ; we 
 neither perceive whether and how far their connection 
 is necessary, nor, a priori, whether it is possible." As 
 neither the mathematicians nor the philosophers had 
 cleared up the darkness, Riemann set himself to do 
 so. His self-imposed task was that of " constructing
 
 RIEMANN'S METHOD 113 
 
 the notion of a multiply extended magnitude out of 
 general notions of magnitude. It will follow from 
 this that a multiply extended magnitude is capable 
 of different measure-relations, and consequently that 
 space is only a particular case of a triply extended 
 magnitude. But hence flows as a necessary con- 
 sequence that the propositions of geometry cannot be 
 derived from general notions of magnitude, but that 
 the properties which distinguish space from other 
 conceivable triply extended magnitudes are only to be 
 deduced from experience. Thus arises the problem, 
 to discover the simplest matters of fact from which 
 the measure-relations of space may be determined ; a 
 problem which from the nature of the case is not 
 completely determinate, since there may be several 
 systems of matters of fact which suffice to determine 
 the measure-relations of space the most important 
 system for our present purpose being that which 
 Euclid has laid down as a foundation. These matters 
 of fact are like all matters of fact not necessary, 
 but only of empirical certainty ; they are hypotheses." 
 Riemann, like Clifford in the passages referred to 
 in the Introduction to the present volume, thus sets 
 himself to the analysis of the principles and universals 
 which have to be disentangled for the comprehension 
 of the concrete individuality of our spatial experience. 
 He divests himself of humanistic tendencies, and his 
 investigation becomes a highly abstract one. For his 
 result is that space proper, taken in itself, is no more 
 than a three-dimensional manifold devoid of form 
 (not an easy conception to understand, inasmuch as 
 three dimensions and manifoldness seem to imply 
 some form), and that space possesses definite shape or 
 form only in virtue of material contents which not
 
 114 MATHEMATICAL PHYSICS 
 
 only fill it but determine its metric relations. If 
 matter is displaced in space it will therefore carry 
 its own metrical field along with it. The material 
 content transferred from one position to another 
 may thus be continuously deformed in the process, 
 and yet in ultimate analysis remain congruent with 
 itself, inasmuch as it carries with it the metrical field 
 which it produces. In a manifold of a continuous 
 character the metric relations encountered must 
 have their explanation sought, not in any character 
 of space itself, but in that which fills it in a fashion 
 which is determined by ' binding forces ' acting inde- 
 pendently. Einstein's ' gravitational field/ in his 
 general theory of Relativity, has since been said to 
 be an illustration of such a binding force. 
 
 Riemann aims at bringing us in this fashion to a 
 true conception of the nature of space when freed 
 from the shapes and measurements which are im- 
 parted to the objects in it by the empirical and 
 arbitrary apprehension of individual phenomena. 
 Space becomes under his analysis a highly abstract 
 conception of a purely general character. It is an n- 
 dimensional continuum. But it becomes continuous 
 only in virtue of success in eliminating variety in its 
 contents by the employment of methods confined to 
 the infinitely small. Geometry is now a differential 
 geometry. Only by means of infinitesimal treatment 
 can we eliminate contingent variations in experience. 
 ' Affine ' geometry which takes cognisance of finite 
 distances, as in the case of Euclid, ignores the neces- 
 sity of grappling with the difficulty. Riemann will 
 not have it so. He excludes from the domain and 
 scope of his infinitesimal geometry the finite distances 
 with which the affine method concerned itself. Since
 
 INVARIANCE 115 
 
 his day Weyl has criticised even Riemann, as will be 
 seen later on, for having assumed that it is possible 
 to compare the lengths of two line elements at finite 
 distances from each other, and has insisted that it is 
 not permissible to use comparisons at a distance in 
 the geometry of the infinitely near. This may be right. 
 The conception of the infinitely near appears as essential 
 if we are to eliminate discontinuity in the manifold 
 taken in itself. It seems that, as Riemann suggests, 
 this can be accomplished only if we confine ourselves 
 for the basis on which we are to build to linear dis- 
 placements relative to a point, and remember that 
 there is no place in such a purified conception for 
 thinking of the infinitesimal displacements of any 
 separate points as equal or unequal. Following Gauss, 
 Riemann came in sight of a much more general view 
 of such displacements in which they appear as no 
 more than what are called ' components/ These 
 vary, but not in the form of changes such as we find in 
 empirical space. It is within the analytical field in 
 which for mathematicians a point is determined that 
 these components are alone definable, and that an 
 adequate description, independent of shape and 
 measurement, can be given of their relations to the 
 point as one in pure space. That is how we come to 
 in variance. It is a quality only of space in its most 
 abstract and conceptual aspect. The relations dealt 
 with as invariant in the tensor method which is alone 
 appropriate to them belong, according to such mathe- 
 maticians as Weyl, to a point and not to space treated 
 as an empirical whole. The tensor is a linear 
 form which may contain several series of variable 
 components, dependent on the co-ordinate system 
 adopted, for the immediate neighbourhood of a point. 
 9
 
 116 MATHEMATICAL PHYSICS 
 
 Confining himself to infinitely small quantity the 
 mathematician is able to make his basic conception a 
 linear one, and his infinitesimals line elements at the 
 point in question. This enables him not only to treat 
 space as continuous for final metrical purposes, but 
 even to regard the Pythagorean principle as to the 
 squares of these line elements as strictly true. He 
 can do so if, but only if, he confines himself to infini- 
 tesimal relations as his foundation. 
 
 But the doubts I have referred to in connection 
 with what was called ' affine ' geometry led to 
 further doubts about Euclid. If the axiom of 
 parallels which Lobatschefsky and Bolyai had 
 brought into disrepute was not well founded, 
 could we safely assume that space was homo- 
 geneous ? Might it not present different characters 
 as we proceeded, such that b^ its very nature 
 it gave altered forms to its contents, instead of 
 leaving them self-subsistent and characterised by 
 Euclidean straightness in dimensions ? It seemed as 
 though at least in the domain of the infinitely great 
 such a question might be of much practical import- 
 ance. Need the dimensions of space consist only of 
 three ? It is true that our ordinary picture of space is 
 as of three dimensions, and we cannot draw on paper 
 any adequate picture of it as having more than three. 
 We exhibit the position of a point in it by using three 
 dimensions and no more, and the co-ordinated lines 
 are sufficient to describe the position of any point 
 which is at rest. If we want to exhibit a point in 
 motion we can only use the three-dimensional picture 
 if we add to it what is merely symbolic, a co-ordinate 
 standing for the change in time which is implied by 
 motion. But this shows that, for our description of
 
 DIMENSIONS 117 
 
 physical reality, the three dimensions of space are not 
 enough. If we wish to describe nature we know well 
 that we often have to describe in terms of more than 
 three standards of reference. It does not matter 
 whether we call them co-ordinates or vectors ; the 
 point is that an indefinite number of such standards 
 may be required for our account of phenomena. 
 If we wish to describe scientifically the behaviour of 
 the molecules of an assemblage of mixed gases we 
 must know the vector action of the molecules of each 
 gas. The relevance of this is to show that, wherever 
 we are dealing with what is in its nature manifold, 
 we may have to employ in description an indefinite 
 number of magnitudes, which we can call co-ordinates 
 or vectors or what we please, representing the con- 
 tinuous elementary functions within that manifold. 
 Now, Euclidean space may turn out to be no final 
 form, but only one got by leaving out of account 
 other dimensions which we cannot picture but which 
 are required to make intelligible the actual behaviour 
 of the objects in our world. We must not assume 
 that the space which gives its form to the surface of 
 the earth itself is uniform in the fashion conceived 
 by Euclid. Gauss doubted it, and his doubts were 
 carried so far that Riemann, one of his successors at 
 Gottingen, found himself driven to a new conception 
 of geometry in which space might theoretically have 
 an indefinite number of dimensions, such that, 
 although we could not make a picture of them on a 
 paper surface, they could explain certain limitations 
 which Euclid's geometry had seemed to impose on 
 our interpretation of our actual observation of the 
 behaviour of things. It is Riemann's idea which 
 Einstein has developed further in his explanation of
 
 118 MATHEMATICAL PHYSICS 
 
 the apparent contradiction of current physical reason- 
 ing by the observed deflection of starlight and the 
 perihelion of the planet Mercury. It is therefore 
 worth while to ask what Biemann meant when he 
 declared himself compelled to search for a founda- 
 tion of geometry which should be wider than that 
 conceived by Euclid. 
 
 " The transition/' says a prominent contemporary 
 mathematician, 1 " from the geometry of Euclid to that 
 of Biemann turns on an idea analogous to that in 
 physics of action at infinitely close quarters. For 
 example, take Ohm's law. We determine by observa- 
 tion that the stream flowing through a conducting 
 wire is proportional to the differences in potential 
 at the beginning and the end of the conduction. But 
 we are satisfied that in this result of measurement of 
 the current in a long wire we have not got before us 
 a law of nature exactly manifested throughout, but 
 that such a law can be inferred from the measurement 
 when referred to an infinitely small section of the 
 conductor. It is really so that we come to the 
 formula that underlies Maxwell's theory. From the 
 differential law we proceed backwards in mathe- 
 matical fashion to the integral law embodied in what 
 we observe, if we presuppose relations that are 
 throughout homogeneous. Just so with Riemann's 
 geometry. The basic fact for Euclid is that the 
 square of the distance of two points is a quadratic 
 form of the relative co-ordinates of the two points. 
 If we look on this law as strictly valid only if 
 the two points are infinitely near each other, we 
 come to Riemann's geometry, and are at the same 
 time lifted above the necessity of a more exact 
 
 Wyl, Raum, Zeit, Matcrie, 4th Ed., p. 81. Cf. English Tr., p, 91.
 
 RIEMANN'S GEOMETRY 119 
 
 determination of what is meant by the co-ordinates, 
 since the Pythagorean principle just referred to 
 is invariant whatever may be the transformations. 
 The transition from Euclidean * distant ' geometry 
 to Riemannian ' near ' geometry corresponds to 
 that from the physics of action at a distance 
 to the physics of action at infinitely close range. 
 The geometry of Riemann is that of Euclid so 
 formulated as to conform to the spirit of continuity, 
 and by being so formulated it assumes a much more 
 general character. Euclidean geometry is con- 
 structed for the investigation of the straight line and 
 the plane ; these are the problems to which it is 
 directed ; as soon as we pass to infinitesimal geometry 
 it is most natural and rational to build on the in- 
 finitesimal principle of Riemann. In this fashion we 
 escape from complication, and are preserved from 
 entanglements with a geometry of finite distances 
 which may not be in accordance with facts. In the 
 space of Riemann, analogously, a surface is indicated 
 as a two-dimensional manifold by means of a para- 
 meter representation x { = x t (HI u 2 ). If we apply 
 the resulting differentials, the fundamental metrical 
 
 8x 
 form of Riemann's space, we get dx t = du t -}- 
 
 Bx 
 -i du.,. We thus obtain for the square of the inter- 
 
 val of two infinitely close points on a surface a 
 quadratic differential form of dui, du 3 (as in Euclidean 
 space), and the metric of the three-dimensional space 
 of Riemann transfers itself immediately to every 
 surface lying in it and converts it into a two-dimen- 
 sional Riemannian space. Thus, while with Euclid 
 space is taken to be of a much more specialised nature
 
 120 MATHEMATICAL PHYSICS 
 
 than the possible surfaces in it that is to say, as 
 flat with Eiemann the conception of space has just 
 the degree of generality that is necessary to remove the 
 discrepancy. The principle of interpreting the world 
 through its relations in the infinitely small is the 
 governing motive both in the physics of action at 
 close quarters and in the geometry of Kiemann." 
 
 Kiemann said that in a Euclidean space of four 
 dimensions Euclidean geometry would apply to a 
 three-dimensional linearly represented collection of 
 points, but that curved three-dimensional spaces, 
 which may exist just as readily in four-dimensional 
 space as curved surfaces can in three-dimensional, 
 were in a different case. Was it not possible that 
 the three-dimensional space of our perception should 
 be really a curved space ? It does not appear, indeed, 
 as if imbedded in four-dimensional space, yet it may 
 be that its intrinsic measurement-relations are such 
 as cannot consist with space being flat. It may be 
 that a sufficiently close measurement of our space 
 after the fashion of a minute geodetic survey of the 
 surface of the earth, would show that its space was 
 not flat. Gauss was indeed at one time so impressed 
 with this doubt that in the year 1821 he measured 
 the triangle formed by the tops of three hills not far 
 from his observatory at Gottingen, the Inselberg, the 
 Brocken, and the Hoher Hagen, with a view to bring- 
 ing the question to the test by ascertaining whether 
 the sum of the angles of the triangle diverged from 
 that of two right angles. No such divergence was 
 actually ascertained, but this he thought might be 
 due to its falling within the limits of possible error 
 in using the instruments. The test remains unmade 
 in this fashion, though Einstein and others have
 
 MOTION AND SPACE 121 
 
 made it in other regions of observed space and 
 have claimed that the doubts of Gauss and Riemann 
 turn out to have been well founded. 
 
 Logically there seems to be no difficulty in 
 the Riemann view. It is true that we imagine 
 that space has only three dimensions. But this 
 is a rash conclusion. Things in space are always, 
 as we find when we inquire closely, in motion, and 
 motion implies time. It may be inapt to employ 
 the word ' dimension ' as a name for the time relation, 
 but this relation has to be very fully taken into 
 account, especially if space and time are only abstract 
 constructions from the fundamental manifold or 
 continuum in which the world really exists. And 
 as regards logic, we can treat space mathematically 
 as having any number of dimensions we please, and 
 reason about it on this footing. We have, in short, 
 here as elsewhere, to be fully aware of conventional 
 habits. 
 
 There are some things which the mathematicians 
 tell us that we may indeed hold to. We may keep 
 to the view of space as being for many purposes a 
 three-dimensional manifold. We may keep, at the 
 other extreme, to the view that its infinitesimally 
 small line elements can be compared with one 
 another in independence of their position and direction, 
 and that the square of the length of the interval 
 between two neighbouring points may be described 
 by the use of suitable co-ordinates in a quadratic 
 differential form. Such an assumption is said by 
 mathematicians to be founded on good sense, for, 
 inasmuch as every transformation from one co- 
 ordinate system to another carries with it a formula 
 of linear transformation for the differentials of the
 
 122 MATHEMATICAL PHYSICS 
 
 co-ordinates, a quadratic differential form must always 
 pass into another such form. This reasoning, however, 
 does not seem to give any ground for the assumption 
 of the Pythagorean law of the quadratic form in 
 preference to a biquadratic form, or to one of an 
 even higher power. But perhaps the preference for 
 the Pythagorean form is founded on experience. 
 
 Let us see what this signifies. It has brought us 
 to regard as inadequate the familiar idea of Euclid's 
 space as an independently existing framework in 
 which matter is embedded. Space has no meaning 
 apart from the world that exists in it, and that is 
 straight or curved only inasmuch as space is itself 
 straight or curved. Differences in curvature may 
 exist everywhere. For Newton the curvature of 
 space itself was o. For Lobatschefsky and Bolyai 
 the curvature was different but still a constant. For 
 Riemann it could be anything anywhere. Objects 
 in it may thus be constantly undergoing deformation. 
 
 But for Riemann's methods there are still principles 
 which do not vary and that are recognisable as 
 permanent through all changes. At these he arrives 
 by the use of his infinitesimal methods. The co- 
 ordinates of a point indefinitely near to another point 
 can be exhibited as functions of the latter point. 
 He is able to establish a system in which the functions 
 can be determined mathematically in independence 
 of their actual measurement or shape ; in other words, 
 as logically antecedent to the results of the observa- 
 tion that is really based on and implies them. The 
 relative co-ordinates, dx, etc., of the neighbouring 
 point are the logical components of a lineal element 
 in the point from which the departure is made, or in 
 other words of an infinitesimal displacement from it
 
 GAUSSIAN CO-ORDINATES 123 
 
 of the neighbouring point, which is dependent for its 
 quality and character on that of the first point. The 
 question is one, not of measurement or shape we 
 have not yet got to these although starting from 
 experience in which they appear but of mathematical 
 analysis of what is implied in the definition we give 
 to the position of the first point in what is primary 
 in observed space. What we are concentrating on is 
 not the distribution of matter itself, but the field of 
 activity of the point-events at which we arrive by 
 the method of limits when we use an infinitesimal 
 basis for calculation. We want to find a way of 
 expressing the field of activity of point-events that 
 are indefinitely close to the point-event from which 
 we depart. 
 
 Now this is what Riemann, by his new conception 
 of the character of space, and Gauss, by some yet 
 earlier work, have enabled mathematicians to do. 
 Gauss discovered that curvature could be denned 
 by differential analysis in terms of inherent metric 
 relations alone of the surface. He devised for this 
 purpose what are called Gaussian co-ordinates, 
 lines of curvature on a surface which can be drawn 
 across each other through every possible point on 
 it, and which define the position of the point. They 
 remain for differential analysis invariant in their 
 properties through all deformations of the surface, 
 provided it is not destroyed by being torn, and can 
 be applied to the case of three-dimensional surfaces. 
 Each point can in this way be made to correspond 
 with some number in a completely ' dense ' series 
 of real numbers. This gives us what mathematicians 
 (though not metaphysicians) mean by continuity. 
 Riemann extended this principle to quadratic
 
 124 MATHEMATICAL PHYSICS 
 
 differential forms of three or more variables. Their 
 relations were not numerical but of tensor form. 
 Tensor relations are such when they characterise 
 unambiguously and essentially a linear algebraic form 
 of such a nature that by itself, apart from measure- 
 ment, it describes the character of the magnitude to 
 which it has reference. They are expressed as the 
 right-hand side of an equation descriptive of the 
 magnitude of an infinitesimal interval between two 
 points, such that this side contains analytically ascer- 
 tained components which remain invariant however 
 much the measurement and shape in the infinitesimal 
 interval may be conceived as altered through the 
 system of empirical measurement of objects adopted. 
 The tensor relation does not express explicitly or 
 implicitly any ordinary quantitative measurement of 
 the intrinsic character of the interval. But it is 
 a function of that intrinsic character, and yields 
 information which does not depend on measurement 
 of shapes in a particular system of objects. It holds 
 for all co-ordinates of points that can be derived 
 by mathematical transformation of the co-ordinates 
 in that system. It appears to be logically a residuary 
 result obtained by eliminating description of what 
 is individual in objects, and to be itself descriptive 
 only in terms of the highest generality. It is thus 
 that the new method has made possible exact know- 
 ledge of what lies beyond the limits to which alone 
 the old notions were confined. The method, which 
 in the hands of Gauss and Riemann was applied only 
 to space, has, by Minkowski and Einstein, been 
 extended to the investigation of the underlying 
 manifold or continuum in which space and time 
 have not yet been distinguished by the abstractions
 
 TENSORS 121 
 
 we make in daily life. If this continuum was to 
 be capable of description we should have expected 
 a method for the ascertainment of certain definite 
 qualities possessed independently of formed space 
 and time to be supplied to us, and this the mathe- 
 maticians have provided by recent tensor theories. 
 The theories do not give us the definite measure- 
 ments which physical science requires, but they 
 guide us towards conceptions which are essential 
 if we are to interpret these measurements, and to 
 render them congruent as they occur in varying 
 situations and under varying conditions.
 
 THE PHILOSOPHICAL SIGNIFICANCE OF 
 OTHER SUBJECTS 
 
 CHAPTER V 
 
 MATHEMATICAL PHYSICS (continued) 
 
 IF we start from what is individual in the actual 
 world and is therefore different from either space or 
 time taken in abstraction and by themselves, the mere 
 fact of change in events, we find that its consideration 
 involves discrete as well as continuous aspects that 
 imply each other, aspects such as position and motion. 
 These aspects we hypostatise through reflection into 
 what are for us the developed notions of space and 
 time. Both are required as logical moments in that 
 which we resolve through abstract distinctions. Posi- 
 tion is a spatial ' now/ It does not remain at rest 
 or static, because of the time-moment that is inherent 
 in its character. It passes by its very nature into what 
 is different position. What is ' now ' at the limiting 
 instant becomes ' then/ or, if it has not appeared, 
 it is to be. The ' now * is the mere limit through 
 which the past is .distinguished from the future. 
 Change, or what we mean when we speak of motion, 
 is inherent in the object of reflection. We thus 
 resolve into the point-instant. What it is in logic 
 it is for us only as a limiting ideal in reality. Taken 
 by itself space implies and passes over into time, and 
 analogously time into space. For analysis the actual 
 involves both as its logical moments. 
 It is of the essence of our procedure when we 
 
 126
 
 COINCIDENCE IN CHANGE 127 
 
 observe to make this resolution. The double character 
 of the outcome affects the result profoundly. The 
 resolution which we make implicitly in what we call 
 our experience is bound to be always relative to the 
 observer. He splits up the continuum, of which he 
 is primarily aware as unresolved, in ways which are 
 always dependent on himself. Mere animals, defi- 
 cient as they are in concepts, apparently do not 
 measure space and time as we do. They are aware of 
 objects as coincident or non-coincident, but their 
 reasoning does not seem to go much beyond this 
 or to enable them to measure in any form resembling 
 miles or yards. They know when they are tired or 
 hungry, and of the concurrence of certain conditions 
 with the place of rest or feeding. It is important 
 knowledge for their practical purposes. We our- 
 selves depend for much on such awareness of coin- 
 cidence. The co -incidence of the top of the thread 
 of mercury with a mark on a thermometer is experi- 
 enced as also coincident with a certain temperature. 
 It is to the notional idea of coincidences between 
 what we describe reflectively as intervals between 
 point-events that we turn when we erect symbolically 
 the structure even of our tensor theories, eliminating 
 by abstraction all shape and measurement. That 
 is how we put together our theory in order to get 
 knowledge of relations between changing events 
 which are always inherent in the ultimate foundation 
 of what we observe, and are not merely relative 
 to our individual circumstances in observing. 
 
 When in reflection we resolve the passage of bare 
 events of which we are primarily aware only as in a 
 state of change we can carry out the elimination of 
 the irrelevant to its final result. This gives us, if
 
 128 MATHEMATICAL PHYSICS 
 
 we proceed on the principle, analogous to that of 
 infinitesimal analysis, which Professor Whitehead 
 has called the method of Extensive Abstraction, a 
 timeless or instantaneous space, and also a mere 
 spaceless succession which we treat as pure time. 
 Yet these are only limiting notions, valuable as ideals 
 and as guides in method, but without correspondence 
 to any concrete individuality directly disclosed by 
 observation. Indeed in the reflection which aims at 
 being most abstract and free from the moment of 
 the particular it is simply as limiting notions that we 
 get at them, notions expressed, like all other mathe- 
 matical conceptions, by symbols or images. 
 
 Bergson's ' duration ' is analogous to pure time. 
 It is only, as he tells us, by spatialising it, as by 
 representing it on the dial of a watch, that we can 
 measure or even represent duration, and in so doing 
 we transform its character. It is therefore the pure 
 flow in duration that the metaphysician, the man 
 who carries logical analysis further than the physicist 
 does, refers to when he speaks of the duration with 
 which Bergson is concerned. The physicist himself, 
 the astronomer, for example, never gets to bare time. 
 Einstein's doctrine of Relativity, with its introduction 
 of the transformation in standpoint effected by 
 change in motion and position in the gravitational 
 field, shows that this is so. Whatever be the full 
 truth about Einstein's doctrine, he seems at least to 
 have established that the measurement of time in 
 physics is relative to particular standards of situation 
 automatically forced on the observer. Even the 
 velocity of light is, for his general theory, in truth 
 no absolute constant. The interpretation of its path 
 must alter with the curvature of the space existing
 
 THE VELOCITY OF LIGHT 129 
 
 in the particular gravitational field under observation. 
 An astronomer on a remote star, with a distribution 
 round him of heavenly bodies different in form from 
 that of an observer on the earth, will estimate coinci- 
 dences and simultaneities of the instants at which 
 light-signals appear differently from the observer on 
 the earth. The velocity of light must remain rela- 
 tively constant, but it will have a different interpreta- 
 tion, in point of measurement and direction. Now 
 that the aether is generally considered to have been 
 deposed from the status of being an independent 
 entity disclosed to us, and now that the absolute 
 frameworks of time and space have gone with it, 
 the astronomers have no absolute standard to measure 
 by excepting the velocity of light itself. We are 
 forced, as observers, to treat the velocity of light as 
 a constant, because back to it we always have to 
 come as basic in the rendering of our experience. 
 We have to accept it as a final physical standard 
 with reference to which we estimate, and for that 
 reason we bring out our resolution of velocity in a 
 form that does not vary. The time and space units, 
 such as miles and seconds, preserve their proportions 
 in the resolution of the velocity. That is why this 
 does not appear to vary. But the units themselves 
 alter in significance. They are not themselves con- 
 stant, although the velocity is so which their pro- 
 portions are used to define. The necessity of finding 
 some congruence in nature drives us into taking the 
 velocity of light as being the most suitable constant 
 in observation. Possibly we might have chosen 
 other physical constants, the velocity of sound, for 
 instance, but immense complications and difficulties 
 would have ensued. Yet what does this constancy
 
 130 MATHEMATICAL PHYSICS 
 
 signify in the case of the velocity of light ? Some- 
 thing that may have a wholly different interpretation 
 for differing observers, even when they start from 
 it as their ultimate standard. If the astronomer 
 says that he is measuring time he is thinking of 
 something which varies in character from what the 
 logician means by measurement with an absolute 
 standard, as much as when he is measuring the 
 space which he observes in contrast to the instan- 
 taneous space of the latter. He is concerned, not 
 with a limiting notion, nor even with the logical 
 conditions which render congruence possible, nor, 
 on the other hand, with anything of which he is 
 immediately aware, but with the outcome of a set of 
 inferences which he makes from supposed facts 
 without being explicitly conscious of their true 
 hypothetical basis. 
 
 The Morley-Michelson experiments awakened the 
 world from its dogmatic slumber in this region of 
 knowledge, and the Fitzgerald-Lorentz contraction 
 hypothesis could not restore the tranquillity which 
 had been broken. Einstein has brushed the perplexity 
 aside with his principle. He says that it arises simply 
 through ignoring that all physical measurement, 
 whether of time or of space, is relative and not 
 absolute, and is dependent on the situation and con- 
 ditions of the observer ; on whether he can properly 
 be assumed to be at rest, or whether he is not just as 
 much moving with accelerating velocity and in paths 
 of a kind which may present no analogy to straight 
 lines. If the world is in final result one in which 
 time and space are not independent entities, but 
 dimensions which we construct by the abstractions 
 we make, as Minkowski held, the notion that there can
 
 THE RELATIVITY OF MEASUREMENT 131 
 
 be any absolute external standard for the estimation 
 of measurement or shape disappears. We are thrown 
 back in any inquiry into the ultimate nature of con- 
 gruence to regarding it as being what arises out of 
 the foundational character of knowledge itself. The 
 supposed constant velocity we observe in light be- 
 comes the outcome of assumptions that work suffi- 
 ciently for daily practice, but only mislead when we 
 come face to face with deeper and more remote 
 problems, the solution of which physical science itself 
 has to ignore. The propagation of a light-ray is the 
 highest velocity our physical conditions have enabled 
 us to observe. In this sense it has a special value, 
 inasmuch as it links time with space ; the bare succes- 
 sion of instants at one point with the relation of order 
 of points along a line. But a final constant it cannot 
 be, however impracticable it may be for observation 
 to get behind it. Reflection drives us to insist on a 
 deeper lying standard, accessible at least to the power 
 of abstract methods. There is no such thing as a 
 time system the same throughout the universe. 
 What we find is a set of diverging mathematical 
 systems of location of events in types of linear suc- 
 cession, which are measured on a basic physical 
 hypothesis according to varyingly applied rules. 
 
 If we could take mind, for the practical purposes of 
 our daily lives in the observatory and elsewhere, as 
 the subject which is inseparable and indistinguishable 
 from the object which falls along with it into the 
 single entirety of knowledge, we should find a way 
 of deliverance from our troubles. Complete con- 
 gruence would be intelligible. But we cannot take 
 mind to be such a subject, at all events as we are 
 conscious of it at our ordinary practical level, and 
 10
 
 132 MATHEMATICAL PHYSICS 
 
 as belonging to our usual order in reflection. It ex- 
 presses itself in our ordinary consciousness in organic 
 form, as an individual human mind with a period 
 and situation in a physical world. Such an expres- 
 sion may be itself only relative. But it is the ' this ' 
 which we have to make our point of departure and 
 we cannot rid ourselves of it. We may resolve its 
 interpretation into universals of thought. These, how- 
 ever, do not exhaust it, or free us from the moment 
 of particularism. Mind as we find it is individual, 
 and as such a particular fact in our object world. 
 To cover completely such individual uniqueness a 
 description would be necessary that was unambigu- 
 ous, what the Germans call eirideutig. But through 
 universals we can never render any such description, 
 however much abstract knowledge the universals 
 may convey. The knowledge they give is always 
 reflective and of a general and indirect type which 
 is inadequate to the exhaustion of the concrete 
 immediacy with its moment of the particular. This 
 does not mean that the particular is some entity 
 by itself. If it were we could describe it in general 
 language, and this is just what we cannot do. It is 
 a notional limit to our intellectual series of progres- 
 sively abstract conceptions, which itself lies outside 
 that series. Human minds, conditioned as they are, 
 can never exhaust what is unique and essentially 
 concrete in individuality, though we may make 
 progress endlessly towards its description in general 
 language. We have seen how this is so with the 
 ' here ' and the ' now.' Mind at a reflective level 
 higher than ours might conceivably escape the diffi- 
 culty that is self-imposed. The distinction between 
 general and particular is after all one which knowledge
 
 LIMITATIONS IN OUR EXPERIENCE 133 
 
 has itself established, and which therefore falls within 
 knowledge. If, then, knowledge had before it all 
 such distinctions as having been made within itself, 
 together with its own procedure in making them, 
 it would be of a nature higher than our human 
 knowledge in that it was free from the relativity 
 which the limitation in our standpoints imposes on 
 comprehension. For us, in whom mind expresses 
 itself by giving to its quality as intelligence to 
 an organism in which the senses and the intellect 
 have their definite characters and are what they are 
 in so far as they realise purposes, knowledge must 
 remain conditioned, the limitlessness of its abstract 
 range notwithstanding. Something of this kind 
 appears to have been in the mind of Max Planck 
 when he wrote what was quoted at the beginning 
 of the last chapter. As it expresses itself in us 
 knowledge does so in the medium of sense as well as 
 thought. That is because of the conditions under 
 which it realises itself in space and time and life in 
 them. It is these conditions that determine its 
 finite character. But it is none the less on that 
 account knowledge, the inherent power of which is 
 to resolve indefinitely into universals the actuality 
 which comes before it. The particular moment in 
 this it can never exhaust. That is because its aspect 
 as intelligence is only one of the aspects of such 
 knowledge. In another aspect it depends for its 
 material on sensation, and so depends because of the 
 nature of the object-self in which it manifests itself 
 as knowledge. But it discloses for us the inherent 
 significance which is inseparable from reality and 
 gives it its meaning. In bringing out in that reality 
 its conceptual aspect it provides the means for ex-
 
 134 MATHEMATICAL PHYSICS 
 
 tending knowledge inferentially. A distinguished 
 contemporary mathematical-physicist makes an ob- 
 servation about the differential equations in which 
 Clerk-Maxwell has expressed the character of the 
 electro-magnetic field which illustrates this quality 
 in the procedure of knowledge : 
 
 " Their beauty of form is by no means unessential. 
 It unveils the simplicity of the processes of nature, 
 which remain concealed for direct apprehension 
 because of the limitations of our senses, and only dis- 
 closes itself to the understanding that can analyse." ' 
 
 We are now in a position to see what Einstein has 
 really accomplished. He has done for the world of 
 externality generally what Clerk-Maxwell did for the 
 electro-magnetic field. He has investigated the re- 
 lations between objects in the external world by 
 means of a searching analysis in which his concep- 
 tions are wider than those of the older physicists, 
 and the analysis is consequently less limited by con- 
 ventional assumption. The method has the charac- 
 teristic quality of all scientific method. It first 
 assembles the facts as experience, purified as far 
 as practicable from tacit assumption, and presents 
 them in the relatively direct awareness which is the 
 Btarting-point in such experience. It then resolves 
 them into universals, which now attain a more general 
 form because of the extent to which the analysis 
 has been carried. 
 
 What is called his ' special theory of relativity/ 
 that which he had reached by 1905, had brought 
 Einstein to this point. He had shown how to so 
 formulate the laws of physics that they should assume 
 an expression in which they would be true and 
 
 1 Born, Die Relativitats-theorie Einsteins, 2nd Ed., p. 134.
 
 THE RESTRICTED THEORY OF RELATIVITY 135 
 
 comparable with each other for all kinds of system 
 appearing to an observer, provided that these systems 
 were moving relatively with uniform velocity and recti- 
 linearly. Given these conditions all measurements 
 of space and time relations made by an observer in 
 one system could be translated into the measurements 
 made by another observer in a different system. 
 The measurements would have different meanings 
 and would be different if compared by a common 
 standard. But they would be capable of being 
 rendered congruent, provided it was remembered 
 that their differences resulted from the differences 
 in the situations and conditions of the respective 
 observers. In this way Einstein got results analogous 
 to those reached by Lorentz. But he got at them 
 much more naturally if his theory of the relativity 
 to each observer of the measurements of his space 
 and time was right. Lorentz had to assume a 
 contraction of the observer and his instruments due 
 to the effect of a supposed variation in the resistance 
 of the aether. Einstein had superseded the hypo- 
 thesis alike of absolute Newtonian space and time 
 and of a substantial aether itself. An aether absolutely 
 at rest was only established if motion relative to it 
 could be detected by observation. The experiments 
 of Morley and Michelson had shown that no such 
 motion could be detected. The contraction hypothe- 
 sis, which had been artificially resorted to in order 
 to explain this negative result, was now superseded 
 by an explanation of a mathematical kind, in reality 
 simpler and less obscure, in which the aether became 
 a general appellation, not for some independent 
 entity analogous to Newtonian space, but for some 
 sort of collective basis underlying phenomena.
 
 136 MATHEMATICAL PHYSICS 
 
 It became apparent to Einstein that his theory 
 must be carried further if it was to furnish a full 
 explanation. The world before us does not consist 
 of inertial systems in uniform and rectilinear motion 
 relatively to each other. It displays changes in the 
 positions of bodies which alter in rate of motion, 
 in virtue of accelerating velocities and paths that 
 are not rectilinear but curved in every kind of fashion. 
 The planets do not move along the straight lines 
 which for Newton were natural and only altered by 
 gravitation. Are inertia and gravitation, then, two 
 different forces ? Or is it possible to resolve them 
 into manifestations of a more general form of change 
 that explains them equally ? The experiments made 
 by Eotvos with the torsion balance had seemed to 
 show that inertial and gravitational force were 
 de facto equivalent. How were these so-called forces, 
 with their apparent equivalence, to be explained ? 
 This is the problem which Einstein claims to have 
 solved by his later and general theory of relativity, 
 which develops the special theory until it appears 
 as merely a special case of a principle of far wider 
 ambit. Its original framework was too narrow to 
 include all the facts with which he was confronted. 
 In the developed theory this framework is widely 
 extended. It gives us a set of further principles into 
 the terms of which we can translate nearly all, if 
 not all, of the laws of physical science so far as they 
 are at present known to us. 
 
 In order to understand the real significance of 
 Einstein's wider doctrine it is essential to have in 
 mind its significance for the theory of knowledge, 
 a subject on which his mathematical exponents are 
 not always clear. Much of the repugnance shown
 
 THE BASES OF THE GENERAL THEORY 137 
 
 to accepting the principle of relativity in physics 
 is due to the idea that Einstein is trying to resolve 
 reality into relations merely arising out of the stand- 
 point of the observer. But this is not the case. 
 What the principle, properly conceived, does is to 
 resolve in this fashion relations of shape and measure- 
 ment but not the actual fact out of which they are 
 differentiated. That fact is the Minkowski * world/ 
 with its time-like dimension. Such a world may be 
 capable of further analysis by the methods of mathe- 
 matical logic, and of analysis still more thorough by 
 methods which are of a metaphysical nature. 
 
 But for the physicist who has to deal with it 
 Minkowski's ' world/ the manifold or continuum 
 out of which space and time are constructed by the 
 observing mind and differentiated, is itself treated 
 as self-subsistent and as possessing an independent 
 existence closed against the intrusion of that mind. 
 The author of the Concept of Nature, Professor 
 Whitehead, does not in that book dissent from this 
 general principle as held by Einstein. He simply 
 treats the principle as one which his method assumes 
 provisionally. This is a convenient assumption for 
 the purposes of mathematical physicists, and if it 
 be borne in mind that the assumption is one only 
 provisional, arising from the application in science 
 of Goethe's maxim that he who would accomplish 
 anything must limit himself, the procedure is legiti- 
 mate. What, then, is this so-called four-dimensional 
 reality which Relativity-physics takes for its starting 
 point ? 
 
 Professor Whitehead employs methods in answer- 
 ing this question which carry him further than those 
 of the school of Einstein do, further even than such
 
 138 MATHEMATICAL PHYSICS 
 
 writers as Cassirer, Schlick, and Weyl. But his pro- 
 cedure is still that of a mathematician. It belongs, 
 however, to the new domain of mathematical logic 
 as to the area and character of which he and Mr. 
 Bertrand Russell have been so prominent as pioneer 
 exponents. Professor Whitehead, by analysis of 
 the ultimate elements in meaning, comes to what 
 is the final phase of nature for the physicist, for whom 
 nature is in its substance closed to mind. It is what 
 he calls the ' passage of nature/ the changing nature 
 of events not yet elaborated by abstraction from their 
 concrete character into abstractly defined objects. 
 They are the contents of the ' specious present ' 
 in which they occupy duration, and extend into as 
 well as supersede each other in the change which is 
 essential in duration. By the abstractions which 
 are constructed in our reflection we shape them into 
 objects, as different in their definiteness from the 
 mere event-world on which they are based as are 
 the space and time of the Einstein relativist from the 
 bare activity in the continuum. If we carry such 
 abstraction far enough, employing what is in effect 
 a method of limits analogous to that of the infini- 
 tesimal calculus in pure mathematics, we arrive at 
 instantaneous points and spaceless instants, and at 
 the notions of space apart from time and of time 
 apart from space. But these notions, however 
 valuable and even necessary in directing and shaping 
 knowledge, are only limiting notions, and have no 
 counterpart in any unique or concrete individual 
 objects of experience. It is thus that we come to 
 space and time as relations, not, I think, between 
 events but between objects, shaped by the mind of the 
 individual observer in his reasoned experience. How
 
 SPACE-TIME SYSTEMS 139 
 
 far a horse or a dog so shapes the relations of objects 
 is a more difficult question. The animal, in so far 
 as it possesses intelligence, is certainly aware of 
 coincidences and of simultaneities in events, and 
 distinguishes and reasons about the passage of nature 
 in a fashion based on them. But how far its reflection 
 extends is a question on which psychologists have not 
 yet provided sufficient materials for a judgment. 
 
 In the cases of individual men each mind fashions 
 a space-time system of its own. These space-time 
 systems are all individual. But, inasmuch as their 
 individualities and consequent differences arise from 
 the conditions under which reflection takes place, 
 upon what in the end prove to be co-ordinates of 
 reference determined by whether the observer is at 
 rest or in motion, and in the latter case on whether 
 his motion is in straight paths or curved, differences 
 in the results of the resolution of the basic fact of 
 the changes present in his awareness result. For 
 us who are men on the earth where the variations 
 in situation and condition among ourselves is so 
 slight as to be negligible, these differences are so 
 small as to escape attention. But when we are 
 observing a region as to which we are relatively in 
 rapid motion, and in which the forms in the gravita- 
 tional field are consequently different from those 
 which present themselves to us at close quarters on 
 the earth, serious discrepancies between our results 
 and those which have to be regarded as natural to 
 an observer in such a distant region must be taken 
 into account. An observer under these different 
 conditions will analyse the contents of his specious 
 present, of the ' duration ' within which fall the 
 events of which he is aware, differently from an
 
 140 MATHEMATICAL PHYSICS 
 
 observer on the earth of these events. Differences 
 in shape and measurement will emerge for those who 
 are observing under these varying conditions. The 
 process may in each case seem to those who put 
 it into operation one so natural that they are un- 
 conscious of it. None the less is it true that it is a 
 process of inference depending on distinct premises 
 and with distinct results. The man on the earth 
 observing the field of the sun seems to himself to be 
 at rest. He is really moving round the sun at a high 
 velocity, and an observer on the sun must be aware 
 of him as not at rest but as changing position in this 
 fashion. The space-time system of each, as resulting 
 from the analysis unconsciously made, is thus an 
 individual and divergent space-time system. To 
 render these systems into harmony requires mathe- 
 matical inquiry based on some principle of congru- 
 ence among them. The constant velocity of light 
 may serve for practical purposes as such a constant. 
 But if the ultimate basis of congruence is to be 
 discovered, and c is to be invested with further- 
 reaching significance, the investigation must be 
 carried beyond the limit to which merely physical 
 mathematical methods can carry it. The final basis of 
 congruence may have to be sought in the foundational 
 character of knowledge, in the light of which it dis- 
 closes itself, not as any event common to time and 
 space, but as that in which identity underlies all 
 knowledge of difference, and for which alone time 
 and space and the events in them have significance 
 and are there. 
 
 Into the larger epistemological problems thus 
 arising neither the mathematician nor the physicist 
 enters. The former directs his methods to the
 
 MATHEMATICIANS AND PHYSICISTS 141 
 
 deduction of wider concepts as the abstract and precise 
 foundations of concepts of a narrower nature. His 
 method is one, not so much of syllogistic inference as 
 of making explicit implications, of further determin- 
 ing a content which is implicit in his propositions. 
 The physicist, on the other hand, is concerned 
 only with the character of the actual in experience. 
 This he defines by observation and experiment, 
 and expresses the result inductively in universals, 
 in the form of equations which are of a nature so 
 general that they cover everything material that 
 can be expressed in point of principle, as the result 
 of observation of the individual objects on which 
 attention is turned. The physicist thus looks for 
 facts in experience as his basis. But he has an 
 ideal in common with the mathematician. The 
 geometry of the latter ought to accord with the 
 generalised observation of his colleague. It is a 
 serious reflection on mathematics and physics if 
 there is a gap between them. The explanation of 
 the difficulty is well stated by Professor Eddington 
 at p. 175 of his book on Space, Time, and Gravi- 
 tation. Speaking of the difficulty of identifying in 
 imagination the abstract geometrical qualities of 
 the world with physical forces, such as those of 
 electricity and magnetism, he asks : " How, for in- 
 stance, can the change in the length of a rod taken 
 round a circuit in space and time be responsible for 
 the sensations of an electric shock ? The geome- 
 trical potentials (k) obey the recognised laws of electro- 
 magnetic potentials, and each entity in the physical 
 theory charge, electric force, magnetic element, 
 light, etc. has its exact analogue in the geometrical 
 theory ; but is this formal correspondence a sufficient
 
 142 MATHEMATICAL PHYSICS 
 
 ground for identification ? *' To this question he 
 seems to me to give the correct answer from an 
 epistemological point of view. ' The doubt which 
 arises in our minds is due to a failure to recognise 
 the formalism of all physical knowledge. The sugges- 
 tion ' This is not the thing I am speaking of, though 
 it behaves exactly like it in all respects/ carries 
 no physical meaning. Anything which behaves 
 exactly like electricity must manifest itself to us as 
 electricity. Distinction of form is the only dis- 
 tinction that physics can recognise ; and distinction 
 of individuality, if it has any meaning at all, has no 
 bearing on physical manifestations." That is what 
 Gauss and Riemann and the modern school of Ein- 
 stein have in substance maintained strenuously. 
 There is another name, too, as closely associated 
 with the principle as that of any of the others, and 
 this is the name of Hermann Minkowski. 
 
 Minkowski was born in 1864 and he died at the 
 early age of thirty-five under an operation for appen- 
 dicitis. He was a Russian, whose genius led to a 
 Chair being made for him at the University of Got- 
 tingen. As I write, a portrait of him is before me. 
 It is the picture of a very young-looking man, with 
 energy and imagination stamped on every feature. 
 The Slavs are like the Celts in this respect. They 
 may be deficient in staying power compared with us 
 who are of Saxon descent, but for flashes of insight 
 they are hard to match. 
 
 Minkowski was a teacher. He was little known 
 in his time to the general public. But when the 
 orations of the statesmen and divines of the West 
 have in the main passed into the oblivion which 
 swallows up what is transitory, there will probably
 
 MINKOWSKI 143 
 
 endure an address delivered by this professor that is 
 likely to be read even three hundred years hence. 
 It was an address delivered on 21st September, 1908, 
 shortly before Minkowski died, to a meeting of 
 learned persons at Cologne. Learned as many of 
 them were I doubt their having taken in much of 
 the deep significance of the words they listened to. 
 The fiery Slav speaker, flourishing only his stick of 
 ' ktihne Kreide* ' his bold chalk/ and operating with it 
 on the black-board, sought to draw for his audience 
 a picture of the world as in truth four-dimensional, 
 with space and time ' degraded to mere shadows/ 
 leaving nothing of their substance save ' a sort of 
 unitedness of the two/ The burden imposed on the 
 audience was not diminished by the unusual charac- 
 ter of the mathematics which the lecturer employed 
 freely. To listen to the address must indeed have 
 been a strain, and yet the occasion was a great one 
 in the history of knowledge. There is an aspect 
 in which the grasp of Minkowski on this occasion 
 suggests itself as of more far-reaching power than any 
 effort to interpret physical reality made before or 
 after his time. 
 
 It is worth while to linger over the theme of the 
 orator. For there is underlying it a conclusion which 
 has not always, I think, been fully appreciated the 
 real reason for the choice of the velocity of light as 
 the constant by reference to which the mathematical 
 physicist actually interprets the varieties of his 
 possible experience. 
 
 Minkowski's own view of the general result he 
 had reached may be given in the words used by him 
 as the conclusion of the first part of his famous ad- 
 dress : " For the future we shall find in the world
 
 144 MATHEMATICAL PHYSICS 
 
 no longer one space but an infinite plurality of spaces, 
 just as in three-dimensional space there is an infinite 
 plurality of planes. Three-dimensional geometry has 
 become a chapter of four-dimensional physics/' His 
 purpose was, with the suggestiveness of the concep- 
 tion of a four-dimensional world, to so enlarge the 
 conception of its geometry that this could express 
 all the genuine features of that world. But he was 
 holding firmly the idea that to actual experience of 
 the character of that world geometry must refer 
 back for the test of its own applicability and truth. 
 No doubt geometry is in substance a branch of 
 deductive knowledge. Yet in the end it is found to 
 depend for the truth of its deductions not merely on 
 the abstract fashion in which they are reasoned out 
 but on the conformity with reality of its primitive 
 assumptions or postulates. That was why Gauss 
 demanded that a test should be made of the con- 
 formity of the postulates of Euclidean geometry to 
 an experimental mensuration of the surface of the 
 earth. To be a science which fits in with the entirety 
 of knowledge the postulates of geometry must accord 
 with exact observation of individual facts. It can 
 resolve into universals as much as it pleases, but it 
 can never in this fashion completely express reality. 
 Back it must come .in the end to experience of the 
 object world, and such experience is to be sought, 
 not in the universals of mere logical reflection, but 
 in unique and unambiguous individual objects in 
 perception. We may resolve these into universals 
 indefinitely, but exhaust them we cannot. The 
 logical moment of the particularity of nature will 
 always confront us as a limiting notion which the 
 methods of our geometry cannot eliminate.
 
 HIS DEMAND FOR A PHYSICAL CONSTANT 145 
 
 In order to compare the space-time systems we 
 discover, and to embrace them for this purpose in 
 a universal system, we require a physical constant, 
 a c, to operate with. There must be some ratio 
 between the relations of time and space in change. 
 If the ratio is merely ideal we shall be unable to 
 connect our abstract reasoning with the facts of 
 nature which we wish to express in our equations, 
 and so to reduce these last to precise form with the 
 aid of our mathematical expressions. That is how 
 we come to make such use of what is an apparent 
 constant in observation, the fact of the velocity of 
 light as being uniform for us. Perhaps we may find 
 another such constant in the electro-magnetic field. 
 If we do find another such critical velocity it will 
 equally serve our purpose. We learn from the 
 mathematicians that if our constant c is an infinite 
 magnitude we come to a relation between the space 
 and time co-ordinates of a point on a surface which 
 gives that surface a Euclidean or Newtonian character. 
 But such a character cannot be the actual one, for 
 otherwise we should not be able to account for a 
 good many facts which observation discloses. Nor 
 can we do without a definite standard of physical 
 constancy in our c. If it is to be our guide in inquiry 
 it must be an individual fact, and cannot be any 
 mere general possibility for reflection. Therefore, 
 declares Minkowski, with a view to surmounting 
 this difficulty, it will not do for science to imagine 
 that we have only to deal with unlimited abstract 
 possibilities within which c may be treated as varying 
 from infinity with a minus sign to infinity with a 
 plus sign. For a mathematician who gives free 
 rein to his imaginative capacity will try to discover
 
 146 MATHEMATICAL PHYSICS 
 
 whether, in the result, the phenomena of nature do in 
 fact present invariance in the relations of space and 
 time. He will not remain content with theoretically 
 unrestricted logical limits, but he will be compelled 
 to search within a range which is definitely finite, 
 inasmuch as it is restricted to the greatest unit for 
 the ' gewdhnlichen Masseinheiten dusserst grossen c,' 
 which we find in experience. Such is the interpreta- 
 tion Minkowski's language seems to me to bear. He 
 was not troubling himself over metaphysical diffi- 
 culties. The velocity of light presents us with a 
 practically limiting fact in our actual experience, 
 and he adds that we may find its analogue in the do- 
 main of electricity. He thus brings to a head his 
 exhibition of geometry as an aspect of four-dimen- 
 sional physics : " Now that mathematics has shown 
 in this connection more ingenuity than usual in 
 laying itself alongside of the instincts of the public, 
 it has at least the satisfaction of knowing that, 
 thanks to its fortunate antecedents in combination 
 with a highly developed sense of the necessity of 
 looking well ahead, it is able to bring together the 
 deep-reaching consequential results of such a re- 
 fashioning of our conception of nature." 
 
 We have now seen why the desire was dominant 
 with Minkowski to base his four-dimensional physical 
 world on observed facts, and why for him no geometry 
 was adequate to the requirements of knowledge which 
 could not provide for this. It remains to ask what 
 this four-dimensional physical world really meant 
 with him. He saw clearly that Newton had assigned 
 an insufficient importance in his scheme to time. 
 Although space and time had different meanings, 
 there was no place in space excepting at a time, and
 
 HIS FOUR-DIMENSIONAL WORLD 147 
 
 no time excepting at a place. A space-point at a 
 time-point must be described through four co-ordi- 
 nates, to give it value as a ' world-point/ The 
 multiplicity of all thinkable systems of value in terms 
 of the four necessary co-ordinates he called his 
 ' world/ In order to avoid a gap in the picture 
 Minkowski makes the (epistemologically) dubious as- 
 sumption that in every place and at every time there 
 is something that can be perceived, as belonging to 
 such a * world/ something which may be spoken of as 
 substance, or a substantial point. He assumes that 
 we can not only perceive a world-point but can thus 
 recognise it when it again appears at another time. 
 The outcome of Minkowski J s conception is that in the 
 phenomena of nature what we recognise is never 
 anything but the four-dimensional world with three 
 co-ordinates for space and one for time. It can be 
 artificially represented in a diagram showing the lines 
 and curves which result when the relation of the 
 space co-ordinates to the time co-ordinate is varied. 
 If we made such a diagram in accordance with 
 Euclid's geometry all straight lines drawn from the 
 centre of a circular plane surface would have the same 
 measurement, for the standard of curvature would 
 be that of a plane circle. Time does not affect the 
 diagram. But in Minkowski's diagram, as employed 
 at Cologne, the lines representing time and space 
 are not independent in the same fashion. They 
 affect each other, and the standard of curvature of 
 the surface on his black-board is made that of an 
 hyperbola. 
 
 The result is that the movement of a point from 
 the origin of its space-and-time co-ordinates has to be 
 expressed differently and means something different 
 11
 
 148 MATHEMATICAL PHYSICS 
 
 from its character with Euclid. What are called the 
 fundamental invariants in this new geometry never- 
 theless remain the same when the co-ordinates are 
 moved round their origin. For convenience in mathe- 
 matical calculation Minkowski substitutes an artificial 
 and imaginary expression for the time relation, which 
 is removed in the expression of the final result of his 
 equations in order to restore to them an exact physical 
 meaning. For physical significance comes back in 
 the end always to the series of real numbers. Hia 
 purpose is to preserve throughout his calculations the 
 true analogies of form between the space-and-time 
 co-ordinates which are left out of sight in Euclidean 
 representations. In order to exhibit the real re- 
 lation of space to time it is necessary to provide for 
 representation of the cases where world-points are 
 sending out light to the situation where the co- 
 ordinates originate so as to distinguish them from 
 cases where world-points have received light from that 
 situation as the origin. In the former time will be 
 represented as less than nothing ; in the latter it 
 must be greater than nothing. For this distinction 
 his diagrams provide. They show, in addition, cases 
 in which no distinction at all in time can arise. 
 
 The diagrams are highly artificial because they 
 present only static pictures. But they show what 
 relations of space to time emerge in Minkowski's 
 doctrine and the principle of fundamental invariance 
 which underlies them. They enable the relations to 
 be made the subject of mathematical calculation, and 
 provide for the possibility of comparing the results 
 in different systems. In any event they show how 
 changes in time must be taken into account as of 
 equal importance with changes in space in the descrip-
 
 MINKOWSKTS 'WORLD POSTULATE' 149 
 
 tion and the estimation of the significance of physical 
 phenomena. 
 
 Minkowski himself did not adopt the expression 
 ' Relativity ' for the outcome of his postulate of the 
 necessity of going deeper down than appearances 
 suggest for a foundation of invariance in the relations 
 of his world-points. " Inasmuch/' he says, " as the 
 meaning of the postulate is that in phenomena we 
 find only the four-dimensional world in space and 
 time, but the projection in space and time can take 
 place with a certain amount of freedom, I prefer to 
 give to my statement the title of ' postulate of an 
 absolute world/ or more shortly ' world postulate/ J 
 The important points in his theory are from the out- 
 look of philosophy two. First of all he pronounces 
 for a so-called absolute world of which we are aware 
 and which we can describe apart from relativity in 
 measurement with the precision which mathematical 
 methods permit. In the second place, the description 
 is one which consists, not merely in resolution into 
 the abstract universals of mathematics, but in direct 
 reference to actual physical objects in a condition of 
 change, such as the changing path of a ray of light, 
 which are individual and unique in character. This 
 is no mere geometry. It is physics. A pure geometry 
 would be altogether deductive. Even Euclid's geo- 
 metry is not pure, for it turns on postulates about the 
 character of space which can look for any verification 
 they possess only to experience. Such verification 
 has now been challenged. It is said that the postu- 
 lates on which Euclid relied do not conform to the 
 nature of the real world. 
 
 The existence as a self-subsistent entity of such a 
 four-dimensional world, taken as present to con-
 
 150 MATHEMATICAL PHYSICS 
 
 sciousness apart from any moulding interference from 
 the observing mind, is the postulate on which the 
 modern doctrine of relativity builds. If methods of 
 a logical and metaphysical order are applied to its 
 investigation such a world may turn out to be further 
 resoluble by reflection. But with the complications 
 such methods might disclose the physicist is not con- 
 cerned. He treats the four-dimensional world as 
 ' closed to mind/ It is for him absolute, and its 
 fundamental characteristics are to be the same for 
 all observers, however situated and whether at rest 
 or moving. But these characteristics are of a very 
 general character, antecedent to shape and measure- 
 ment. They depend on functions of the relations to 
 each other of the world-points. Such functions are 
 made capable of differential expression by applying 
 to them the doctrine of tensors. The possibility 
 of doing this and of so arriving at relations that are 
 invariant, however the time-and-space co-ordinates 
 of situation in the world as experienced mould each 
 other, affords the footing on which the results of such 
 moulding, and the varying appearances in the different 
 space- time systems which arise for perception, can 
 be compared, rendered congruent, and reduced in 
 calculation to each other's terms. The abstractions 
 of mathematics are thus sought to be made applicable 
 to the unique and individual natures of the objects 
 of perception, and a large part of mathematics itself 
 becomes a deduction from the results of observation 
 of the actual world. The assumption of Newton 
 that his space and time were actual but unchanging 
 frameworks in which the objects of nature exist is 
 accordingly replaced by the principle that there is an 
 indefinite multiplicity of space- time systems which
 
 THE PASSAGE OF NATURE 151 
 
 depend for the shapes and measurements that appear 
 in them on the relation of the observer to what he 
 observes. It is where there is practical uniformity 
 in this relation, as in the case of most observation 
 by those on the earth of objects, that the space- time 
 system appears to be the same for all observers. But 
 wherever differences among these in situation and 
 conditions exist on a considerable scale, as in the 
 cases of calculated results of observation by observers 
 in different positions in the firmament, the space- 
 time systems may vary materially, with practical 
 consequences. 
 
 What we really apprehend when we eliminate by 
 abstraction the elements that we ourselves have 
 contributed is therefore, for Minkowski and the 
 school of Einstein that agrees with him, a ' passage 
 of nature/ a series of changing events in which 
 objects with the definite relations which are what we 
 mean byspace and time have not yet been constructed. 
 Our constants in such comparison as this mere aware- 
 ness admits of are not yet shapes or measurements. 
 Nor, inasmuch as what we are seeking to describe 
 is a concrete world, can they be mere mathematical 
 deductions. These constants must be sought in a 
 phenomenal domain where we can find changes of a 
 kind critical in this respect, that their magnitude is 
 recognised as being in each case a limiting one for 
 our observation. In so far as these magnitudes 
 cannot in point of fact be exceeded they are treated 
 as if they were individual and unique facts, which 
 we can employ as standards capable of being referred 
 to in comparison and as bases in calculation. When 
 we measure them we use in part deductive methods 
 based on the assumption that they are final and
 
 152 MATHEMATICAL PHYSICS 
 
 constant. The measurements must always eome 
 out with the same result, inasmuch as they consist 
 in no more than expressions referred in the terms 
 of the varying space-and-time relations of the 
 observer to the unique and final fact which he is 
 observing. The space-and-time calculations will be 
 expressed differently as the systems of the observers 
 differ. But if they are true calculations they must, 
 by their very nature, yield just the same outcome 
 about the relative measurement of the change 
 observed at the outset, however different may be 
 the significance of the space-and-time units in which 
 that outcome is expressed. That is why Morley 
 and Michelson, and all other observers who since 
 their time directed experiments to the point, have 
 found the velocity of light to have a constant 
 measurement of about 186,300 miles a second. No 
 doubt much has to be said about the interpretation 
 of the miles and seconds and their relation. But 
 the cardinal feature is that the measurement not 
 only does result, but on the principle of a four- 
 dimensional world must result, in formally invariant 
 answers to the question put. 
 
 We never see space unmoulded by time or time 
 unmoulded by space. Instantaneous space, a pure 
 collection of static points, is a convenient abstraction 
 for the purposes of the mathematician. But the 
 physicist observes nothing of the sort, and if, per 
 impossibik, he could he would retain no picture of 
 it in his consciousness. What we observe, and what 
 alone we can image to ourselves, is a change or 
 passage from point to point in which points are 
 distinguished. It is the same with time. Get rid 
 by abstraction of separation in space, and there is a
 
 MATHEMATICS AND THE ACTUAL 163 
 
 mere empty series, in which the only distinction is a 
 merely numerical one between names for what is, 
 what was, and what may be. Minkowski exhibited 
 this by means of a highly artificial diagram to which 
 reference has been made, and showed that if an 
 attempt were made on a purely mathematical and 
 deductive footing to apply it for the description of 
 all conceivable rays moving in the world of actual 
 perception, with the critical velocity which we 
 experience in connection with light, a further case 
 would occur. There would be of necessity excluded 
 from our possible experience regions in which we 
 could not have the velocity of light as a standard. 
 Such regions are mathematical constructions which 
 point beyond possible experiences. They are in- 
 structive. But they belong to the aspect in which 
 knowledge passes beyond what is actual, in its pro- 
 cess of analysing only through abstract distinctions 
 which knowledge itself establishes. For Minkowski, 
 as for Einstein, in the system of the actual world it 
 can be demonstrated that a velocity greater than 
 that of light is impossible. This is a result which 
 follows from the principles on which their kinematics 
 are based. There has been a good deal of complaint 
 about it. People refer, for instance, to the beta 
 rays of the radio-active substances, which appear to 
 possess a velocity which may approach that of light, 
 and ask why these rays cannot become so accelerated 
 as to exceed in their velocity that of light. But the 
 school of Einstein reply that the mass of a material 
 particle, and therefore its inertial resistance, can be 
 shown mathematically to tend to become impossibly 
 great in proportion as the velocity of the particle 
 approaches that of light, and that the attainment of
 
 154 MATHEMATICAL PHYSICS 
 
 the latter velocity can be proved to be on this account 
 impracticable. Our ideas, not only in kinematics but 
 also in dynamics, have to be refashioned because of 
 the new conception of our world. The refashioned 
 dynamical principles, as held by the adherents of 
 relativity, allow of mathematical proof that the 
 inertial resistance of a moving particle to acceleration 
 by means of any finite force is such that this resist- 
 ance increases to infinity and precludes the attain- 
 ment of the velocity of light.
 
 THE PHILOSOPHICAL SIGNIFICANCE OP 
 OTHER SUBJECTS 
 
 CHAPTER VI 
 
 MATHEMATICAL PHYSICS (continued) 
 
 THE four-dimensional world is the bridge between a 
 domain of abstractions and a concrete world filled 
 with individuality as perceived. Stationed on this 
 bridge Einstein and his disciples look impartially 
 in both directions. But it is now evident why they 
 refuse to separate geometry from mensuration, and 
 why they lay such stress on facts of actual experience, 
 such as the velocity of light and of energy manifesting 
 itself in the electro- magnetic field. What Gauss 
 was straining after when he introduced curvilinear 
 co-ordinates for the ascertainment of the positions 
 of the points on every kind of two-dimensional 
 surface ; what Riemann grasped at when he en- 
 larged, as he did, the limits of possible conceptions 
 of space and of its geometry, has been brought, in 
 the view of Einstein and his disciples, within their 
 reach by the introduction of the continuous manifold 
 of the four-dimensional world. 
 
 We can now see the real step forward which 
 Einstein seeks to attain by his general theory. He 
 has Minkowski's space-time world of change before 
 him. This gives him the facts of nature so inter- 
 preted to apprehend in their fundamental relations. 
 Change in the position of bodies relatively to each 
 other was explained by Newton as motion in an 
 independently existing Euclidean space. But every 
 
 106
 
 156 MATHEMATICAL PHYSICS 
 
 such change of position of this developed kind may 
 arise equally, so far as its appearance in our experience 
 is concerned, if we assume that it is the observer who 
 has changed position while the object observed has 
 remained at rest. The apple appears to fall to the 
 earth. But if the earth itself, with the observer on 
 it, were moving with accelerating velocity it would 
 overtake the mere inertial motion upwards of the 
 apple, and so produce the appearance of its falling. 
 If the reality of what is happening must be sought 
 in a four-dimensional continuum, where relative and 
 measurable rest and motion are unmeaning and 
 unbroken change is a basic characteristic, the actual 
 truth may lie just as well in the latter explanation 
 as in the other, which depends on the assumption 
 that the earth and the observer are definitely at rest. 
 The sun appears to go over the earth in a curve, and 
 was generally believed to do so for many centuries. 
 We now know, but only by inference and as the 
 result of interpretation, that the earth goes round the 
 sun. So, it is said, it can be shown of every such 
 phenomenon of nature that it is at least capable of 
 Einstein's alternative explanation. 
 
 Gravitation is not different from inertial motion. 
 They are equivalent, if we bear in mind that they 
 are equally open to the alternative explanation 
 which reduces each to an illustration of the other, 
 disguised by the circumstance of the observer being 
 himself arbitrarily in motion. Now Minkowski, as 
 well as Einstein, has shown us that the ultimate 
 world is one which may be interpreted as a series of 
 world-points in activity or change. It is by making 
 assumptions as to rest and motion, which really are 
 assumptions as to the rest or motion of the observer,
 
 COINCIDENCE 157 
 
 that we have got by abstraction to our conceptions 
 of space and time as independent of each other. 
 They have in truth no independent existences. They 
 are ways in which we treat reflectively the world 
 of changing point-events which we are to hold to as 
 final physical reality. Euclidean geometry is just 
 one out of many possible ways of doing this. Theory 
 and experiment alike (such as were the experiments of 
 Eotvos already referred to) point to the wider concep- 
 tion of relativity as the possible explanation of many 
 facts. One thing which what we call direct aware- 
 ness discloses to us when we eliminate our theories 
 is the coincidence in time and space of material 
 points at the same time and in the same space. We 
 cannot even say of a line, when we attempt to describe 
 it merely by such coincidences, whether it is straight 
 or otherwise. For that implies standards which bare 
 coincidence does not warrant. If we examine the 
 procedure of the exact sciences we find that all their 
 definite determinations arise by assuming at least 
 the principle of such coincidence. Every actual 
 measurement proves in ultimate analysis to be a 
 demonstration that a point coincides with another 
 point on something resembling a scale. Whether the 
 measurement is of length, of time, of force, of mass, 
 of electrical current, or of chemical affinity, it is 
 always the same : all determinations are of coinci- 
 dences in time and space. In the language in which 
 Minkowski describes his ' world-points/ they are 
 identified through the encounters in the space-time 
 manifold of world-lines, and physics is the science of 
 the relations of the points so identified. The doctrine 
 of Minkowski seems, as he stated it, to be expressed 
 more pictorially than the stage he is dealing with
 
 158 MATHEMATICAL PHYSICS 
 
 warrants ; but in point of principle it is hardly 
 different from the result reached in his analysis of the 
 passage of events in nature by Professor Whitehead. 
 Both seek to reach reality by stripping it of artificial 
 incrustations with which it is invested by the minds of 
 particular observers. It is these incrustations which 
 the principle of relativity peels off. 
 
 Impressive as the writings of Minkowski are, by the 
 freshness and power of his statements, they suffer 
 from the defect earlier referred to. His wonderful 
 command of mathematical instruments tempts him 
 too often to try to express in the shape of diagrams 
 the relationship of the time and space which he has 
 reduced to ' shadows/ and which involve each other 
 conceptually inasmuch as they spring from a common 
 root. These diagrams are of course only spatial, and 
 convey nothing excepting symbolically of the character 
 of that change in which time consists. Moreover, as 
 Minkowski is essentially an empiricist, in so far as he 
 is aiming at exhibiting three-dimensional geometry as a 
 branch of four-dimensional physics, it is to experience 
 that he comes in the end for the constants that the 
 principle of congruence which is essential for him 
 necessitates. These he finds in maximum velocities 
 which we cannot get beyond in an experience of the 
 character of our own, the velocities of light and the 
 electro-magnetic field. Conceivably there may be 
 more general constants. Pure mathematics can suggest 
 and deal with such hypothetically. But in so far 
 as it does PO pure mathematics is a deductive and 
 merely logical process based on what is unverifiable in 
 the world of reality. Accordingly Minkowski avoids 
 hypothetical constants and bases his reasoning on 
 relationships to those which he finds in experience.
 
 CRITICISM OF MINKOWSKI 159 
 
 He is careful to confine himself within this limitation. 
 But his diagrams and some of his mathematical ex- 
 pressions of a different kind have given an impulse to 
 a good deal of talk which goes outside the limits which 
 the method imposes. If we are dealing with a maxi- 
 mum velocity, such as that of light is found in obser- 
 vation to be, it is quite true that we have before us, 
 as he suggests, a complete line of demarcation between 
 the past and the future. But this is in reality an em- 
 pirical or practical demarcation, and is not in itself one 
 which guides towards the conception of a reversal of 
 the history of events, or to any timeless or neutral 
 object world. Much more of new principle than what 
 relates merely to measurement of position is involved 
 in such a conception. While it is true that there 
 is in our experience, possible as well as actual, in one 
 sense no absolute simultaneity any more than there is 
 absolute motion, this has its significance as due to the 
 unavoidable intrusion of relativity into the observer's 
 procedure. There is another sense in which, in the 
 ultimate four-dimensional world, there is both ab- 
 solute simultaneity and absolute change. These may 
 be only limiting notions, but experience implies them 
 as notions on which its significance and reality are 
 ultimately based. It seems, therefore, dangerous to 
 speak of events as causing events in their past ; there 
 appears to be here confusion between the different 
 characters which belong to what are physical and, 
 therefore, arbitrary standards, and to what are really 
 general and theoretical constants. The structure of 
 possible experience, assuming that it is to be regarded 
 as if made actual, does not seem to admit of such a 
 merely mathematical representation. 
 Perhaps the very enthusiasm with which Minkow-
 
 160 MATHEMATICAL PHYSICS 
 
 ski expressed himself lias given rise to a tendency in 
 his school to go beyond what he himself said. At all 
 events, some of his disciples have been careful even 
 when they seek to follow him in his principle. One 
 who knows his work well and is among the most dis- 
 tinguished of these disciples has been cautious in this 
 respect. There is a suggestive attempt at description 
 of the four-dimensional world in a book to which I 
 have already referred, Die Relativitats-iheorie Ein- 
 steins, by Professor Max Born of Gottingen, a second 
 edition of which has recently appeared. Prof. Born 
 is not only a physicist but a mathematician, with 
 grasp of modern methods of differential analysis. It 
 seems useful to state the way in which he has formu- 
 lated the Minkowski-Einstein position, even without 
 including all the diagrams and equations which 
 Prof. Born uses. 
 
 At page 238 of his book Professor Born observes 
 " that the totality of marked-out world-points is 
 what is determinable in the actual. The four-dimen- 
 sional continuum is in itself devoid of structure ; it 
 is only the factual relations of the world-points in it 
 which observation discloses that express in it what 
 corresponds to measurement-relation and geometry. 
 In the world that confronts us we have, so far, the 
 same conditions that we have learned to recognise 
 even in the geometry of surfaces. The mathematical 
 method of treatment is accordingly the same in each. 
 Suppose that we introduce Gaussian co-ordinates into 
 our treatment of the four-dimensional world, we con- 
 struct a network or mesh-system of marked-out world- 
 points. It implies that we may think of space as 
 filled with matter arbitrarily in motion in all direc- 
 tions, matter which may turn and deform itself, but
 
 PROFESSOR MAX BORN 161 
 
 always preserves a continuity in its relations ; it is 
 what Einstein has likened to a kind of mollusc. In 
 this domain we draw three sets of lines cutting each 
 other, which we number and distinguish by the letters 
 x, y, 2. In the corners of the net of meshes which is 
 so produced we now think of clocks as placed. They 
 may go at any rate so long as the differences between 
 the results of clocks that are very close to each other 
 in space is very small. The total system is now not 
 a rigid one ; it is an altering mollusc of relations. In 
 the four-dimensional world there corresponds to it 
 a system of Gaussian co-ordinates, consisting in a 
 network of four-numbered surface sets, x, y> z, t. All 
 moving rigid relational systems are naturally just 
 special forms in this self-deforming relational system. 
 It is meaningless from our general standpoint to regard 
 rigidity as something given a priori. Moreover the 
 separation of space from time is wholly arbitrary, for 
 just as the rate of the clocks is wholly arbitrary and 
 cannot be assumed to have more than a principle of 
 continuity in its change, so the space itself, as no more 
 than the totality of all simultaneous world-points, is 
 likewise without physical reality of its own. For if 
 the Gaussian co-ordinates were chosen differently the 
 world-points that were simultaneous would be dif- 
 ferent. What, however, do not change in the transi- 
 tion from one system of Gaussian co-ordinates to 
 another are the points in which the actual world-lines 
 intersect, the marked-out world-points which exhibit 
 for our reflection coincidences in time and space. 
 All the actually determinable facts of physics are thus 
 qualitative relations of position of these world-points, 
 and they remain unaltered by the change in the 
 Gaussian co-ordinates.
 
 162 MATHEMATICAL PHYSICS 
 
 " Such a transformation of the Gaussian co-ordi- 
 nates of the space-time continuum means the transi- 
 tion from one relational system to another arbitrarily 
 deformed and moved. The satisfaction of the demand 
 that we should assume in the laws of nature only what 
 is actually ascertainable involves the postulate that 
 these laws must be found as invariant when arbitrary 
 transformations of Gaussian co-ordinates, x, y, z, t, are 
 made into others, x 1 , y 1 , z 1 , t 1 . This postulate obviously 
 covers the general principle of relativity, for among 
 the possible transformations of x, y, z, t are those 
 which express the transition from one three-dimen- 
 sional system to another in any kind of motion. But 
 the postulate goes further, in that it includes also 
 arbitrary deformations of space and time. It is in 
 this way that we come to the foundation of a general 
 doctrine about space, on the basis of which alone the 
 principle of a complete relativity can be carried out/' 
 
 This passage in Bern's book illustrates the inter- 
 pretation he has put on the ground conception 
 of his predecessor at Gottingen, Minkowski. In 
 agreement with the latter he claims to be describing 
 the four-dimensional world, not as a mathematical 
 abstraction, or even as a geometry based on a priori 
 postulates about the nature of space, but as indica- 
 tive of the ultimate source of our experience. He 
 goes on to show the relation of this character to 
 the general principle of relativity as formulated by 
 Einstein. On his exposition of this last the space 
 at my disposal only permits me to touch briefly. 
 His task is in the first place one mainly of pure 
 mathematics. The interval between two world- 
 pointi expresses what corresponds or is at least 
 analogous to a space-and-time relation in the four-
 
 THE EQUATION FOR AN INTERVAL 163 
 
 dimensional world. Its characteristics will vary with 
 the relation in which what corresponds to space and 
 time in combination occurs there. An equation can 
 easily be found which will define this relation if 
 co-ordinates can be assumed represented by Eucli- 
 dean straight lines, e.g. in regions where there is no 
 gravitational field apparent. There the special theory 
 of relativity for the relations which obtain when 
 systems are in rectilinear and uniform motion rela- 
 tively to each other, and the Lorentzian formula for 
 transformations, hold good. The equation expresses 
 a principle which would then be completely invariant 
 in all such transformations. We could even apply it 
 to sufficiently small fractions of a curved surface. But 
 we must not forget that we are really concerned with 
 intervals in the continuum which are of the nature, 
 not of straight lines, but more generally of geodesic 
 lines, the directest possible, but depending in point of 
 form on the character of the space-time region in 
 which we find them. We are not to think of this 
 as flat space or as an independent entity in which 
 lines are artificially carved out in curved form. It 
 is rather itself curved by its nature. A ball when 
 thrown from the hand gravitates towards the earth. 
 The Newtonian explanation by the action of a 
 gravitational pull may be replaced without theoretical 
 difficulty by the conception of the space itself as 
 exhibiting a relation of curvature created by the 
 accelerated motion of the observer and the earth 
 on which he stands. There are no absolute paths 
 or shapes any more than measurements. In the 
 four-dimensional world all is in a state of change, 
 and this will account for the appearance of gravi- 
 tation and its identification with inertial motion. 
 12
 
 164 MATHEMATICAL PHYSICS 
 
 All such diversities in motion are actual facts for 
 observation, and they supersede the hypothesis of a 
 pulling force acting at a distance, which is no longer 
 essential so soon as we understand the circumstances 
 fully. A geodesic line is no straight line in Euclid's 
 sense. Euclid made an assumption of finality in his 
 axiom of parallels for which observation afforded no 
 real warrant. 
 
 So soon, therefore, as we turn to the infinite varie- 
 ties of curvature which the geodesical possibilities of 
 the continuum offer we have to look for a less re- 
 stricted equation for the description of the interval 
 than that which suffices when the spatial relation is 
 conceived as Euclidean. Such a Euclidean line can 
 no longer be taken as the standard to which the inter- 
 vals conform. For their continuity we must now 
 look further. With space altering its form in its 
 combination in change with time we can, by applying 
 what are analogous to the curved co-ordinates intro- 
 duced by Gauss, reach a new standard. The geodesic 
 lines may vary in curvature, but if they do so with 
 continuity of a general character formulas can be 
 found which will express the invariant quality or 
 relation in this continuity of character. Such for- 
 mulas have been discovered by the researches of pure 
 mathematicians. I have myself ventured to attempt a 
 slight, but only a slight, account of them in chapter v 
 of The Reign of Relativity and it is not necessary to 
 pursue the subject further here. Those who desire 
 to enter into details will find them, not only in the 
 books there referred to, but still more fully in Professor 
 Weyl's treatise on Raum, Zeit, Materie, to which 
 reference has already been made. 
 
 The outcome of the matter is that, just as in the
 
 GEODESIC LINES 166 
 
 theory of surfaces the structure was composed of what 
 could be called geodesic lines, so here in the four- 
 dimensional world we figure to ourselves geodesic lines 
 which represent the shortest or most direct intervals 
 between the world-points in the space- time continuum, 
 and the invariant character which these intervals 
 possess enables us to compare them. For quantitative 
 measurement in space and time we have to resort 
 to observation and experiment for our materials. 
 But an equation of a tensor nature gives a result 
 which is invariant, however the measurements and 
 its systems may differ. This result is free from rela- 
 tivity. But just on that account it can be no more 
 than a framework into which the actual measurement 
 is finally built. Through the instrumentality of a 
 tensor expression which is covariant for whatever 
 particular quantities are introduced as the result of 
 observation, we become able to render congruent and 
 so comparable the phenomena of different systems 
 of relativity. 
 
 Such appears to be the basis on which Einstein has 
 sought to bring together physics and geometry. 
 Minkowski's deposition of space and time from the 
 status of independent entities seems to have fitted in 
 completely with his own principles. When Einstein 
 introduced his new idea of the gravitational field he 
 effected a great revolution. The assumption of a 
 force pulling at a distance became, conceptually at 
 least, unnecessary. It had always been unintelli- 
 gible, and it was now replaced by the view that all 
 we observe is change in positions relatively to each 
 other and particularly to ourselves, the observers. 
 This required new conceptions of space and time, as 
 no longer objectively self-subsistent, but as relations
 
 166 MATHEMATICAL PHYSIOS 
 
 into which we resolve change, which is what we really 
 observe. Thus space-time systems presented them- 
 selves as varying with the situation and motion, 
 accelerated or uniform, of the observer. Gravitation 
 and inertia became different appearances of the same 
 fact. Then it was evident that the principle of rela- 
 tivity must be extended to the idea conveyed by 
 mass. For energy became capable of a natural 
 interpretation in terms of variation in the path of 
 its radiation. Mass displayed itself as simply a 
 form in which energy appears, and matter became, 
 no more indestructible substance, but merely con- 
 centration of energy. For example, it has been shown 
 by Sir J. J. Thomson that, if a conductor charged 
 with electricity has to be moved or stopped, addi- 
 tional force will be necessary simply on account 
 of the charge. For the conductor has to carry its 
 electrical field with it, and force is needed to set 
 the field moving. This electrical field is inertial, 
 and its inertia is indistinguishable from mass. 
 More energy introduced adds to the mass. Is there 
 any other meaning than this in mass ? For the 
 general theory of relativity, in which electrical and 
 magnetic fields as domains of causal activity dis- 
 play merely manifestations of energy, the phenomena 
 of inertia of mass must always appear. The electron 
 and the atom become illustrations of the principle. 
 We arrive finally, after yet further mathematical 
 analysis, at a highly general conception which it is 
 suggested should be called action, as descriptive of 
 the fundamental reality in physics. There are 
 restrictions on the theoretical possibilities as regards 
 the relation of mass proper to energy. For example 
 it is demonstrable, as has akeady been observed,
 
 FURTHER QUESTIONS 167 
 
 that the amount of its mass in the case of a moving 
 particle increases in proportion as its velocity ap- 
 proaches that of light. That is because mass is not 
 different from motion and increases with it. The 
 appropriate equations show that where the velocity 
 tends to equal that of light the mass will approach 
 infinity. It follows that it is impossible with any 
 finite force to give the particle a velocity which can 
 exceed that of light, for its inertial resistance would 
 in that case be infinite and prevent it from attaining 
 to such a velocity. 
 
 These are some of the questions which the investiga- 
 tions of Einstein force upon us. There remain points 
 on which much work has yet to be done. One of 
 these at least is far-reaching. The modern concep- 
 tion of the atom suggests that light is the outcome of 
 the production by electrons inside the atom of waves 
 of energy which proceed in every direction. For such 
 a phenomenon physicists used to be content with the 
 formulas which have been current since the introduc- 
 tion of Maxwell's equations. Of late many physicists 
 have felt compelled to give up the adequacy of these 
 formulas as sufficient for description of what happens 
 inside the atom, and to assume other laws, formulated 
 by Max Planck in 1900. These are the laws be- 
 longing to the quantum theory. They have been 
 developed in their application by physicists such as 
 Bohr, and an account of the general considerations 
 which make some such principle seem inevitable will 
 be found in Mr. J. H. Jeans's recently published 
 Report on the Quantum Theory. Here we come on 
 discreteness, to use a term which has one meaning in 
 logic and a different one in mathematics (a difference 
 to which reference will be made later on), in the
 
 168 MATHEMATICAL PHYSICS 
 
 aspect of the four-dimensional world which can no 
 more be neglected than can its aspect of continuity. 
 How far the character of such phenomena is suscep- 
 tible of having light thrown on it from epistemological 
 considerations is a question which I have already 
 mentioned. It may be that the general character of 
 experience is such that continuity is logically impos- 
 sible apart from discreteness, just as time has even in 
 logic no significance apart from space. The unique 
 quality of the actual in experience and the conse- 
 quent impossibility of exhausting it by the universals 
 of science suggest such considerations. The general 
 theory of relativity would hardly be an adequate 
 description of our actual experience if it asserted only 
 continuity in the phenomenal world. 
 
 It is material to the strength of Einstein's position 
 that it is just this assertion that he does not make. 
 His doctrine is one which is no abstract mathematical 
 idea resting in the air. It is a development of 
 ideas gathered from an experience which has merely 
 been simplified when described as one ultimately 
 concerned with the form of structure of the four- 
 dimensional world of experience, an actual manifold 
 and also a continuum. This structure is characterised 
 by discreteness as much as by continuity. Its 
 phenomenal quality is that of the individual and self- 
 contained object in knowledge. It is not to the point 
 to say that it is a world of which we never ourselves 
 have actual experience. If this objection were a 
 good one it would be fatal to progress in exact physical 
 science. The application of all methods depending 
 on limits, which cannot be considered as more than 
 vanishing relations or rates of change, would be ex- 
 cluded in inquiry into the real nature of experience.
 
 GENERALITY IN MATHEMATICAL METHOD 169 
 
 But such methods are essential in modern science. 
 They deal, it is true, only with general characters and 
 are not exhaustive, but they alone enable us to 
 ascertain the full significance of what we observe. 
 They guide us towards macrocosmic principles by 
 which we interpret the individual objects which we 
 encounter in empirical knowledge. They enable us 
 to predict possibilities in developed observation, and 
 tell us what we may exclude from the region of the 
 possible. More perfect instruments and better con- 
 ditions may enable the observer to become directly 
 aware of objects which under existing conditions he 
 cannot reach. But the abstract deductions of the 
 mathematician do more, for they limit the region 
 of the possible and direct the observer to what alone 
 he can with hope of success search for. 
 
 Mathematical investigation into the character of 
 reality often does more than this. It alters for us the 
 significance of what seems to appear, and banishes 
 false and distorted images of the possible. Einstein's 
 teaching, for example, has made it unnecessary for us 
 any longer to attribute to space an independently self- 
 subsisting nature, such as might admit of its being 
 regarded as a cause of physical happenings. It is no 
 more necessary to-day to give it such a character than 
 it is to believe in a real contract when legal theory, in 
 order to secure justice by means of a fiction which no 
 suitor in the Courts of Justice is allowed to traverse, 
 imputes a contract which everyone knows never to 
 have been actually made. For space conceived as the 
 field required for causal action most mathematical 
 physicists are now content to substitute change in the 
 position of a moving observer, relatively, it may be, 
 to a background of distant masses like the heavenly
 
 170 MATHEMATICAL PHYSICS 
 
 bodies, as the explanation of what appears differ- 
 ently to the observer who assumes himself to be 
 stationary. It is the same with the apparent inter- 
 action of molecules. What is popularly meant by 
 causative action at an even infinitesimal distance is 
 a conception no longer required in physics. But 
 we may still talk in familiar Newtonian terms, if 
 we remember that they cannot be ultimately relied 
 on as guides. There is convenience in so doing, for 
 Newton's results approximately conform to most 
 of our experience. We may even speak of the 
 ' aether ' if we bear in mind that the only scientific 
 significance left to it is that of the empty and 
 varying spatial system which forms the scene of 
 gravitational and electro-magnetic fields. But such 
 an aether is no substance. It has no independent 
 existence. It has no fixed and unalterable points or 
 paths in it. It does not admit of being described as 
 anything to which by itself motion is relative. It is 
 just a nomen collectivum, to which Einstein himself 
 does not object if its only real meaning is kept in 
 memory. 
 
 The theory of relativity in its wider significance is 
 thus a further attempt which science has made 
 towards the interpretation in terms of universals 
 of an actual world. It is no mere collection of mathe- 
 matical abstractions, deduced from general princi- 
 ples. It is a new interpretation of the meaning 
 constitutive of reality towards which we have 
 been driven by observation of the actual. It has 
 brought us to see that the part which mind plays 
 in the fashioning of our knowledge of what we 
 call facts is larger than we had supposed. The 
 relativity of such knowledge becomes everywhere
 
 SIGNIFICANCE OF RELATIVITY 171 
 
 apparent and account has to be taken of it. But the 
 character of such relativity can now be in part ex- 
 plained and its variations can be reduced to principles. 
 The method is just the same as that followed in a 
 developing fashion by science since the days of Bacon. 
 The history of the genesis of Einstein's theory is an 
 illustration of how science never stands still, but is 
 always being impelled by reflections of a dynamic 
 nature. But scientific knowledge is not the less 
 scientific knowledge because it does not stand still. 
 
 Hitherto we have been concerned with the world of 
 physics and therefore with reflection belonging to a 
 certain order in knowledge. It is the standpoints to 
 which that order is confined that give to knowledge 
 in it the character of relativity in a deeper sense than 
 that in which Einstein and his disciples use the word. 
 Just as we refuse even from a scientific point of view 
 to try to bifurcate nature after the fashion of the 
 Victorian physicists; just as we decline to try any 
 more to draw a line separating objectivity from sub- 
 jectivity, or primary from secondary qualities ; so 
 we come to regard the actual aspects which nature 
 presents as representing, not self-subsisting entities, 
 but standpoints within the entirety of knowledge. 
 
 Even if we take the view that the work of the 
 school of relativity in mathematical physics is of 
 too limited a character in itself to throw all the 
 light we require on the nature of knowledge, it has 
 opened up the character of its procedure. I do 
 not refer to the specific achievements of the school 
 of Einstein. These may have to be remodelled as 
 research goes on. Even if, for instance, the work 
 of Weyl (to be referred to presently) in setting up 
 a fresh and more general theory of the character
 
 172 MATHEMATICAL PHYSICS 
 
 of interval relations is superseded, we shall have 
 
 gained much from his attempt to enable the laws 
 
 of the field of electro-dynamics to be referred to 
 
 electric charge as the reality behind gravitation and 
 
 the appearance of the world in space and time. 
 
 For he, like Einstein, has brought to light in a fresh 
 
 fashion points to which attention must be given if 
 
 what is actual is to be fully explained, distinctions 
 
 forced upon us between our relative and arbitrary 
 
 identification of events and their measurement, and 
 
 certain intrinsic qualities which do not vary either 
 
 in these events or in our particular measurements 
 
 of them with the altering standards of observers. 
 
 Mathematicians have taught us that such distinctions 
 
 must be made, and they have further taught us how 
 
 to describe sufficiently these intrinsic qualities by the 
 
 introduction of tensors. This method enables us to 
 
 separate what is merely relative to the position of the 
 
 observer in the results of his observation from what 
 
 is not relative but always the same. It does not carry 
 
 us to any pictorial or actual view of reality. But 
 
 it does enable us to generalise in a way that would 
 
 not otherwise be possible, and to gain new knowledge 
 
 of the intrinsic character of the actual by a resolution 
 
 into universals of a kind much farther-reaching than 
 
 was possible before the tensor method was discovered. 
 
 This, however, is only one of the great examples 
 
 which the most modern mathematics offers to the 
 
 would-be student of the nature of knowledge. A 
 
 familiar illustration of new ideas has been already 
 
 referred to. The principle of what the Germans call 
 
 Nahewirkung, action at infinitesimally close distance, 
 
 has been introduced into the study of physics with 
 
 tremendous consequences. It has been equally
 
 UNIVERSALS AND CATEGORIES 173 
 
 familiar, as we saw, in the study of pure space since 
 Riemann adopted it for that purpose, and it now 
 extends to time, since time and space are no longer 
 treated as separate entities, but rather as abstractions 
 made from different standpoints in the consideration 
 of a four-dimensional world. 
 
 The question is whether the lessons so taught are 
 without application when we come to aspects of 
 nature other than those which belong to mathematics 
 and physics. One thing is clear. In all cases we are 
 in search of what we call laws of nature, uniformities 
 which have to be explained as consequences of reasons 
 of a general character. We can only study the 
 phenomena in their unique individuality by describing 
 their characteristics in the language of universals, 
 and this means that we must seek for relations that 
 are not individual merely but general. Adequate 
 concepts are therefore essential. We have to try 
 hypothesis after hypothesis, based on such concepts, 
 by the test of their fitting the individual facts which 
 have to be explained. But if, as I have sought to 
 show in The Reign of Relativity, knowledge has 
 many standpoints from which the object which is 
 relative to it is always moulded, then the conceptions 
 chosen as the bases of hypothesis must be such as are 
 appropriate to the particular standpoint from which 
 we are observing. The entirety of knowledge seems 
 to consist in a plurality of general standpoints which 
 belong to different orders in thought. These orders 
 must not be confounded. Nor can the categories 
 appropriate only to one order be employed when we 
 are dealing with problems which belong to another. 
 It is failure to remember this which has led to the 
 contradictions that arise when mind is treated as a
 
 174 MATHEMATICAL PHYSICS 
 
 thing and knowledge as its property. The same sort 
 of contradiction arises when, by the employment of 
 conceptions which do not fit the facts, we try to 
 describe what is living as a mechanism. The essential 
 feature in mechanism is externality to each other 
 in space and time of the components. Even in 
 physics infinitesimally conceived this is strictly true. 
 Cause and effect and change in the form of substance 
 resulting from their action are the relevant categories. 
 They are not the less the categories of the relevant 
 standpoint when we succeed in exhibiting matter 
 as simply a form of energy. What is characteristic 
 in the general relationship is that, in ultimate 
 analysis, what we call the cause when completely 
 described is indistinguishable spatially and tempo- 
 rarily from its effect. Yet our standpoint makes us 
 treat them as separable entities in the field of action, 
 even when we look on that field as really four-dimen- 
 sional. 
 
 Before concluding these observations on the doc- 
 trine of relativity in our measurement of space and 
 time it seems right to refer to another recent develop- 
 ment of that doctrine. In chapter v of The Reign 
 of Relativity I drew attention to the philosophical 
 significance of the tensor method. The tensor method 
 is capable of extension in a variety of ways. Its 
 object is the elimination of the irrelevant by bringing 
 the object in a highly abstract fashion under a very 
 general yet exclusive concept. For instance, we can 
 partition space in many different ways, by employing 
 co-ordinates which may be rectangular or polar or 
 oblique or straight or curved. The space-systems so 
 fashioned will consequently vary, and so will measure- 
 ments and mesh-systems based on the co-ordinates.
 
 INTRINSIC CHARACTERISTICS 175 
 
 But there are mathematical formulas which are 
 applicable for description of the character of an in- 
 definitely small interval in space, although the co- 
 ordinates and the measurements and mesh-systems 
 employed differ in different sorts of space. Such 
 formulas teach us the character of space independent 
 of shape and measurement in it. There are character- 
 istics of space ascertained by this sort of abstraction 
 which enable us to discriminate between intrinsic 
 characteristics of space constant under varying con- 
 ditions, which are antecedent in logic to shape and 
 measurement, but which must be ascertained if we 
 wish to ascertain completely the nature of the space 
 we are dealing with. The same thing, mutatis 
 mutandis, is true of time. Shape and measurement 
 in both space and time depend on the perceptions of 
 the observer and his situation and conditions. But 
 the general character of his space and time may be 
 of a kind that is invariant, while the results of his 
 observation will have different meanings according 
 to the particular space-system in which the observa- 
 tion takes place. There was formerly failure to take 
 account of this. That was why, when the eclipse of 
 the sun took place in 1919, the rays passing from the 
 distant stars were found to be deflected differently 
 from what the ordinary physicist had predicted. 
 He had not allowed for variation in the system in 
 which the phenomenon would have to be observed. 
 The law of gravitation, which applies to light on the 
 principle of relativity, as much as it applies to what 
 is popularly called matter, is indeed for Einstein a 
 law which in its general form holds whatever the 
 special position of the observer may be. It defines 
 the geodesic line of a particle, regarded as if attracted
 
 176 MATHEMATICAL PHYSICS 
 
 by gravitation to another, as describable in terms of 
 the character of the four-dimensional world, the 
 space-time continuum. The description is given with 
 the help of a tensor equation which expresses the 
 relation of an event-particle to an indefinitely close 
 event-particle. The equation is based on the charac- 
 teristic functions of the co-ordinates of one of the 
 event-particles, and assumes continuity or invariance 
 in the fundamental quality of the space-time, treated 
 as being what physicists call ' absolute/ 
 
 But here a doubt has come in. The attribution of 
 continuity or invariance in the underlying quality of 
 the space-time with which the physicist is dealing 
 is the outcome of his differential method, which is 
 concerned with the infinitely near. If all we had 
 to deal with were two infinitesimally close space- 
 time systems, the real character of which was that 
 of limiting notions inseparable in some logical order, 
 it would be natural to assume continuity between the 
 space-time of the point-event we started from and 
 space-time infinitely near it. This may be a legiti- 
 mate assumption in answering questions arising out 
 of Einstein's theory of gravitation. But can we 
 properly assume invariance of character when we 
 have to compare the intervals in two sets of such 
 points if the sets . are at a finite or observable 
 distance from each other ? Can we assume that 
 if we transport whatever is the equivalent of an 
 infinitesimal rod or clock for measuring coincidences 
 from one position to another at an actual distance 
 from it, the measurements we obtain will be based 
 on the same fundamental character for both parts 
 in space ? In the first instance, we know that they 
 cannot, because the shapes and measurements must
 
 WEYL'S DOUBTS 177 
 
 be dependent on the observer and how he is related 
 to the object. But can we in this case eliminate 
 these variables as physicists have become able to 
 do in the case of gravitational fields, by estimating 
 fundamental qualities which are invariant for all 
 gravitational systems ? For the new problem of 
 comparing intervals distant from each other we cannot 
 apply, in the same fashion at all events, the limiting 
 notion of the infinitely near. It may prove necessary 
 to bridge over the distance between the intervals to 
 be compared by determining in a complete chain each 
 of the intermediate intervals separately and ascer- 
 taining a definite unit of interval at every intermediate 
 point in the continuum. For only if we can do this 
 shall we be brought back to the geometry of the 
 infinitely near and that continuity in fundamental 
 character which is the foundation of the tensor system. 
 The intermediate intervals may vary and yet preserve 
 continuity in their variations if only their relation 
 of position as regards each other is in each in- 
 stance a continuous one. If that be so a further 
 calculation will be possible, in which the particular 
 character of each successive interval, what is some- 
 times called its ' gauge/ is made amenable to tensor 
 treatment. Now the problem is by no means a 
 merely speculative one, as to whether there is latent 
 an untested feature in Einstein's method of estimating 
 the underlying character of space and time. It is a 
 practical problem. For the characteristics of the 
 electro-magnetic field apparently render it necessary 
 to consider the question definitely. Weyl, in his 
 book, Raum, Zeit, Materie, already referred to, has 
 been a pioneer in this region. He discusses it at 
 pp. 257-8 of the recently published Fourth Edition
 
 178 MATHEMATICAL PHYSICS 
 
 (cf. the Eng. Trans, at p. 282). Starting from the 
 proposition that in nature we know no really funda- 
 mental expressions of force excepting those of gravi- 
 tation and of electrical energy, he says that the 
 physical science of our time renders it plausible 
 that all the other expressions of force can be built 
 up indirectly out of the intermediate values of these 
 two. The result will then be that the world is a 
 (3 -f- 1) dimension metrical manifold, and that all 
 the phenomena of the physical field are the objective 
 expressions of the metrical qualities or structure of 
 that world. He is willing to use, as synonymous with 
 the word ' metric/ the phrase ' condition of the sether ' 
 in order to emphasise the objective character of the 
 metric ; but no one must build up a false picture from 
 the employment of this phrase. The terminology 
 employed just affirms the ground-principle of infini- 
 tesimal geometry, that the field of direction, and along 
 with it gravitation, vary with what may be called in 
 guarded language the condition of the SBther. The 
 antithesis between ' physical condition ' and ' gravi- 
 tation ' is sought to be transcended in the new con- 
 ception, and a completely unified standpoint is 
 attempted. Variation of relativity in magnitude in 
 co-ordinate systems must be added to that as regards 
 motion of Einstein. What we call matter is to be 
 exhibited as mere metrical structure. Descartes' 
 dream of a purely geometrical physics is to be 
 realised in a fashion of which Descartes himself 
 never dreamt. 
 
 " Newtonian mechanics," says Weyl, " and also the 
 special theory of relativity, assumed that uniform 
 translation is just a specific condition of motion in the 
 intersecting points of axes of vectors, and that the
 
 THE RELATIVITY OF MAGNITUDE 179 
 
 position of the axes at one moment determines their 
 position at every other moment. But this is irrecon- 
 cilable with the plainly appearing principle of the 
 relativity of motion. Yet, without coming into gross 
 conflict with facts, we can satisfy this principle, 
 only, however, if we hold fast to the concept of the 
 infinitesimal displacement of a vector set of axes 
 as if a parallel one. But we must regard the affine 
 connection which the displacement defines as something 
 physically actual, standing in dependence on the con- 
 dition of matter because of a law of nature obtaining 
 in it (the field of direction). The property established 
 empirically in the case of gravitation, the equality 
 of inertial and heavy mass, shows finally that in the 
 field of direction gravitation is contained as well as 
 inertia. It was thus that the general theory of rela- 
 tivity obtained a specifically physical meaning in 
 addition to its original meaning in the geometry of the 
 world. On just as good evidence as the relativity 
 of motion is based the principle of the relativity of 
 magnitude. We must have the courage to hold firmly 
 to this principle, according to which the magnitude 
 of a body at one moment does not define its magnitude 
 at another moment, and this notwithstanding the 
 existence of rigid bodies. But no one is able to do 
 this without coming into gross conflict with funda- 
 mental facts, if he is not at the same time prepared to 
 hold firmly to the concept of infinitesimal congruent 
 extension; that is to say, we must ascribe to the 
 world, in addition to its determinations of measure- 
 ment, a metrical connection in addition. We must, 
 however, see in this no geometrical property, which 
 belongs to the world only as a phenomenal form, but 
 an actual state of the field of physical reality." 
 13
 
 180 MATHEMATICAL PHYSICS 
 
 It is for this reason, he suggests, that we are driven 
 by the facts of the spreading character of action and 
 of the rigidity of bodies to base the affine connection 
 on what lies at a deeper level, a fundamental metrical 
 property of the world. And we are brought into sight 
 of the identification of certain co-efficients with elec- 
 tro-magnetic potentials, just as we have identified 
 certain others with the potentials of the gravitational 
 field. 
 
 I have cited Weyl with no intention of being so rash 
 as to indulge in speculation as to whether he is right 
 or wrong. I wished simply to show the extent to 
 which mathematicians are trying to interpret physical 
 phenomena in terms of universals. Weyl goes beyond 
 Einstein, while accepting the general theory of relati- 
 vity. Einstein, he says, assumes that in the trans- 
 ference of distances by congruent transference we are 
 dealing with what is integrable and that intervals at 
 finite distances can be compared on the footing that 
 their magnitudes can be expressed in terms of each 
 other. But this, for Weyl, is just as much in conflict 
 with the principle of the relativity of magnitude as is the 
 point of view of Galileo and Newton with that of the 
 relativity of motion. A wider principle is, according 
 to Weyl, required, if the phenomena of the electro- 
 magnetic field are to be accounted for and full har- 
 mony with Maxwell's conceptions is to be attained. 
 And the wider principle, if it is introduced, means the 
 modification of Einstein's laws and the recognition 
 of a newly conceived world-curvature determining 
 the very foundation of metric relations. A further 
 form of tensor expression must follow. 
 
 One is reminded, in reading Weyl's description of 
 these new possibilities, of the famous conclusion of
 
 DOUBTS AS TO WEYL'S EXPLANATION 181 
 
 Riemann's essay on the hypotheses which lie at the 
 foundations of geometry in which he says that if the 
 actual reality underlying space is not a discrete mani- 
 fold, the ground of the relations in its measurement 
 must be sought in binding forces for the demonstra- 
 tion of which we must look to a science other than that 
 of geometry physics. These words, says Weyl, in a 
 passage which is interesting to us over here, fell on 
 the ears that were deaf to them of Riemann's con- 
 temporaries, deaf men all excepting one. And that 
 one, he says, was W. K. Clifford. 
 
 But a doubt arises in the minds of those who are 
 concerned with philosophy, which always has to look 
 at things as a whole. The school of Einstein has told 
 us that it is in Einstein's explanation of the gravita- 
 tional field, as a set of forms produced by the move- 
 ment of the observer in varying courses relatively to 
 the bodies observed, that the origin and meaning of 
 that field are to be found. But it does not seem so 
 apparent that the variations in the characters of 
 magnitudes to which Weyl has directed attention can 
 be explained by any such principle of mere general 
 relativity to situation in observation. Weyl appears 
 to say that the explanation of variation in magnitude 
 or gauge must be sought in some objective quality of 
 reality independent of the observer, for otherwise the 
 electro-magnetic laws cannot be accounted for. But 
 if so the phenomena of the electro-magnetic field 
 contain features which relativity to the observer 
 alone, such as Einstein holds to be sufficient, appar- 
 ently cannot account for. How are the two principles 
 of variation to be combined into one ? They are not 
 the same, and they belong to different aspects of ex- 
 perience. What is the true character of the real accord-
 
 182 MATHEMATICAL PHYSICS 
 
 ing to Weyl ? Relativity to knowledge appears to be 
 insufficient to explain his new qualities of invariance. 
 For these seem to belong absolutely to reality itself 
 and not to depend on our knowledge of it, as in the 
 case of the Einstein principle of gravitation. This 
 is a point which we who are mere philosophers 
 would like the mathematical physicists to clear up 
 for us. I shall presently call attention to the way in 
 which this point has been discussed. It is suggested 
 by more than one recent writer that not only Weyl 
 but Riemann himself have created difficulties by 
 tacitly assuming that concepts do not enter into 
 the reality which is foundational of the phenomenal 
 world of relativity itself, and have been looking for 
 self-subsisting entities, disguised by being called 
 ' invariants/ instead of for laws. 
 
 The attention of the few German mathematicians 
 who are also trained in logic and metaphysics is being 
 directed to the subject. Cassirer has approached the 
 general problem in his recently published book, Zur 
 Einsteinschen Relativitdts-theorie. His purpose is to 
 bring the work of philosophy and mathematical 
 physics into harmony. The results of the latter can- 
 not claim finality. For they develop, he says, no 
 more than the significance which space and time 
 possess in our empirical and physical measurements. 
 That significance the physicist may progressively 
 vary. It is for the theory of knowledge to interpret, 
 from a fuller point of view but equally progressively, 
 the significance from time to time thus brought to 
 light, and this interpretation may reveal a good deal 
 of that undetected ' anthropomorphism ' against 
 which Goethe long ago warned men of science. ' The 
 symbols " (at p. 127 of the book) " which are made
 
 CASSIRER'S VIEW 183 
 
 foundations! by the mathematician and the physicist 
 in their outlook on externality, and by the psycholo- 
 gist in his view of the inner world, must be inter- 
 preted as being merely symbols. So long as this 
 interpretation is not clearly made the true philoso- 
 phical insight, that into the character of the entirety 
 as such, is not attained, but a merely partial ex- 
 perience is hypostatised into that of a whole. From 
 the standpoint of mathematical physics the entire 
 content of immediate qualities, not merely differences 
 in sense perception, but the qualities of our conscious- 
 ness of space and time, threatens to tumble into 
 fragments. For the metaphysical psychologist, on 
 the other hand, all that is actual is to be sought in 
 this immediacy, while all mediate knowledge through 
 concepts has the value only of arbitrary convention, 
 adopted to serve practical purposes/' 
 
 Cassirer, who is an accomplished mathematician, 
 thinks that there is a real gap between the views of 
 space and time held by Kant and those of Einstein. 
 For the doctrine of the latter these are always em- 
 pirical and not pure transcendental forms. Even if, 
 with Einstein, we grasp characters in them which are 
 invariant in the face of all possible transformations, 
 these characters are independent of the results of con- 
 crete measurements and particular conditions. They 
 must be, therefore, conceptual and not intuitive. 
 While the object in perception is not for the Critical 
 Philosophy any absolute picture with which we can 
 compare our ideas, but a ' conception in relation to 
 which our ideas have synthetic unity/ for Einstein 
 the real object is no picture at all, but a physical 
 interpretation of one, assuming the form of equa- 
 tions the systems of which are covariant through all
 
 184 MATHEMATICAL PHYSICS 
 
 arbitrary transformations. The relativity which thus 
 arises is itself of a purely logical and mathematical 
 nature. The object of physics is indeed a phenomenal 
 object, but it no longer depends on any subjective 
 contribution. Kant's standpoint is, therefore, insuffi- 
 cient for the doctrine of relativity and does not 
 harmonise with it. 
 
 Cassirer goes to the real root of the question of the 
 objective significance of the conceptions used by 
 mathematicians when they speak about the character 
 of experience in space and time as rendered in shape 
 and measurement. Such experience the mathema- 
 tician interprets exclusively under his own system 
 of abstractions, which brings out its real character 
 from his own standpoint. 1 Mathematical physics 
 knows no limit in this recognition. It must follow 
 its path unbrokenly ; it dare not halt in its task of 
 finding the general conceptions that for itself are true 
 in the object which it has before it. Its duty is to 
 render what can be counted into pure number, quality 
 into quantity, particular form into general scheme of 
 order, and by means of this process to comprehend. 
 Philosophy would strive in vain were it to seek to 
 arrest the process at any particular point in it. Its 
 task is rather to indicate that, while it recognises fully 
 the significance of the mathematico-physical concep- 
 tion of the object, it recognises it as a logically 
 limited conception, limited by the standpoint em- 
 ployed. For as soon as we pass from the domain of 
 physics we alter not merely the means but the aim 
 of knowledge, and give it a new character. Logical 
 structure and aesthetic consciousness may be quite 
 different in nature and yet not in conflict. There is 
 
 1 fur Einsteiruschen Relativitdts-thcorie, p. 121.
 
 STANDPOINTS AND ENTITIES 185 
 
 a divergence not of entities but of standpoints. There 
 has been a change in the sort of meaning. There is 
 in each sort more than mere passive awareness dis- 
 closes. Concepts of different kinds go to the con- 
 stitution of reality of different kinds, and the orders 
 in reflection must be recognised as distinct and must 
 not be confused. 
 
 This view of the character of reality is at least akin 
 to that discussed in The Reign of Relativity, and in 
 the earlier portion of the present volume. The inter- 
 pretation of the concreteness of individuality, and 
 of the part played in its constitution by universals, 
 is not materially different. Space is an example. 
 Geometrical space depends on the assumption of the 
 equivalence of all positions and directions, and their 
 distinction from each other. While metrical Eucli- 
 dean space is brought under the postulate of isotropy 
 and homogeneity, the space of awareness through 
 touch and sight is anisotropic and non-homogeneous. 
 So it is with time also, and with the difference between 
 what we mean when we speak of the continuity of 
 awareness and that which we define by the con- 
 structive methods of mathematics in relation to 
 number. Continuity in logic and in philosophy is 
 thus something different from what is meant when 
 the expression is used in the theory of number. A 
 principle such as that of levels in knowledge and 
 reality alike seems to present itself as the solution of 
 such difficulties for Cassirer. He insists that the true 
 objects of modern science are not entities, but laws. 
 The confusion which is apt to arise comes from as- 
 sumptions about the character of what is empirically 
 * given/ Our particular sensations are not in them- 
 selves the known and intelligible elements in know-
 
 186 MATHEMATICAL PHYSICS 
 
 ledge. There are no absolute or self-contained sen- 
 sations. Knowledge is no mere framing of 'pictures/ 
 The true object is conceptual but none the less reality. 
 The relativity theory ought not to seek to present it in 
 mere pictorial form, but rather as a physical inter- 
 pretation in the form of equations and systems of 
 equations in which the altering substitutions are 
 covariant. " The relativity which is thus brought 
 about is of a purely logical and mathematical 
 character. By means of it the object in physics is 
 indeed determined as a phenomenal object, but to 
 its phenomenal nature subjective arbitrariness and 
 subjective contingency no longer pertain. For the 
 ideality of the forms of knowledge and of their con- 
 ditions on which physics as a science depends both 
 guarantees and assigns a ground for the empirical 
 reality of all that is meant when we speak of facts and 
 their objective validity/' * For example, the inter- 
 position between the ideas about empty space and 
 about matter of the conception of the ' Field ' since 
 the days of Faraday and his ' Lines of Force ' has 
 taught us not to base the conception of matter on 
 that of its field, but to regard matter as merely 
 position in such a field. So also in electro-dynamics. 
 So in the analyses of the intrinsic relations of measure- 
 ment within the four-dimensional space-time world, 
 the riddle of gravitation and of force acting at a 
 distance is resolved and we are satisfied with the 
 ten components of the gravitational potentials of the 
 Einstein doctrine. In the form he has given them 
 they serve equally what is required in definition of the 
 metrical properties of four-dimensional space, and, on 
 the other hand, for the expression of the properties 
 
 1 Zur Einsleinschen'Relativitdte'theorie, p. 57.
 
 CASSIRER AND THE MATHEMATICIANS 187 
 
 of the gravitational field. We obtain a unification 
 of definite relations of function which vary in 
 implication with the relative inertial systems in 
 which we express them. Dynamics tends to become 
 more and more a purely metrical system, but a 
 system in which the conception of metric has ob- 
 tained a generalisation and extension of a new kind, 
 inasmuch as the metrical relations of Euclidean 
 geometry become only a special case in a system 
 which is far wider in scope. 
 
 Throughout his book Cassirer has gentle words of 
 caution for mathematicians who talk as though their 
 symbolic descriptions of the encounters of world-points 
 were actual pictorial descriptions. He brings out 
 the magnitude of the services which will be required 
 from those trained in mathematical logic before we 
 cease to suffer from obscurity and confusion arising 
 from the unrestrained use of merely figurative lan- 
 guage. " When, for example/' he says at p. 85, " in 
 the mathematical foundation of the relativity theory 
 the formula is given for the ' interval ' between two 
 infinitely neighbouring points, x 1} z 2 , x & x t> an d 
 x l + dxit z a H~ dx 2 , X 3 + ^3' x * + ^4> this must 
 certainly not be thought of in the ordinary way as a 
 rigid Euclidean line, inasmuch as by introducing time 
 as a fourth dimension we are dealing, not with a 
 magnitude of space, but with one of motion. Yet the 
 foundational form of co-existence and succession, 
 and of their mutual relation and union, is unmistak- 
 ably present in this expression of the general line 
 element. Not, however, because the theory here, as 
 people at one time thought, presupposes space and 
 time as already given from the imputation of such 
 circular reasoning it is absolved but in the sense
 
 188 MATHEMATICAL PHYSICS 
 
 that it cannot dispense with the spatial and temporal 
 form and function in general." The history of physics, 
 he says, is the history not of the discovery of a simple 
 series of facts, but of the discovery of ever fresh 
 special methods of thought. Modern science knows 
 that a definite spatial and temporal order of pheno- 
 mena only exists for knowledge in so far as knowledge 
 is progressively bringing such an order into being, 
 and that the only method of bringing it into being 
 is through the work of science in thinking out laws. 
 But the task, from such a point of view, remains a 
 permanent one for reflection, and becomes for it 
 sharper and more severe the more reflection makes us 
 conscious that a final solution is never possible. Just 
 because the unity of space and time seems ever to flee 
 from empirical apprehension and empirical measure- 
 ments, in reflection we realise that we must always 
 persist in seeking that unity and must make use for the 
 purpose of ever sharper and more novel instruments. 
 It is the merit of the relativity theory that it has 
 adopted no new way of doing this, but not the less, 
 by employing the fundamental principle of the co- 
 variance of the universal laws of nature throughout all 
 arbitrary substitutions, has established a principle by 
 means of which reflection can direct the idea of rela- 
 tivity which it has evolved from itself. 
 
 Thus for Cassirer the renunciation of this idea that 
 the world of so-called direct perception is of a character 
 that is simple and obvious is at the same time the 
 guarantee that it includes a more important self- 
 containedness both for thought and in its own system. 
 Space, to take an example, has its real ground, not 
 in something existing apart from and independent of 
 it, but as the ideal basis which discloses itself in the
 
 CASSIRER AND RIEMANN 189 
 
 progress and building up of a knowledge of what is 
 real. He criticises Riemann's famous question as 
 to the ' binding forces ' which may be required for 
 the explanation of its laws. Rather, he says, we 
 ought to give up the idea of space as something 
 existing in itself, to be explained like other realities 
 that are the outcome of binding forces, and to ask 
 whether that a priori function, that general ideal 
 relation, which we name as space, does not contain 
 in itself various possible forms, and among them 
 those whose part it is to yield an exact and exhaustive 
 presentation of definite physical relations and definite 
 fields of energy. The development, he adds, of the 
 general theory of relativity has answered this question 
 in the affirmative ; it has shown that which for Rie- 
 mann was a geometrical hypothesis, a mere possibility 
 for reflection, to be an actual mode of our knowledge 
 of the actual. The Newtonian dynamics have 
 become kinematics and the kinematics have been 
 resolved into geometry. Only, by taking a step 
 further in the region of empirical knowledge, we have 
 widened the content of geometry and have substituted 
 one more complex for the simple Euclidean type of 
 geometrical axioms. We have thereby acquired 
 fresh means for bringing to light the relations in the 
 real and the structure of what is empirical but mani- 
 fold. We have to look on the pure space-time 
 manifold as the logical prius, not as if it were in any 
 sense heralded and given as an entity outside and 
 antecedent to physical experience, but as forming the 
 principle and fundamental condition of all empirical 
 knowledge of physical relations. For example, when 
 the notion of the special three-dimensional manifold 
 that has a constant measure of curvature, o, is
 
 190 MATHEMATICAL PHYSICS 
 
 enlarged into the notion of a system of manifolds with 
 different constant or variable curvatures, we are 
 provided with new conceptual symbols which 
 express not things but the possible relations which 
 result from their laws. Minkowski's ' postulate of 
 an absolute world ' resolves itself in the end into the 
 postulate of an absolute method. " The general 
 relativity of all positions, times, and measuring in- 
 struments must be the final word of physics, because 
 the reduction to relativity, the resolution of the object 
 of nature into pure relations of measurement, forms 
 the kernel of procedure in physics, inasmuch as it is 
 the fundamental function of physical knowledge." 
 But Cassirer guards himself at this point. It is true 
 that the mathematical method can recognise no 
 barrier in the path of its own procedure. It can 
 convert the value of time into an imaginary quantity, 
 as Minkowski showed, whereby all actuality and all the 
 qualitative difference which time as a form of inner 
 sense seems to possess appear to become annihilated 
 or inverted. Philosophy is quite aware of this. Its 
 duty is not to contradict the claim of what is the 
 method only of a standpoint, but to point out the 
 limitations of the sphere of the knowledge to be got 
 from it. The limitation of this knowledge is inherent 
 in that of its standpoint and its method. There are 
 other standpoints and methods which yield the actual 
 in a form which mathematical reasoning does not 
 touch. Differences in meaning fashion different kinds 
 of reality. Speculations about the experiences which 
 those would have who made journeys with the 
 velocity of light require careful recognition of the 
 limits of the domain within which the methods of 
 mathematical physics are confined by its standpoint.
 
 HANS REICHENBACH 191 
 
 In another recently published book, Relativitdts- 
 theorie und Erkenntniss a priori, an equally well- 
 furnished writer, Hans Reichenbach, goes further. It 
 is for him the mistake of Kant to have made pro- 
 nouncements about the subjective elements in physics 
 which had not been brought to the test of experience. 
 It is only now, when experience has established in 
 physics the relativity of co-ordinates, that we can 
 treat the ideality of space and time as demonstrated. 
 If Weyl is right a new conceptual element has been 
 discovered in metrics, a form of description analogous 
 to that arising out of the situation in which we find 
 ourselves with co-ordinates. The concept of the 
 object has changed, and with it the estimate of 
 the part knowledge has taken in the constitution of 
 our perceptions. This may alter progressively, and 
 affords the ground on which we must conclude that 
 the formulation of the nature of direct knowledge 
 cannot be given in such unrestricted pronouncements 
 as that space is merely ideal, but only in the enuncia- 
 tion of mathematical principles. The procedure of 
 eliminating by means of formulas of transformation 
 the subjective aspect in description out of objective 
 significance therefore takes the place of the Kantian 
 analysis of the part played by reason. The Kantian 
 table of categories becomes primitive in comparison 
 with the modern theory of in variance. 
 
 In Reichenbach's view, since all the results of 
 direct experience are only approximations, it is quite 
 admissible to regard them, collectively and as the 
 outcome of induction, as exhibiting a more general 
 principle. It is both logically and technically pos- 
 sible to ascertain inductively new principles of order 
 which exhibit a continuous enlargement of those
 
 192 MATHEMATICAL PHYSICS 
 
 hitherto employed. We may call such generalisation 
 continuous inasmuch as the new principle passes for 
 approximately realised cases into the old one. Kant's 
 mistake was to analyse perception as if he could get 
 at its nature by analysing reason. He thus really 
 sought after axioms instead of categories. No doubt 
 perception is determined by reason, but the character 
 of this influence of reason is expressed only in per- 
 ception. Reason is no system of final principles, but 
 a faculty which becomes fruitful only in its applica- 
 tion to concrete cases. Kant's standpoint was limited 
 by its conventionality. The object for reason does 
 not stand still. It is the merit of the relativity 
 principle that it has transferred the question of the 
 validity of geometry from pure mathematics to physi- 
 cal experience. Reichenbach takes exception to 
 WeyFs criticism of Einstein referred to earlier. It 
 is not necessary, he says, to give up altogether the 
 notion of an unvarying length for an indefinitely 
 small measuring-rod. It may be that Weyl's view of 
 the more elastic and general character of such a rod is 
 a possible one, but whether it is so depends not on 
 considerations of infinitesimal geometry but on what 
 experience discloses. Physical results do not depend 
 on geometrical necessity. Rather do our notions of 
 our object in science, of reality and of its characters, 
 depend on gradual and progressive precision in inter- 
 pretation. The part played by reason is, not to offer 
 unalterable elements in an ordered system, but to 
 make provision for apparently arbitrary elements dis- 
 closing themselves within its system. The concep- 
 tion of the object in knowledge can thus be alterable 
 and progressive, in accordance with the development 
 of principles in an ordered system. That the real in
 
 HIS CRITICISM OF WEYL 13 
 
 physical science can be described in terms of the 
 metrical relations of four co-ordinates is as certain as 
 the validity of physical science itself taken as a 
 whole. It is only the special form assumed that is the 
 problem of empirical research. Still, there may come 
 a time when we shall have to enlarge our principles 
 and our conception of the physical object, as the 
 result of further experiment ; only such enlargement 
 will proceed on a basis of continuity. A priori may 
 mean antecedent to direct knowledge, but not for all 
 time or independently of experience. We fall, more- 
 over, into a mistake when we suppose that our metric 
 gives us geometrical images, instead of those that 
 indicate a merely physical condition. What ties us 
 so tight to the employment of Euclidean geometry is 
 that we think we come by it to pictures of actual 
 things. But as soon as we see that knowledge is 
 here something quite different from the display of 
 resembling shapes, and that the real metrical relation 
 has a different meaning, we are prepared to give up 
 the instinctive tendency to look on Euclidean geo- 
 metry as a necessary form of reality. It is this 
 confusion between the two kinds of image that makes 
 it difficult for the untrained mind to accept Riemann's 
 geometry. It is no assertion of the doctrine of rela- 
 tivity that what was formerly the Euclidean picture is 
 now a picture of something curved. What is really 
 asserted is that there is no such subjectivity, and that 
 what is expressed in metrical relations is something 
 other than a repetition in images of objects. We can 
 indeed form geometrical pictures, but they may not 
 suffice for the characterisation of empirical facts. It 
 is not that such pictures are in themselves false, but 
 that they may not be applicable to the actual facts.
 
 194 MATHEMATICAL PHYSICS 
 
 The task of the theory of knowledge is to explain the 
 nature of knowledge by analysing the content of 
 experience, without reference to artificial images and 
 analogies. 
 
 What is most interesting in the criticism of Kant 
 by Cassirer and Reichenbach is that it is directed 
 against the attempt of the Critical Philosophy to 
 break up the unity of the object in experience, and 
 thereby knowledge itself. The conclusions of these 
 two writers, if they do not explicitly assert the con- 
 ceptual character of the actual which Aristotle and 
 Plotinus contended for long ago, and which the ob- 
 jective idealists of the last century finally came to, are 
 much more in harmony with it than is that teaching 
 of Kant which they criticise. 
 
 It may well be that, notwithstanding the claims put 
 forward on his behalf by enthusiastic disciples, but 
 never, so far as I know, by himself, Einstein has not 
 come in sight of the ' binding laws ' which Riemann 
 thought might be discovered as lying at the founda- 
 tion of the spatial relations manifested in experience, 
 and that it would be superfluous for him, as a mathe- 
 matical physicist, to search for them. It may equally 
 well be that such an investigation as Einstein has so 
 far made into the differences between what is only 
 relative in space. and its invariant characteristics is 
 no final one. Experience may compel an enlarge- 
 ment of Einstein's conceptions, taking account of 
 more than the effect of the presence of a gravitational 
 field, and including characteristics lying beyond 
 any subjectivity of the kind to which Weyl takes 
 exception. The interpretation of the actual may have 
 to be enlarged, and perhaps in the end again and 
 again enlarged ; for our knowledge, conditioned as
 
 ABSENCE OF FINALITY 195 
 
 it is, never can attain finality in the interpretation of 
 what must seem to confront us as if independent. 
 But the distinctions, here as elsewhere, all fall within 
 knowledge and are its creatures. That is why our 
 human knowledge is always in the nature of progres- 
 sive interpretation of the given, and that is why the 
 general theory of relativity may have to be extended 
 so as to provide for the admission of suggested novel 
 constants. But this will not have been, if it turns out 
 so, merely because of some new self-contained fact 
 which confronts us. It will happen because there 
 is no such finality in the concepts or systems of univer- 
 sals we employ as prevents us from developing them 
 without breach of continuity into ideas which make 
 practicable in the interpretation of what is actual a 
 larger outlook and a deeper insight. 
 
 14
 
 CHAPTER VII 
 
 BIOLOGY 
 
 THIRTY-EIGHT years ago, I wrote, in conjunction with 
 my brother, now Professor J. S. Haldane, an " Essay 
 on the Relation of Philosophy to Science." ' We were 
 both interested at the time in the theory of know- 
 ledge, to which that Essay was devoted. Since those 
 days he has continued work at problems in physiology, 
 while I have been occupied with other subjects. 
 Nevertheless I have not ceased to follow his in- 
 vestigations with keen interest. Some of their early 
 forms are described in the Essay to which I have 
 alluded. Other inquiries of a still more searching 
 character have been developed by him in the course 
 of the years which have elapsed between 1883 and 
 to-day. The results have been recorded in a succes- 
 sion of books and papers on which I have drawn freely 
 in what follows. His Mechanism, Life, and Person- 
 ality was first published in 1913. A new edition 
 appeared in 1921. Organism and Environment was 
 published in 1917, and The New Physiology in 1919. 
 A further volume by him on Respiration and the 
 Physiology of Breathing is passing through the press 
 while I write. 
 
 As I have said he is a physiologist, immersed in 
 laboratory investigation, and I am not. But a good 
 deal of reading and discussion has tended to strengthen 
 
 1 Published in a volume called Essays in Philosophical Criticism, 
 by various authors. (Longmans, 1883,) 
 
 196
 
 THE INTERPRETATION OF LIFE 197 
 
 the view, first formed more than thirty-eight years 
 ago, of theory and practice alike as disclosing that 
 life can only be interpreted and rendered in terms of 
 life. The understanding of this fact, if it be one, 
 is vital for philosophy itself. Approaching the con- 
 ceptions of biology from different standpoints and with 
 minds differently trained, my brother and I, in the 
 old Essay to which I have referred, had come to the 
 conclusion that in observing and recording the be- 
 haviour of living organisms conceptions are freely used 
 which belong to an order in knowledge different 
 in character from that to which the conceptions of 
 mechanical science belong. " It is not the case/' 
 we wrote in those days, " that the fittest survive 
 after the fashion in which the roundest shot only 
 reach the bottom of the sloping board used by shot- 
 makers to eliminate those that are imperfect. De- 
 velopment is in all cases the realisation of what was 
 not there at the beginning of the process. Yet the 
 resulting difference is not conceived as impressed 
 from without, but as freely produced from within 
 itself by that which develops. A little consideration 
 shows that such branches of biological science and 
 morphology become possible only through the con- 
 ception of development/' Further on, referring to 
 morphological identity, we said : "If there were 
 no point of view higher than that of mechanism, 
 such conceptions as those which have now been 
 briefly examined would be meaningless. But it is 
 just because there is such a point of view, possibly 
 by reason of the fact that the phenomena which it 
 embraces are constituted through higher categories 
 than those of spatial and temporal arrangement, that 
 as science advances men are driven back to the use
 
 198 BIOLOGY 
 
 of these higher conceptions in spite of their attempts 
 to dispense with them. For such attempts lose their 
 meaning as soon as it is recognised that to abandon 
 them in no sense implies the admission of an exception 
 to the uniformity of nature. The man who insists on 
 regarding organisation and development as mechanical 
 and the man who insists on the existence of supra- 
 mechanical substances and causes, are alike dogma- 
 tists, whose principles are really untrue to those 
 facts of common sense with which science and philo- 
 sophy alike must start. If, then, a critical examina- 
 tion of categories can reconcile the truth which lies 
 at the bottom of each point of view, and, without 
 for a moment seeking to intrude into the domain 
 of observation and experiment, yet throw light on 
 conceptions which are necessarily used in obtaining 
 and arranging the results so reached, surely such a 
 criticism becomes a matter of the last importance/' 
 And a little later : " It is no doubt quite correct 
 to lay stress upon the mathematico-physical relations 
 of matter, and to reason from them in an abstract refer- 
 ence. But even such appropriate abstractions, when 
 hypostatised in thought into real existences, share 
 the general fate of all other abstractions, and give 
 rise to contradictory conclusions. We can no more 
 consistently represent to ourselves matter as con- 
 stituted by the reciprocal determination of points of 
 attraction and repulsion in space, than we can con- 
 ceive matter and energy as independent existences. 
 Such abstract conceptions, however great their 
 value as regulative, i.e. for the purpose of advance 
 in knowledge, are not adequate as descriptions of 
 a reality which is essentially concrete and inexhaus- 
 tible in its properties. . . ." " The history of the past
 
 SCIENCE AND PHILOSOPHY 199 
 
 relations of science and philosophy has shown that 
 so long as the spheres of inquiry remain in 
 different hands in the hands of persons who are 
 more or less ignorant of each other's subjects so long 
 will science have cause to reject many of the inferences 
 of philosophy as the intrusion into her domain of 
 something akin to a priori reasoning. But it is no 
 less true that under these conditions the philosopher 
 must have equal cause to complain of the man of 
 science, in that he perpetually raises difficulties 
 insoluble for himself in his own department by the 
 dogmatic application of mistaken categories." 
 
 It is not without interest to compare with this 
 something said in the recent book by Professor 
 Cassirer already quoted. I translate a passage in 
 which he is dealing with what is in appearance a 
 different subject, Newton's principle of inertia. 1 
 ' The difficulty, however, which remains in the 
 structure of classical mechanics for the formulation 
 of the principle of inertia, lies in the circular reasoning 
 out of which there seems to be no way of escape. 
 In order to make intelligible the meaning of the 
 principle we make use of the notion of ' equal times/ 
 But a useful physical measure of equal times we can 
 only obtain, on the other hand, if we assume the law 
 of inertia, in both its content and its validity, to 
 be already there. In point of fact mechanics has 
 sought since Carl Neumann's well-known memoir on 
 the Principles of the Theory of Galileo and Newton, 
 which first set going the modern discussion of the law 
 of inertia to define ' equal times ' as those within 
 which a body left to itself traverses equal distances. 
 Maxwell also, in his account of the Newtonian me- 
 
 1 Page 22.
 
 200 BIOLOGY 
 
 chanics, treats the law of inertia as a pure definition 
 of measurement. Newton's first law he declares in 
 precise language tells us under what conditions 
 there is present no external force (' Matter and 
 Motion '). In the development of mechanics the 
 law of inertia is even more definitely recognised as 
 substantially what it signified for Galileo. It stands 
 good to-day no longer as a direct empirical description 
 of given processes in nature, but as that regulative 
 axiom, that fundamental hypothesis, by means of 
 which the new science of dynamics ascribes a definite 
 form to measurement. Inertia appears no longer as 
 an absolute and inherent property of things and of 
 objects, but as the free determination of a definite 
 measuring rod and symbol of measurement, by means 
 of which alone we can hope to attain to a collective 
 and systematic interpretation of the laws of motion. 
 Herein only lies the root of its reality, of its objective 
 and physical meaning. Thus here also, within the 
 historical development of physics itself, measuring 
 divides itself more and more clearly from what is 
 measured, that with which at first it seemed to 
 coalesce. And so there are dividing themselves 
 more and more clearly the observable data of ex- 
 perience from what must be presupposed and used 
 as the condition of observation and measurement." 
 
 In the preceding chapter I drew attention to the 
 fashion in which concepts and laws enter into physical 
 reality and mould it. The conceptual character of 
 the actual follows from the general principle of the 
 relativity of reality to knowledge, and on this point 
 Cassirer and Eeichenbach, with regard to physical 
 science, appear to present a view in harmony with 
 that given of biological science in the Essay of 1883
 
 THE BUSINESS OF PHILOSOPHY 201 
 
 which I have already quoted. In this chapter I 
 propose to follow the principle into illustrations from 
 experience. But just as my personal knowledge in 
 the case of physics has been mainly derived from the 
 study of books and only to a small extent gained 
 in the laboratory, so in the instance of biology I have 
 drawn mainly and freely on the results worked out 
 and recorded by my brother and by others during 
 long years of practical as well as theoretical in- 
 vestigation. 
 
 The business of philosophy is to inquire into the 
 character of the various standpoints which combine 
 in the constitution of experience, and to ascertain 
 the differences in the aspects of reality which its 
 relativity to these standpoints brings about. The 
 results of metaphysical inquiry under the various 
 systems which make up its history are not, as was 
 pointed out in some detail in The Reign of Relativity, 
 so inconsistent as is popularly believed. The question 
 in each case has been in the main one of emphasis or 
 stress laid. There has been concentration on aspects 
 that have varied with the tendencies of the period. 
 We find the same thing in literature and in branches 
 of knowledge that do not depend on quantitative 
 measurement. Even when this last is prominent 
 modern science, as we saw in the preceding chapter, 
 has progressively given to quantitative measurement a 
 conceptual significance. It is no longer practicable 
 to dissociate intelligently any one branch of knowledge 
 from a place within the entirety of knowledge. For 
 this proposition the Relativity physics of our time 
 affords the most recent evidence. In the case of 
 biology the task of philosophy is therefore analogous 
 to its task in the case of physics. It has to ascertain
 
 202 BIOLOGY 
 
 and scrutinise the conceptions which give meaning 
 and so actuality to its subject-matter, life, and in 
 which life presents itself as a phenomenon. 
 
 Although life is prima facie very unlike the me- 
 chanism considered in physics it is none the less 
 conceptual, in the sense that what Cassirer in the 
 case of physics calls " laws/' or what I have called 
 meanings or interpretations, are what give it objective 
 existence. The determining quality of that existence 
 may be most easily seen by contrasting the laws that 
 obtain in the domain of life with those of physics. 
 In the latter we start with a causal relation of succes- 
 sion, in which the cause is taken as something separate 
 from the effect. As knowledge progresses we reduce 
 the relation to one of succession, as Einstein has done 
 in the case of gravitation, and as has been accom- 
 plished by the reduction of matter and energy to 
 phenomena of position and change in the " field." 
 It is the uniformities or laws that obtain in the field 
 that give objectivity to its contents, and these operate, 
 from the point of view of the physicist who has to treat 
 them abstractly, by way of succession according to 
 principles. 
 
 But when we turn to life we find ourselves con- 
 fronted with phenomena which are of a character 
 quite different. They are what they are only from a 
 standpoint at which conceptions diverse in logical 
 character from those of mathematics and physics 
 appear in them. It is no more mere causation or 
 mere succession of events that we have before us. 
 These we can and do impute to the new phenomena 
 when we regard them abstractly or partially from 
 a special standpoint which is not the obvious one. 
 But if we take in the determining character of what
 
 THE CHARACTER OF LIFE 203 
 
 we observe we notice in it something quite different 
 from the governance ab extra of physical science. 
 Living organisms behave. They behave in fulfilling 
 what need not be and generally are not, so far as 
 observation teaches, conscious purposes. But the 
 details of both their structure and their activities 
 exhibit maintenance of something which we cannot 
 help recognising and which we call the life of the 
 organism. In so far as its life dominates the pheno- 
 mena in connection with an organism these phenomena 
 are determined from within and not from without. 
 The life of an organism has the character of a whole 
 which has no existence save in its parts. But, except- 
 ing as belonging to its proper whole, the part on the 
 other hand does not live. Its structure and activities 
 are totally altered when it is removed from its place 
 and function in that whole. Its end as a subordinate 
 whole is to be an organ of the bodily whole and it is 
 the fulfilment of this end that does not merely give 
 it but is its life. In living the organ behaves in 
 fulfilment of this end, but the end is not antecedent 
 in time to the organ, the behaviour of which it 
 controls, as is a cause to its effect. It is actual only in 
 the behaviour in which it expresses itself. It acts 
 presently and not before or after the event, although 
 its operation may endure through a tract of time and 
 result in a developing course of change. It is a universal 
 which is real through the particulars to which it gives 
 meaning in constituting the individual in which it 
 and these become actual. That individual may 
 itself be determined by what bears some analogy to 
 the field in physics, the species to which the individual 
 belongs. But it is the fulfilment of the end of 
 which life is the expression that characterises and is
 
 204 BIOLOGY 
 
 constitutive of the species, and is in that relation 
 determinative of the individual members, along with 
 their conduct and course of life. Nowhere does the 
 relation of life present itself as one of cause external 
 to effect. In every case we seem to see behaviour 
 in fulfilment of immediately present and inherent 
 ends. Reality is disclosing itself in a fresh aspect, 
 and the concepts to which it owes its meaning are 
 the concepts of a standpoint wholly different from 
 that of the mathematician who deals with order in 
 externality and the physicist who is really con- 
 cerned with the same relation. 
 
 Of course we may say with full truth that in the 
 domain of life our knowledge extends to these other 
 aspects also, and that apart from them the realm of 
 life would be an abstraction. Physics and chemis- 
 try are required by the biologist in his investigation 
 into the phenomena of the living organism. Without 
 their help he could not solve physical problems which 
 have to be solved, connected with quantity of energy 
 taken in and given out, as well as with countless 
 other problems. But the addition of the results got 
 by such methods of knowledge appears to be wholly 
 inadequate to the description of the characteristic 
 phenomena of life. The physical and chemical 
 methods yield valuable abstractions, but they do not 
 solve the problem of the actual for the biologist, any 
 more than they solve that of the artist or even the 
 student of human nature. 
 
 In order to see how this appears so let us look at 
 the characteristics of life. In the interpretation of 
 the living organism we seem to find that the concep- 
 tions which force themselves on us in physics and 
 chemistry, those of the relations of matter and energy
 
 PHYSICS IN THE STUDY OF LIFE 206 
 
 and of chemical structure and its changes, fall short 
 of what is necessary for the expression of the facts. 
 These physical and chemical conceptions are indeed, 
 as we have already seen, not what an easy-going 
 anthropomorphism has taken them to be. They are 
 themselves interpretations which have been sim- 
 plified by the criticism of the school of relativity. But 
 even in a crude form they have been of the utmost 
 value as working hypotheses, which have enabled us 
 up to a certain point, but up to a certain point only, 
 to express and to predict phenomena. They belong 
 to knowledge in one of its many aspects, and their 
 limitations appear to be due to insufficiency in the 
 standpoint from which we bifurcate our world into 
 knowledge and its objects. No doubt, as I have said, 
 they are beginning to be modified. They have been 
 affected by such new ideas as those of the relativity 
 of shape and measurement, the resolution of mass 
 into inertia, the electro-magnetic theory of energy, 
 the discovery of the periodic law and its application 
 in chemistry, the transmutation of chemical elements 
 in connection with radio-activity, the light cast by 
 Faraday's discovery that in electrolytic dissociation 
 of matter the ions which result have definite electrical 
 charges, and the still further light which the electron 
 theory is throwing on the structure of the atom. Still, 
 the old-fashioned conceptions have in their time 
 proved valuable handmaids, and if they are now grown 
 too infirm to do their old work we have still to be 
 grateful for them. But in the region of life they have 
 played only an auxiliary and not a leading part. 
 Auxiliary, because they permitted us to take the 
 living body, not as living structure, but as a thing 
 self-contained and independent of its environment,
 
 206 BIOLOGY 
 
 and, on this very dubious assumption, not borne out 
 by observation, to apply exclusively the methods of 
 the physicist and the chemist. No doubt much 
 information of provisional value is to be got in this 
 way. By adopting it, and treating the body as a 
 heat-producing machine, Lavoisier gave the world 
 a clear and useful working hypothesis. What it 
 failed to take account of was that the heat-produc- 
 tion was organically regulated. Moreover a further 
 price has had to be paid for such a picture of life as 
 mechanism. Anatomy and physiology, particularly 
 anatomy, have been profoundly influenced by the 
 a priori conception of the living structure as being 
 inherently a mechanical structure. One result has 
 been that medicine has found itself divorced in a 
 large measure from sciences which ought to have been 
 its foundation at every turn. When presently we 
 come to the character of life we shall find it to lie in 
 the preservation of what is normal with the organism. 
 It has normal conditions up to which it maintains 
 itself and so preserves its continued existence. In 
 the maintenance of these normal conditions health 
 consists. Such normals are for anatomy usually 
 conceived as being no more than mere external struc- 
 tures, and for much current physiology as no more 
 than mere averages. But are such relations not 
 rather manifestations of the life of the organism 
 regarded as a whole ? The various functions, such as 
 breathing, oxygenation, digestion, metabolism, com- 
 bine to maintain life, and in this maintenance the 
 structural activities of the various organs adapt them- 
 selves to what they perform. The whole determines 
 the parts and subsists in their co-ordinated activities. 
 Just as in society human beings try to live up to
 
 NORMALS 207 
 
 normal standards of conduct, which keep their lives 
 on a level with the lives of others, and strive to avoid 
 getting into the bankruptcy or the police court, so 
 the organism tends to maintain a continuously healthy 
 life and to avoid deficiencies which may destroy that 
 life. 
 
 The practical purpose of the physician is to restore 
 or maintain health. What is health ? It is what is 
 biologically speaking normal, the condition in which 
 the body is maintaining all its functions in an 
 efficient state and as an entirety. What the doctor 
 sees in the sick man is a perversion of his normal 
 condition, and he watches the effort of nature to 
 get rid of this perversion and tries to assist with 
 medicines and nursing. He has to understand what 
 the process means. If he knows how breathing is 
 normally regulated he will distinguish between 
 various reasons for abnormal breathing, and so in 
 the cases of other symptoms. That will be because 
 he is an experienced practitioner who has seen such 
 things often and has dealt with them. For if 
 he had to depend on knowledge of physics and 
 chemistry merely, or even of anatomy and physiology 
 as explained in textbooks which seek to exhibit 
 them as illustrations of .mechanical laws, he could 
 not know adequately how he stood. His subject 
 is not these things, but an organism that is alive. 
 Scientific knowledge of mechanical and chemical laws 
 is very valuable, but taken by itself it is not enough. 
 That is why so many practical doctors hold these 
 studies in lighter esteem than they should. The 
 proper study of medicine requires them, but it 
 requires knowledge of a physiology based on what 
 health really means, and on how it can be maintained
 
 208 BIOLOGY 
 
 under varying conditions of environment. It requires, 
 too, a pathology which will teach how health tends 
 to reassert itself under abnormal conditions, and a 
 pharmacology which will teach, not merely the action 
 of drugs in the abstract, but how they can be used, 
 all the conditions being taken into account, with 
 well-founded hope of assisting nature to re-establish 
 normal conditions in the particular living organism. 
 
 We have seen how the laws of physics and the 
 reality of phenomena for the physicist depend on 
 the interpretations which are made from a definite 
 standpoint and enter for us into their existence. 
 So it is with biology. We have to determine our 
 standpoint and its relation to other and different 
 standpoints if we wish to get at that meaning of the 
 data which makes them what they are both for us 
 and in themselves. In physics the data are taken as 
 external to and independent of each other. That is 
 of the essence of the procedure of the mathematical 
 physicist. His symbols take no cognisance of be- 
 haviour as exhibited in life or purposive action. 
 But when we are observing a living organism this 
 is just what we must take account of. We cannot 
 get at the meaning or the reality of our data if we 
 take them as if existing in isolation from each 
 other. It is characteristic of the phenomena with 
 which we are here concerned that the details of form, 
 movement, and chemical composition which we dis- 
 tinguish in them are essentially and not accidentally 
 connected with each other. ' We are accustomed to 
 the fact that a limb, or even a bone, of a certain build 
 is associated with a whole body of a certain build. 
 We know also that if an animal is breathing we may 
 expect to find its heart beating and all its other organs
 
 RELATIVITY IN PHYSIOLOGY 209 
 
 in a state of more or less evident activity. We 
 associate together the details of structure and activity 
 as those of a living animal ; we think and speak of it 
 as alive, and we regard its structure and activities 
 as the expression or manifestation of its life. What I 
 wish to maintain is that in so regarding a living 
 organism we use an hypothesis which is for biology 
 just as intelligible, just as elementary, just as true 
 to the facts known, and just as good a scientific 
 working hypothesis, as is the hypothesis of the in- 
 destructibility of matter for physics and chemistry/' l 
 The ordinary physician who does not trouble him- 
 self with speculative questions and who is not the 
 prey of " unconscious assumption " takes much this 
 view of his patient. It is when we come to the domain 
 of theory that controversy arises. If reality is really 
 relative to standpoint in knowledge there is no more 
 difficulty in accepting the facts as they seem to 
 present themselves than there is for Einstein in 
 accepting the velocity of light as a constant, the same 
 for an observer at rest in relation to its source as for 
 an observer in motion to or from that source. But 
 for those who have not made their own the principle 
 of the relativity of reality to knowledge throughout 
 the sciences, an insuperable dilemma seems to them 
 to present itself when they are asked, here as else- 
 where, to believe in the reality of the world as it 
 seems. They think that they must either reduce the 
 phenomena with which they are confronted to in- 
 terpretations which are purely mechanistic, or that 
 they must admit the presence of some influence of 
 which science can take no account consistently with 
 the only principles which they admit. They hold 
 
 1 The New Physiology, p, 31.
 
 210 BIOLOGY 
 
 themselves forced to a choice between a consistently 
 mechanistic view or one which admits a special 
 vital principle as causally operative. We shall 
 have to consider the first of these alternatives in 
 some detail. Meantime it is enough to take one 
 illustration as disclosing an initial difficulty in its 
 way. If there is any feature that is clearly present 
 in a living organism it is its capacity not only to 
 maintain but to reproduce its own structure. But 
 when we try to state such a process of reproduction 
 in mechanical terms we have to state it as the neces- 
 sary result of certain simple properties of simple parts 
 which interact in the event. For a mechanical 
 explanation the reacting parts must first be given. 
 Unless an arrangement of parts with definite properties 
 is given, it is meaningless to speak of mechanical 
 explanation. If the matter is to be carried far enough 
 the description must become one in the differential 
 equations of mathematics. Now, as has been remarked 
 in the volume I have just quoted l : " To postulate 
 the existence of a self-producing or self-maintaining 
 mechanism is thus to postulate something to which 
 no meaning can be attached. Meaningless terms 
 are sometimes used by physiologists ; but there is 
 none so absolutely meaningless as the expression 
 ' mechanism of reproduction/ Any mechanism there 
 may be in the parent organism is absent in the process 
 of reproduction, and must reconstitute itself at each 
 generation, since the parent organism is reproduced 
 from a mere tiny speck of its own body. There can 
 be no mechanism of reproduction. The idea of a 
 mechanism which is constantly maintaining or re- 
 producing its own structure is self-contradictory. 
 
 1 At page 142.
 
 THE CRYSTAL AND GROWTH 211 
 
 A mechanism which reproduced itself would be 
 a mechanism without parts, and therefore not a 
 mechanism. " 
 
 In a crystal we have a good example of apparent 
 self -increase. If we lower the temperature of water 
 to below the freezing-point without allowing it to 
 freeze, and then throw into it a small crystal of ice, 
 the fragment increases spontaneously and becomes a 
 larger crystal. The molecules of water attract each 
 other and fall into a physical arrangement in which 
 by their disposition in space they occupy more space 
 than before the water to which they belong is frozen. 
 The crystal is also constantly giving off and taking 
 up molecules of water from its environment. So far 
 there is some semblance of analogy between the 
 crystal and an organism. But the semblance breaks 
 down. The arrangement of the molecules in the crystal 
 is a mere repetition, but in the organism there is 
 individual variety of detail controlled by unity, not 
 necessarily of detail but of plan. How this plan 
 will accomplish itself we cannot predict on mathe- 
 matical or physical principles. We are dealing with 
 a living individual structure possessing properties 
 which are highly complex and which vary in each case, 
 not only with the structure itself but with the en- 
 vironment, minute differences in the character of 
 which may affect profoundly the activity of the 
 living structure which depends on that environment 
 for its growth. 
 
 The mechanistic explanation encounters difficulties 
 at every turn, of which that referred to is only an 
 illustration. But the explanation offered by what is 
 called ' vitalism ' is confronted by difficulties which, 
 if of another kind, are just as great. The theory of 
 15
 
 212 BIOLOGY 
 
 vitalism is that ordinary physical and chemical 
 explanations, useful and necessary as they are for 
 the study of the living organism in certain of its 
 aspects, do not account for its behaviour or the con- 
 trolling influence which gives rise to its distinctive 
 activities. These the vitalists therefore look for in a 
 controlling power which is apparent only in life and 
 which is quite different from any with which we be- 
 come familiar in the inorganic world. In the autonomy 
 of living organisms we have their essential quality 
 and the record of their history. Such autonomy 
 arises from a vital ' force ' or ' principle ' which is 
 operative in bringing about their distinctive activities. 
 The older vitalists apparently regarded this vital 
 ' force ' as being something superadded to mechani- 
 cal action and arrangement, which, like the mechanists, 
 they took to be characteristic of nature in its organic 
 as well as its inorganic aspects. Of late, under the 
 leadership of teachers like Driesch, they have sub- 
 stituted the expression ' entelechy ' as a better 
 description of the vital principle the controlling 
 influence of which they hold to be manifest. 
 
 But such vitalism, even in the form which Driesch 
 gives it, seems to prove either too little or too much. 
 Too little, in so far as a large field in the behaviour 
 of the living organism is left to be explained in me- 
 chanistic terms and through mechanistic conceptions. 
 Too much, in that it is not possible to find a line of 
 demarcation showing where the sphere of the one 
 begins and that of the other ends. An entelechy or 
 vital influence becomes itself a sort of mechanism in 
 any view which places it alongside of and co-ordinate 
 with the causes and effects which belong to mechanism. 
 It is a world of externality in order to which we are
 
 'VITALISM' 213 
 
 held bound, and such an order of externality is 
 different in its very nature from that of which the 
 level is one at which ends and the organs which 
 express them are indistinguishable alike in space and 
 time. The other way is to take the course which we 
 adopt when we are concerned with ethics, with beauty, 
 and with the religious consciousness. In these cases 
 we do not look for different entities. What we con- 
 template is reality with a difference in meaning due 
 to difference in standpoint, reality that in this way 
 owes its very nature as a fact confronting us to its 
 relativity to the kind of knowledge for which alone 
 it is actual. Concepts of the nature of unlversals 
 enter here into the constitution of individual facts, 
 just as they do at the standpoint of the mathematical 
 physics of relativity when the velocity of light is 
 disclosed as a constant, or when an ' interval ' in an 
 underlying four-dimensional world is stripped by 
 reflection of all quality of shape and measurement, 
 and yet is not the less accepted as the ' invariant ' 
 foundation in all relations of externality. Such a 
 view of things is no doubt an unfamiliar one to the 
 man in the street, whose mind is encrusted with the 
 only half- thought-out conventional assumptions which 
 serve him best in the rough practice of everyday 
 human intercourse. But they are not sufficient for 
 science, nor even for the man in the street himself, 
 and unless their relativity is recognised as bound 
 up with standpoint in knowledge they exercise a 
 distorting influence upon its conceptions. We are 
 becoming more and more aware, as generation after 
 generation makes further progress in exact thinking, 
 how essential it is that we should always be on the 
 alert for the misleading intrusions of merely con-
 
 214 BIOLOGY 
 
 ventional assumptions, and should never leave out 
 of sight the possibility that the categories we habitu- 
 ally employ may require criticism and revision. The 
 true question is not why we should adopt a mechanis- 
 tic or a vitalistic attitude in considering the phenomena 
 which life displays. The real question is whether 
 either one or the other is required. For if we are at 
 liberty to look at the facts as the closest observation 
 appears to disclose them, and just as tiny seem to 
 present themselves, without twist towards one hypo- 
 thesis or bias towards the other, then we may take the 
 course that is natural in the interests alike of science 
 and of common sense. If I am right in the general 
 conclusions about the relation of reality to know- 
 ledge which I have already set forth, the history of 
 philosophy teaches us, on a distinct balance of 
 testimony, not only that we are free to do this, but 
 that the course is the only one which we can legiti- 
 mately take without imperilling the advance of know- 
 ledge generally. The facts of life will on this footing 
 be facts which can be rendered only in terms of the 
 concepts of life. These afford no warrant for the 
 notion that we can reduce life to mechanism and so 
 end to cause any more then they afford warrant 
 for the notion of a vitalistic cause which is none 
 the less a cause in that its effect is life. The level 
 or degree in knowledge from which the facts 
 present themselves when we apprehend what is 
 living has its own conceptions, and these are the 
 conceptions appropriate to the standpoint to which 
 the knowledge of nature in its aspect as biological 
 is relative. What we have to do is to look at the 
 facts as they present themselves, and simply to 
 observe what their implications are. If these indicate
 
 THE STANDPOINT IN BIOLOGY ! 
 
 the standpoint as one which is unmistakably appro- 
 priate, then the doctrine of the general character 
 of knowledge and of its relativity tells us that the 
 standpoint is one which we need not hesitate to 
 accept. 
 
 When we observe life we are observing objective 
 nature just as much as we observe mechanism when 
 we examine the heavens with the telescope or the 
 resolution of white light into its component colours 
 with the spectroscope. Both modes of observation 
 depend on interpretations which turn on standpoint 
 in knowledge, but they are interpretations which 
 enter into and fashion the actual, meanings which 
 determine what is real. In studying the living body 
 we do not separate off and specify occurrences as due 
 to separate parts in the fashion we find them separated 
 off and specified in a machine. In nervous responses 
 and especially in conscious responses the whole 
 nervous system and indirectly the whole organism 
 with its environment are involved. The response is 
 the response of the living body as an entirety, and not 
 merely that of the brain or any other particular organ. 
 It is their fulfilment of an organic unity, their contri- 
 bution to the maintenance of the normal life of the 
 organism, that makes inappropriate as an explanation 
 the otherwise indefinable and inexhaustible com- 
 plexity of what we are confronted with in the en- 
 deavour after interpretation as physical and chemical 
 reactions. It is only their clinging to an a priori 
 metaphysical view, held most often unconsciously, 
 that makes so many try to render the phenomena of 
 life into physical and chemical conceptions ; a meta- 
 physical view really no better than that at another 
 extreme held by the interpreters in a different sense
 
 21 BIOLOGY 
 
 of the phenomena of the liquefaction of the blood of 
 some long-deceased saint. Perception involves acti- 
 vity of reflection in the selection of what is perceived 
 and the abstractions which are made in the different 
 forms of knowledge. The standpoints overlap, and 
 it is by collecting the results arising from the em- 
 ployment of their respective conceptions that we 
 constitute and arrange the various sciences. The 
 idea of the physical world as one made up of self- 
 existing matter and energy is the outcome of a useful 
 and necessary working hypothesis. But not less 
 useful and necessary is that of life as a phase of the 
 actual that is independent of this hypothesis, and is 
 of a character epistemologically distinct from it. 
 The purpose in all science is to find order and 
 intelligibility in its objects, and different standards 
 of reference may be required by sciences which prove 
 on that account to be of logically different characters. 
 A plurality of standpoints may be required for the 
 comprehension of an individual object, and the 
 meanings sought for may have to belong to more 
 orders than one. But the natures of these meanings 
 have to be kept distinct in reflection. The biologist 
 takes cognisance of physical and chemical changes 
 as the sensuous data which he must ascertain in the 
 course of interpreting them. It is by bringing the 
 results into a larger whole that he arrives at physio- 
 logical knowledge and sees behind changes in form, 
 in electrical activity, in oxygen absorption, in the 
 outward signs of muscular activity, the metabolic 
 activity of living organisms. Life manifests itself 
 both as structure and activity. But in each case the 
 manifestation is of what is living. The structure 
 expresses living activity, and the ceaseless metabolic
 
 STRUCTURE AND ACTIVITY 217 
 
 change of which visible structure is the outward 
 expression is a phenomenon closely related to what 
 we call nutrition. The changes in the retina when 
 light falls on it are in part chemical, but they are not 
 the less metabolic or structural activities. So are the 
 activities of nerve cells, muscle cells, gland cells, or 
 any other living cells. Even the greater visible 
 movements of the body are but the outer signs of 
 metabolic activity. In metabolism the food of the 
 organism is converted into the products which the 
 organism requires for the maintenance of its life. 
 The processes are during health of exquisite regu- 
 larity and delicacy, </wasi-purposively directed so as 
 to maintain life. Even in ordinary nutrition nothing 
 remains still and inactive. Living structure is really 
 alive and full of molecular activity, and expresses 
 directions and velocities which this activity takes. 
 Substances are constantly being taken up from and 
 given back to the environment ; and even when 
 these substances do not seem to be used up in 
 nutrition, as in the case of inorganic salts, there is 
 a constant molecular interchange between the cell 
 and its environment. Cell secretion, cell respiration, 
 and cell nutrition seem to be only different forms in 
 which molecular activity thus directed appears. 
 
 A good illustration of the great part played in life 
 by metabolic activity is afforded by observation of 
 the way in which the circulation of the blood is regu- 
 lated. The blood brings to the tissues the various 
 substances required for their normal life, and removes 
 from them substances which are then carried to other 
 tissues or to secretory organs. It also conveys heat. 
 That it also carries oxygen and carbonic acid is 
 another among its many functions. The flow of
 
 218 BIOLOGY 
 
 blood through any part of the body depends partly 
 on the difference in blood pressure between arteries 
 and veins, and partly on the resistance to flow from 
 the arteries through the capillaries to the veins. 
 The blood pressure in the veins is lower than that 
 in the arteries and varies because of variations in 
 resistance due to the varying calibre of the small 
 vessels. The stimuli which determine these variations 
 appear to originate in accumulation of products of 
 metabolism, or through deficiency of the substances 
 required in it. In some way such as this it appears 
 that the flow of the blood through the different parts 
 of the body is regulated in accordance with the re- 
 quirements of each part, so that during extra activity 
 in any part there is a correspondingly greater blood 
 flow. Greater oxygen consumption is accompanied 
 by increased circulation, and so is increased pro- 
 duction of carbonic acid in the venous blood. The 
 pumping action of the heart, although the primary 
 motor power, is not the regulator of the circulation of 
 the blood. It is the state of contraction in the blood- 
 vessels that governs the rate of circulation. We come 
 back for ultimate explanation to the metabolic 
 activity of the living body as a whole. The blood 
 circulates at such a rate as is sufficient to keep its 
 composition approximately constant at any part of 
 the body, and the rate of flow seems to be greater or 
 less at any part in proportion as the causes tending 
 to disturb the composition of the blood are greater 
 or less at that part. Among the chief of these causes 
 is consumption of oxygen and liberation of carbonic 
 acid. The circulation rate is largely determined by 
 the latter processes, and varies, just as the breathing 
 varies, in such a way as to keep the gas pressures
 
 CIRCULATION OF THE BLOOD 219 
 
 in each part of the body approximately constant. 
 The phenomena illustrate what was said by Claude 
 Bernard as long ago as 1878, when he declared that 
 " all the vital mechanisms, varied as they are, have 
 only one object, that of preserving constant the 
 conditions of life in the internal environment." 
 
 Such a picture as this of the regulation by the 
 living organism of the circulation of its blood is surely 
 no picture of any mechanism. It is a picture of 
 what belongs to a wholly different domain. Such a 
 system of self-conservation can hardly more be repre- 
 sented in the equations or diagrams of mechanics 
 or the reactions of chemistry than could the pro- 
 ceedings of a Parliament. The conceptions required 
 for the definition and expression of what is happen- 
 ing belong to an order that is of a wholly different 
 kind. When we remember that the organism that 
 behaves thus was originally a speck of organic 
 matter which grew up inheriting the modes of 
 behaviour of its parents, and becoming one out of 
 a countless number of other similar living beings 
 all conducting themselves in the same fashion, 
 the attempt at a mechanistic interpretation which 
 depends on chance, and on rejecting end as distin- 
 guished from mechanical cause, becomes an apparently 
 hopeless one. Nor would common sense have per- 
 mitted it to be made had it not been for the super- 
 stition that all real knowledge and all reality must 
 be reducible to one order, and that the most abstract. 
 For a theory of knowledge which discovers the actual 
 only in what is concrete and individual, and which 
 therefore finds itself compelled to explain from above 
 downwards, and not from what is most abstract 
 upwards to what is less so, the apparent difficulty
 
 220 BIOLOGY 
 
 which throughout the history of reflection has stimu- 
 lated the mechanistic attempt, is a difficulty which 
 is really non-existent, inasmuch as it arises from a 
 misconception. 
 
 Hardly less remarkable than the organisation for 
 circulation of the blood are the arrangements by which 
 it is kept supplied with oxgyen and carbonic acid. 
 These last appear to be equally unintelligible from a 
 standpoint confined to mechanical arrangements. 
 It has been found that the breathing, which is governed 
 by a special centre in the brain, reacts with almost 
 incredible delicacy to minute changes in the reaction 
 of the blood. It controls the reaction by regulating 
 the amount of carbonic acid in the blood, which of 
 course varies according as the breathing increases or 
 diminishes. 
 
 That the respiratory centre should respond in the 
 exact fashion it evidently does to change in the re- 
 action of the blood is in itself extraordinary, but what 
 is not less extraordinary is the fact that in the arterial 
 blood the amount of carbonic acid remains during 
 rest almost completely steady. Various kinds of acid- 
 forming and alkali-forming substances are constantly 
 being introduced! with great frequency into the body 
 by the food. And yet the reaction of the blood 
 hardly varies at all under normal conditions, even 
 when tested by the exquisitely sensitive indicator 
 of the percentage of carbonic acid in the air of the 
 lungs. It is indeed important that this should be 
 so, for the indications are that disturbances more 
 minute than those which are ordinarily measured in 
 chemical tests may make a prodigious difference to 
 physiological processes. 
 
 What regulates the reaction or the hydrogen-ion
 
 THE KIDNEYS 221 
 
 concentration of the blood ? It is now known that 
 the most important agent is the action of the 
 kidneys. It was for long common knowledge that 
 the urine varies in acidity or alkalinity according to 
 the diet. What was not known until it was recently 
 discovered is that under ordinary conditions the 
 variations in hydrogen-ion concentration of the urine 
 are enormously greater than those of the arterial 
 blood. 
 
 This astounding fact seems to be due to the re- 
 sponsiveness of the epithelial cells in the kidney. 
 These answer so precisely to the demands arising 
 from variations in the hydrogen-ion concentration in 
 the blood that the very smallest variation in this 
 concentration, in the acid or alkaline direction, 
 stimulates them to excrete in the urine what is acid 
 or alkaline with an intensity which is far in excess 
 of any proportion to the state of the blood at the 
 moment, bringing about the result that the con- 
 dition of the blood in this respect is kept practically 
 constant. 
 
 There appears to be good reason to believe that in 
 the case of other features in the blood, such as the 
 salts and amount of water in it, a similar quasi- 
 purposive regulation is exercised by the kidneys. 
 The delicacy with which they discharge this kind of 
 function, in such a way as to preserve the normals 
 required for the circulation of blood of the proper 
 kind by the organism, is of a character that would 
 appear miraculous were it only explicable by the phy- 
 sicist or the chemist as taking place apart from the 
 phenomena that pertain to the order of life. The 
 gland cells of the kidneys eliminate urea, for example, 
 with such thoroughness that there is present as the
 
 222 BIOLOGY 
 
 result in a given volume of urine usually about ten 
 or fifteen times as much of urea as in the same volume 
 of the blood. When the kidneys secrete sugar there 
 may be as much as twenty or thirty times more sugar 
 in the urine than there is on the average in the blood 
 which they purify from it. When the kidneys 
 excrete with this remarkable power it is because the 
 concentration of the substance excreted is above 
 what the normal conditions of the blood permits. 
 Not only is the normal maintained there, but if the 
 concentration in the blood falls for any reason below 
 it the kidneys cease to excrete the substance. The 
 capacity to do this work may be, of course, interfered 
 with by pathological conditions. Minute doses of 
 certain poisons or the want of oxygen may disturb it, 
 and it may be heightened by the administration of 
 drugs. 
 
 It has been found, too, that if a large quantity of 
 water is drunk, the water which becomes present in 
 the blood in an undue amount is excreted into the 
 bladder without there being passed with it from the 
 kidneys the ordinary normal constituents of the 
 blood. However we look at the matter, what we 
 find in the case of the kidneys is the same kind of 
 regulation for preservation of the normals of the 
 living body that has been referred to in connection 
 with other organs. Whether it be breathing or 
 circulation or the activities of the structures which 
 form the liver or the kidneys the same type of phe- 
 nomenon presents itself. We can neither perceive 
 the actual living object excepting as manifesting the 
 character that is distinctive of life, nor can we describe 
 it in any terms belonging to an order more abstract 
 than that which life forces on our recognition.
 
 LIFE CONTRASTED WITH MECHANISM 223 
 
 It is only the difference between life and the usual 
 balancing of mechanical arrangements that enables the 
 subordination of the processes of life in the fulfilment 
 of the end of conserving it to preserve life through con- 
 tinuous change of material. The moulding influence 
 of the whole is a normally unbroken and self-sustaining 
 one which, within limits, is capable of adapting the 
 environment and incorporating it. But the preser- 
 vation of life depends on conditions so intricate and 
 so delicate that a very small departure from such 
 as cannot be controlled may bring it irrevocably to 
 an end. 
 
 The illustrations just given show how different a 
 living body is from a machine, an aggregate of parts 
 which can be dissociated and afterwards put together 
 again. The unity of the organism is wholly unlike 
 this. It consists in its activity in maintaining its 
 structure and activities right through a life history. 
 We have given no adequate account of its character 
 when we call it an aggregate of material. For it is 
 much more, and is different in nature from such an 
 aggregate. It is in a constant state of change of 
 taking in and of giving out its material, and of trans- 
 forming it with exquisite and quasi-purposive delicacy. 
 Not only molecules but living cells are being taken 
 in, given off, and developed afresh. Between the 
 organism and its environment no other line of real 
 demarcation can be drawn excepting one referred to 
 the ambit of the power of life itself, as forming what 
 is distinctive of the individual organisms, in the 
 exercise of control. Do the blood and the lymph 
 belong to the organism or to its environment ? A 
 merely mechanical answer cannot be given. So of 
 the gas in the lungs and the food in the intestines.
 
 224 BIOLOGY 
 
 It is the normal activity of structure that affords 
 the only solution. What we have before us seems to 
 possess a kind of unity which we cannot explain or 
 even describe in terms other than its own. It is a 
 unity that persists through change in material which 
 after a time has become complete. The conceptions 
 that are appropriate to this unity, and to such a 
 unity exclusively, are as distinctive as those which 
 are characteristic in physics or chemistry. And they 
 belong in both cases to reality as much as to knowledge. 
 
 The more we consider the results which the work of 
 physiologists is placing on record in an always in- 
 creasing degree, the further does merely mechanistic 
 explanation seem to recede, and the more cogent 
 does the evidence seem that the organs of the body 
 exercise their respective functions in the economy 
 of the whole more like human beings acting together 
 in a society than like the parts of a machine. Human 
 beings they do not really resemble, because their 
 action is apparently not conscious, and is only quasi- 
 purposively directed. The old idea was that pheno- 
 mena of this nature might be explained as due to 
 some sort of intra-cellular mechanism. But by de- 
 grees the extraordinary proportioning to the needs 
 of the entire organism with which the organs discharge 
 their tasks, and the fashion in which they adapt that 
 discharge from time to time to conditions that are 
 constantly varying, produced a sense that the pro- 
 blem was not so simple a problem as it had been taken 
 to be. The old methods of investigation proved 
 incapable of attaining their aim. 
 
 When we turn to what biological science tells us 
 of pathology we have suggested to us not less strongly 
 that in illness, as in health, the standpoint for inter-
 
 PATHOLOGY 226 
 
 pretation must not be other than that of life itself. 
 In a fever there may be a higher temperature than 
 what is normal. But this does not signify for the 
 experienced physician that his business is to look out 
 for some purely chemical source of production of heat 
 within the fevered body. The rise of temperature 
 depends on disturbance of the power of regulating 
 body temperature, and usually signifies that the 
 body has been attacked by an army of hostile 
 microzoa which the forces of healthy nature are 
 contending with and seeking to destroy. When 
 a cold in the head extends downwards into the 
 bronchial tubes we interpret it as meaning that some 
 invasion of this kind has taken place, an invasion 
 which the forces of nature may not be strong enough 
 in some people or at some ages to contend against. 
 The physician may think it necessary to inoculate 
 in order to render such an invasion more difficult. 
 When he does so he is opposing life to life, and not 
 mechanism to mechanism. 
 
 Take again the case of the alarming disturbance of 
 function known as diabetes. This disease depends 
 essentially on a failure in self-regulation in the 
 interests of the whole by living organs. Carbohy- 
 drates like fruit and bread and potatoes are a very 
 important form of food, containing as they do sugar 
 and starch. All the more complex forms of car- 
 bohydrate have to be converted into sugars, such as 
 glucose and lavulose, before they can be utilised in the 
 body. The process takes place in the alimentary canal 
 under the influence of various ferments. When the 
 sugar assimilated has got through the wall of the bowel 
 it is carried by the portal vein to the liver, which 
 converts about half of it into glycogen and stores it
 
 226 BIOLOGY 
 
 up. The remainder goes into the blood and is 
 eventually taken up by the muscles. The process 
 of assimilation and storing requires the presence of a 
 sufficient quantity of the internal secretion of the 
 pancreas, and " the supply of what is termed the 
 necessary hormone may be influenced by the state 
 of the pancreas itself, by changes in other ductless 
 glands which aid or oppose the pancreas, and also 
 by certain nervous impulses." I take this descrip- 
 tion from the account of the pathology of the meta- 
 bolic process involved given in an article in The 
 Edinburgh Medical Journal for November 1921, 
 written jointly by Dr. Murray Lyon, Lecturer in 
 Clinical Medicine at Edinburgh University, and by 
 Dr. Meakins, the Professor of Therapeutics there. 
 The blood, this article goes on to tell us, normally 
 contains a small quantity of glucose which in the 
 fasting state averages O'l per cent. This circulating 
 sugar is drawn upon during muscular activity, and 
 more glucose is liberated from the liver to replace the 
 loss. An increase in the amount of sugar present in 
 the blood occurs in certain emotional states, such as 
 fear or anger or great excitement. This is due to 
 the action of certain nerve centres. In other cases 
 where the increase of sugar in the blood is due to diet, 
 the authors say that the rate of absorption of glucose 
 from the intestine has become faster than the rate 
 of assimilation by the tissues, so that sugar accumu- 
 lates in the blood. Where there is great pathological 
 disturbance of the system sugar may be formed by 
 the conversion by the organism of proteins and 
 fats into sugar. 
 
 It is obvious that what takes place during what 
 is here described is due to imperfect regulation by the
 
 DIABETES 227 
 
 living organism of certain of its normal processes. 
 The pancreas apparently plays an important part in 
 such regulation, and it has been known for long that 
 by interfering with it diabetes may be artificially 
 produced. But other organs are involved, for if 
 there is not co-operation between these organs in 
 maintaining the normal level of the processes con- 
 cerned, the symptoms will appear. These may 
 assume various menacing forms. The sick man may 
 waste away from inability to metabolise the car- 
 bohydrates necessary for the maintenance of life, 
 or, for want of carbohydrate conversion, acids may be 
 formed in the blood by disturbance of the normal 
 regulation of reaction in the body. The foreign acid 
 produced will bring about coma and death if it is 
 present in sufficient quantities. 
 
 I have referred to this phase of metabolism because 
 it is another illustration of the fashion in which the 
 living whole exercises regulation of the processes in 
 which it is actual and which constitute its life. When 
 these processes are interfered with the health of the 
 living being is affected and its life may be brought to 
 an end. The facts seems to point to a control which 
 is incapable of a mechanistic explanation. We seem 
 always driven ,to the notion of life realising and 
 maintaining itself in a flux of material which is 
 constantly being taken in and given out. There is 
 continuous nutrition, and continuous reproduction 
 also, of cell and other life in the healthy subject, 
 and this takes place consistently with behaviour in 
 the fulfilment of a further end which is accomplished, 
 that of growth and development through a course 
 of life, from conception to death, in the interest of 
 the species. 
 16
 
 228 BIOLOGY 
 
 I will take yet another piece of testimony to this 
 from the records of results established, this time 
 by biologists. There is a microscopic unicellular 
 organism which is found in rivers and ponds and 
 is called Arcella. It is specially interesting when 
 examined under the microscope, since there are 
 observed in it gas-bubbles within its protoplasm. 
 When these bubbles appear they make the animal 
 lighter, so that it can come to the surface of the 
 water. It has been discovered that a comparatively 
 slight deficiency in the normal oxygen percentage 
 of the water causes the Arcella to develop bubbles 
 at once and so to come to the surface. What takes 
 place is a visible intra-protoplasmic gas secretion, 
 and the gas seems to be oxygen. Now what the 
 Arcella does is no isolated thing without parallel in 
 other cases of living organisms. The secretion of 
 oxygen in the swim-bladders of fishes was discovered 
 a hundred years ago by the French physicist and 
 chemist, Biot. He was engaged in survey work on 
 the Mediterranean, and he noticed that deep-sea 
 fishes caught with a line at great depths came to the 
 surface with their swim-bladders distended with gas 
 or even bursting. He examined the gas and found 
 it to be, not ordinary air, but oxygen. He observed 
 that the greater the depth from which the fish was 
 taken the more did the gas in the swim-bladder 
 approximate to pure oxygen. In the end later re- 
 search showed that the secretion of this oxygen was 
 under the control of the nervous system, the secre- 
 tory nerve being one of the branches of the vagus. 
 
 As nearly pure oxygen has been obtained from the 
 swim-bladders of fishes living at a depth of 4,500 feet, 
 it is apparent that oxygen may be secreted into this
 
 THE SWIM-BLADDER IN FISHES 229 
 
 bladder and retained in it at a pressure of over 
 120 atmospheres, while the partial pressure of the 
 oxygen in the surrounding sea-water is only one- 
 fifth of an atmosphere. It seems to follow as the 
 inevitable inference that the liberation of oxygen 
 and its retention by the semi-liquid wall of the swim- 
 bladder is the result of an active physiological process 
 in the living cells lining the walls, and cannot be 
 explained mechanically. This and other evidence 
 seems to show that living animal cells have the power 
 of liberating or secreting free oxygen, and do so in, 
 accordance with the requirements of the organism 
 as an entirety. They seem to work for the main- 
 tenance of whatever are the normals under the 
 conditions which obtain from time to time. 
 
 In these and countless other instances we find that 
 a living activity cannot be made intelligible apart 
 from its relation to other living activities. What it 
 accomplishes is apparently directed to the maintenance 
 of the normal condition of the organism. The parts 
 of a machine are intelligible in independence of and 
 as external to each other, and they can be put to- 
 gether by a process of addition. The structures and 
 activities of the parts of a living whole appear quite 
 differently. They are functions within wholes which 
 are determined as such through control by ends. 
 To comprehend life we have to employ conceptions 
 which do not belong to mathematics and physics but 
 which are essential in the phenomena of life. It is 
 no question of mere forms of knowledge. We do not 
 tend to distort some reality existing apart from these 
 conceptions by bringing it under them. The reality 
 forces them on us. It is what it is only inasmuch 
 as they enter into the actual with which we are
 
 230 BIOLOGY 
 
 confronted. Why do many men of science struggle 
 to resist this conclusion, and take the actual to 
 have no other relations than such as consist in 
 externality to each other of entities and actions ? 
 Because of their unconscious metaphysics . They think 
 of minds as things, looking out of boxes called skulls, 
 on entities which exist in themselves without any 
 relation to knowledge. But both the mind and its 
 object seem rather to fall within knowledge, and we 
 have therefore to ascertain what knowledge means 
 before we can indulge in any such unverified hypo- 
 theses as are current. If the object of knowledge be 
 always individual, with logical moments which are 
 real only as belonging to it, and if of these moments 
 some are of a universal character, belonging to thought, 
 while others are in the nature of vanishing particu- 
 lars, asymptotic limits in analysis which are actual 
 only if and as they are set in universals of reflection, 
 then we get to a new notion about our experience. 
 It is always individual in form, concerned with what 
 is just this and unique in the universe. But the in- 
 dividual object that is just this individual is what 
 it is only because of its setting in knowledge, and the 
 mind or subject which we take to know it is in the 
 same case. Both fall within a fuller and less abstract 
 entirety, experience no longer taken to be a property 
 of a ' thing/ but as founded in knowledge. Now 
 knowledge has an infinity of forms which it assumes. 
 These vary with the relation to it of its world and 
 with the ends which it sets before itself. We always 
 have relativity to knowledge itself as the result. The 
 forms of knowledge which we employ in our study 
 of life we seem to employ not because of any arbitrary 
 choice, but because in the actual world in which we
 
 CHARACTER OF BIOLOGICAL EXPERIENCE 231 
 
 as men have our stations and our duties we find them 
 there as readily and as truly as we find those of the 
 sciences which require a fuller measure of abstraction 
 from the actual. It is no question of entities, for 
 there are none such independent of knowledge. It is 
 a question of standpoints within the entirety of the 
 knowledge to which we and our objects alike belong. 
 Knowledge seems to be the foundational fact. It 
 is, still more than in the case of the velocity of light, 
 a constant which we always presuppose. Knowing, 
 and not being, comes first in fact as in logic. But 
 to understand the meaning of this we must eliminate 
 from our imaginations the picture of knowledge as 
 a property of a thing in space and time. Indeed 
 space and time, as the physicists themselves are 
 telling us to-day, are constructions relative to the 
 observer, by which bare change is differentiated into 
 relations which depend on standpoint.
 
 CHAPTER VIII 
 
 PSYCHOLOGY 
 
 THERE are few scientific words that have been used 
 with such varying meanings as 'psychology/ The 
 general and popular idea about it is that this science 
 is concerned with forms of activity displayed by 
 something usually called 'the mind/ which can be 
 scrutinised in complete detachment from himself by 
 an observer who turns the lantern of introspection 
 in upon his private soul, thus held out for observation. 
 But in another view of the science it is that of the 
 behaviour of the organism, equally regarded as ex- 
 pressing what is ' mental/ but as an external object. 
 Such behaviour includes everything from merely reflex 
 action in neural processes to the manifestations that 
 people call intelligent. The two views are more 
 often than not sought to be correlated and brought 
 into combination. 
 
 Aristotle, however, would tolerate neither of these 
 opinions. He smiles at those who hold them as 
 being the victims of obsessions. Nor is it really to 
 the point to say that he knew nothing of the advances 
 which modern science was to make. If he had known 
 the entire physiology of the nervous system as it is 
 understood in our own times, it is plain that for him 
 it would have been irrelevant for the solution of his 
 problem. He had rejected the notion according to 
 which mind and body are two self-subsisting and 
 mutually exclusive forms of being. They were for 
 
 232
 
 ARISTOTLE AND PSYCHOLOGY 233 
 
 him logical phases in the concrete reality of everyday 
 life, the individual reality in considering which the 
 observer, not aware of limits to which his procedure 
 is subject, is apt to detach each from the other 
 and to hypostatise it into a separate thing. For 
 Aristotle reality was what it was in virtue of the 
 meaning which it expressed. Behind its relation to 
 knowledge we therefore could not go. The soul 
 represents the true meaning of the body, so that body 
 cannot accurately be said to exist apart from soul, 
 and it is through soul that bodily processes attain 
 their true significance. Soul and body are for 
 Aristotle not simply a harmony of independent 
 existences. They fall rather within a unity in which 
 the bodily functions require us to have knowledge of 
 the soul in order to bring out their full significance 
 and reality. ' We must then," he says, in the De 
 Anima, " no more ask whether the soul and the body 
 are one, than ask whether the wax and the figure 
 impressed on it are one, or generally inquire whether 
 the material and that of which it is the material are 
 one/' Matter cannot be separated from form. 
 Reality is that which it becomes. The object and 
 the capacity to perceive it are correlatives, differing 
 only in the way in which they are approached. They 
 are different aspects of a single actuality, one side of 
 which expresses itself in the activity of perception, 
 and the other in the concrete individual thing 
 perceived. 
 
 It is not sufficient to dispose of Aristotle's view to 
 say that it is two thousand years old, and was that 
 of one who knew nothing of modern scientific results. 
 It is true that he had no understanding of the 
 Baconian principle as we have applied it. It is true
 
 234 PSYCHOLOGY 
 
 that he was unacquainted with our sciences of 
 measurement and of quantitative research. But he 
 had the sense of ancient Greece for quality, and, 
 possessing this sense, he had an almost unrivalled 
 gift for detecting unconscious metaphysics and for 
 dragging to light crudeness in philosophical assump- 
 tion. It is not clear that our sense of quality in this 
 respect has advanced beyond that of the great Greek 
 thinker. 
 
 We must, therefore, in approaching the considera- 
 tion of modern psychological methods, bear in mind 
 the Aristotelian criticism of the assumptions which 
 are apt to disclose themselves as their foundations. 
 But with this word of caution, that the methods 
 cannot be used for erecting any structure more 
 reliable in point of finality than the character of these 
 assumptions warrants, we may turn to the psychology 
 based on methods which, in their fashion, have proved 
 highly fruitful. We may approach it from the stand- 
 point at which the physiology of the brain and nervous 
 system forms its instrument. Or we may rely on 
 introspective methods as our instrument for getting 
 at the character of mind. Or we may proceed by 
 both paths. 
 
 As to the second and third of these methods of 
 approach, objection has been taken. Those who 
 belong to the school of * Behaviourism ' raise strenuous 
 doubts about any other plan than one. They warn 
 us that we must look to external observation, and to 
 that alone, for the meaning of mind. They deny that 
 introspection is a reliable or valid method of acquiring 
 knowledge of its nature. Results supposed to be so 
 reached are not really scientific. It is only what we 
 do, and not what we think, that can be accurately
 
 BEHAVIOURISM 235 
 
 ascertained. When we imagine that we are observing 
 our own thinking we are in truth only observing our 
 behaviour as living organisms in the habit of express- 
 ing themselves in forms of action which we call 
 intelligent. The study of the behaviour of other 
 animals is the k*y to the study of the behaviour of 
 human beings. What we add in the latter case is a 
 construction by inferences which are artificial and 
 unwarranted. It is, for instance, not any psychical 
 idea that leads the bee to fashion the cells in the 
 honeycomb as it does. It is not prevision, but 
 instinct developed in response to stimulus. This, as 
 even writers who do not accept the full principle of 
 the Behaviourists say, may be traced to biological 
 origins. Professor Lloyd Morgan, for example, in the 
 second chapter of his well-known book on Instinct 
 and Experience, restricts the term ' instinctive/ in a 
 biological acceptation to which he gives a large scope, 
 to congenital modes of behaviour dependent upon 
 inherited dispositions within the lower brain centres. 
 " The sequence," he says, in summing up the outcome 
 of this chapter, " of instinctive experience, correlated 
 with a physiological sequence in the cortex, though 
 it is a conscious sequence, and though it affords data 
 for an associating process, is not in itself a psychical 
 process proper, because its course is not determined 
 by conscious relationships, but is determined by 
 purely organic and physiological relationships, com- 
 parable to those which subserve the digestion of food. 
 It is just for this reason that I do not regard it as 
 conative, since I conceive that it is of the essence of 
 conative process that it is determined by conscious 
 relationships with their attendant psychical values." 
 There are, as I have already suggested, some
 
 236 PSYCHOLOGY 
 
 possible obscurities which are ignored in the various 
 views just alluded to. Before we can proceed to 
 study mind we must know what we mean by mind. 
 Is it anything that can be adequately represented as 
 merely an object in space and time for the observer ? 
 Or do space and time present themselves excepting 
 in relations, and in relations which vary, to mind ? 
 Is mind separable in our experience from our know- 
 ledge about it ? And can mind be described in any 
 way which goes behind itself as presupposed in all 
 of them ? 
 
 It is evident that it is indispensable in the investiga- 
 tion of mind to study the biological organism in 
 which what we call mind expresses itself. But how 
 are we to approach this study ? One way is to define 
 in advance the object of our researches as the dis- 
 covery of physical and chemical laws which are 
 assumed to be all that life means. Some of the 
 difficulties which attend this assumption we saw 
 earlier when considering physiology. If the final 
 category is to be the form of mere succession in 
 external series the facts appear impossible to account 
 for. And yet this category seems to be the only one 
 permitted to themselves by the school of philosophers 
 in which Mr. Bertrand Russell, to whose book on 
 Mind reference will be made later on, is a brilliant 
 leader. 
 
 Another way is to take as primary the biological 
 category of end, as operative immediately and pre- 
 sently, in contrast with the cause which is treated as 
 an entity distinct from its effect. This is the method 
 with the aid of which, as we have seen, some phy- 
 siologists are now studying life itself. Behind the 
 terms in which life is spoken of for everyday purposes
 
 ALTERNATIVE METHODS 237 
 
 of recognition they do not go. They dread, when 
 tempted to do so, the effects of unconscious assump- 
 tions. In this restricted fashion we may safely aim 
 at understanding life, but not consciousness. 
 
 A third way is to abstain from taking the world of 
 actual experience to contain only a single type of 
 entity or of relation. If reality is not from every 
 point of view separable from our knowledge of it, 
 but is fashioned by concepts which in giving it mean- 
 ing give it also existence, it is necessary to attend to 
 the character of the concepts employed in its inter- 
 pretation. These are not events or happenings in 
 space and time, or entities separable from the mind 
 observing, but are not the less determinative of the 
 character of what is itself actual, and must have 
 account taken of them. It will therefore be necessary 
 to see what the biological organism yields to observa- 
 tion and experiment, shutting out no standpoint 
 which these appear to disclose. The process will have 
 to be analogous to that appearing in restricted form 
 in physiological research, where the standpoint 
 seemed to disclose itself in what was observed, as it 
 had been found to do in the instance of physical 
 measurement and shape. 
 
 All that I wish to do at this stage is to suggest the 
 great necessity for caution. The methods used in 
 the special sciences are apt to imply fundamental 
 assumptions which, if wrong, turn out to have 
 coloured illegitimately the results apparently reached. 
 The advantage of being critical in the use of domi- 
 nating conceptions is therefore great from the outset. 
 It seems to be the sense of the necessity of this care 
 in some form that has led many physiological 
 psychologists to treat their own work as provisional
 
 238 PSYCHOLOGY 
 
 only. They refuse the reduction of mind to matter, or 
 of matter to mind, as a purpose with which they are 
 not concerned. Just as the aether is a name for that, 
 whatever it may be, in which the phenomena of the 
 magnetic field in physics exist, so they are content 
 to assume provisionally what is called a soul. But 
 about this they make no pronouncement excepting 
 that it is the domain in which neural processes dis- 
 close the production of psychical processes. Experi- 
 ence, they think, may in course of time throw further 
 light on the question. For the present the only safe 
 attitude is that of a sceptical agnosticism which leaves 
 the problem of whether the soul is more than a sum 
 of physical events unanswered. They think that 
 experience shows that some neural process invariably 
 accompanies every state of consciousness in the 
 higher as well as in the simpler phenomena of mind. 
 But on the implications of this they are of opinion 
 that they cannot safely pronounce. The science of 
 psycho-physics has not up till now in their view 
 enabled them to offer a judgment on the question, 
 and it may turn out to be one which their methods 
 cannot solve. 
 
 Not the less these restricted methods have very 
 great value. If we interpret them as the methods 
 which are appropriate for investigating the behaviour 
 of the living individual, in doing what may be more 
 than merely physical or even physiological and is 
 called mental, we have not yet got an adequate 
 definition. We do not know so far what mind means. 
 But we have excluded methods which deal with what 
 is looked at only as mechanical, such as the leverage 
 of the body in pulling up a weight, or only as physio- 
 logical, such as the influence of the living structure
 
 LIMITATIONS OF METHODS 239 
 
 taken as a whole on the functions of each of its 
 organs. This does not mean that the employment of 
 these methods may not prove to be of the highest 
 importance as aids in psychological research. Just 
 as mathematics and physics and chemistry are 
 required in physiology, so these and physiology itself 
 are of vital importance for the psychologist. But it 
 does mean that the primary domain of psychology is 
 one in which certain of the distinctive features are 
 those of conscious action, and that where even what 
 is akin to it, like instinct, has to be included for study 
 along with conscious purpose, this must be done with 
 contrast in view to action that is consciously directed. 
 Purpose as against mere biological end is what tends 
 to mark off this region, and its conceptions go beyond 
 those of end, taken to be no more than end. There 
 is a difference not merely in the character of the 
 facts but in that of the standpoint and interpretation 
 adopted. We no longer in our abstraction exclude 
 sensation and feeling, although we have to take 
 account of factors that do not in themselves come 
 directly within the range of consciousness, inasmuch 
 as they belong to what is external. 
 
 On the other hand, we are aware that beyond our 
 private sensations we do not get in external percep- 
 tion. When we say that we all see the same sun, 
 moon and stars, what we really mean is that we all 
 invest our private sensations with a meaning which 
 is the same as the meaning that others give to their 
 sensations. Into his particular sensations none but 
 the individual who has them can penetrate. Percep- 
 tion is everywhere a business of interpretation, of 
 the recognition of logical identity in difference. 
 Thoughts are no mere happenings in space and time.
 
 240 PSYCHOLOGY 
 
 If they were we should never be cognisant of the 
 thoughts of our neighbours. Even the fullest psycho- 
 logical investigation must therefore, if it stops short 
 of a philosophy of some kind, fail to carry us to com- 
 plete understanding of the world external to ourselves. 
 Nor does our internal world, as revealed by intro- 
 spection or by even the vaguest self -consciousness, 
 stand in any better case. The barest feeling is what 
 it is for us only by virtue of its being distinguished in 
 some form of knowledge. It is recognised by being 
 classified, however loosely. It is so classified only by 
 virtue of the general or universal aspect it presents, 
 an aspect which has no subsistence apart from a 
 particularism that takes shape in an individual form 
 which is actual only in that both moments enter into 
 it. No doubt if we can resolve the universals of 
 knowledge here and elsewhere into something more 
 foundational, say self-subsistent entities succeeding 
 each other in order of externality, we shall get further. 
 But this requires us to become metaphysicians of 
 a particular school, like, for instance, Mr. Bertrand 
 Kussell, and even when we think that we have at 
 last arrived, it is only to find ourselves confronted 
 once again with the individual in its form of concrete 
 universality. Behind the fact that in some form 
 we always know we seem unable to get. But if 
 so neither the physiology nor the psychology of the 
 day, nor both in combination, bring us any nearer 
 the solution of the problem of the character of the 
 ultimate reality. Their value is to enable us to 
 study scientifically a particular aspect which presents 
 itself in a special domain of that reality, and in this 
 respect they are analogous to mathematics and 
 physics. Such study is, like study in these other
 
 CONFUSION OF STANDPOINTS 241 
 
 fields, of far-reaching importance. But its limits have 
 to be understood. When some of the most modern 
 physiological psychologists inform us that they feel 
 bound to recognise psychical processes as reacting on 
 neural processes, and that there is a ground of unity 
 of psychical process, they sometimes go on to call this 
 the ' soul/ It may be necessary for them to employ 
 some such appellation. But the meaning they seem 
 to attribute to the name is one that defines some 
 self-subsistent entity. The alternative interpretation 
 appears to be to look on the organism, say of a human 
 being, as the expression of more levels than one 
 in a hierarchy of knowledge. If the actual is only 
 actual through its relation to knowledge, if in 
 knowing we are always more than we take ourselves 
 to be, and are exercising no mere activity of a thing 
 in space and time, then we shall no longer worry 
 ourselves with the task of finding a metaphysical 
 meaning for ' soul/ We shall take the expression as 
 signifying that the plane of knowledge is more than 
 merely physical or even biological. We shall say 
 that when we find the neural processes as apparently 
 disclosing psychical reality we are recognising in 
 them a fuller character belonging to their actual 
 nature when it is investigated from this standpoint. 
 In other words, we shall take the facts as we 
 find them, refusing to be deterred by metaphysical 
 assumptions that they cannot be what they seem. 
 We shall, in short, take seriously, here as elsewhere, 
 the relativity of reality to its mode of apprehension 
 by mind. Such mind can therefore be itself no 
 effect and no substance, for these presuppose it as 
 their foundation. Not the less it is there for us 
 to study in the varying forms in which it expresses
 
 242 PSYCHOLOGY 
 
 itself, and one of these is its self-display in the 
 intelligent activity of the organism. 
 
 If we can in this way free ourselves from our 
 unconscious assumptions we may find ourselves 
 delivered from embarrassment in approaching the 
 problems of physiological psychology and of intro- 
 spective psychology alike. They both present illus- 
 trations of knowledge that is only of a particular 
 kind or degree and is therefore relative. But not the 
 less on that account do they belong to knowledge, 
 and knowledge which may be of scientific value. 
 When people talk of neural and psychical processes 
 as causally related we shall not deny the truth of 
 their observations. We shall only interpret the word 
 * causally ' in a different sense. The uniformities 
 will not be the less on that account ascertainable by 
 science. Nor shall we trouble ourselves over diffi- 
 culties about ' epiphenomenal ' aspects or the de- 
 scription of consciousness as being of this nature. 
 What we seek for is freedom to observe and record 
 the facts without distraction, and this freedom the 
 fuller view of knowledge and of the relation to it of 
 reality seems to permit us. It leaves us at liberty 
 to be grateful for the light which physiologists, by 
 study in minute detail of the structure and functions 
 of the nervous system, are throwing on the behaviour 
 of the organism. It leaves us not less grateful for 
 the increased refinement which introspective psycho- 
 logical methods have introduced into the study of 
 mental phenomena, such as those of association, 
 aided by new experimental adjuncts which biology 
 helps to furnish. 
 
 Physiology is now enabling us to understand more 
 completely than before the great part played in the
 
 THE VALUE OF PHYSIOLOGICAL METHODS 243 
 
 life of the organism by reflex action. Movements 
 which are reflex are such as are determined by a 
 chain of purely physiological processes. Some 
 physical stimulation, for instance of a sense-organ 
 of the skin, is transmitted through the sensory nerves 
 into the spinal cord, along certain neural channels in 
 the cord, and out along the motor nerves that pass to 
 the muscles, the contractions so stimulated in them 
 bringing about movements. It seems, if we take the 
 ordinary view that the organism and the soul are 
 separate entities, and not different aspects of one 
 reality, as though there could be no point at which 
 mind intervenes in such reflex action. In a carefully 
 guarded sense this is so. But the statement has to 
 be made subject to two qualifications. In the first 
 place such action does not appear to be merely 
 * causal ' in the meaning in which the word is used 
 in physics. A stimulus is of an order different from 
 that of such a cause. It is adequately intelligible 
 only on the footing that it is a phenomenon of life 
 dependent on the presence of the living organism as 
 an entirety and controlled by ends. It is no case 
 merely of events fashioned by external causes. In 
 order that the stimulus may operate the life of the 
 organism as a whole must come into play. You 
 cannot produce reflex action in a corpse. Even 
 when the living body is in deep sleep or uncon- 
 sciousness, as under the influence of a drug, it is 
 still a living body conducting itself as such, and 
 it is in this aspect that it presents the phenomena 
 of reflex action apart from consciousness of it. 
 In the second place the view that in the relation 
 of soul to life we are concerned with difference in 
 standpoint as distinguished from entity excludes 
 17
 
 244 PSYCHOLOGY 
 
 the idea that we are to inquire how soul and body 
 act on each other as causes. No doubt there are 
 many aspects of our objective world in which we do 
 not find mind expressed. But this does not imply 
 that it is somehow physically excluded. All our 
 conceptions of the orders which confront us in 
 apprehension are the outcome of a process of abstrac- 
 tion. From pure mathematics upwards this is so. 
 Whether in the course of progress towards fuller 
 comprehension we shall not discover at any point 
 that we require conceptions significant of mind in 
 order to make complete interpretation possible, we 
 cannot tell a priori. The transition, for example, 
 in biology from end apparently unconsciously 
 realising itself to consciously directed purpose, is 
 not a difficult transition for introspective psychology, 
 and it may be that for physiological psychology the 
 two orders in reflection will turn out to have been 
 isolated merely as the outcome of abstraction. 
 Indeed the progress of the latter science seems to 
 indicate more definitely than ever that this must be 
 kept in view. For recent research, such as that of 
 Professor Sherrington and others, seems to preclude 
 the old notion that the effects of external stimulation 
 of the sensory nerves always terminate at some place 
 in the brain where a soul which there encounters 
 and interprets them has sensations, and itself, in 
 response, produces active movement in the motor 
 nerves. We now know that the brain resembles the 
 spinal cord, and that stimulation passes through 
 channels of a highly complicated and differentiated 
 nature to the motor nerves, in a fashion akin to the 
 reflex action in the spinal cord. But even if it be 
 true that neural process can be separated from
 
 PROFESSOR MoDOUGALL 245 
 
 psychical process, it seems pretty clear that all 
 psychical process is accompanied by neural process. 
 
 Some very important questions which arise in this 
 connection are discussed by Professor McDougall in 
 his book on Physiological Psychology. He points out 
 the value, in connection with the physiological 
 phenomena which he describes, of the new knowledge 
 which is coming into being about speech, about sleep 
 and fatigue, and about what is popularly called 
 mental life. But he adds that the objective methods 
 of psychological study presuppose a basis attainable 
 only by subjective or introspective methods. The 
 work of the physiologist, however valuable, is there- 
 fore valuable as possessing an elucidative rather than 
 an independent character. To that observation I 
 venture to make this addition. There is no field of 
 knowledge in which there is not required more than 
 one order of conception for its interpretation. The 
 conceptions which enter into and fashion our ideas of 
 individual objects always belong to a plurality of 
 orders in knowledge, and therefore, in the objects 
 themselves, to the reality which is relative to it. The 
 physiology of an intelligent living organism can 
 hardly be exhaustively studied apart from the fact 
 of intelligence. 
 
 The observation I have just made, agreeing so far 
 with Professor McDougall, is no merely academic one. 
 There is prevalent a tendency to regard the behaviour 
 of the mind as though it could be accurately described 
 only in terms of physiology or physics. Even a very 
 competent exponent of educational systems does not 
 hesitate to tell us that for accurate and easy thinking 
 about education it is necessary " to select the facts 
 about which to think, and, above all, to choose facts
 
 246 PSYCHOLOGY 
 
 which, are simple, even if imaginary like the line 
 which represents the direction of a hedge. Thus, in 
 formulating principles of education we shall, for the 
 most part, focus our attention upon the comparatively 
 simple material aspects of the brain, rather than upon 
 the mind or soul, of the person being educated." 
 This is written by a man who has not only a high 
 and comprehensive view of education, but is far 
 removed from being a materialist. He believes, like 
 Professor McDougall, in the directing influence of a 
 real soul upon the organism, in ' interaction/ But 
 the result of his principle in investigation is to direct 
 his study of mental phenomena away to ' neuroses ' 
 and ' neurograms or neural dispositions/ and to find 
 this standpoint appropriate for an investigation of 
 the objects to be aimed at in education. Now that 
 physiology is a valuable adjunct and a necessary one 
 in the study of psychology, few would question to-day. 
 It plays the part that mathematics, physics and 
 chemistry all do as a necessary adjunct in biology. 
 Every field of study analogously implies the bringing 
 to bear of various orders in reflection. The reflection 
 is abstract and inadequate if it is confined to one 
 standpoint. But there is always an aspect which is 
 characteristic and dominant as marking off the 
 particular field. Its reality, always relative when 
 understood fully, but yet characteristic, is what 
 marks off the subject matter from different subject 
 matters. Now education is characterised by being 
 pre-eminently concerned with freedom in develop- 
 ment. To understand free mind as expressed in a 
 biological organism we have indeed to make full use 
 of the light that is cast on the behaviour of intelligent 
 persons by sciences which take no account of conscious
 
 EDUCATION AND PSYCHOLOGY 247 
 
 and self-directed purpose or of personality. But 
 these can give us nothing by itself adequate. They 
 are required as the physiologist requires physical 
 science. But they can take no account of the 
 phenomena of self-consciousness, inasmuch as these 
 latter are actual only at another level in the hierarchy 
 of knowledge. And such knowledge in its entirety 
 is implicitly presupposed as the origin and foundation 
 of all the distinctions which fall within its field, and 
 so make reality what it is. 
 
 We shall see later how introspective psychology 
 has tended of late to make an hypostatisation which 
 is analogous, though quite different. The point is 
 that although hypostatisations of this sort may be 
 necessary for limited purposes, as they are with the 
 mathematician, they are but partial guides to the 
 character of the actual, and are admissible only for 
 definitely limited purposes. If the closely limited 
 nature of the purposes is not interpreted and kept in 
 view such methods may be very misleading. Not only 
 in education but in practical medicine the failure to 
 consider this is giving rise to uneasiness among those 
 whose daily concern is with the facts of human life. 
 The medical practitioner has been of late complaining 
 of ' preliminary studies/ such as chemistry and 
 physiology, as being of little use. He is wrong. They 
 are of great use if only they are undertaken with 
 sufficient width of outlook to prevent them from 
 degenerating into what is too abstractly conceived. 
 In the same way the complaints about the use of 
 physiological and psychological methods in the 
 teaching of education are misplaced. The subjects 
 are highly valuable if taught with the warning that, 
 although they yield light, they are not exhaustive or
 
 248 PSYCHOLOGY 
 
 even adequate sources of light. Here, as elsewhere, 
 more standpoints than one are essential in interpreta- 
 tion. The soul which has to be educated is that of 
 a free and conscious person, however the personality 
 is conditioned in physical expression. It is therefore 
 primarily more than the mere physical expression in 
 a brain and nervous system that must always be in 
 view. 
 
 The study of this physical expression casts none the 
 less much light on the organisation of the soul and 
 of its modes of activity. The human organism marks 
 the highest point attained in biological evolution, and 
 the principles of heredity and of growth assist in the 
 understanding of its evolution. In man the family 
 of vertebrates reaches a much higher level in cerebral 
 development than in the case of any other member of 
 that family. The brain constitutes a segment which 
 is not, as in the cases of vertebrates of a low type, 
 merely one of a series, but is a part of the body 
 possessing a special dominating importance and con- 
 trol. In order to provide for great freedom of action 
 in dealing with the environment special sense organs 
 which have been developed to a high level acquire not 
 less highly developed nervous connections with the 
 ganglia of the most important segment. The brain 
 of man is related to the spinal cord, and to its own 
 basal ganglia, analogously to the relation which 
 obtains in the cases of animals lower than man. But 
 the brain itself in his case has reached a higher stage 
 in development. The cerebral hemispheres depend, 
 no doubt, on the greater number and complexity of 
 what constitute the factors in the culminating portions 
 of the nervous system that are its basis. But that 
 which distinguishes it in man is still more the enor-
 
 THE BRAIN IN MAN 249 
 
 mously increased and complicated multitude of neural 
 arrangements which become increasingly organised 
 as experience of life progresses. It is pre-eminently 
 in man that the cerebrum is capable of so adapting 
 its structure and its functions as to bring about 
 habits in action and dispositions peculiar to indi- 
 viduals. Here, as everywhere else in the brain, the 
 nerve-cells do not exist in isolation. For purposes 
 of nutrition and growth they may be regarded each 
 by itself. But they really discharge functions in the 
 interests of the entirety of the body, and depend for 
 their lives on co-operation of the parts within the 
 whole to which they belong. Such nerve-cell organ- 
 isations are generally spoken of to-day as neurones, 
 a term which seems to have been chosen as indicating 
 that cells do not really exist isolatedly. The neurone 
 includes not only a nucleus of the cell, but proto- 
 plasmic substance which surrounds that nucleus. It 
 is out of such neurones that nerve fibres are built up. 
 As to how nervous impulses are conducted along 
 nerve fibres little seems to be known with any degree 
 of certainty. There are waves of electrical energy 
 which travel from the point excited when a nerve is 
 stimulated, but much more than this fact is required 
 for an adequate description of the character of 
 nervous impulses. We seem here to be in the region 
 of self- adaptation in response to ends to be fulfilled, 
 and beyond anything which merely mechanical 
 descriptions fit. As far as I can find, the action 
 which takes place when the neurone is stimulated is 
 of a metabolic character. The living cell substance 
 alters its composition, and gives rise to some form of 
 energy. On the other hand, it restores itself after- 
 wards from its environment in the fashion referred
 
 250 PSYCHOLOGY 
 
 to earlier when we were concerned with biology. If 
 this be so no merely chemical explanation can be 
 sufficient. Here, as elsewhere, the categories of life 
 yield the only terms in which life can be described. 
 
 In the complicated living system in which the 
 organism consists neurone is related to neurone. 
 They combine in sensori-motor arcs or systems in 
 which the nervous impulse is conducted from sense 
 organ to muscle. This requires the junction of at 
 least two neurones, a sensory or afferent and a motor 
 or efferent neurone. Chains of neurones may be 
 joined in this fashion. The junctions are known to 
 physiologists as synapses. 
 
 In the work already referred to Professor McDougall 
 gives an account of synapses, and dwells on the 
 importance of their capacity to resist the passage of 
 energy from neurone to neurone. This capacity to 
 resist may be much affected by the state of the blood, 
 by drugs, and by influences such as were discussed 
 when we were considering the nature of life in the 
 last section. Professor McDougall points out that 
 repetition of the process of transmitting energy across 
 a synapse tends to lower its capacity for resistance, 
 and that a permanent lowering thus brought about 
 appears to be the mode of formation of neural 
 habits, and so of high moment. " If," he says, 1 " the 
 conclusions just stated are well founded, the part 
 played in the nervous system by the synapses is 
 supremely important, for it is the various degrees of 
 resistance of the innumerable synapses, variable by 
 the several influences enumerated above, that guide 
 the course of the excitation-process initiated in any 
 sensory neurone, as it spreads from neurone to 
 
 1 Physiological Psychology, at p. 32.
 
 NEURONES AND SYNAPSES 251 
 
 neurone through the maze of the nervous system, 
 and determines its issue by this or that group of 
 motor neurones to this or that group of muscle 
 fibres. For, as was said in Chapter I, the sensori- 
 motor arcs, even those of the spinal level, are not 
 commonly simple and isolated from one another, 
 but are combined to form neural systems of various 
 degrees of complexity. And no one system is com- 
 pletely isolated from the rest, for, if the nervous 
 system is in a state of abnormal excitability, a 
 stimulus applied to any small group of sensory 
 neurones may initiate an excitement which spreads 
 throughout a very large part of the nervous system 
 and throws almost all the muscles of the body into 
 contraction. But when the nervous system is in a 
 normal condition, the excitation-process resulting 
 from a stimulus of moderate strength applied to a 
 sensory neurone, or a group of sensory neurones, 
 spreads through a limited system of arcs and excites 
 a co-ordinated contraction of one group of muscles 
 only. The neural system was defined as a group of 
 sensori-motor arcs so connected that when any one 
 part of it is excited through a sensory neurone the 
 excitement tends to spread to the rest of them. 
 We now see that such a system consists of neurones 
 connected together by synapses of low resistance, 
 and we can understand how simple systems, con- 
 sisting of a few neurones united by synapses of the 
 lowest degree of resistance, may be connected 
 together by synapses of rather higher resistance to 
 form more complex systems, and these again by 
 synapses of still higher resistance to form still more 
 complex compound systems. We can understand, 
 too, that since the resistances of the synapses are
 
 252 PSYCHOLOGY 
 
 liable to temporary variations from various causes, 
 the effects produced in the nervous system by a 
 stimulus of given character and intensity applied to 
 any group of sensory neurones may be very different 
 on successive occasions." 
 
 The passage just quoted throws light on much that 
 is matter of daily psychical experience. Our quick- 
 ness in apprehension, our readiness to respond to 
 perceptions, are subject to physical conditions. We 
 may vary in capacity from day to day. The explana- 
 tion here given is of a kind that is much more than 
 merely mechanical. It is more than merely bio- 
 logical. It is an explanation that applies to the 
 living structure regarded as having a psychical 
 aspect. Not one in which the psyche is a thing 
 apart from the brain and nervous system, but one in 
 which these are looked upon as capable of signifying 
 reality at a stage that is higher and more concrete 
 than what is disclosed merely by the microscope. 
 Apart from introspective experience the phenomena 
 described would lose half their significance. In man 
 and the intelligent animals the organism presents 
 itself as factual at a level that is more than merely 
 biological, and apart from the conceptions it expresses 
 and that are peculiar to such a level it would lose 
 much of its meaning and be no longer actually what 
 it is for us. 
 
 In man, too, there are regions in the organisation of 
 his nervous system whichmarkhis progressive develop- 
 ment from the lower vertebrates. To these he is 
 closely allied by what we find in the region of the 
 spinal level, and the reflex system which connects 
 excitement of the sensory nerves with the stimulation 
 to movement of muscles and groups of muscles.
 
 THE SENSORY AREAS 253 
 
 Here, as elsewhere in the body, the neurones are 
 grouped into sensori-motor networks or arcs. But 
 the sensory paths are prolonged so as to reach the 
 arcs of the cerebral hemispheres. If we look at a 
 physiological drawing of the brain we notice located 
 on it various areas as being the sensory areas for 
 the different senses. The visual area is in one 
 place, the auditory, tactile, and olfactory areas in 
 others, and the region of the muscular sense in one 
 different. Nervous fibres pass down through the 
 grey material of the cortex from these various 
 sensory areas to join the various motor mechanisms 
 of the spinal level. The afferent neurones of the 
 sensory parts of the body appear to be closely con- 
 nected, in the sensory areas of the cortex, with 
 efferent neurones that connect with motor systems 
 of the same region. It is in the cerebral hemi- 
 spheres that the passage of excitation of the nerves is 
 attended with consciousness in the form of sensibility. 
 Pain and pleasure are experienced as connected with 
 these sensation-reflexes. As Professor McDougall 
 observes (at p. 49 of the book already quoted) : " At 
 every moment very many different stimuli are playing 
 upon my sense-organs. Variously coloured rays of 
 light are entering the eyes, waves of sound fall upon 
 the ears, the skin receives stimuli from the clothes 
 and all other objects in contact with the body, the 
 contractions of skeletal muscles excite the nerves of 
 the ' muscular sense/ and many of the nerves of the 
 visceral system are almost constantly stimulated. 
 Some of these stimuli excite only pure reflexes like 
 those just mentioned, but most of them excite sensa- 
 tions and sensation-reflexes. Of all the objects that 
 thus excite sensation my attention is given to only
 
 254 PSYCHOLOGY 
 
 one at any moment, only one of them is at that 
 moment an object for me in the psychological sense 
 of the word, and if I am absorbed in thought my 
 attention is given to none of them. Nevertheless, 
 all these sensations, excited by objects to which no 
 attention is paid, are present to consciousness in an 
 obscure manner, they constitute a field of undis- 
 criminated or marginal sensations, and are the 
 principal constituent of the rich and massive, though 
 vague, background of consciousness on which the 
 object of attention at any moment stands out as the 
 most prominent feature of the state of consciousness." 
 
 Experience points to the fact that we do not have 
 sensations atomically, as if succeeding one another 
 or as co-present in isolation. They seem to belong 
 to a field out of which we can only bring them under 
 attention by act of abstraction in which they are 
 singled out and distinguished amid a multitude of 
 other sensations, in an entirety to which all of them 
 belong. It may be that the stimuli themselves are 
 always complex, and that the feeling is excited in 
 the sensory areas of the cortex of the brain. It may 
 well be also that assistance can be got in under- 
 standing the principle of the association of ideas by 
 looking at the facts from a physiological point of 
 view. For the structure and functional activities of 
 the different parts of the brain disclose a basis on 
 which physical association takes place, and this 
 cannot be dissevered from the corresponding psychical 
 association. Moreover, the functions of the brain 
 are localised functions, and it is not irrelevant that 
 the sensory nerves which communicate with them 
 are nerves having individual and specific functions. 
 
 There is evidence that points to the cell junctions or
 
 CELL JUNCTIONS AND MENTAL ACTIVITY 255 
 
 synapses as being the region in which psycho-physical 
 processes really manifest themselves most plainly. 
 For the organisation of neural processes in systems 
 seems to consist chiefly in the establishment of these 
 junctions, and their development. The less complete 
 the development the greater the psychical manifesta- 
 tion appears to observation to be. When the point 
 has been reached at which resistance is overcome the 
 psychical manifestation tends to disappear. Pro- 
 fessor McDougall observes under this head, 1 that 
 " what we have to accept as a well-established view 
 is that some part or parts of the sensori-motor arcs of 
 the intermediate level, where they traverse the cere- 
 bral cortex, are of a highly peculiar constitution, such 
 that the process of transmission of the ' nervous 
 impulse ' assumes in them a very special or specific 
 character, that this highly specialised nervous sub- 
 stance is not of one character in all cases, but exhibits 
 a certain number of varieties which give rise to a 
 corresponding number of kinds of psycho-physical 
 processes, each of which excites one of the elementary 
 qualities of sensation." It does not appear that any 
 ordinary physiological explanation can be found of 
 how these processes come to be brought together in 
 the unity which characterises mental activity. The 
 factors in mental unity are not atomic as they are in 
 chemical combination, in which they remain separate 
 entities even while combining. What happens 
 appears to belong to a different order in experience. 
 It is not necessary or even logical to assume that 
 this different order implies a substance, existing in 
 itself and yet different from other physical substances. 
 The soul, if the term may be used, is not to be assumed 
 
 i Ub. sup., p. 61.
 
 256 PSYCHOLOGY 
 
 to be a thing. When I look round on the rich world 
 that surrounds me it is not a collection of causal 
 processes subsistent by themselves that I see. It is 
 rather a world which requires all orders of reflection 
 for its explanation, and levels of objectivity which 
 express conceptions beyond those of physical and 
 biological science. The ethical and the beautiful 
 aspects of reality are not to be got rid of by any 
 attempt to reduce them to relations in which they 
 cannot even be expressed. It is more consonant with 
 common sense to start with what is actual, and 
 explain physical relations as reached downwards by 
 abstraction from what is more concrete. Just so the 
 brain conceived purely biologically, not as expressing 
 function in a living and intelligent human being, 
 but only as it appears when dead on the dissecting 
 table, seems to be no adequate representation of 
 the brain conceived as the organ of mind, in a 
 man into whose individuality all the varieties of 
 ethical and social relationships enter. It is the 
 old story of trying to exhaust the individual by 
 universals. The process is one which can never 
 operate exhaustively or reach a conclusion. There 
 is always some level lying beyond which the con- 
 centration of abstract reflection and observation 
 excludes. So far, but only so far, does such reflection 
 yield truth. 
 
 This consideration becomes still more apparent 
 the further we proceed with the study of the brain 
 in the higher animals. The perceptual organisation 
 is a complex of sensori-motor arcs of various physio- 
 logical levels. It is not merely sensory nerves in 
 the area where sensation arises that we observe 
 contributing to mental process. We find arcs of a
 
 SENSORI-MOTOR ARCS 257 
 
 higher level which are indispensable for the evoking 
 of images, and for co-ordinating motor impulses. 
 The control of the muscles of the body ; the inhibition 
 of the activities of other parts of the nervous system 
 by the drawing to itself of energy in the case of the 
 part that is for the moment dominant ; the diminu- 
 tion in other systems caused by the activity of the 
 perceptual system which is in action, these are 
 among phenomena which physiological psychology 
 brings under study. As correlative to psychical 
 process they enable us to get light on its operation. 
 But they do not exhaust the necessity for a further 
 standpoint in that study. The brain consists of 
 almost innumerable systems of neurones, organised 
 with varying degrees of completeness and intimately 
 interconnected. Some of these systems are congenital, 
 while others are built up during the course of life 
 through its activities. Instinct appears to belong at 
 least mainly to the inheritance that is congenital. 
 
 But there are phenomena which seem to require a 
 further standpoint for their explanation. Diversion 
 of the passage of energy by ' drainage ' throws some 
 light on the difference between attention and in- 
 attention. More, however, is required in order to 
 make intelligible the further phenomena of volitional 
 as distinguished in experience from automatic move- 
 ment. Here what we call ' will/ action in which 
 self-consciousness is present, confronts us. Professor 
 Stout, in his Analytic Psychology, dwells in detail on 
 the differences we encounter here. 
 
 These differences are not absolute. Volition shades 
 into automatism as the result of habit. But when 
 we are carrying out the result of conscious reflection 
 the successive phases of action are not detached
 
 258 PSYCHOLOGY 
 
 from each other and do not follow a time order which 
 usage has established. What determines the order 
 and form of action in conscious volition is the con- 
 ception of the process as a whole, and of an end to 
 be realised in it. The distinction is the old one 
 between cause and end, but the end is here a con- 
 sciously adopted end, and therefore a purpose. This 
 is what actual experience of the facts seems to 
 teach us. 
 
 Now it is no doubt true that in the higher levels of 
 a fully developed brain the organisation is of a very 
 complex nature, so complex that physiology can 
 to-day describe it only in the barest outline. Even 
 if we assume, what is almost certainly true, that 
 every process disclosed by introspection has a neural 
 counterpart, this assumption in itself guides us but 
 little in psychological interpretation of the phenomena 
 of volition as observed from the standpoint of ordinary 
 physiology. If we include ends as disclosing them- 
 selves in operation from that standpoint, we are 
 still a long way from having before us conscious 
 purpose, with its apparent freedom both in selection 
 of order in succession and in shaping and even 
 creating. We seem here to be beyond the level, not 
 only of physical, but of biological conceptions. To 
 import the notion of a self-subsistent entity, physi- 
 cally different from the neural processes in which 
 it expresses itself, is to court confusion. If the 
 assumption is only the outcome of a restricted meta- 
 physical assumption, it seems safer to throw over 
 this assumption and to turn to the possibility that 
 reality, here as elsewhere, may disclose itself as 
 possessing levels or degress which have their counter- 
 part in the levels or degrees of the conceptions in our
 
 CONSCIOUS PURPOSE AND PHYSIOLOGY 259 
 
 knowledge to which all reality appears to be relative. 
 If an effort of will discloses itself as a voluntary 
 concentration of attention upon some object, it may 
 be a percept or idea, and if its physiological correlate 
 is a high degree of concentration of the energy of the 
 brain along some system of paths, then we may have 
 to look upon the higher phases of brain organisation 
 as being expressive of more than mere biological ends. 
 Unless we make up our minds that we are free to do 
 so it is difficult to see how we can attain to any 
 explanation that is adequate to the facts. A human 
 being, living in society, obeying its laws, manifesting 
 even the minimum of intelligence and self-deter- 
 mination that is required to make him human, 
 endowed with ethical, aesthetic and religious qualities, 
 is not to be explained merely biologically. Why 
 should the phenomena of his brain be so explained 
 any more than those of the complete personality ? 
 In the living and intelligent being the brain belongs 
 to his personality, and expresses it in the same 
 fashion that any other of his aspects does. If the 
 methods of necessity employed when the brain taken 
 by itself has to be studied do not admit of the 
 conceptions which personality implies, that warrants 
 only the inference that these methods are, like other 
 methods employed in science, of necessity abstract, 
 and inadequate as a means of attaining to the fullest 
 truth about the nature of the domain of reality in 
 which we find ourselves. 
 
 It is here that the limits of the assistance which 
 physiology can render to psychology appear to come 
 in. Of great assistance to the psychologist these 
 methods undoubtedly are. But they play the part 
 which mathematics, physics and chemistry play for 
 18
 
 260 PSYCHOLOGY 
 
 biology itself, and no further part. Experience as an 
 entirety is wider than all these, which constitute only 
 certain of its forms. 
 
 We are thus driven to the use of introspective 
 methods in supplement of those which physiology 
 provides. But here, too, we find ourselves often 
 confronted with the limitations sought to be imposed 
 on us by the mind which limits its categories. If the 
 self is assumed to be a ' thing/ capable of being 
 sufficiently studied as though it were only such, we 
 inevitably fall into trouble. Metaphor drawn from 
 the domain of mere observation at arm's length 
 becomes rampant. If the soul is only intelligible as 
 deriving meaning and therefore reality in virtue of 
 distinctions made within knowledge, it cannot be 
 interpreted excepting as an object which knowledge 
 discloses, an object which will be inadequately 
 conceived unless it is recognised that its reality is 
 relative to knowledge such that no one level is ex- 
 haustive. A view obtained from a single standpoint 
 may be of great value, but it does not disclose the 
 full truth. It is only by letting knowledge exhibit 
 its own development and its own stages in that deve- 
 lopment that we can interpret the actual adequately. 
 
 What is called ' psycho-analysis ' proceeds on this 
 limited footing. It treats the self as a thing to be 
 studied apart from its relativity to the categories 
 employed. We have always to work in this way in 
 our finite investigations, but we have not the less to 
 bear in mind the limitation of the results reached. 
 How closely limited these may become by the 
 metaphors drawn from other levels of knowledge we 
 shall see if we take as our example one of the best- 
 known systems of psycho-analysis.
 
 FREUD 261 
 
 About forty years ago Dr. Sigmund Freud of 
 Vienna, afterwards Professor in the University there, 
 made certain investigations into cases of hysteria. 
 He caine to the conclusion that the origin of the 
 hysteria in these cases was the unconscious repression 
 by the patient of the presence of hidden experiences, 
 mental dispositions which had passed into the region 
 of the unconscious, and which had originally been 
 attended by emotion. The memories of these experi- 
 ences had passed into unconsciousness, but were not 
 the less active and were being unconsciously repressed. 
 Upon his studies Freud founded the well-known 
 theory which is elaborated, with a multitude of 
 illustrations, in his book on The Interpretation of 
 Dreams. By him the force which represses un- 
 pleasant thoughts and keeps unconscious wishes from 
 getting through into the region of conscious know- 
 ledge, is called the ' censor/ The term ' wish ' is 
 used in his psycho-analysis as covering all sorts of 
 yearnings and ambitions. Of these a great many are 
 in existence but do not come into consciousness, 
 owing to repression by the censor. They constitute 
 none the less a working basis for dreams, neurotic 
 symptoms such as stammering, and many sorts of 
 mental conflict. The dream is a true expression of 
 unconscious mental content, and is the fulfilment of 
 a repressed wish. A mass of latent ideas is condensed 
 into the momentary dream as it is remembered on 
 awakening, and to find its basis requires analysis of 
 the dream itself. It is generally forgotten because 
 of the dominant wish to forget the ideas on which it 
 is based. This wish is a form of ' resistance/ One 
 valuable function of dreaming is to make sleep 
 possible by rendering such ideas momentary and
 
 262 PSYCHOLOGY 
 
 unrecognisable by the sleeper. The only sort of 
 dream which disturbs sleep is the nightmare, which 
 is an anxiety dream. For Freud hysteria is the 
 result of the effort of the mind to disguise its un- 
 pleasant thoughts and experiences. That is why it 
 takes the form of mental conflict. It is due to ideas 
 which are not harmonious with the rest of the patient's, 
 personality. When these ideas are repressed the 
 repression gives rise to peculiar mental states, to 
 loss of memory, or even to behaviour and physical 
 conditions which may characterise hysteria, such 
 as stammering (an anxiety form of nervousness), 
 paralysis, blindness, loss of sensation, feeling of 
 unreality and so on. The true way for the physician 
 of dealing with such pathological conditions is to 
 explore their origin with a view to detecting and 
 breaking down the resistances in the past which have 
 produced them. How has all this come about ? 
 Only an exploration of what the real working of our 
 minds has been can show. The value of preventing 
 experience early in life of the undue working of fear 
 or shyness may thus prove of much use in preventing 
 the acquisition of abnormal habits later on. This 
 sort of penetration into the origin of symptoms 
 in nervous pathology constitutes at the same time 
 their treatment. The unconscious but yet present 
 motives and desires which are disclosed in various 
 physical disturbances, and even in some manifes- 
 tations in ordinary life, are got rid of if they are 
 brought into consciousness. Freud has inquired into 
 the dreams in particular of persons mentally afflicted, 
 and claims to have been able to trace the genesis of 
 delusions, morbid fears, hysteria and insane ideas. 
 The basic conception of his psycho-analysis is the
 
 PSYCHO-ANALYSIS 263 
 
 existence of definite division between the individual 
 consciousness and its unconscious basis. The method 
 of psycho-analysis is not the usual disclosure by the 
 patient in answer to the questions of a physician of 
 the history of his affliction. In that case the patient 
 can offer the records only of his self-consciousness. 
 It is the reduction of the contents of consciousness 
 to the sub-conscious origins with which psycho- 
 analysis is concerned. It affects on this account to 
 be a new science. Dreams, symptomatic action, and 
 what are called association tests, are among the 
 means by which each symptom in the patient's 
 mental life is sought to be resolved. What are called 
 his ' emotional transferences ' are examined with a 
 view to ascertaining possible reasons for resistance to 
 the analysis, and when these reasons are made 
 explicit they tend to disappear, so that the subject 
 is brought to a utilisation of his mental energy in a 
 way more profitable than that of expending it in 
 unconscious neurotic conflict. The art required 
 implies considerable scientific study and training. 
 As might be anticipated, the sexual instinct has a 
 high place among the reasons hidden in the region of 
 the unconscious which are operative. But there is a 
 large school of psycho-analysts who hold that Freud 
 has gone too far in this direction, and give more room 
 to other tendencies in nature. 
 
 What distinguishes the new method from old ones, 
 depending only on introspection and suggestion, is 
 held to be that what the new method aims at is to 
 remove something definite, the influence exercised 
 by the abnormal mental resistances, while the other 
 methods merely aim at adding something. The 
 object of psycho-analysis is to produce self-know-
 
 264 PSYCHOLOGY 
 
 ledge, not to hypnotise or to reduce mere surface 
 effects which may recur for want of removal of their 
 causes. The analytic process of the new school 
 seeks to transfer into a fresh and safe channel the 
 emotions brought to light. What the physician has 
 to do is to unlock the door which resists the emer- 
 gence of the hidden complex, and this he does scien- 
 tifically and sympathetically until it disappears and 
 the patient becomes normal and the symptoms 
 disperse. The hidden complex consists in ideas with 
 emotion attaching to them. They are there, but an 
 unconsciously exercised purpose has shut them in, 
 so that they emerge in dreams and other symptoms 
 not under the control of conscious and free mental 
 activity. Much of ' forgetting ' is really unconscious, 
 and so involuntary repression. In the phenomena of 
 duplex personality and in somnambulism this makes 
 itself apparent. The hidden vital energy or instinct 
 is sometimes called the * libido/ This is by no 
 means always of a sexual nature. It may assume 
 the form even of hunger. 
 
 The unconscious is for the school I am referring to 
 the domain in which lie the contents of the self of 
 which we are not aware. It is spoken of as ' uncon- 
 scious ' mental life, an expression which is sometimes 
 preferred to ' sub-conscious ' or ' subliminal/ inas- 
 much as it does not suggest any spatial relationship. 
 In this domain of the unconscious are stored up wishes 
 and ideas, often impossible of fulfilment in actual life, 
 and they are kept there by the censor of consciousness. 
 When these wishes and ideas seem to be fulfilled in 
 dreams it is because the censor of awakened intelli- 
 gence has been feeble or absent, and has allowed them 
 to slip past it as dreams. Often the unconscious
 
 THE UNCONSCIOUS AND SUBLIMATION 265 
 
 wishes and ideas get through in only symbolic form, 
 and then psycho-analysis traces their existence 
 through the symbols. Myths may be the symbolic 
 expressions in this sense of a whole race. 
 
 Sublimation, or the refining away of baser qualities, 
 is the process which the physician of this new school 
 employs. It is the unconscious conducting of the 
 repressed emotions into a new channel. The patient 
 is guided away from mere resistance, and the mental 
 energy, instead of being expended on mere resistance, 
 is directed to fashioning the emotion into some good 
 shape. Sublimation along religious lines is common. 
 The patient, being made aware of his buried mental 
 processes, becomes gradually released from the 
 oppression of their fixed character, and the conflict 
 arising from inner resistance yields. The energy of 
 the unconscious self is no longer pent up, but transfers 
 itself in the patient, now aware of it and duly encour- 
 aged, into fresh channels. Moreover, the unconscious 
 is the region where character lies, and the contents 
 of this region must therefore be transformed if the 
 character is to be improved. The character of a 
 person may be largely dependent on childish im- 
 pulses and reactions against them. Thus a spoiled 
 child tends to become an impatient adult, and a day- 
 dreaming boy may grow into an unduly taciturn 
 man. The origins must in all such cases be detected 
 and brought to light. A healthy self-consciousness, 
 no longer repressive, but seeking to use the hidden 
 tendencies for good ends, will do the rest. 
 
 Such is a bare outline of the doctrine of Freud and 
 of those who have found in him their teacher. It is 
 obviously not a scientific doctrine to the same 
 degree as is physiological psychology. It aims
 
 266 PSYCHOLOGY 
 
 rather at practice. It is therapeutic, an art at least 
 as much as a science. Its nomenclature and its 
 descriptions are based largely on metaphors which, 
 however useful for practical purposes, throw but 
 little light on the ultimate character of reality. It 
 is not surprising, therefore, that even those who 
 recognise in Freud's teaching the initiation of a new 
 method of inquiry should have developed much 
 criticism of its foundational assumptions. We shall 
 see presently why this has been so. For the moment 
 it is enough to say that objection is taken to the 
 drawing of a sharp boundary line between the 
 conscious self and an apparently numerically different 
 unconscious self, with a censor, also outside con- 
 sciousness, guarding the gateway between the two. 
 Such a picture is said to be merely metaphorical, and 
 to be also untrue of the phenomena of the mind. 
 Psychologists who employ more strictly scientific 
 expressions have raised a number of points about 
 this, some of which require attention. 
 
 Investigators who rely on introspective methods, 
 as well as some whose attention has been concen- 
 trated mainly on physiological study, have been busy 
 over various questions. One of these relates to the 
 proper significance of the expression ' unconscious/ 
 Another is concerned with the place in the science of 
 mind of ' instinct/ A third refers to the character- 
 istics which distinguish instinct from mental activity 
 proper. Looking at this last question, there has been 
 discussion over what is called the * All or None ' 
 principle as characteristic of instinctive reaction. 
 This principle signifies that the amount of the 
 reaction does not depend on the amount of the 
 stimulus, but that, if a neural stimulus takes place
 
 INSTINCT AND CONSCIOUS PURPOSE 267 
 
 at all, it always results in a reaction in full force. 
 It has been suggested that in this lies a quality which 
 distinguishes instinct from conscious action, in which 
 the extent of the action in volition is proportioned to 
 the object sought to be accomplished. In physiology 
 there are some reactions of the ' All or None ' type 
 which are familiar. We are here dealing with stimu- 
 lation and not with causation proper. If Professor 
 Lloyd Morgan is right in the passage quoted earlier, 
 in which he treats instinct as a function of the sub- 
 cortical centres, it is intelligible that a slight stimulus 
 should in all normal cases release the same amount 
 of stored-up energy. It is said that the extensor 
 thrust reflex, obtainable by touching the skin beneath 
 the pads of a dog's hind foot, which remains within 
 wide limits unaltered although the strength of the 
 stimulus is varied, illustrates the principle. But 
 it is pointed out that, however true the application 
 of the principle may be in the case of certain nervous 
 reactions in physiology, it does not fit the facts in 
 many cases of instinctive behaviour, such as those in 
 which the emotions of fear or anger are instinctively 
 exhibited as varying with the character of the object. 
 Obedience to the principle is therefore no sufficient 
 general characteristic of pure instinct. 
 
 It is accordingly held by some recent writers that 
 while instinct is innate it cannot be sharply marked 
 off from the rest of mental content by any such 
 principle. It may display a cognitive side, and 
 often enters into cognition proper, inasmuch as it 
 renders possible, in virtue of innate disposition, 
 perception and discriminative treatment of objects 
 independently of previous individual experience. We 
 see this in the case of men of high aptitudes. The
 
 268 PSYCHOLOGY 
 
 power of calculation, for example, seems in certain 
 individuals to be due in large part to a natural free- 
 dom from uncertainty in apprehension through which 
 they predominate over others. Yet such capacity is 
 properly treated as an intellectual one, although it 
 apparently depends on unconscious as well as on 
 conscious quality and varies with the subject to which 
 it is applied. 
 
 In order to avoid the difficulty so arising it has 
 been of late suggested that a distinction should be 
 drawn between mental structure and mental function- 
 ing, and that we may accept the view that conscious- 
 ness is not co-extensive with the whole field of the 
 psychical. Mental structure may be outside con- 
 sciousness, while mental functioning may be within 
 it. Thus the observation of the structure would be 
 limited to a merely ' behaviourist ' method, aided by 
 inference from introspection. The mind would 
 consist in this view not merely of ideas or presenta- 
 tions but of the structure which regulates their 
 appearance, a structure which would form the 
 domain of the unconscious. 
 
 This brings up at once the difficulty first referred 
 to of drawing a line of demarcation between the 
 conscious and the unconscious. Freud does not allow 
 himself to be embarrassed on this point, but his 
 escape from it is largely due to his copious use of 
 metaphorical expressions. Is there any definite 
 line of demarcation between the two different sets of 
 facts ? There is of course much of which we are 
 not immediately conscious which yet influences 
 us. What significance is to be attached to tele- 
 pathic methods we hardly yet know. But much 
 that has been learned and has since been appa-
 
 THE CONSCIOUS AND THE UNCONSCIOUS 269 
 
 rently forgotten is still present for some purposes, 
 hidden, it may be, in ' the pit of the ego/ as it 
 has been called without prejudice, but capable of 
 being brought back into actual knowledge. The 
 limits of the field of the object of self-consciousness 
 are neither physical nor fixed. The process in 
 awareness appears to be dynamic and to stand for 
 nothing static. Thought is always qualifying feeling, 
 and feeling is continuously giving actuality to thought. 
 They are never divorced in our actual experience. 
 When we use the methods of psychology in its current 
 forms we seem to arrest the process and to stereotype 
 what is only one aspect in which by our abstract 
 methods we force it to present itself. For practical 
 use we may draw a distinction between the domain 
 of the conscious and that of the unconscious. We 
 may even employ this distinction for scientific ends 
 if we remember how artificial it is. But it does not 
 seem to correspond to the full reality or to give 
 adequate expression to the full truth. 
 
 If the principle on which this book and its prede- 
 cessor, The Reign of Relativity, are founded be a 
 reliable one we are delivered from the embarrassment 
 of having to look to either physiological or intro- 
 spective psychology for the ultima ratio. These are 
 sciences which, like other sciences, fashion in their 
 standpoint the aspects which the actual presents for 
 them. The brain and nervous system which the 
 physiological psychologist is dealing with are, let us 
 assume, those of a living man. Well, they are just as 
 much expressive of human personality as is any other 
 aspect of the individual man. They are expressive of 
 more than mere life. They are the manifestation of a 
 soul. Of course when they are dead and laid out on the
 
 270 PSYCHOLOGY 
 
 dissecting table they are so no more. Mind is no longer 
 expressing itself in them. What is a means is no longer 
 fulfilling its function. It is in virtue of concepts, 
 which are not happenings in space and time, but are 
 logical identities in difference, that we cognise and 
 recognise personality. I have given the reasons for 
 saying this in Chapter VII of The Reign of Relativity. 
 All that physiology can yield is a science, limited in 
 the character of the reality which is relative to its 
 particular standpoints, as are the abstract characters 
 with which physics and chemistry deal. That is no 
 reproach to the particular sciences concerned. It is 
 not really their aim to go beyond their special under- 
 takings. If knowledge be in truth the entirety, and 
 the standpoints of the special sciences represent 
 levels within its hierarchy, this is intelligible. We 
 are dealing, not with entities, but with forms which 
 our experience assumes. It is the doctrine of 
 Aristotle, of Plotinus, and of some of the modern 
 leaders in philosophy. What it warns us against is 
 the treatment of knowledge as an attribute or 
 activity of a thing. If we treat it so we may be 
 using a valuable abstract method, as we do in 
 mathematics. But although valuable as being in- 
 dispensable for the concentration which is required 
 for the extension of exact research, such knowledge 
 is of a limited order. It cannot guide us to the 
 ultimate truth about the reality it is concerned 
 with because it has fashioned that reality into its 
 own restricted image before moving at all. 
 
 Let us then rather regard the active and intelligent 
 man as having in his brain and nervous system, 
 while he remains active and intelligent, what is akin 
 to the rest of his personality and interpretable only
 
 LIMITS OF PSYCHOLOGICAL METHODS 271 
 
 at its level. Physiological psychology can give us 
 help in studying phases of his self-expression, but it 
 cannot reach his personality. The reason is that 
 the soul is no thing, nor any structure in space or 
 time, but an aspect in which the human organism 
 presents itself at certain standpoints. At these the 
 brain while, but only while, it lives and acts is an 
 integral manifestation of personality. Physiological 
 psychology is therefore just physiology with intro- 
 spective psychology brought to its aid. 
 
 Then introspective psychology itself is no less a 
 science which has fashioned the actual in its own 
 image. In this science we look into our minds, 
 holding them out for inspection after the fashion 
 which John Locke made famous. No doubt there 
 have been here immense advances in method, made 
 since his day. Experiment in the laboratory has 
 made such advances possible. But the standpoint 
 and the categories or conceptions implied by him 
 have not varied. The mind is treated as a thing to 
 be observed ab extra, and not as self-disclosing. 
 Such a standpoint gives us much. It has yielded a 
 body of knowledge which includes, not only what 
 is contained in the textbooks of psychology, but 
 much of what is included in treatises on logic. Still, 
 from this standpoint, the inquirer does not regard 
 knowledge as being foundational or what is always 
 presupposed along with the distinctions which its 
 dynamic character is ever setting up within itself. 
 Among those are the differences between reality and 
 unreality, present and past, truth and error, good and 
 evil, beauty and ugliness, universal and particular. 
 It is only in terms of knowledge itself that these get 
 the meaning which is constitutive of their actuality.
 
 272 PSYCHOLOGY 
 
 Our own minds we come at as signifying what is 
 thus established within a system of knowledge outside 
 of which we cannot travel even in thought. In 
 being apprehended as objects for knowledge these 
 minds get their meanings for it and for the fashion of 
 their reality with a significance and appearance 
 which depend on standpoint. 
 
 These considerations appear somewhat to reduce 
 the importance of the distinction between the domain 
 of the conscious and that of the unconscious. It 
 may be that the search for a definite line of demar- 
 cation is a vain one. There is no reason why, for 
 purposes belonging to a psychological standpoint, 
 we should not recognise aspects of reality falling 
 within the system which includes all knowledge, 
 instinct and conscious selection, and connect these 
 aspects in our physiological studies with structural 
 arrangements in the spinal system and the lower 
 brain centres and arcs. But we must not leave out 
 of sight that even for the physiologist the life of the 
 organism is that of a whole, in which the life of the 
 whole not only influences, but is indispensable to 
 that of every organ or part. So with introspective 
 methods. It is not clear that we can treat the 
 conscious and the unconscious as separate entities. 
 The methods which do so appear indeed to have more 
 practical than scientific value. Within our experience 
 the one shades off into the other. Much of our 
 highest activity in reflection, in conduct, in art, is 
 unconscious of itself. It is not on that account 
 irrational nor does it belong to a different self. It is 
 mind developing itself in its own activity. As has 
 often been pointed out, by among others Professor 
 Stout, psychologists are apt to ignore the constructive
 
 THE FOUNDATION OF ASSOCIATION 273 
 
 side of mental process even in its lower phases. When 
 I have experienced in the past a particular sweet 
 taste, in connection with a particular appearance of 
 sugar, it does not follow that association means that 
 the sense of sweetness associated with the appearance 
 of another piece of sugar is the particular sweetness 
 previously experienced. It is surely a new idea of 
 sweetness connected with the appearance or concep- 
 tion of the present bit. A universal of reflection 
 enters into the concrete individuality of the sugar 
 as I conceive it. There is here a construction based 
 on an inference from past experience which does not 
 belong to direct awareness. There may be and are 
 regions which have no counterpart in any actual 
 experience. But when elements come from them 
 into my awareness they come into the world of my 
 conscious experience, and there attain reality. There 
 is no other real world. There may be what is loosely 
 called ' double personality/ two centres in the same 
 individual from which memory is differently focussed. 
 A line of demarcation between two series in experience 
 may exist. But it is a shifting one, for otherwise 
 there would be two individuals. What I am at the 
 moment unconscious of is something beyond what I 
 am actually aware of. But it falls within the iden- 
 tically same mental activity which I bring to bear 
 on other experience, and it is in this respect at least 
 continuous with it. The unconscious is therefore no 
 world which is subsistent in itself and apart from me. 
 Although outside my present experience it is con- 
 tinuous with it. For bare feeling by itself would be 
 non-existent because meaningless. There can be no 
 other world of bare feeling, and when the limits 
 within which I am aware are extended they are so
 
 274 PSYCHOLOGY 
 
 extended just by the increased scope of my recognition 
 through concepts, and not merely by the intrusion 
 of what has no actual existence apart from these 
 concepts. The notion of an unconscious existence, a 
 ' subliminal self/ to use the phrase of the late Frederic 
 Myers, seems to be an hypothesis founded on a 
 metaphor which will not bear criticism. There is 
 only one object world for the self, an object world 
 which is always expanding or diminishing, but which 
 owes its significance to the constructive activity of 
 intelligence operating in universals. This is the fact 
 from which we start in human intelligence, and the 
 view which the evolution theory gives us does not 
 contradict it. For that view, while true from its 
 own standpoint, is only a relative one which does 
 not explain the basic starting-point of the knowledge 
 within which the object world it postulates has a 
 place but only a place. 
 
 The principle of evolution or development is one 
 which we find only in a world of externality. We get 
 at it by the study of different organisms, or different 
 stages of the life of the same organism, in such a 
 world. Introspective psychology may get light by 
 supplementing its own methods with those used in 
 physiology. It has done so in the case of the associa- 
 tion of ideas, and the explanation which weakening of 
 synapses under the influence of habit throws on this. 
 But sensations are never presented for it as self- 
 subsistent things, or as entities existing independently 
 of each other. The character of our actual experience 
 excludes the possibility of this. A particular is 
 always defined through a universal, even in the 
 recognition of contiguity in time or space, and the 
 unique individual object of knowledge always implies
 
 PERSONALITY 276 
 
 both particular and universal as logical constituents 
 so implied. That seems to be of the very essence of 
 what in experience we name existence. 
 
 The point I am pressing is that there are essential 
 limitations to the kind of information about the 
 ultimate nature of mind that psychological methods 
 can furnish us with, whether they be physiological or 
 introspective. Psychology is just as good a science 
 as any other, for there is a similar limitation in the 
 case of every special science. It has fashioned reality 
 in its own image by the use of exclusive conceptions. 
 It therefore is no guide to the final reality which 
 requires knowledge in the entirety of its forms for 
 its full interpretation. It is the tendency which its 
 practical applications carry with them to restrict the 
 significance of their subject and to regard it mechani- 
 cally that suggests caution in their use. There is 
 little danger when psychological methods of inquiry 
 are directed to such practical questions as arise in 
 industry as to industrial fatigue and about applying 
 human energy in factories, the reduction of monotony, 
 and the increase of interest in work and the distribu- 
 tion of rest periods. Valuable guidance, much of it 
 of a negative kind, may be gained by psychological 
 inquiry into the conditions of study in schools. But 
 the system of education generally appears to be a 
 subject too great to be reduced to psychological 
 principles. It is concerned with human personality, 
 and this is not adapted to mechanistic consideration. 
 The free self-determining soul requires influences in 
 its development which depend on conceptions of a 
 larger order. To attempt to employ unrestrictedly 
 those of one that is narrower is to fall into a very 
 common form of what we call pedantry. 
 19
 
 276 PSYCHOLOGY 
 
 With this qualification we may fully approve of the 
 new use which is being made of psychological work in 
 education. Genetic psychology throws light on 
 instinct, on habit, and on the effect of environment. 
 It teaches that even very young children require a 
 form of education in mental habits. It gives new 
 meaning to what was written by Froebel and by even 
 Rousseau. It throws light on method in class-rooms, 
 and on the badness of old and familiar methods of 
 teaching languages and other subjects. The teacher 
 ought therefore to be sufficiently instructed in this 
 kind of psychology, and there are now good practical 
 textbooks which can guide him. But do not let the 
 teacher imagine that the main source of his activity 
 should ever be sought for merely in studies of this 
 kind. It depends much more on his own personality 
 and knowledge, and on his power of bringing these 
 to bear suggestively on the youth with which he is 
 in daily contact. 
 
 I referred earlier to ' Behaviourism/ The most 
 consistent statement of the principle is to be found 
 in such books as Psychology from the Standpoint of a 
 Behaviourist, by Professor John B. Watson, who has 
 taught it at the Johns Hopkins University. 
 
 In his writings the reader does not find any reference 
 to consciousness, or to such terms as ' sensation/ 
 ' perception/ ' attention ' or ' will/ Even thinking and 
 memory are redefined in terms of physical behaviour. 
 Attention, for instance, signifies for Professor Watson 
 the attainment of a form of bodily organisation and 
 of its function. The method of studying the mind is 
 for him genetic, and if the student could grasp the 
 genesis of the various types of its genetic organisation, 
 he would be able to understand the organism as a
 
 PROFESSOR JOHN B. WATSON 277 
 
 whole. For mind is just a mode of its functions. He 
 insists on the necessity of looking at the influence 
 of the entirety of the organism in interpreting its 
 activity, just as do modern physiologists generally. 
 Language, for instance, is implicitly what we really 
 mean by ' thought process/ We have no right, 
 according to his view, to separate the biological 
 activities which we name as intelligent from other 
 ' organisation processes/ Nor are we any more at 
 liberty to treat consciousness as a correlate of cortical 
 activity. All we really actually do is to watch our 
 own expressions to ourselves. They are words which 
 we utter inchoately, and the thought we take them 
 to present to our self -observation is " not different in 
 essence from tennis-playing, swimming or any other 
 overt activity, except that it is hidden from ordinary 
 observation, and is more complex and at the same 
 time more abbreviated so far as its parts are con- 
 cerned than even the bravest among us could dream 
 of." Everything in science and in art, and in religion, 
 Professor Watson claims to be able to interpret thus. 
 Instinct is a combination of congenital reflexes 
 unfolding serially under appropriate stimulation. 
 The reflexes form here a chain. Emotion and instinct 
 are not separated by any sharp line. Both are 
 hereditary modes of action. But " in emotion the 
 radius of action lies within the individual's organism, 
 whereas in instinct the radius of action is extended 
 in such a way that the individual as a whole may 
 make adjustments to objects in his environment/' 
 The former is " implicit mass action," while the latter 
 is " explicit definatised and localised action/' The 
 method of observation in Behaviouristic psychology 
 differs from that in physiology mainly in this, that
 
 278 PSYCHOLOGY 
 
 while physiology directs observation to part reactions, 
 psychology deals with the adjustments of the 
 organism as a whole. 
 
 Now there are points of real value made by the 
 Behaviourists. They insist rightly that it is as a 
 whole that the living organism must be studied if it 
 is to be understood as intelligent. They lift us to this 
 extent above the standpoint of mechanistic biology 
 and treat this as inadequate. Much light is to be 
 got by such interpretation of certain of the activities 
 of the organism. Movements may express reflection, 
 for example. But can we limit the meaning with 
 which we have invested such movements by categories 
 appropriate only to external existence ? Does not 
 mind come first, with the meanings which have no 
 significance, and therefore no reality, excepting in and 
 for mind ? Apart from being the expression of such 
 meanings what were the words uttered by a human 
 being more than the letters printed in the book he 
 holds ? In each case we can give what lies before us 
 a restricted and merely mechanical significance. But 
 is this the full truth about them ? Is not the truth 
 the whole, and does not the whole truth and the 
 whole reality depend on our starting from facts as 
 they present themselves at a standpoint that is fuller 
 and higher ? 
 
 I have now brought to a point sufficiently definite 
 for the end I had in view this survey of the field 
 where the methods of psychology are put in operation. 
 The outcome is apparently to disclose here again the 
 relativity of reality to knowledge.
 
 CONCLUDING REMARKS
 
 CHAPTER IX 
 
 CONCLUDING REMARKS 
 
 THE actual, as we have seen, does not subsist apart 
 and in isolation, but depends on the form of know- 
 ledge in which it gets meaning. The relativity 
 of reality to that knowledge has a wider significance 
 than it possesses even in modern physics. There 
 are variations due to modes of apprehension other 
 than those merely of measurement and of shape. 
 Equally with the latter these other variations are 
 introduced by dominating concepts which determine 
 the character of a reality apprehended and actual 
 only in and through them. 
 
 It seems as though we start in every instance from 
 what is concrete and individual, some fact that as it 
 appears in our initial awareness is unique. The truth 
 about such a fact depends for every form of know- 
 ledge on how knowledge, setting out from what 
 appears to be its direct object, resolves that object 
 into meanings. It is what is in the highest degree 
 concrete that always presents itself as our point of 
 departure. We do not build up anything in the 
 world that appears to confront us by putting together 
 fragmentary units. For at such units themselves 
 we can only arrive after a process of abstraction. 
 They are come to mediately, and are general and not 
 particular in character. We may present to ourselves 
 the outcome of our reflections as scientific conceptions, 
 
 281
 
 282 CONCLUDING REMARKS 
 
 or they may assume the shape, as in ethics, art and 
 religion, of values. But they always bring us back 
 to the actual as being individual and unique in its 
 nature, through the union in it of moments that are 
 both particular and universal, isolable at most in our 
 analysis. It is to the actual in this form that we 
 always return as our basis. Knowledge of this kind 
 as essentially presupposed in the starting-point, the 
 ' that ' which is reality, makes this so. Behind the 
 fact of such knowledge we neither get nor can get, 
 nor are we able to resolve this fact of knowledge 
 itself into any terms which do not actually pre- 
 suppose it at every turn. 
 
 If the ideal of our knowledge, as wider than it 
 takes itself to be in the limited outlook of our daily 
 life, is kept before us in the special applications of our 
 endeavours to develop its significance, it becomes 
 a principle which prescribes a fresh standard for our 
 efforts. 
 
 It is so that we are brought face to face with 
 forms of value which make a demand on us that is 
 imperative : 
 
 "That low man goes on adding one to one, 
 
 His hundred's soon hit: 
 This high man, aiming at a million, 
 Misses an unit." 
 
 We seem to come back for our starting-point to a 
 world that is never in itself any region of merely 
 scientific abstractions. It is rather the rich concrete 
 individuality which Max Planck seems to ask for in the 
 passage from his book on the Conservation of Energy 
 quoted early in the fourth chapter. No one of the 
 sciences, in their various orders in knowledge, presents 
 such a world to us exhaustively. An infinity always
 
 THE REAL CHARACTER OF EXPERIENCE 283 
 
 stretches beyond each partial presentation, and no 
 abstract procedure can take us far into that infinity. 
 It is for this reason that Goethe makes Mephistopheles 
 tell the student in Faust that those who set them- 
 selves to analyse and describe life begin by ignoring 
 its link with spirit. Thereby they get life into their 
 hands but only as a collection of dead fragments. 
 The spiritual bond is missing : 
 
 " Encheiresin naturae nennt's die Chemie 
 Spottet ihrer selbst, und weiss nicht wie." 
 
 The outcome of such methods, and of their ethical 
 counterparts, Goethe sums up in the cry of the angels : 
 
 "Die hast sie zerstort, 
 Die sohone Welt." 
 
 To set out from the world as it seems to be there 
 in all its fulness and in all its aspects is therefore inevit- 
 able if we are to attain to truth which will take account 
 of the whole. Knowledge of a range such that this ful- 
 ness and these aspects should have their places in it as 
 belonging to a single entirety, the unendingness of our 
 human effort to comprehend will not permit. Its 
 incompleteness must remain at all points apparent 
 for an ideal knowledge, in which universal and par- 
 ticular should not seem to fall asunder in the activity 
 of thought nor appear as if even possibly independent. 
 But for us, conditioned as we are by our station in 
 nature, reflection, though limitless in its range, has 
 not power enough to bring together such a vision. 
 Its completion must remain no more than an ideal. 
 But it is yet an ideal which guides and must guide us. 
 It is implicit, whether in science we resolve our object 
 more and more penetratingly through general prin-
 
 284 CONCLUDING REMARKS 
 
 ciples, or whether as in Humanism we lay the chief 
 stress on values, and on the concrete unity of what 
 absorbs us by its very individuality. A Riemann 
 and a Newman are swept along by different purposes. 
 Yet their objects are analogous, for they both seek 
 to describe the meaning of the actual. The method 
 is different in science from what it is in poetry or 
 religion. In science the meaning is sought to be 
 thrown into the form of abstract universals, so wide 
 in their range that, like the w-multiply-manifold, they 
 apparently take us away from the individual reality 
 which it is their function to render. But that is not a 
 reproach to the method. For its object is no more 
 than to deal with a certain aspect of reality, an aspect 
 necessary to be dealt with if the meaning of reality 
 is to be developed and its nature made pregnant for 
 knowledge. All science is of this order. Like geometry, 
 it must start from experience, and it comes back to 
 experience interpreted in the new rendering given. 
 
 The fallacy that appears to have underlain many 
 attempts at the explanation of nature and that 
 has caused them to fail has arisen from ignoring this 
 basic principle of all knowledge. The metaphysical 
 assumption is made, generally unconsciously, that 
 what are in truth only abstractions are individual 
 objects confronting us. Even in the most modern 
 physics we find the four-dimensional continuum 
 spoken of as though it were something that, in the 
 form in which abstract reflection in the end brings us 
 to it, can be made an actual object in perception. 
 It cannot be so made. That is no barrier to analysis, 
 but such an analysis yields the universals of science 
 and not the concrete individuality of objects which we 
 take ourselves to perceive directly.
 
 THE PERILS OF ABSTRACT METHODS 285 
 
 It is but too often not only philosophers, but the 
 votaries of science who have fallen into the meta- 
 physical slough. Theologians, hardly less in their 
 own fashion, encounter a similar peril in their difficult 
 path, difficult when they seek to apply the conceptions 
 of one order in knowledge to what truly belongs to a 
 different order. The function of philosophy must 
 always be at least to provide a searching criticism of 
 categories, for without such criticism entanglements 
 in untested assumptions are apt to prevail. That is 
 why philosophical writers like Professor Gentile 
 express themselves almost violently in insisting on 
 the work required to-day from metaphysics, and on 
 the necessity, in the interest of knowledge generally, 
 of the study of philosophy. 
 
 It may serve a useful purpose to illustrate these 
 views by contrasting them with one that is different. 
 There is to-day hardly any writer who treats his 
 subject with more apparent lucidity than Mr. Bertrand 
 Russell. Not only is his style admirable, but he is 
 well equipped with scientific learning. He is an 
 accomplished mathematician, and a pioneer in the 
 new method of criticism known as mathematical 
 logic. Recently he has published a book entitled 
 The Analysis of Mind, in which his gifts are apparent. 
 
 The comment which I shall venture to make on 
 this book is that, like his previous books, it is in truth 
 written by a metaphysician who has not satisfactorily 
 weighed the legitimacy of the categories he employs. 
 For Mr. Russell, whatever he may say, and however 
 he may object to be looked on as one, is a meta- 
 physician of a pronounced sort. At the back of his 
 mind, throughout the new volume, is the faith that 
 physics is the most fundamental science now in
 
 286 CONCLUDING REMARKS 
 
 existence. He does not attribute to physics, in its 
 modern form, a belief in the existence of matter in 
 the old-fashioned interpretation of the word. Matter 
 is rather for such physics a construction from events. 
 To Mr. Russell it appears as neither mental nor 
 material, but as a ' neutral stuff ' out of which both 
 what is mental and what is material emerge by 
 construction, a view which he holds to fit in well with 
 the outlook of modern psychology. 
 
 Such a conclusion must of course meet with the 
 sharpest antagonism from Gentile and other Italian 
 writers, for whom mind is ultimate and is pure 
 activity, antecedent to any object form it may impose 
 on itself, and as such the source of constructions 
 which have meaning only as the outcome of that 
 activity. But without adopting all the language of 
 the Italians it becomes apparent that in the phrases 
 used by Mr. Russell an assumption is made which 
 has never passed without challenge, a challenge which 
 he can hardly be left to ignore without having met it. 
 His method assumes that it is possible to get behind 
 knowledge, and to explain it in terms other than its 
 own. For him there are final data out of which 
 knowledge emerges. These are, as I interpret him, 
 not atoms of matter, which is a construction of reflec- 
 tion, but particulars in the form of entities or events. 
 Such when correlated constitute a momentary condi- 
 tion of some unit which may emerge as physical. 
 Scientific understanding of such correlation and its 
 subject matter, if it were perfect, which it is not, 
 would exhibit the causal laws of the world in terms 
 of these particulars, and these causal laws would be 
 applicable in physics and psychology equally. For 
 physics and psychology do not really differ in their
 
 MR. BERTRAND RUSSELL 287 
 
 material. Mind and matter alike are logical con- 
 structions. The variety which obtains in the rela- 
 tions between the final particulars distinguishes the 
 study of these relations into that of physics and that 
 of psychology. Even in what Mr. Russell terms 
 mnemic causation there is a causal unit consisting 
 of a group of particulars with a given place for pas- 
 sive observation at a given time, and it is this sort 
 of grouping that distinguishes subjectivity. Habit, 
 memory and thought are explained as being its 
 developments, and consciousness is only a complex 
 but far from universal characteristic which appears 
 in the course of that development. Thus all our 
 data, both in physics and in psychology, are subject 
 to what may be properly called psychological causal 
 laws. " Physical causal laws, strictly speaking, can 
 only be stated in terms of matter, which is both 
 inferred and constructed, never a datum. In this 
 respect psychology is nearer to what actually exists/' 
 In a perfected science, he adds, all these causal laws 
 would assume the form of differential equations or 
 of finite-difference equations, if the theory of quanta 
 should prove correct. 
 
 Now what are these final data for Mr. Russell, and 
 what are their correlations apart from their meaning 
 for us ? Nothing at all ! We cannot even state pro- 
 positions about them, and much less attribute any 
 existence to them, excepting in terms of thought. 
 A bare sensation has no significance apart from our 
 knowledge about it, and as a pure particular, dis- 
 tinguished from nothing else, it never comes into 
 existence. No doubt we affect to give the go-by to 
 this foundational fact in our every-day life. We try 
 to treat intelligence itself as an object which we
 
 288 CONCLUDING REMARKS 
 
 detach as one among others in the world. We see 
 a micro-organism, apparently at the bottom of the 
 scale of life, seeming to experience some sensation. 
 We interpret it accordingly. There are many objects 
 in the external world which express even purposive 
 intelligence and freedom. That is because they con- 
 form to that order of conception and display it as 
 belonging to their reality. But such reality is always 
 relative to knowledge. In so far as this is so know- 
 ledge is not itself an event, or a property of a thing, 
 or a happening in space and time. It is the founda- 
 tion on which rests the reality of all these. Such 
 reality signifies nothing intelligible unless for know- 
 ledge. It is inseparable from meaning. If we could 
 exhibit the whole of the world that confronts us 
 individually with all its phases we should get no 
 further than an object world which was there for 
 mind. Intelligent organisms would appear as having 
 been evolved in such a world, but the whole theatre 
 on the stage of which such evolution unrolled itself 
 would have significance and be something only as 
 present to the intelligence in which the full course 
 of evolution was a fact, significant only for knowledge. 
 Intelligence can therefore be itself, when properly 
 interpreted, no mere phenomenon in such a world. 
 It is rather that within which subject and object 
 alike fall, distinguished only through the founda- 
 tional activity of intelligence itself. 
 
 Such was the outcome of the reflection of the 
 ancient Greeks, and we have yet to be shown how 
 to get behind their analysis. Hardly by suppressing 
 that which lies at the root of all science and all know- 
 ledge. The object in these possesses its reality only 
 as relative to the form of knowledge in which it
 
 ORDERS IN KNOWLEDGE 289 
 
 appears. It is never intelligible excepting as assigned 
 to some order or orders in that knowledge. The 
 recognition of beauty and of truth and of degrees 
 higher than those at which we live our daily lives, 
 is as real as the recognition of causal relations and 
 the entities which stand so related. They are all 
 constructions within knowledge. But when know- 
 ledge in this interpretation of the word is recognised 
 as their basis it is not taken to be an event falling 
 within that object world, which is its own creature. 
 It is more than personal. It is an entirety within 
 which all distinctions, including those between reality 
 and unreality, as well as truth and error, fall. Such 
 distinctions are closely connected with the station 
 within nature which is inevitable for us as individuals 
 who are at the same time subjects in knowledge. We 
 are intelligent organisms and our stations condition 
 the scope of our intelligence, although they do not 
 affect its penetrating power so far as we can exercise 
 it. For the entirety, to be which is of the essence of 
 knowledge as such, exhibits itself at degrees or levels 
 at which, taken in separation, we have only aspects 
 of the whole. It is the tendency to assume that the 
 particular orders of knowledge which concern a 
 particular science are the only orders in which know- 
 ledge is actual that gives rise to the difficulty which 
 Greek thought surmounted. 
 
 We can no doubt exercise our individual freedom 
 as intelligent beings by pursuing abstract methods 
 freely. But when we do so, we do it at the risk of 
 shutting out the fulness of reality. We may, for 
 limited purposes, conceive the basal facts of know- 
 ledge as being a succession or an aggregate of psycho- 
 logical entities. But if we interpret mind on this
 
 290 CONCLUDING REMARKS 
 
 footing without qualification, it will cease to be 
 intelligible how human beings who are really shut 
 into the mutually exclusive possession of such indi- 
 vidual sensation can be aware of an identical world 
 as confronting them all in their awareness. It is 
 only through identity in reflection, through thoughts 
 which are no ' happenings ' but are in the full logical 
 sense the same thoughts throughout differences, that 
 we can have a common world or communicate with 
 each other. 
 
 Mr. Russell is such an admirable writer, and in his 
 own subjects his understanding is so acute, that one 
 hesitates before venturing to remonstrate with him. 
 But he sometimes, his great quality notwithstanding, 
 appears to assume, as though there could be no 
 question about it, that the standpoint from which he 
 approaches the most difficult questions is the only 
 standpoint open to reasonable beings. Now it may 
 be right, as William James did, to question the 
 reality of consciousness regarded as an entity, and to 
 assign to it only subordinate functions. That may 
 well be a legitimate mode of approach from the point 
 of departure we make when we treat consciousness 
 as a biological fact, or as an object in the procedure 
 of empirical psychology. But is this the only signi- 
 ficance which the word possesses ? May consciousness 
 not also mean a form of knowledge within an order of 
 thought different from this ? It has more often than 
 not been so treated in the history of philosophy, and 
 it seems better not to ignore the circumstance. 
 
 Take, again, the insistence of Mr. Russell in other 
 books than the Analysis of Mind on the title of the 
 standpoint of mathematics to predominate. There 
 is no science which is more distinguished by the
 
 THE MEANING OF CONTINUITY 291 
 
 resolute abstractness of its methods. The exclusion 
 of all the aspects of reality, excepting those of the 
 order in externality with which it is concerned, has 
 been the source of the mathematician's power. 
 But it is an exclusion which shuts out other and 
 necessary significances in the real. ' Continuity ' for 
 example has a special meaning in mathematics. In 
 logic and metaphysics the word is used in a quite 
 different sense, and yet those who so use it have been 
 reproached by Mr. Russell for ignoring the mathe- 
 matical use. They would not, I think, deny Mr. 
 RusselFs just title to pronounce against them on any 
 purely mathematical ground. But they would deny 
 that this meaning which they attach to the word 
 ' continuity ' is the same as that which the mathe- 
 maticians attach to it, or that the latter have an 
 exclusive title, like that to a trade name. 
 
 Even if we were to start by conceding to Mr. 
 Russell, what he presses for in his Principles of Mathe- 
 matics, the non-existential character of propositions 
 (other than those which assert existence) and " the 
 pluralism which regards the world, both that of 
 existents and that of entities, as composed of an 
 infinite number of mutually independent entities, 
 with relations which are ultimate, and not reducible 
 to adjectives of their terms or of the whole which 
 these compose," we should not be much further on 
 with the problem of continuity. For the purpose 
 of a science which pursues from its exclusive stand- 
 point an abstract method we should have bifurcated 
 the object in knowledge from the activity of know- 
 ledge itself, but we should not have faced the difficulty 
 with which philosophical, as distinguished from 
 merely mathematical logic, is thereby confronted. 
 20
 
 292 CONCLUDING REMARKS 
 
 When we count even such separate entities, we count 
 them in virtue of a continuous quality or identity 
 which pervades them, so that every unit, however 
 small or great, is a distinguishable part within some 
 whole made up of such parts. We cannot enumerate 
 without knowing what is being enumerated. The 
 relation which is thus essential in the meaning we put 
 on the process implies both the nature of the continuity 
 and the rule under which a discrete aspect arises. 
 Quantity, in other words, implies quality as in- 
 separable from it. Thus continuity involves discrete- 
 ness, and the latter not less the former. The two 
 conceptions have no intelligible significances apart 
 from one another. That is because the essential 
 character of the reflection out of which meaning 
 comes is to be dynamic, and is ever passing beyond 
 the distinctions it makes into what it is contrasting 
 them with. 
 
 No one wishes to challenge the right of mathe- 
 maticians to use such words in another sense, provided 
 that there is borne in mind the different use made of 
 them by metaphysicians in contemporary thought, 
 and also long before mathematics began to adopt 
 the expressions to its special purposes. 
 
 It is, of course, of assistance to point out that a 
 series may be said to be ' compact ' when no two 
 terms are finally consecutive, but between any two 
 there are others. It is true that in what mathe- 
 maticians mean by continuous motion the moving 
 body occupies at a given instant a certain position, 
 and at other instants other positions, but that the 
 interval between any two instants and any two 
 positions is always finite, while the continuity of the 
 motion is shown in the fact that however near
 
 MATHEMATICS AND PHILOSOPHY 293 
 
 together we take the two instants and the two posi- 
 tions, there is an infinite number of positions still 
 nearer together which are occupied at instants that 
 are also still nearer together. In this sense the 
 moving body never ' jumps ' from one position to 
 another, but always passes by a gradual transition 
 through an indefinite number of intermediary 
 positions. 
 
 This is excellent, but it does not tell us what we 
 want to know, the relation to each other of the con- 
 ceptions of continuity and discreteness. For light on 
 the significance of this, we are driven back to the 
 underlying interpretation by philosophical logic to 
 which I have referred. Mathematical writers like 
 Cassirer are well aware of this. 
 
 Much that is analogous could be said about the 
 contrast between the meanings of the word ' infinite/ 
 as used in mathematics, and the word as interpreted 
 in philosophy. The two interpretations are not 
 inconsistent, simply because they are the outcome 
 of different purposes, and consequently of different 
 standpoints. Neither supersedes the other, just for 
 that reason. 
 
 But it is now time to return to the principles laid 
 down in Mr. Russell's Analysis of Mind. My objection 
 to them is that indicated. He seems to me to take 
 a particular outlook in knowledge as though it could 
 throw light on the full meaning of the object in know- 
 ledge relatively to knowledge as an entirety. His 
 method is a valuable one if restricted to the purposes 
 of a particular form of science. My criticism is that 
 this form of science does not yield the complete truth, 
 nor take us beyond aspects into which the true object 
 is fashioned by a method which is necessarily partial
 
 294 CONCLUDING REMARKS 
 
 and abstract. The categories employed appear to 
 require to be critically examined. 
 
 But having said this, I do not wish to be understood 
 as lacking in appreciation of the merits of the in- 
 vestigation made within its self-imposed limits. Mr. 
 Russell never fails to inspire me with admiration for 
 his clearness in expression, and for his knowledge in 
 his own department. He is deservedly reckoned as 
 one of the most eminent of contemporary inquirers. 
 In lucidity of statement, I wish indeed that I could rise 
 to his level. Not the less, when he enters on a crusade 
 against schools of thought different from his own, I 
 have sometimes also wished that he had shown more 
 appreciation of what those who belong and have 
 belonged to such schools really said. I know how 
 difficult philosophy is, and how much it needs, what 
 Goethe asked for, a long tract of time through which 
 those who are engaged in its work can co-operate. 
 And if that co-operation is to be effective, it must be 
 based on a sustained effort at mutual understanding 
 of divergent methods. That seems to me to be 
 essential for us finite and fallible searchers after 
 truth. 
 
 Now although in his Analysis of Mind Mr. Russell 
 is more gentle about other people than he has always 
 been in other books, he not the less tends to ignore 
 that there may be great differences of opinion about 
 method in the approach to the problems with which 
 he concerns himself. 
 
 Treated from a particular Victorian standpoint, 
 that in which mind and secondary and tertiary quali- 
 ties were ' bifurcated/ to use Professor Whitehead's 
 expression, from nature, the analysis is of great use. 
 It has the value which the standpoint of Newton con-
 
 THE USES OF MR. RUSSELL'S METHOD 296 
 
 tinues to possess, the principle of Relativity notwith- 
 standing. But it has this value only on the footing 
 that it is concerned with a special form of scientific 
 investigation, directed to obtaining distinctness in 
 knowledge by confining itself to conceptions which 
 exclude all excepting one or two of the many aspects 
 which the actual possesses. On this footing the book 
 is a genuine contribution of an original nature to the 
 psychological inquiry into reality. It resembles the 
 contributions of physics and chemistry to biology. 
 The views expressed in the Analysis of Mind throw 
 new light, the limitation of standpoint being kept in 
 view, on several important questions. From this 
 standpoint there is much to be said for rejecting 
 the idea of consciousness as an entity, and for the 
 appreciation of what is of assistance in the ' be- 
 haviourist ' contribution to method. We may agree 
 with Mr. Russell in thinking that instinct is dis- 
 tinguished from knowledge by requiring no prevision 
 of the biological end which it serves. We may, 
 however, feel colder when he seems to suggest that 
 punishment is an outcome of vindictive impulse. 
 It is surely much more. It is an advance towards the 
 explanation of facts when he tells us that for him 
 mnemic phenomena comprise that large class of 
 responses of the organism which can only be brought 
 under causal laws by including past occurrences in 
 the history of the organism as part of the causes of 
 the present response, and that it is only mnemic 
 phenomena that belong to the domain to which he 
 limits experience. A chain of experience, or a 
 ' biography/ becomes in this way what distinguishes 
 science dealing with living organisms from physics. 
 The proximate cause here may consist, not only of a
 
 296 CONCLUDING REMARKS 
 
 present event, but of this together with a past event. 
 Of course that compels Mr. Russell to supersede laws 
 of causation by laws of change, and so to come to 
 order in externality as foundational of reality. He 
 and Professor Alexander appear to hold views which 
 do not here diverge in essentials. But it is not unim- 
 portant that Mr. Russell should point out that all 
 that we can know empirically is approximate and 
 liable to exceptions, and that exact laws embodied in 
 differential equations may be true, but cannot be 
 known to be so. In other words, they are conceptual. 
 A piece of matter is not a single existing thing, but 
 a system of existing things. ' When several people 
 simultaneously see the same table they all see some- 
 thing different ; therefore ' the ' table which they are 
 supposed all to see, must be either an hypothesis or a 
 construction." Correlation of points of view is neces- 
 sary. So we come to views of the world from different 
 places as ' perspectives/ Physics, on the other hand, 
 is not troubled by this multiplicity, because what it 
 attends to is changes in appearance according to the 
 same law. This is followed by an acute discussion 
 of introspection and of ' images. 3 Through ' mnemic 
 causation ' we get to perception, in which sensation 
 is the theoretical core, but the actual experience is 
 perception, always complex. The ' subject ' is a 
 logical fiction, like a mathematical point. Belief is 
 * the most mental thing we do/ It is an actually 
 experienced feeling, nothing merely postulated. A 
 memory-belief confers on a memory image its 
 meaning, and refers us to an object which existed in 
 the past. The causation of images is divergent from 
 that of sensations. Images may be vague. But 
 such generalised pictures can be used to form concepts,
 
 MR. RUSSELL ON KNOWLEDGE 297 
 
 united by the presence of an act of judgment. This 
 leads to an inquiry into the structure of judgments 
 and of what we call, erroneously, abstract ideas. 
 Knowing is not any " mystic unity of knower and 
 known." It is " a very external and complicated rela- 
 tion, incapable of exact definition, dependent upon 
 causal laws, and involving no more unity than there is 
 between a signpost and the town to which it points." 
 Of belief and of sensation itself we may be conscious 
 but are not necessarily so. The function of con- 
 sciousness and thought is to enable us to act with 
 reference to what is distant in time or space, although 
 that may not be presently stimulating our senses. 
 Such a reference is possible through association and 
 habit. Consciousness is " far too complex and 
 accidental to be taken as the fundamental character 
 of mind." What we call ' subjectivity ' is the 
 characteristic of ' perspectives ' and ' biographies/ 
 the characteristic of giving a view of the world from a 
 certain place. 
 
 For Mr. Russell, therefore, knowledge is not the 
 ultimate foundation of reality. We can go behind 
 and resolve it into realities that in fact as well as in 
 logic are antecedent to itself. The difficulties which 
 I have already dwelt on as hindrances to this opinion 
 I will not repeat. The opinion itself has, however, 
 been stated nowhere that I know of more acutely or 
 impressively than it has been by Mr. Russell. His 
 book must be studied in order to appreciate its 
 excellence of its own kind. For all that I have been 
 able to do here is to draw attention to certain points 
 in it. 
 
 If the conclusions come to in this book and in its 
 predecessor, The Reign of Relativity, are well founded,
 
 298 CONCLUDING REMARKS 
 
 there is a criterion of truth in our knowledge which 
 always must be kept in view. It is not enough that 
 our opinions should merely appear to harmonise with 
 what observation of their object is taken to disclose. 
 For that observation may have been directed from an 
 outlook that is too narrow. If knowledge enters into 
 reality and moulds it, whether in physics or in any 
 other domain, we must be sure that the character of 
 the method brought to bear is not stretched beyond 
 the limits of that to which it is directed. If this last 
 is always individual and concrete in its nature, and 
 if the purpose is to find the general conceptions in 
 which that nature can properly be described, we 
 have to be careful. For our object is individual, 
 in so far as it reveals its particular aspect only as set 
 in universals apart from which the particularity would 
 have no meaning and no reality. We have, there- 
 fore, in order to get at the types of universal which 
 are appropriate to any individual object of investiga- 
 tion, to remember that these types must be not only 
 general, but as matter of experience characteristic of 
 it. We do not really impose them on the object. 
 It is on us that they ought to be imposed, and our 
 knowledge is relative to them. The phenomena of 
 the ethical world are not those with which mathe- 
 matics deals, nor is the type of the one form reducible 
 to that of the other. The characters of the universals 
 to which analysis is directed are different in each case, 
 and we have to bear in mind the necessity of accepting 
 the appropriate order when seeking to resolve that 
 which is individual into the general conceptions 
 through which alone it is intelligible. No doubt we 
 can choose conceptions arbitrarily, and adopt a stand- 
 point in our investigation determined by them. But
 
 THE DIFFERENT ORDERS IN EXPERIENCE 299 
 
 to do so is to court disaster. For certain categories 
 are found in our experience to be sufficient for the 
 actual facts we are dealing with, facts of which they 
 are the expressions while others are not. We come 
 to this when we exclude the idea that knowledge 
 is a mere property of a thing, and accept the view 
 that both subject and object fall within it as their 
 foundation. 
 
 On what principle then are we to fashion our 
 abstractions ? Surely by considering first the sort of 
 fact with which we are dealing. If that fact is life, we 
 ought not to assume that we can render our con- 
 ceptions of it into those of physics. We may have to 
 do this in order to describe certain aspects which living 
 organisms present, but these may be neither the only 
 nor the dominant aspects of the actual in such a case. 
 The criterion required is that we should satisfy our- 
 selves by observation of the actual as to the cate- 
 gories required in its study. Thus the relativity of 
 knowledge gets a further significance, for it is only 
 relative knowledge that we have when the standpoint 
 is one that is not such as to cover the full reality. 
 
 A view like this does not affect the accepted criterion 
 of truth in science. It rather insists on that criterion 
 being applied in a more thoroughgoing form than is 
 common. The various branches of inquiry relate to 
 special domains, and we fall into error if we apply 
 general conceptions appropriate only to the character 
 of one domain to description of what is of the order of a 
 different domain. It is observation that tells us in 
 each case with what character we are really con- 
 cerned. We are not in difficulty over this if we 
 are careful to start in our study with what is concrete, 
 and not with some abstract distortion of its nature,
 
 300 
 
 CONCLUDING REMARKS 
 
 due to insistence on a special standpoint arbitrarily 
 adopted. There may be many standpoints from 
 which we can view an individual fact. The question 
 is which of these can account for fact in the starting- 
 point, the actual as experience shows it to be. 
 
 The variety of order in which knowledge presents 
 itself, if we do not distort but observe it in its self- 
 development, gives us the key to the variety of its 
 standpoints. Its universals are not difficult to find; 
 But it is one thing to find them and quite another to 
 hold fast to them when found. Most of the confusion 
 which has characterised the history of reflection has 
 been due to the assumption that a particular set of 
 universals would prove sufficient for the description 
 of objects differently characterised in facts disclosed 
 in nature. The inquirer has again and again pursued 
 in consequence a path which has led him away from 
 these facts. 
 
 If there is a service which philosophy can render 
 with more advantage to science than any other, it is 
 probably to keep reminding men of science never to 
 forget to criticise their categories before employing 
 them. 
 
 THE END
 
 INDEX 
 
 Active Reason, 38 
 
 .Ether, the, 91, 109, 238 
 
 Arcella, the, 228 
 
 Aristotle, 1, 2, 3, 5, 7, 38, 232, 233 
 
 Arnold, Matthew, 76 
 
 Association and Contiguity, 15, 
 
 273 
 Astronomical Expedition of 1919, 
 
 41 
 Athens, 81 
 
 Bacon, 9, 233 
 
 Beethoven, 68 
 
 Behaviourism, 234, 276, 277, 278 
 
 Bergson, 10, 128 
 
 Berkeley, 36, 80 
 
 Biot, 228 
 
 Blood, circulation of the, 217 
 
 Bolyai, 111, 116, 122 
 
 Born, Max, 109, 160, 162 
 
 Browning, 70 
 
 Browning's ' Grammarian,' 67 
 
 Carr, Wildon, 23 
 
 Cassirer, 182 et seq. 
 
 Cayley, 12 
 
 Censor, the, 261 
 
 Character in men, 66 
 
 Church, Dean, 71 
 
 Clifford, W. K., 10 et seq., 27, 181 
 
 Continuity, 291, 292 
 
 Copernicus, 38 
 
 Croce, 23 
 
 Crystals, 211 
 
 Descartes, 178 
 
 Diabetes, 225, 226, 227 
 
 Dialectic, 19, 59 
 
 Donnellan Lectures, preface, 31 
 
 Eddington, 141 
 Education, 245, 247, 275, 276 
 Einstein, 38, 40, 41, 43, 45, 47, 
 57, 90, 110, 111, 117, 128, 130, 
 134, 153, 155, 165, 168, 176, 
 180, 181, 194 
 
 End contrasted with Cause, 48, 
 
 202 et aeq. 
 
 Euclid, 12, 110, 111, 118, 119, 149 
 Experience, 61, 64 
 
 Faraday, 111, 186 
 'Field,' the, 111 
 Finality, 22 
 Freud, 261 et seq. 
 
 Gauss, 91, 115, 117, 120, 123, 161 
 Gentile, Giovanni, 23, 25, 27, 286 
 God, 20, 21 
 Goethe, 2, 3, 4, 5, 18, 22,68, 82, 90, 
 
 96, 137, 283 
 Gravitation, 156 
 Greeks, the, 5, 8, 19, 21, 37, 59, 110 
 
 Haldane, J. 8., preface, 196 
 Hegel, 73, 74 
 Helmholtz, 90, 98 
 Heynacher, Max, 3 
 Humanism, preface, 31, 35 ef seq. 
 Humanism in Germany, 94 
 Hume, 36, 80 
 Huygens, 107 
 
 Idealism, 21 
 India, 21, 93 
 Individuality, 30, 60 
 Infinitesimal Geometry, 114 
 Instinct, 266, 267 
 In variance, 115 
 Ireland, 79 
 
 Jeans, J. H., 167 
 
 Kant, 21, 37, 111, 183, 192 
 
 Keats, 77 
 
 Kelvin, 107 
 
 Kidneys, the, 221 
 
 Kirchhoff, 107 
 
 Knowledge, 5, 20, 27, 36, 52, 274 
 
 Lavoisier, 206 
 Leadership, 67 
 
 301
 
 302 
 
 INDEX 
 
 Life, 48, 49, 202 et seq., 223 
 Lobatschefsky, 111, 116, 122 
 Locke, 36, 80 
 
 McDougall, 245, 246, 250, 253, 255 
 
 Mass, 153, 166 
 
 Maxwell, Clerk-, 111, 134 
 
 Milton, 76, 78 
 
 Minkowski, 10, 111, 142 etseq., 190 
 
 Montaigne, 82 
 
 Morgan, Lloyd, 235 
 
 Neoplatonism, 21 
 Neurones, 249, 251 
 Newman, Cardinal, 72, 284 
 Newton, 38, 39, 107, 108, 109, 122, 
 
 136, 150 
 Normals, 207 
 Number, 11 
 
 Oxford Movement, the, 71 
 
 Particulars, 51, 54 
 Pathology, 225 
 Pericles, 81 
 
 Personality, 16, 87, 275 
 Planck, Max, 107, 167, 282 
 Plato, 2, 80 
 Plotinus, 2, 38 
 Plutarch, 82 
 Points, 25 
 
 Psycho-analysis, 260 et seq, 
 Ptolemy, 43 
 
 Quantum theory, 65, 167 
 
 Badhakrishnan, 93 
 Realism, 21 
 Realism, New, 23, 27 
 Beichenbach, Hans, 191 et seq. 
 Reign oj Relativity, preface 
 Relations, external, 5 
 
 Relativity of knowledge, 36, 83 
 
 Religion, 88 
 
 Riemann, 12, 13, 15, 91, 110, 112, 
 
 115, 117, 119, 120, 124, 189, 284 
 Russell, Bertrand, 138, 236, 285 ; 
 
 his " Analysis of Mind," 285 et 
 
 seq. 
 
 Sainte-Beuve, 81 
 
 Schoolmen, 21 
 
 Seeley, 97 
 
 Self, the, 53 
 
 Sensation and general knowledge 
 
 7 o 
 /, 
 
 Shakespeare, 77, 82, 97 
 Sherrington, 244 
 Stimulus, and cause, 243 
 Stout, 257, 272 
 Subject, the, 17 
 Sylvester, 12 
 Synapses, 250, 251 
 
 Tensors, 42, 124, 174 
 
 Thomson, J. J., 166 
 
 Thought, no event in the world, 
 
 13, 14 
 Time, 26, 27 
 
 Uniqueness, 65, 59 
 Universals, 51, 54 
 Upanishada, 93 
 
 Value, 85 
 Vitalism, 211 et seq. 
 
 Watson, John B., 276, 277 
 Weyl, 13, 115, 118, 171, 177, 178 
 Whitehead, A. N., preface, 105, 
 
 137 138 
 Wordsworth, 68, 76, 77, 79 
 
 Printed by Hoztll, Walton A Viney, Ld., London and Aylesbury, England.
 
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