MacTutor
William Clifford
Times obituary
PROFESSOR CLIFFORD'S LECTURES AND ESSAYS *
The feelings of the many personal friends of Professor Clifford on reading these volumes must be like those of the survivors of a shipwreck who, on the morning after the storm, contemplate on the wreck, on the beach, the deep remnants that the capricious sea has revealed from the rich contents of the sea that she has engulfed. Their joy at the sight of each relic is insufficient to compensate for the sad memories it awakens of equally precious ones that are lost. Nor is this feeling attributable merely to the fact that an early death has snatched from us a thinker of great power. Many such might pass away without exciting these feelings of regret. The world would be grateful for anything it had actually received from them, and would not concern itself with speculations as to how much greater might have been their achievements had more time been allowed them. But none who personally know Professor Clifford could thus banish the thought of what might have been -- of the future which was denied him. For his life we are not that of the solitary thinker whose greatness is first learned by the world and mastered by his associates. Himself intensely human and delighting above all things in human society, it was his greatest pleasure to take his friends with him into the most rectitude of his mind and to lavish on them his richest thoughts. To them to read or lecture was inward part of his thoughts and savings which he chose to put into literary form. Hence, in their views of him, promise and performance were inextricably mixed. It must seem to them, as though death had drawn an arbitrary line between the portion of his work which is to survive and that which must pass away. The true reward of a life and character in which the personal element has such prominence is the affection and reverence of friends and contemporaries and of this no one had a larger share than Professor Clifford. And as in considering the reward of such a life we may not neglect this personal element, so also we must take it into account in estimating the work that he has done. In the influence that he exercised over all who were brought into contact with him, and in the stimulus he thus gave to the cult of the ideas which he himself cherished, will be found the complement of the labours whose results are now before us. But this part of his life's work can never be fully recognized by the world at large, however anxious those may be who have profited by personal intercourse with him to acknowledge their debt. If, however, any words can adequately describe the man in his relations to those around him, it has been done by the author of the biographical sketch which is prefixed to these volumes. The name of the author would be a sufficient guarantee that his work would possess all that literary skill and intellectual power could give to it; but no mere literary skill could have given such a touching picture of the personal charm of Professor Clifford or of the picturesque variety of his life and thoughts, and no mere întellectual effort could have criticized his character and its bearing upon the theories that he held with so just an appreciation and so positive a sympathy, Its tender grace speaks throughout of one who mourns a dear comrade, and who feels that he honours him best by preserving to the world the fresh memory of their friendship.
The present question, however, with regard to Professor Clifford's works is not their suggestiveness to those who knew the author, but their value to the general reader in the state in which they actually exist. And many a friend of the author who first took them up and remembered his versatile genius and his keen enjoyment of all realms of intellectual activity must have trembled lest they should be found to consist of fragmentary pieces of work, too disconnected to do justice to his powers of consecutive reasoning and too varied to have any effect as a whole. Fortunately, these fears are groundless. It is true that in form these papers are disconnected, but the very circumstances that gave them birth have caused them to manifest a unity of purpose and a cognatenoss of subject which render them in everything but form a con- nected whole. Indeed, so completely is this the case that Professor Clifford had, it seems, the ideas of recasting them and publishing them in a single work under the name of "The Creed of Science," and even went so far as to sketch its table of contents. If we compare the existing papers with this table of contents, we at once see that, with one or two trifling exceptions, they would have all found their place in the projected book, and would have needed but little modification for that purpose beyond such as would be necessary to prevent repetition. It is not only in subject that the various papers are closely related. There is also a singular consistency of view and of method throughout. This can be seen by comparing his lecture at the Royal Institution in March, 1868—which was his first public utterance, and was delivered within about a year of his taking his degree at Cambridge — with his article on "Cosmic Emotion," which is almost the last that he wrote. The latter shows, of course, considerable advance in grasp of the subject, but there is no substantial modification of view or even of method. This we shall presently show was not accidental; but it suffices to remark that it renders the work as valuable as though it were in a more connected form, while the fact that all the papers are preserved in their original form gives us a better insight into the mind of the author and the aims and tendencies of his labours.
The key to Professor Citford's writings is to be found in the special characteristics of genius as manifested in his mathematical work, that work which unquestionably represents the main bent of his mind, and in which his power is most conspicuously shown. His chief strength in mathematics consisted in prodigious faculties for reasoning by analysis, using that phrase in its broadest sense. He is of a comparatively simple kind, capable only of determining, under special circumstances, the modifications which must be made in it to suit different or more general conditions. This power of apparently reasoning from the particular to the general, and of passing from one proposition to the corresponding one when some change had been made in the conditions essential to its truth, was inborn with him. It was the ruling passion of his mind, and it was mainly to the exercise of this faculty that are due his splendid contributions to our mathematical knowledge. No sooner had he a theorem in plane geometry than he sought for its analogue in solid figures. No sooner had he a theorem relating to our ordinary space than he sought its analogue in the impossible spaces in which he delighted. Nor was he content to deal thus with single theorems. He would throw himself mentally into the altered circumstances, and would not rest until he had constructed a complete system to suit them, drawing each portion of it by analogy from the corresponding truths of the system he was thus transplanting. In this way he would feel his way amid the impenetrable darkness of four-dimensional space, or non-Euclidean geometry, with the same ease that he would have shown in dealing with the relations of ordinary and possible space; and would speak thereon with a certainty and clarity that seemed incredible even to those who were his competitors in other branches of mathematics. Indeed, he would often talk of such matters in so vivid a way that it was a contested point among his friends whether he had not some occult mental picture of these non-existent and impossible regions. We do not think that he had. It was perhaps by means of mental pictorial representations that he was able to realize the properties of these new and strange regions, but by his intrinsic power of allowing for change of conditions. If a man has to pass at some period of his existence into a world where two and three made six, or where two straight lines could enclose a space, Professor Clifford would have been the proper person for him to consult. He would have told him how far he could retain his previous habits and what new ones he must cultivate. It was not only in dealing with mathematical questions that his peculiarity showed itself. Often, when in conversation some theory, possible or impossible, was suggested, either in earnest or in joke, he would pretend to adopt it and proceed to help work it out in all his bearings, keeping with wonderful skill and consistency to the new hypothesis, however self-contradictory or impossible it might appear to be. And this was not the ordinary testing process of the inductive philosopher, who followa out a hypothesis to its legitimate consequences in order to test its admissibility by the truth or falsehood of the deductions. It was not in any sense analytical, but was purely constructive. He loved to clothe the hypothesis with all the detail that would naturally belong to it if it were an actuality. And rightly to understand Professor Clifford's philosophical work, we must view him thus. His was an eminently constructive mind, taking pleasure less in dissecting out causes than in pursuing their consequences in all their complexity of result.
Towards the end of his College course, during the earlier part of which he had not occupied much with scientific questions, Professor Clifford became acquainted with the discoveries of Mr. Darwin and Mr. Herbert Spencer. We shall not linger to discuss the greatness of the change initiated by these discoveries. The world has now no parallel instance of the sudden introduction of ideas so deep-reaching in their influence over human thought at a time when the facilities for the transmission of ideas among civilized mankind were so great. And, consequently, there has never been, and probably never will be, such a sudden transformation throughout the whole intellectual horizon. These views will sound exaggerated to many; the universal recognition of the magnitude of the change must be left to a succeeding age, but the nature of this change is already sufficiently apparent. We may learn the rapidity with which the change has taken place by the fact that these discoveries, once the subject of such blind and unmeasured abuse, are already becoming fully understood and fairly treated by all parties. The more enlightened men of all schools are beginning to feel that they have been delivered from the danger of basing their arguments upon a riddle ill-read; a danger which constantly besets all Churches sufficiently venerable to respect tradition, since so much of the exegesis and argument which have become associated with their teaching must date from ages of great scientific ignorance. Thus the controversy is narrowing itself to the true issue—the extent to which the new doctrines are applicable to the solution of the mysteries that surround us in nature. On this point the variety of opinion is necessarily infinite. Of those who accepted the new teaching in its entirety was Professor Clifford. After the lesson which the world had just received, to the extent to which an increase in knowledge may explain what had previously seemed utterly inexplicable, it was in his eyes an unworthy as well as a foolish act to doubt the universality of science, and any attempt to plead the vastness of the unknown as an excuse for our hesitation to yield implicitly to the teaching of that which was known seemed to him to be to use our own ignorance as a cloak for self-deception. He expresses this with his characteristic grace of thought in the following passage from his lecture on Body and Mind:
The papers which deal with strictly physical subjects do not require to be noticed separately here. In the first place, they are already widely known and have deservedly become favourites among the vast body of educated people who take an interest in science—a distinction which they owe not merely to their scientific merit but to the charm of a style, the beauty of which it would be hard to overpraise, and which enabled him to couch his exposition in the most vivid and picturesque language without in the least sacrificing the more important element of accuracy. And, in the second place, these papers are not written from the point of view of scientific instruction. The direct teaching of physical science he left to those who had considered it their specialty, and he treated physical discoveries as a philosopher seeking to learn from them lessons of far wider and more general application. Thus his more direct physical teaching is made subservient to and incorporated with his philosophy. This was what led him to choose for his scientific lectures subjects which are of such special interest to all at the present moment. We are at an epoch when all attention is concentrated upon what may be termed the minute anatomy of matter. The ultimate constitution of bodies and the laws that govern the elements of which they are composed are being investigated from all points, and the discoveries that have already been made have only served to stimulate the eagerness of the search. Professor Clifford was deeply impressed with the idea that the Atomism that characterizes recent physical science was a phase of development in all scientific research, and believed that some parallel step was needed to be taken in other sciences; and hence he made a study of all the Iatest discoveries tending to throw light upon these matters, and thus was able to take his studies into the most recondite mysteries of molecular phenomena.
As the fundamental principle of the system which he accepted was, as we have seen, that all knowledge has arisen from experience, it is clear that no place was left in it for the so-called necessary truths of the exact sciences. And hence in a series of papers he examines the nature and genesis of the ideas of space and number which are supposed to be obedient to these à priori laws. This portion of his work is of special interest and importance, inasmuch as his splendid mathematical power enables him to tread firmly on this slippery ground on which so many astute thinkers have just their footing. The question on which one naturally looks with most closeness, for his opinion, is that of the much-discussed axioms of Euclid Here he, as one of the first geometers of the age, could speak with exceptional authority, and his treatment of the matter is strikingly original. He unravels the Gordian knot of the supposed absolute truth of these axiomas by showing that we do not know, after all, whether they are true or not. Taking in aid the work of Lobatchewsky and Riemann, he proves that any one of these familiar geometrical principles, such as that "two straight lines cannot enclose a space", might be untrue and yet all human experience be unable to detect it, so that it is conceivable that even those axioms may be conclusions too hurriedly arrived at, which may ultimately be found to be incorrect, and which must in the meanwhile be relegated to the position of assumptions, to which, although they are justified by experience, we can only assert what they are sufficiently accurate for our present state of knowledge. It may seem strange that any one should hint a possibility that, after all, two straight lines can enclose a space. But it is not a mere paradox that is suggested. It has been found possible to construct consistent systems of geometry upon hypotheses which would not exclude such an occurrence, and, although it taxes Professor Clifford's unrivaled power of exposition to make it plain, he is entitled to the credit of having offered to us alternatives which we cannot say are impossible. It would be quite characteristic of the progress of science that we should thus have to call in review our fundamental mental hypotheses. They are usually framed in a time which is incapable of testing them severely. One can imagine the world resting for ages in the belief that radiant light always goes in straight lines, and that this should come to be regarded as a necessary truth, until some very accurate experiment showed the existence of diffraction and the tendency of light to go round a corner. And, theoretically speaking, these considerations apply with immensely greater force to the present case, for, on the hypothesis used by Professor Clifford, not the most accurate experiment which we could devise would suffice to detect the minute differences that would be caused by the change from the old assumption to the new one. Thus he has the right to say that we ought not to ascribe to these laws any further validity than as being correct to the utmost limit of our present instrumental accuracy. In the theoretical truth of all this we agree fully with Professor Clifford, and we greatly admire the skill with which he handles so intricate a question. But, so far as the position of the axioms is concerned, we doubt whether the appeal to non-Euclidean geometry helps the matter much; and still less do we think that he is justified in his estimate of the effect of Lobatchewsky's work. According to him:-
Strange to say, the necessity of keeping in view the limits of legitimate inference from experience is the point most constantly insisted on throughout these volumes, a fact which is worth remembering by those who accuse the scientific school of desiring only to substitute one set of dogmas for another. It might well have been expected that one who so earnestly preached the sufficiency of science would be led to dwell rather on what it can tell us than on the limitations to which even it is subject; and the temptation to do so was rendered greater by the fact that he did not think that any actual danger was to be apprehended under present circumstances from an exaggerated faith in the authority of the dicta of science. But the moral evil of permitting mankind to erect for itself an idol out of some supposed absolute and universal uniformity in nature appeared to him too serious to be risked; and hence he continually impresses on his readers that they may not seek for absolute certainty any more than they may decline to avail themselves of the light which they actually have. The aim of science is to help man's needs, not to provide him with such intellectual inconsistencies as abstract or absolute truths. We cannot refrain from referring here to a passage in his well-known address to the British Association at Brighton:
Such, then, is his view of the origin of morality in the past. He has no fears about its future. In his belief it will no less strongly bind the beards and consciences of men when its true connection with the interests of the community is perceived than it has in times past, when its nature and functions were less understood. But even if this is to be granted to him, the world would not find in these ideas the equivalent of all that it at present possesses The older systems of morality gave definite rules of conduct, and thus put before mankind ideals which, if difficult or impossible of attainment, at least told in which direction it should strive. But if we substitute for all these definite rules of conduct the single one that we are to do our best to promote the efficiency and development of the social organism, we are left sadly in doubt as to what we are to follow and what elude. When the common duties of life have been performed, whence can we learn how further to aid society Nature knows but one test for increased efficiency, and that is survival; but this test is only applied by her to what has been done, and not to what is proposed to be done. Are we, then, condemned to go blindly blandering on and to have as our sole reward the consciousness that if we have gone wrong our work will be brought to naught? Is there to be no criterion by which we are to distinguish the good impulses from the mistaken ones? Professor Clifford evidently felt deeply the want of such a criterion and the imperfection of the system which he advocated, if none such could be found. And he tries to supply one. He points out that there are two ways in which a race may undergo change. The variation may come from within, or it may be forced upon it from without by the action of the external environment; and he would have us regard a variation as a good one, just in proportion as the former element is more strongly marked in it in comparison with the latter. His argument is that the progress of development in simplified nature is an advance from the less to the more highly organized, and that anything that tends to increase organization tends to raise the organism in the scale of being. In those changes which come from without the organism is affected as any dead matter of such kind would be, and the influence upon it will be to produce greater fixity and less capacity for change; while, on the other hand, the changes that come from within are likely to increase the organization and to give greater capacity for further adaptation. To use his own words
We have attempted, in what we have written here, to give a sketch of a mind most difficult to describe in its powers, its strangeness, its uniqueness. It is no wonder we treasure every relic he has left us, not only because he was taken from is so young, but because to great a proportion of his working years was encroached on by the cruel malady which bore him away. Yet these years were far from wasted, since his intellectual activity continued unabated almost to the very end; while the moral beauty of his nature was brought out in fullest sorrow. The devotion of his friends throughout was intense, for he had the rarest gift of winning friendship, being himself so loving, so sympathetic, so quaint of humour, and so completely untainted by worldliness, that he over preserved something of the appealing charm of childhood. He delighted in little children and they delighted in him, as the simplicity of his character gave them a sense of comradeship with him. But his love for his own children passes all words and was a guage of the depth of his feelings. The triumph of the brave spirit over the suffering body, his brilliant calm, and gentle cheerfulness, were viewed with reverence by all who surronnded him. When the weak voice could scarcely be more heard, its whispers were still of bright conception, of fresh suggestions, of thoughts of truth and wisdom. Nor were these poured into unworthy ears, for over his sick bed bent in succession the noblest and best among our leaders of thought. They loved him in life, they cherish his memory, and they trust that those who make acquaintance with the the writings of this young philosopher -- whether they agree with him, or whether they differ from him -- will think of him with something of the kindly tenderness which he called forth from all who personally knew him.
[*Lectures and Essays by the late William Kingdon Clillford, F.R.S. Edited by Leslie Stephen and Frederick Pollock. Two volumes. Macmillan and Co., London, 1879]
PROFESSOR CLIFFORD'S LECTURES AND ESSAYS *
The feelings of the many personal friends of Professor Clifford on reading these volumes must be like those of the survivors of a shipwreck who, on the morning after the storm, contemplate on the wreck, on the beach, the deep remnants that the capricious sea has revealed from the rich contents of the sea that she has engulfed. Their joy at the sight of each relic is insufficient to compensate for the sad memories it awakens of equally precious ones that are lost. Nor is this feeling attributable merely to the fact that an early death has snatched from us a thinker of great power. Many such might pass away without exciting these feelings of regret. The world would be grateful for anything it had actually received from them, and would not concern itself with speculations as to how much greater might have been their achievements had more time been allowed them. But none who personally know Professor Clifford could thus banish the thought of what might have been -- of the future which was denied him. For his life we are not that of the solitary thinker whose greatness is first learned by the world and mastered by his associates. Himself intensely human and delighting above all things in human society, it was his greatest pleasure to take his friends with him into the most rectitude of his mind and to lavish on them his richest thoughts. To them to read or lecture was inward part of his thoughts and savings which he chose to put into literary form. Hence, in their views of him, promise and performance were inextricably mixed. It must seem to them, as though death had drawn an arbitrary line between the portion of his work which is to survive and that which must pass away. The true reward of a life and character in which the personal element has such prominence is the affection and reverence of friends and contemporaries and of this no one had a larger share than Professor Clifford. And as in considering the reward of such a life we may not neglect this personal element, so also we must take it into account in estimating the work that he has done. In the influence that he exercised over all who were brought into contact with him, and in the stimulus he thus gave to the cult of the ideas which he himself cherished, will be found the complement of the labours whose results are now before us. But this part of his life's work can never be fully recognized by the world at large, however anxious those may be who have profited by personal intercourse with him to acknowledge their debt. If, however, any words can adequately describe the man in his relations to those around him, it has been done by the author of the biographical sketch which is prefixed to these volumes. The name of the author would be a sufficient guarantee that his work would possess all that literary skill and intellectual power could give to it; but no mere literary skill could have given such a touching picture of the personal charm of Professor Clifford or of the picturesque variety of his life and thoughts, and no mere întellectual effort could have criticized his character and its bearing upon the theories that he held with so just an appreciation and so positive a sympathy, Its tender grace speaks throughout of one who mourns a dear comrade, and who feels that he honours him best by preserving to the world the fresh memory of their friendship.
The present question, however, with regard to Professor Clifford's works is not their suggestiveness to those who knew the author, but their value to the general reader in the state in which they actually exist. And many a friend of the author who first took them up and remembered his versatile genius and his keen enjoyment of all realms of intellectual activity must have trembled lest they should be found to consist of fragmentary pieces of work, too disconnected to do justice to his powers of consecutive reasoning and too varied to have any effect as a whole. Fortunately, these fears are groundless. It is true that in form these papers are disconnected, but the very circumstances that gave them birth have caused them to manifest a unity of purpose and a cognatenoss of subject which render them in everything but form a con- nected whole. Indeed, so completely is this the case that Professor Clifford had, it seems, the ideas of recasting them and publishing them in a single work under the name of "The Creed of Science," and even went so far as to sketch its table of contents. If we compare the existing papers with this table of contents, we at once see that, with one or two trifling exceptions, they would have all found their place in the projected book, and would have needed but little modification for that purpose beyond such as would be necessary to prevent repetition. It is not only in subject that the various papers are closely related. There is also a singular consistency of view and of method throughout. This can be seen by comparing his lecture at the Royal Institution in March, 1868—which was his first public utterance, and was delivered within about a year of his taking his degree at Cambridge — with his article on "Cosmic Emotion," which is almost the last that he wrote. The latter shows, of course, considerable advance in grasp of the subject, but there is no substantial modification of view or even of method. This we shall presently show was not accidental; but it suffices to remark that it renders the work as valuable as though it were in a more connected form, while the fact that all the papers are preserved in their original form gives us a better insight into the mind of the author and the aims and tendencies of his labours.
The key to Professor Citford's writings is to be found in the special characteristics of genius as manifested in his mathematical work, that work which unquestionably represents the main bent of his mind, and in which his power is most conspicuously shown. His chief strength in mathematics consisted in prodigious faculties for reasoning by analysis, using that phrase in its broadest sense. He is of a comparatively simple kind, capable only of determining, under special circumstances, the modifications which must be made in it to suit different or more general conditions. This power of apparently reasoning from the particular to the general, and of passing from one proposition to the corresponding one when some change had been made in the conditions essential to its truth, was inborn with him. It was the ruling passion of his mind, and it was mainly to the exercise of this faculty that are due his splendid contributions to our mathematical knowledge. No sooner had he a theorem in plane geometry than he sought for its analogue in solid figures. No sooner had he a theorem relating to our ordinary space than he sought its analogue in the impossible spaces in which he delighted. Nor was he content to deal thus with single theorems. He would throw himself mentally into the altered circumstances, and would not rest until he had constructed a complete system to suit them, drawing each portion of it by analogy from the corresponding truths of the system he was thus transplanting. In this way he would feel his way amid the impenetrable darkness of four-dimensional space, or non-Euclidean geometry, with the same ease that he would have shown in dealing with the relations of ordinary and possible space; and would speak thereon with a certainty and clarity that seemed incredible even to those who were his competitors in other branches of mathematics. Indeed, he would often talk of such matters in so vivid a way that it was a contested point among his friends whether he had not some occult mental picture of these non-existent and impossible regions. We do not think that he had. It was perhaps by means of mental pictorial representations that he was able to realize the properties of these new and strange regions, but by his intrinsic power of allowing for change of conditions. If a man has to pass at some period of his existence into a world where two and three made six, or where two straight lines could enclose a space, Professor Clifford would have been the proper person for him to consult. He would have told him how far he could retain his previous habits and what new ones he must cultivate. It was not only in dealing with mathematical questions that his peculiarity showed itself. Often, when in conversation some theory, possible or impossible, was suggested, either in earnest or in joke, he would pretend to adopt it and proceed to help work it out in all his bearings, keeping with wonderful skill and consistency to the new hypothesis, however self-contradictory or impossible it might appear to be. And this was not the ordinary testing process of the inductive philosopher, who followa out a hypothesis to its legitimate consequences in order to test its admissibility by the truth or falsehood of the deductions. It was not in any sense analytical, but was purely constructive. He loved to clothe the hypothesis with all the detail that would naturally belong to it if it were an actuality. And rightly to understand Professor Clifford's philosophical work, we must view him thus. His was an eminently constructive mind, taking pleasure less in dissecting out causes than in pursuing their consequences in all their complexity of result.
Towards the end of his College course, during the earlier part of which he had not occupied much with scientific questions, Professor Clifford became acquainted with the discoveries of Mr. Darwin and Mr. Herbert Spencer. We shall not linger to discuss the greatness of the change initiated by these discoveries. The world has now no parallel instance of the sudden introduction of ideas so deep-reaching in their influence over human thought at a time when the facilities for the transmission of ideas among civilized mankind were so great. And, consequently, there has never been, and probably never will be, such a sudden transformation throughout the whole intellectual horizon. These views will sound exaggerated to many; the universal recognition of the magnitude of the change must be left to a succeeding age, but the nature of this change is already sufficiently apparent. We may learn the rapidity with which the change has taken place by the fact that these discoveries, once the subject of such blind and unmeasured abuse, are already becoming fully understood and fairly treated by all parties. The more enlightened men of all schools are beginning to feel that they have been delivered from the danger of basing their arguments upon a riddle ill-read; a danger which constantly besets all Churches sufficiently venerable to respect tradition, since so much of the exegesis and argument which have become associated with their teaching must date from ages of great scientific ignorance. Thus the controversy is narrowing itself to the true issue—the extent to which the new doctrines are applicable to the solution of the mysteries that surround us in nature. On this point the variety of opinion is necessarily infinite. Of those who accepted the new teaching in its entirety was Professor Clifford. After the lesson which the world had just received, to the extent to which an increase in knowledge may explain what had previously seemed utterly inexplicable, it was in his eyes an unworthy as well as a foolish act to doubt the universality of science, and any attempt to plead the vastness of the unknown as an excuse for our hesitation to yield implicitly to the teaching of that which was known seemed to him to be to use our own ignorance as a cloak for self-deception. He expresses this with his characteristic grace of thought in the following passage from his lecture on Body and Mind:
In many parts of Europe it is compulsory to leave a part of the land until grown for the brownie to live in, because he cannot live in cultivated ground; and if you grant him this, he will do a great deal of your household work for you at night while you sleep. In Scotland, the piece of ground which is left wild for him to live in is called 'the goodman's croft.' Now, there are people who indulge a hope that the ploughshare of science will leave a sort of goodman's croft around the field of reasoned truth; and they promise that in that cases a good deal of our civilizing world shall be done for us in the dark, by means we know nothing of. I do not share this hope, and I feel very sure that it will not be realized. I think that we should do our work with our own hands in a healthy, straight-forward way. It is idle to set bounds to the purifying and organizing work of science. Without mercy and without resentment, she ploughs up weed and briar; from her footsteps behind her grow up corn and healing flowers, and no corner is far enough to escape her furrow.From such language as this, it is easy to see how deeply he had become imbued with the new teaching. And, this being the case, those special faculties of his mind of which we have spoken enabled him at a bound, as it were, to realize all the consequences of his new beliefs. The ordinary phenomena which accompany the reception of new ideas either by an individual or a society are familiar to all. The old ideas for a long time contrive to keep their place in spite of the introduction of the new ones. It is only by slow degrees that their incompatibility is recognized, and they are modified or got rid of. And even when the process of adaptation is fairly complete, traces of the past state of things are to be found in "survivals"—remnants of former and incongruous modes of thought which linger on, owing their preservation to their insignificance. But with Professor Clifford there was no gradual process of assimilation; there were no "survivals." He seized upon the new doctrines with his accustomed mental fervour, and thenceforth his every line of thought flowed strictly from them. We find in his writings few, if any, traces of conflict, and none of compromise. It is this which has earned for him so unjustly the reputation in some quarters of being an extreme or violent writer. Violent he is; the very completeness of the transformation prevented him from showing the intemperance of thought or language which usually marks conversions. Nor can he be fairly termed an extreme writer. He was merely thoroughly consistent with himself, and any appearance of excess of zeal in the application of the new ideas arose from his delight in exercising his faculty of developing the various consequences that follow from given premises; and it was this which would not let him rest content until he had made us taste with him the philosophy, the polity, the morality, and even the poetry of the new era.
The papers which deal with strictly physical subjects do not require to be noticed separately here. In the first place, they are already widely known and have deservedly become favourites among the vast body of educated people who take an interest in science—a distinction which they owe not merely to their scientific merit but to the charm of a style, the beauty of which it would be hard to overpraise, and which enabled him to couch his exposition in the most vivid and picturesque language without in the least sacrificing the more important element of accuracy. And, in the second place, these papers are not written from the point of view of scientific instruction. The direct teaching of physical science he left to those who had considered it their specialty, and he treated physical discoveries as a philosopher seeking to learn from them lessons of far wider and more general application. Thus his more direct physical teaching is made subservient to and incorporated with his philosophy. This was what led him to choose for his scientific lectures subjects which are of such special interest to all at the present moment. We are at an epoch when all attention is concentrated upon what may be termed the minute anatomy of matter. The ultimate constitution of bodies and the laws that govern the elements of which they are composed are being investigated from all points, and the discoveries that have already been made have only served to stimulate the eagerness of the search. Professor Clifford was deeply impressed with the idea that the Atomism that characterizes recent physical science was a phase of development in all scientific research, and believed that some parallel step was needed to be taken in other sciences; and hence he made a study of all the Iatest discoveries tending to throw light upon these matters, and thus was able to take his studies into the most recondite mysteries of molecular phenomena.
As the fundamental principle of the system which he accepted was, as we have seen, that all knowledge has arisen from experience, it is clear that no place was left in it for the so-called necessary truths of the exact sciences. And hence in a series of papers he examines the nature and genesis of the ideas of space and number which are supposed to be obedient to these à priori laws. This portion of his work is of special interest and importance, inasmuch as his splendid mathematical power enables him to tread firmly on this slippery ground on which so many astute thinkers have just their footing. The question on which one naturally looks with most closeness, for his opinion, is that of the much-discussed axioms of Euclid Here he, as one of the first geometers of the age, could speak with exceptional authority, and his treatment of the matter is strikingly original. He unravels the Gordian knot of the supposed absolute truth of these axiomas by showing that we do not know, after all, whether they are true or not. Taking in aid the work of Lobatchewsky and Riemann, he proves that any one of these familiar geometrical principles, such as that "two straight lines cannot enclose a space", might be untrue and yet all human experience be unable to detect it, so that it is conceivable that even those axioms may be conclusions too hurriedly arrived at, which may ultimately be found to be incorrect, and which must in the meanwhile be relegated to the position of assumptions, to which, although they are justified by experience, we can only assert what they are sufficiently accurate for our present state of knowledge. It may seem strange that any one should hint a possibility that, after all, two straight lines can enclose a space. But it is not a mere paradox that is suggested. It has been found possible to construct consistent systems of geometry upon hypotheses which would not exclude such an occurrence, and, although it taxes Professor Clifford's unrivaled power of exposition to make it plain, he is entitled to the credit of having offered to us alternatives which we cannot say are impossible. It would be quite characteristic of the progress of science that we should thus have to call in review our fundamental mental hypotheses. They are usually framed in a time which is incapable of testing them severely. One can imagine the world resting for ages in the belief that radiant light always goes in straight lines, and that this should come to be regarded as a necessary truth, until some very accurate experiment showed the existence of diffraction and the tendency of light to go round a corner. And, theoretically speaking, these considerations apply with immensely greater force to the present case, for, on the hypothesis used by Professor Clifford, not the most accurate experiment which we could devise would suffice to detect the minute differences that would be caused by the change from the old assumption to the new one. Thus he has the right to say that we ought not to ascribe to these laws any further validity than as being correct to the utmost limit of our present instrumental accuracy. In the theoretical truth of all this we agree fully with Professor Clifford, and we greatly admire the skill with which he handles so intricate a question. But, so far as the position of the axioms is concerned, we doubt whether the appeal to non-Euclidean geometry helps the matter much; and still less do we think that he is justified in his estimate of the effect of Lobatchewsky's work. According to him:-
What Vesalius was to Galen, what Copernicus was to Ptolemy, that was Lobatchewsky to Euclid. There is, indeed, a somewhat instructive parallel between the two last cases. Copernicus and Lobatchewsky were both of Slavic origin, and one of them brought about a revolution in scientific ideas so great that it can only be compared with that wrought by the other. And the reason for the transcendent importance of these two changes is that they are changes in the conception of the cosmos.Surely sympathy with a brother geometer whose tastes greatly resembled his own has carried Professor Clifford too far in this. We have no wish to disparage the value or interest of Lobatchowsky's investigations, and we freely admit that they may tend to impress on the few minds capable of comprehending them the importance of remembering that all knowledge is generalized experience, and that there are limits beyond which this process of generalization cannot be pushed with safety. But this is a very different thing from working a revolution in our conception of the Cosmos. It does not even add anything to the evidence for or against any proposed genesis of our ideas on the exact sciences. The question whether these are, after all, merely due to experience must be decided by other considerations than the possibility of a few minds rising to the conception of crooked space.
Strange to say, the necessity of keeping in view the limits of legitimate inference from experience is the point most constantly insisted on throughout these volumes, a fact which is worth remembering by those who accuse the scientific school of desiring only to substitute one set of dogmas for another. It might well have been expected that one who so earnestly preached the sufficiency of science would be led to dwell rather on what it can tell us than on the limitations to which even it is subject; and the temptation to do so was rendered greater by the fact that he did not think that any actual danger was to be apprehended under present circumstances from an exaggerated faith in the authority of the dicta of science. But the moral evil of permitting mankind to erect for itself an idol out of some supposed absolute and universal uniformity in nature appeared to him too serious to be risked; and hence he continually impresses on his readers that they may not seek for absolute certainty any more than they may decline to avail themselves of the light which they actually have. The aim of science is to help man's needs, not to provide him with such intellectual inconsistencies as abstract or absolute truths. We cannot refrain from referring here to a passage in his well-known address to the British Association at Brighton:
When the Roman jurists applied their experience of Roman citizens to dealings between citizens and aliens, showing by the difference of their actions that they regarded the circumstances as essentially different, they laid the foundations of that great structure which has guided the social progress of Europe. The procedure was an instance of strictly scientific thought. When a poet finds he has to move a strange new world which his predecessors have not moved; when, nevertheless, catches fire from their flashes, arms from their armoury, sustenance from their footsteps, the procedure by which he applies old experience to new circumstances is nothing greater or less than scientific thought. When the moralist, studying the conditions of society and the ideas of right and wrong which have come down to us from a time when war was the normal condition of man and success in war the only chance of survival, evolves from them the conditions and ideas which must accompany time of peace, when the comradeship of equals is the condition of national success, the process by which he does this is scientific thought and nothing else. Remember, then, that it is the guide of action; that the truth we see it arrives at is not that which we can ideally contemplate without error, but that which we act upon without fear; and you cannot fail to see that scientific thought is not an accompaniment or equation of human progress, but human progress itself.The portions of those volumes which will, however, have the largest circle of readers are those which deal with social and metaphysical subjects. It is in this way that Professor Clifford finds most scope for his special powers by following out in detail the results of his hypotheses, and it is here that the richness of his intellect shows itself most forcibly in the variety and originality of the ideas which he presents to us. To appreciate this variety it is necessary to read the book itself, for it rests in some form or other of nearly all the subjects of deepest interest in this age of questioning. To trace the connection between our present ideas and habits, social or otherwise, and man's past history, and to ascertain what, if any, modifications will follow from the general recognition of this connection, formed in his eyes a problem the solution of which did not admit of delay. It was as a contribution to the solution of this problem that he framed his remarkably original and fascinating theory of consciousness, and devoted so much pains to working out the various ethical and social questions which he treats in this part of his works. As a specimen of his results we will take his theory of moral ideas. The existence of moral ideas and of the concept of praise and praise and blame Professor Clifford connects with the social habits of mankind. In the earliest stage of humanity he supposes that man was gregarious; and as this was of great value in preserving the race, all qualities tending to develop it were highly favoured in the struggle for existence. Thus there grew up closeness of relation between the individual and the tribe, and a unity of interest which caused the individual habitually to regard notions and events from the point of view of the tribe and no longer to consider merely their effect upon his own individual self. Hence arose a conception of a tribal self. All the members of the tribe, regarding assumptions from this common point of view, combined to repress those that were injurious to the interests of the tribal self and to encourage those that were beneficial, and the individual members thus taking part in passing the tribal verdict developed the faculty of anticipating its nature, at first in the case of the actions of others, and subsequently of their own. This relation of the action to the tribal self was, in Professor Clifford's view, the earliest form of its moral quality, and this habit of anticipating the tribal verdict was the prototype of conscience. Nor does he think that matters have changed much in these respects. The tribal self has widened until now it embraces whole nations, and even the total of humanity. The crudeness of the judgement as to what is beneficial or injurious bas diminished in the light of wider experience. But the root and essence of morality is and is always to remain the same. Thus the highest morality is that which most contributes to the efficiency of a man as a citizen, and there are no self-regarding virtues. Those who knew the nobleness and beauty of Professor Clifford's life will not need to be told that this idea of all morality being dependent on the relations of our actions to our fellow-mon and not on their relation to ourselves was not with him an excuse for relaxing the stringency of the moral code. On the contrary, it would be difficult to find higher ides of morality than that which animates all those of his writinga which deal with social subjects. And this mode of regarding our relations to our neighbours as supplying the one guiding principle of life brought into prominence with him the sadly-neglected duty of honest inquiry. To let falsehood live when we could aid in killing it, or to be slack in the diffusion of what we know to be truth, was to be guilty of a lie to the community, and this Professor Clifford views as at once cowardly and wicked. When we consider how error has in past ages cramped the energies of mankind and stunted its faculties, we can well understand that to aid, actively or passively, in prolonging its reign must take the first rank among crimes in the eyes of one who defined evil as that which binders the development of the human race.
Such, then, is his view of the origin of morality in the past. He has no fears about its future. In his belief it will no less strongly bind the beards and consciences of men when its true connection with the interests of the community is perceived than it has in times past, when its nature and functions were less understood. But even if this is to be granted to him, the world would not find in these ideas the equivalent of all that it at present possesses The older systems of morality gave definite rules of conduct, and thus put before mankind ideals which, if difficult or impossible of attainment, at least told in which direction it should strive. But if we substitute for all these definite rules of conduct the single one that we are to do our best to promote the efficiency and development of the social organism, we are left sadly in doubt as to what we are to follow and what elude. When the common duties of life have been performed, whence can we learn how further to aid society Nature knows but one test for increased efficiency, and that is survival; but this test is only applied by her to what has been done, and not to what is proposed to be done. Are we, then, condemned to go blindly blandering on and to have as our sole reward the consciousness that if we have gone wrong our work will be brought to naught? Is there to be no criterion by which we are to distinguish the good impulses from the mistaken ones? Professor Clifford evidently felt deeply the want of such a criterion and the imperfection of the system which he advocated, if none such could be found. And he tries to supply one. He points out that there are two ways in which a race may undergo change. The variation may come from within, or it may be forced upon it from without by the action of the external environment; and he would have us regard a variation as a good one, just in proportion as the former element is more strongly marked in it in comparison with the latter. His argument is that the progress of development in simplified nature is an advance from the less to the more highly organized, and that anything that tends to increase organization tends to raise the organism in the scale of being. In those changes which come from without the organism is affected as any dead matter of such kind would be, and the influence upon it will be to produce greater fixity and less capacity for change; while, on the other hand, the changes that come from within are likely to increase the organization and to give greater capacity for further adaptation. To use his own words
The action which has its immediate antecedents within the organism has a tendency, so far as it alters the organism, to make it more organic, or to raise it in the scale. The action which is determined by foreign causes is one in regard to which the organism acts as if inorganic, and in so far as it tends to alter it, it tends also to lower it in its scale.It would be hardly just to take exception to the very general and, we might even add, vague terms in which this passage is expressed. The speculation is put forward in a very guarded and tentative manner, rather as a contribution to the discovery of truth than as representing the final truth itself, and if we could recognize in it any approach to a true principle, we should welcome it, however satisfactory it might be in its present form. But we regret that in this case we can neither follow his reasoning nor accept his conclusion. Take, as a simple example, the case of a change of habitat which exposes a soft-footed race of animals to the necessity of walking on hard ground. The new circumstances might be met either by the cuticle of the foot becoming indurated, or by some internal modification of the organism, which would cause the supply of fresh cuticle to keep pace with the increased waste. Professor Clifford would have us believe that the latter method is essentially the better, and would urge as a reason that when conditions once more changed, the organism would not have the hereditary callosities which the other method would have developed. But it has purchased this at the price of an unnecessary drain on its vital energies during the long ages when the more economical method would have served its purpose and left it more strength for initiating other developments. Who can say whether its gain or its loss preponderates? The one test of the value of an attempt at variation is, as we have said, its success, and we see no reason to think that any general secondary law will be discovered that will enable us to prophesy the result of this test. Growth of knowledge will teach us how to adapt with ever-increasing skill our efforts to the circumstances of each particular case, but that is all we can hope for. The tenacity with which Professor Clifford clung to this principle in spite of all the difficulties that surround it is accounted for by its having, in some way or other, become associated in his mind with the principle of the importance to mankind of the free and spontaneous development of the individual. This is, however, a very different truth, resting on no such doubtful foundations as the hypothesis of which we have spoken. By means of the unconscious working of the survival of the fittest, Nature is working out the problem of how best the organism may be adapted to its environment. It is this which has formed the world of today, and in the vigorous action of the same process lie the best hopes of humanity for the ages to come. But the one condition for this vigorous action is that the individual should be left free to make spontaneous attempts at development. Nature will separate the good from the bad, but she can only pronounce on what is submitted to her judgment Hence it was that, in Professor Clifford's mind, the most hopeless symptom in a race was uniformity, and the most suicidal policy was represssion of individual liberty. In this he was a true representative of the traditions of the Anglo-Saxon race. The organized intellectual slavery to which Comte looked forward as the apotheosis of humanity answered to his conception of the utter destruction of all that is good. This idea was the source of all his political views and is the principal theme of some of his best essays, although he was not in the least an anarchist. The community was with him higher than the individual, and in the completeness of social organization he saw the final triumph of evolution. But it was because he saw in the development of the comununity the one safe path to the complete freedom of the individual.
We have attempted, in what we have written here, to give a sketch of a mind most difficult to describe in its powers, its strangeness, its uniqueness. It is no wonder we treasure every relic he has left us, not only because he was taken from is so young, but because to great a proportion of his working years was encroached on by the cruel malady which bore him away. Yet these years were far from wasted, since his intellectual activity continued unabated almost to the very end; while the moral beauty of his nature was brought out in fullest sorrow. The devotion of his friends throughout was intense, for he had the rarest gift of winning friendship, being himself so loving, so sympathetic, so quaint of humour, and so completely untainted by worldliness, that he over preserved something of the appealing charm of childhood. He delighted in little children and they delighted in him, as the simplicity of his character gave them a sense of comradeship with him. But his love for his own children passes all words and was a guage of the depth of his feelings. The triumph of the brave spirit over the suffering body, his brilliant calm, and gentle cheerfulness, were viewed with reverence by all who surronnded him. When the weak voice could scarcely be more heard, its whispers were still of bright conception, of fresh suggestions, of thoughts of truth and wisdom. Nor were these poured into unworthy ears, for over his sick bed bent in succession the noblest and best among our leaders of thought. They loved him in life, they cherish his memory, and they trust that those who make acquaintance with the the writings of this young philosopher -- whether they agree with him, or whether they differ from him -- will think of him with something of the kindly tenderness which he called forth from all who personally knew him.
[*Lectures and Essays by the late William Kingdon Clillford, F.R.S. Edited by Leslie Stephen and Frederick Pollock. Two volumes. Macmillan and Co., London, 1879]
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