 Chapter 3 of Philosophical Essays by Bertrand Russell This LibriVox recording is in the public domain. Recording by Landon D.C. Elkind at the University of Iowa in Coralville, Iowa. The study of mathematics, Footnote 1, Reprinted from the New Quarterly, November 1907. End of Footnote 1. In regard to every form of human activity, it is necessary that the question should be asked from time to time, What is its purpose and ideal? In what way does it contribute to the beauty of human existence? As respects those pursuits which contribute only remotely by providing the mechanism of life, it is well to be reminded that not the mere fact of living is to be desired, but the art of living in the contemplation of great things. Still more in regard to those avocations which have no end outside themselves, which are to be justified, if at all, as actually adding to the sum of the world's permanent possessions, it is necessary to keep alive a knowledge of their aims, a clear prefiguring vision of the temple in which creative imagination is to be embodied. The fulfillment of this need, in what concerns the studies forming the material upon which custom has decided to train the youthful mind, is indeed sadly remote. So remote as to make the mere statement of such a claim appear preposterous. Great men, fully alive to the beauty of the contemplations to whose service their lives are devoted, desiring that others may share in their joys, persuade mankind to impart to the successive generations the mechanical knowledge without which it is impossible to cross the threshold. Dry pedants possess themselves of the privilege of instilling this knowledge. They forget that it is to serve, but as a key to open the doors of the temple. Though they spend their lives on the steps leading up to those sacred doors, they turn their backs upon the temple so resolutely that its very existence is forgotten, and the eager youth who would press forward to be initiated to its domes and arches is bitten to turn back and count the steps. Mathematics, perhaps more even than the study of Greece and Rome, has suffered from this oblivion of its due place in civilization. Although tradition has decreed that the great bulk of educated men shall know at least the elements of the subject, the reasons for which the tradition arose are forgotten, buried beneath a great rubbish heap of pedantries and trivialities. To those who inquire as to the purpose of mathematics, the usual answer will be that it facilitates the making of machines, the traveling from place to place, and the victory over foreign nations, whether in war or commerce. If it be objected that these ends, all of which are of doubtful value, are not furthered by the merely elementary study imposed upon those who do not become expert mathematicians, the reply it is true will probably be that mathematics trains the reasoning faculties. Yet the very men who make this reply are, for the most part, unwilling to abandon the teaching of definite fallacies, known to be such, and instinctively rejected by the unsophisticated mind of every intelligent learner. And the reasoning faculty itself is generally conceived by those who urge its cultivation, as merely a means for the avoidance of pitfalls, and a help in the discovery of rules for the guidance of practical life. All these are undeniably important achievements to the credit of mathematics, yet it is none of these that entitles mathematics to a place in every liberal education. Plato we know regarded the contemplation of mathematical truths as worthy of the deity, and Plato realized, more perhaps than any other single man, what those elements are in human life which merit a place in heaven. There is in mathematics, he says, quote, something which is necessary and cannot be set aside, and if I mistake not of divine necessity. For as to the human necessities of which the many talk in this connection, nothing can be more ridiculous than such an application of the words. Clineas. And what are these necessities of knowledge, stranger, which are divine and not human? Athenian. Those things without some use or knowledge of which a man cannot become a God, to the world, nor a spirit, nor yet a hero, nor able earnestly to think and care for man. End quote. Laws page 818. Footnote 1. This passage was pointed out to me by Professor Gilbert Murray. End of footnote 1. Such was Plato's judgment of mathematics, but the mathematics do not read Plato. While those who read him know no mathematics, and regard his opinion upon this question as merely a curious aberration. Mathematics rightly viewed possesses not only truth but supreme beauty, a beauty cold and austere like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry. What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever renewed encouragement. Real life is, to most men, a long second best, a perpetual compromise between the ideal and the possible. But the world of pure reason knows no compromise, no practical limitations, no barrier to the creative activity, embodying in splendid edifices the passionate aspiration after the perfect from which all great work springs. Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos where pure thought can dwell as in its natural home and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world. So little, however, have mathematicians aimed at this beauty that hardly anything in their work has had this conscious purpose, much owing to irrepressible instincts which were better than avowed beliefs, has been molded by an unconscious taste, but much also has been spoiled by false notions of what was fitting. The characteristic excellence of mathematics is only to be found where the reasoning is rigidly logical. The rules of logic are to mathematics what those of structure are to architecture. In the most beautiful work, a chain of argument is presented in which every link is important on its own account, in which there is an air of ease and lucidity throughout and the premises achieve more than would have been thought possible by means which appear natural and inevitable. Literature embodies what is general in particular circumstances whose universal significance shines through their individual dress, but mathematics endeavors to present whatever is most general in its purity without any irrelevant trappings. How should the teaching of mathematics be conducted so as to communicate to the learner as much as possible of this high ideal? Here experience must in a great measure be our guide, but some maxims may result from our consideration of the ultimate purpose to be achieved. One of the chief ends served by mathematics when rightly taught is to awaken the learner's belief in reason, his confidence in the truth of what has been demonstrated, and in the value of demonstration. This purpose is not served by existing instruction, but it is easy to see ways in which it might be served. At present, in what concerns arithmetic, the boy or girl is given a set of rules which present themselves as neither true nor false, but as merely the will of the teacher, the way in which, for some unfathomable reason, the teacher pervers to have the game played. To some degree, in a study of such definite practical utility, this is no doubt unavoidable. But as soon as possible, the reasons of rules should be set forth by whatever means most readily appeal to the childish mind. In geometry, instead of the tedious apparatus of fallacious proofs for obvious trusums, which constitutes the beginning of Euclid, the learner should be allowed at first to assume the truth of everything obvious and should be instructed in the demonstrations of theorems which are at once startling and easily verifiable by actual drawing, such as those in which it is shown that three or more lines meet in a point. In this way, belief is generated. It is seen that reasoning may lead to startling conclusions, which nevertheless the facts will verify. And thus the instinctive distrust of whatever is abstract or rational is gradually overcome. Where theorems are difficult, they should be first taught as exercises in geometrical drawing until the figure has become thoroughly familiar. It will then be an agreeable advance to be taught the logical connections of the various lines or circles that occur. It is desirable also that the figure illustrating a theorem should be drawn in all possible cases and shapes, that so the abstract relations with which geometry is concerned may of themselves emerge as the residue of similarity amid such great apparent diversity. In this way, the abstract demonstrations should form but a small part of the instruction and should be given when by familiarity with concrete illustrations they have come to be felt as the natural embodiment of visible fact. In this early stage, proofs should not be given with pedantic fullness. Definitely fallacious methods such as that of superposition should be rigidly excluded from the first. But where without such methods the proof would be very difficult, the result should be rendered acceptable by arguments and illustrations which are explicitly contrasted with demonstrations. In the beginning of algebra, even the most intelligent child finds as a rule very great difficulty. The use of letters is a mystery which seems to have no purpose except mystification. It is almost impossible at first not to think that every letter stands for some particular number if only the teacher would reveal what number it stands for. The fact is that in algebra the mind is first taught to consider general truths, truths which are not asserted to hold only of this or that particular thing but of any one of a whole group of things. It is in the power of understanding and discovering such truths that the mastery of the intellect over the whole world of things actual and possible resides. And ability to deal with the general as such is one of the gifts that a mathematical education should bestow. But how little as a rule is the teacher of algebra able to explain the chasm which divides it from arithmetic and how little is the learner assisted in his groping efforts at comprehension. Usually the method that has been adopted in arithmetic is continued. Rules are set forth with no adequate explanation of their grounds. The pupil learns to use the rules blindly and presently when he is able to obtain the answer that the teacher desires he feels that he has mastered the difficulties of the subject. But of inner comprehension of the processes employed he has probably acquired almost nothing. When algebra has been learned all goes smoothly until we reach those studies in which the notion of infinity is employed the infinitesimal calculus and the whole of higher mathematics. The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our own age has to boast. Since the beginnings of Greek thought these difficulties have been known in every age the finest intellects have vainly endeavored to answer the apparently unanswerable questions that had been asked by Zeno the Eliotic. At last Georg Cantor has found the answer and has conquered for the intellect a new and vast province which had been given over to chaos and old night. It was assumed as self-evident until Cantor and Dedekind established the opposite that if from any collection of things some were taken away the number of things left must always be less than the original number of things. This assumption as a matter of fact holds only of finite collections and the rejection of it where the infinite is concerned has been shown to remove all the difficulties that had hitherto baffled human reason in this subject matter and to render possible the creation of an exact science of the infinite. This stupendous fact ought to produce a revolution in the tired teaching of mathematics. It has itself added immeasurably to the educational value of the subject and it has at last given the means of treating with logical precision many studies which, until lately, were wrapped in fallacy and obscurity. By those who were educated on the old lines the new work is considered to be appallingly difficult, obstruce, and obscure and it is to be confessed that the discoverer, as is so often the case has hardly himself emerged from the mists which the light of his intellect is dispelling. But inherently the new doctrine of the infinite to all candid and inquiring minds has facilitated the mastery of higher mathematics. For hitherto it has been necessary to learn by a long process of sophistication to give assent to arguments which on first acquaintance were rightly judged to be confused and erroneous. So far from producing a fearless belief in reason a bold rejection of whatever failed to fulfill the strictest requirements of logic a mathematical training during the past two centuries encouraged the belief that many things which a rigid inquiry would reject as fallacious must yet be accepted because they work in what the mathematician calls practice. By this means a timid compromising spirit or else a sacerdotal belief in mysteries not intelligible to the profane has been bred where reason alone should have ruled. All this it is now time to sweep away. Let those who wish to penetrate into the arcana of mathematics be taught at once the true theory in all its logical purity and in the concatenation established by the very essence of the entities concerned. If we are considering mathematics as an end in itself and not as a technical training for engineers it is very desirable to preserve the purity and strictness of its reasoning. Accordingly those who have attained a sufficient familiarity with its easier portions should be led backward from propositions to which they have assented as self-evident to more and more fundamental principles from which what had previously appeared as premises can be deduced. They should be taught what the theory of infinity very aptly illustrates that many propositions seem self-evident to the untrained mind which nevertheless a nearer scrutiny shows to be false. By this means they will be led to a skeptical inquiry into first principles on examination of the foundations upon which the whole edifice of reasoning is built or to take perhaps a more fitting metaphor the great trunk from which the spreading branches spring. At this stage it is well to study afresh the elementary portions of mathematics asking no longer merely whether a given proposition is true but also how it grows out of the central principles of logic. Questions of this nature can now be answered with a precision and certainty which work formally quite impossible and in the chains of reasoning that the answer requires the unity of all mathematical studies at last unfolds itself. In the great majority of mathematical textbooks there is a total lack of unity and method and of systematic development of a central theme. Propositions of very diverse kinds are proved by whatever means are thought most easily intelligible and much space is devoted to mere curiosities which in no way contribute to the main argument. But in the greatest works unity and inevitability are felt as in the unfolding of a drama in the premises a subject is proposed for consideration and in every subsequent step some definite advance is made towards mastery of its nature. The love of system of interconnection which is perhaps the inmost essence of intellectual impulse can find free play in mathematics as nowhere else. The learner who feels this impulse must not be repelled by an array of meaningless examples or distracted by amusing oddities but must be encouraged to dwell upon central principles to become familiar with the structure of the various subjects which are put before him to travel over the steps of the more important deductions. In this way a good tone of mind is cultivated and selective attention is taught to dwell by preference upon what is weighty and essential. When the separate studies into which mathematics is divided have each been viewed as a logical whole as a natural growth from the propositions which constitute their principles the learner will be able to understand the fundamental science which unifies and systematizes the whole of deductive reasoning. This is symbolic logic A study which, though it owes its inception to Aristotle is yet in its wider developments a product almost wholly of the 19th century and is indeed in the present day still growing with great rapidity. The true method of discovery in symbolic logic and probably also the best method for introducing the study to a learner acquainted with other parts of mathematics is the analysis of actual examples of deductive reasoning with a view to the discovery of the principles employed. These principles for the most part are so embedded in our raciocinative instincts that they are employed quite unconsciously and can be dragged to light only by much patient effort. But when at last they have been found they are seen to be few in number and to be the sole source of everything in pure mathematics. The discovery that all mathematics follows inevitably from a small collection of fundamental laws is one which immeasurably enhances the intellectual beauty of the whole. To those who have been oppressed by the fragmentary and incomplete nature of most existing chains of deduction this discovery comes with all the overwhelming force of a revelation like a palace emerging from the autumn mist as the traveler ascends an Italian hillside the stately stories of the mathematical edifice appear in their due order and proportion with a new perfection in every part. Until symbolic logic had acquired its present development the principles upon which mathematics depends were always supposed to be philosophical and discoverable only by the uncertain, unprogressive methods hitherto employed by philosophers. So long as this was thought mathematics seemed to be not autonomous but dependent upon a study which had quite other methods than its own. Moreover, since the nature of the postulates from which arithmetic analysis and geometry are to be deduced was wrapped in all the traditional obscurities of metaphysical discussion the edifice built upon such dubious foundations began to be viewed as no better than a castle in the air. In this respect the discovery that the true principles are as much a part of mathematics as any of their consequences has very greatly increased the intellectual satisfaction to be obtained. This satisfaction ought not to be refused to learners capable of enjoying it for it is of a kind to increase our respect for human powers and our knowledge of the beauties belonging to the abstract world. Philosophers have commonly held that the laws of logic which underlie mathematics are laws of thought laws regulating the operations of our minds. By this opinion the true dignity of reason is very greatly lowered. It ceases to be an investigation into the very heart and immutable essence of all things actual and possible becoming instead an inquiry into something more or less human and subject to our limitations. The contemplation of what is non-human the discovery that our minds are capable of dealing with material not created by them above all the realization that beauty belongs to the outer world as to the inner are the chief means of overcoming the terrible sense of impotence of weakness of exile amid hostile powers which is too apt to result from acknowledging the all but omnipotence of alien forces. To reconcile us by the exhibition of its awful beauty to the reign of fate which is merely the literary personification of these forces is the task of tragedy. But mathematics takes us still further from what is human into the region of absolute necessity to which not only the actual world but every possible world must conform and even here it builds a habitation or rather finds a habitation eternally standing where our ideals are fully satisfied and our best hopes are not thwarted. It is only when we thoroughly understand the entire independence of ourselves which belongs to this world that reason finds that we can adequately realize the profound importance of its beauty. Not only is mathematics independent of us and our thoughts but in another sense we and the whole universe of existing things are independent of mathematics. The apprehension of this purely ideal character is indispensable if we are to understand rightly the place of mathematics as one among the arts. It was formally supposed that pure reason could decide in some respects as to the nature of the actual world. Geometry at least was thought to deal with the space in which we live. But we now know that pure mathematics can never pronounce upon questions of actual existence. The world of reason in a sense controls the world of fact but it is not at any point creative of fact and in the application of its results to the world in time and space its certainty and precision are lost among approximations and working hypotheses. The objects considered by mathematicians have in the past been mainly of a kind suggested by phenomena but from such restrictions the abstract imagination should be wholly free. A reciprocal liberty must thus be accorded. Reason cannot dictate to the world of facts but the facts cannot restrict reason's privilege of dealing with whatever objects its love of beauty may cause to seem worthy of consideration. Here as elsewhere we build up our own ideals out of the fragments to be found in the world and in the end it is hard to say whether the result is a creation or a discovery. It is very desirable in instruction not merely to persuade the student of the accuracy of important theorems but to persuade him in the way which itself has of all possible ways the most beauty. The true interest of a demonstration is not as traditional modes of exposition suggest concentrated wholly in the result. Where this does occur it must be viewed as a defect to be remedied if possible by so generalizing the steps of the proof that each becomes important in and for itself. An argument which serves only to prove a conclusion is like a story subordinated to some moral which it is meant to teach. For aesthetic perfection no part of the whole should be merely a means. A certain practical spirit a desire for rapid progress for conquest of new realms is responsible for the undue emphasis upon results which prevails in mathematical instruction. The better way is to propose some theme for consideration in geometry a figure having important properties in analysis a function of which the study is illuminating and so on. Whenever proofs depend upon some only of the marks by which we define the object to be studied these marks should be isolated and investigated on their own account. For it is a defect in an argument to employ more premises than the conclusion demands. What mathematicians call elegance results from employing only the essential principles in virtue of which the thesis is true. It is a merit in Euclid that he advances so far as he is able to go without employing the axiom of parallels not as is often said because this axiom is inherently objectionable but because in mathematics every new axiom diminishes the generality of the resulting theorems and the greatest possible generality is before all things to be sought. Of the effects of mathematics outside its own sphere more has been written than on the subject of its own proper ideal. The effect upon philosophy has in the past been most notable but most varied. In the 17th century idealism and rationalism in the 18th materialism and sensationalism seemed equally its offspring. Of the effect which it is likely to have in the future it would be very rash to say much but in one respect a good result appears probable. Against that kind of skepticism which abandons the pursuit of ideals because the road is arduous and the goal not certainly attainable mathematics within its own sphere is a complete answer. Too often it is said that there is no absolute truth but only opinion and private judgment that each of us is conditioned in his view of the world by his own peculiarities his own taste and bias that there is no external kingdom of truth to which by patience and discipline we may at last obtain admittance but only truth for me for you, for every separate person. By this habit of mind one of the chief ends of human effort is denied and the supreme virtue of candor of fearless acknowledgement of what is disappears from our moral vision. Of such skepticism mathematics is a perpetual reproof for its edifice of truth stands unshakable and inexpunable to all the weapons of doubting cynicism. The effects of mathematics upon practical life though they should not be regarded as the motive of our studies may be used to answer a doubt to which the solitary student must always be liable. In a world so full of evil and suffering retirement into the cloister of contemplation to the enjoyment of delights which however noble must always be for the few only cannot but appear as a somewhat selfish refusal to share the burden imposed upon others by accidents in which justice plays no part. Have any of us the right, we ask to withdraw from present evils to leave our fellow men unaided while we live a life which though arduous and austere is yet plainly good in its own nature? When these questions arise the true answer is no doubt that some must keep alive the sacred fire some must preserve in every generation the haunting vision which shadows forth the goal of so much striving but when as must sometimes occur this answer seems too cold when we are almost maddened by the spectacle of sorrows to which we bring no help then we may reflect that indirectly the mathematician often does more for human happiness than any of his more practically active contemporaries. The history of science abundantly proves that a body of abstract propositions even if as in the case of conic sections it remains 2000 years without effect upon daily life may yet at any moment be used to cause a revolution in the habitual thoughts and occupations of every citizen. The use of steam and electricity to take striking instances is rendered possible only by mathematics. In the results of abstract thought the world possesses a capital of which the employment in enriching the common round has no hitherto discoverable limits nor does experience give any means of deciding what parts of mathematics will be found useful. Utility therefore can be only a consolation in moments of discouragement not a guide in directing our studies. For the health of the moral life for ennobling the tone of an age or a nation the austere virtues have a strange power exceeding the power of those not informed and purified by thought of these austere virtues the love of truth is the chief and in mathematics more than elsewhere the love of truth may find encouragement for waning faith. Every great study is not only an end in itself but also a means of creating and sustaining a lofty habit of mind and this purpose should be kept always in view throughout the teaching and learning of mathematics. End of Chapter 3 Chapter 4 of Philosophical Essays by Bertrand Russell First half This LibriVox recording is in the public domain recording by Landon D.C. Alkind at the University of Iowa in Coralville, Iowa Pragmatism, Footnote 1 reprinted from the Edinburgh Review April 1909 The appearance in the world of a genuinely new philosophy is at all times an event of very great importance more particularly is this the case when the new philosophy embodies the prevailing temper of the age better than any of its older rivals for in that case it is likely to establish itself in popular favor to color the thoughts of the educated and half educated public and to strengthen those elements in the mental atmosphere to which it owes its success it would be a mistake to suppose that new philosophies are always adapted to the age in which they appear but when they are not they fail to win wide acceptance whatever their other merits may be Spinoza for example deserved success as well as liveness yet his works were almost wholly neglected until more than a century after his death because the political and intellectual milieu was not one in which they could thrive Leibniz on the contrary gave scope to the love of calculation which men derived from the discoveries of his time and represented the world as a hierarchy of systems each exactly like the Holy Roman Empire his system therefore ruled the German mind until the ferment which preceded the French Revolution set men's thoughts running in new channels the philosophy which is called pragmatism or humanism footnote one these two names are distinguished by William James and Dr. Schiller in various ways at various times for our purposes it is unnecessary it is unnecessary to consider these distinctions end of footnote one is genuinely new and is singularly well adapted to the predominant intellectual temper of our time as regards its adaptation to the age we shall have more to say when we have considered what it is as regards novelty its authors show a modesty which in our opinion is somewhat excessive pragmatism a new name for some old ways of thinking William James calls his book and Dr. Schiller constantly asserts that his doctrines are those of Protagoras as for Protagoras we know sufficiently little about him to be able to read into him almost any doctrine we please and the appeal to him may be regarded as mainly due to the desire to produce an ancestry which has acquired respectability by the lapse of time with regard to more modern precursors it must be admitted that many philosophers as chief among whom we may mention Nietzsche have paved the way for the new doctrines nevertheless the cardinal point in the pragmatist philosophy namely its theory of truth is so new and so necessary to the rest of the philosophy even to those parts which had been previously maintained by others that its inventors cannot be regarded as merely developing the thoughts of less explicit predecessors the name pragmatism was first invented by Mr. C. S. Perse as long ago as 1878 it was applied by him to the doctrine that the significance of a thought lies in the actions to which it leads in order to estimate the difference between two different beliefs about the same matter he maintained we ought to consider what difference in conduct would result according as we adopted the one belief or the other if no difference would result the two beliefs are not effectively different Mr. Perse's doctrine however remained sterile until it was taken up 20 years later by William James who while retaining the word pragmatism gave it a more sweeping significance the full-fledged philosophy is to be attributed to him and Dr. Schiller jointly Professor Dewey of Columbia University is also to be reckoned among the founders of pragmatism his writings are more technical and less popular than those of James and Dr. Schiller but on certain points his exposition is perhaps preferable to theirs footnote 1 confer especially an article on the experimental theory of knowledge mind new series number 59 July 1906 end of footnote 1 as an introduction to pragmatism it is interesting to read William James's essay on the will to believe first published in 1896 and reprinted in book form in the following year in this essay though the word pragmatism does not appear we find much that is characteristic of James's later views the thesis he is advocating is that in certain cases it is right to believe wholeheartedly in one of two alternatives even when there is no evidence as to which of them is true these cases arise he says when we are compelled to choose between two hypotheses each of which seems to us possible and when it makes a great difference which we choose the instances he has in mind are chiefly questions of morals and religion in a moral perplexity we are compelled to come to some decision since inaction is as much a decision as action in regard to religion also we must act as though it were true or as though it were false we are therefore practically compelled to choose his contention is that in such cases it would be foolish to refuse to have faith merely on the ground that we do not find conclusive evidence on either side of the question to quote his own words our passion nature not only lawfully may but must decide an option between propositions whenever it is a genuine option that cannot by its nature be decided on intellectual grounds for to say under such circumstances do not decide but leave the question open is itself a passion decision just like deciding yes or no and is attended with the same risk of losing the truth end of quote he proceeds to justify himself against the charge of insufficient regard for truth not as he would now by contending that in the absence of other evidence the answer which gives the greatest emotional satisfaction is true but on a variety of grounds tending to show that there are no sufficient moral arguments against thinking it true he points out to begin with that emotions and wishes though often unable to alter our beliefs when these have become established nevertheless play a great part in initially deciding what our beliefs are to be he points out next that our duty in the matter of opinion has two branches one we must know the truth two we must avoid error these two precepts he says have very different results if in cases where evidence is lacking we abstain wholly from either belief we are sure of not incurring error but on the other hand we are sure of not knowing truth if however we decide for one of the alternatives we have an even chance of knowing the truth it follows that those who are just to abstain from belief in the absence of evidence consider it more important to avoid error than to believe truth this horror of being duped he represents as a somewhat contemptible form of cowardice quote our errors he says are surely not such awfully solemn things in a world where we are so certain to incur them in spite of all our caution a certain lightness of heart is healthier than this excessive nervousness on their behalf end of quote the legitimate conclusion from this argument would be that in such cases as William James has in mind we ought to believe both alternatives for in that case we are sure of knowing the truth in the matter if it were said that to believe both is a psychological impossibility we would rejoin that on the contrary it is often done and that those who cannot yet do it need only practice the will to believe until they have learnt to believe that the law of contradiction is false a feat which is by no means as difficult as it is often supposed to be William James proceeds to point out that in the case of religion the choice between believing and disbelieving possesses all the characteristics of the options which according to him ought to be decided by the emotions he tacitly assumes that there is no evidence for or against religion and he points out that by refusing either to believe or to disbelieve we lose the benefits of religion just as much as by deciding to disbelieve quote skepticism then is not avoidance of option it is option of a certain particular kind of risk better risk loss of truth than chance of error that is your faith vetoer's exact opinion he is actively playing his stake as much as the believer is he is backing the field against the religious hypothesis just as the believer is backing the religious hypothesis against the field it is not intellect against all passions then it is only intellect with one passion laying down its law and by what forsooth is the supreme wisdom of this passion warranted duperie for duperie what proof is there that duperie through hope is so much worse than duperie through fear end of quote the conclusion is that although there is no evidence in favor of religion we ought nevertheless to believe it if we find satisfaction in so doing this essay on the will to believe is important because it has been widely read and much criticized both adversely and favorably and because it affords a good introduction to the pragmatist temper of mind some practice in the will to believe is an almost indispensable preliminary to the acceptance of pragmatism and conversely pragmatism when once accepted is found to give full justification of the will to believe we shall therefore before proceeding to pragmatism proper consider briefly what there is to be said on a common sense basis against the doctrines so persuasively set forth in this essay we may observe to begin with the agnostic hypothesis upon which the whole argument rests the hypothesis is that no evidence for or against religion is at present known pragmatists pose as the friends of religion except in Italy and many religious people have accepted them as allies it is therefore worthwhile to emphasize this underlying hypothesis and to point out the very questionable wisdom of accepting it as the basis of a defense of orthodoxy with the truth or falsehood of this hypothesis however we need not concern ourselves in this discussion the question for us is whether granting the hypothesis we can accept the results which William James derives from it let us observe in the first place a confusion which runs through the whole pragmatist account of knowledge namely the confusion between acting on a hypothesis and believing it in the cases which William James has in mind the option between rival hypotheses is he says a forced option that is it is not avoidable quote if I say either accept this truth or go without it I put on you a forced option for there is no standing place outside of the alternative end of quote this statement appears to us to be contrary to many of the plainest facts of daily life if in walking along a country road I come to a fork where there is no signpost and no pass or by I have from the point of view of action a forced option I must take one road or other if I am to have any chance of reaching my destination and I may have no evidence whatever as to which is the right road I then act on one or another of the two possible hypotheses until I find someone of whom I can ask the way but I do not believe either hypothesis my action is either right or wrong but my belief is neither since I do not entertain either of the two possible beliefs the pragmatist assumption that I believe the road I have chosen to be the right one is erroneous to infer belief from action in the crude way involved in the assumption that we must either accept this truth or go without it is to ignore the plain fact that our actions are constantly based upon probabilities and that in all such cases we neither accept a truth nor go without it but entertain it as a hypothesis this applies in particular to the working hypotheses of science a man of science who considers it worthwhile to devise experimental tests of a hypothesis and to construct elaborate theories which use the hypothesis is not on that account to be regarded as believing the hypothesis pragmatists tell us that in such cases the initial unverified belief is a necessary condition for the subsequent established theory and by so doing they make out a case for the usefulness of believing before we have evidence this is however a mistaken analysis of the state of mind of a man who is testing a hypothesis all that is required and all that occurs among careful investigators is the belief that the hypothesis has a greater or smaller chance of being true and for this belief that there is probably sufficient evidence the actual belief that the hypothesis is true when it occurs is apt to be a hindrance since it retards the abandonment of false hypotheses when the evidence goes against them the belief is general it makes people regard experimental verification as unnecessary the Aristotelians who opposed Galileo and refused to give weight to his experiments had faithfully obeyed the precepts revived by William James the matter is however more complicated in such cases as religious beliefs where the chief benefit is derived from the emotional satisfaction of the belief itself not from the useful actions to which it directly prompts but here too the antithesis of accepting or going without is far too crude we may regard the belief as more or less probable entertain a greater or less degree of hope that it may be true and derive accordingly a greater or less proportion of the comfort we should derive from complete belief in practice to adopt the pragmatist test the effect of partial belief is very different from that of complete belief complete belief if the issue is sufficiently momentous will justify persecution assuming as history warrants us in doing that the blood of Protestant martyrs is the seed of the Catholic Church an incomplete belief on the contrary will not warrant the infliction of an indubitable evil for the sake of a gain which may possibly be illusory this affords a pragmatic argument against conceding full belief in such cases as those with which William James is concerned but if as he assumes there is a genuine possibility of the truth of an hypothesis it is in accordance with all the strictest tenets of scientific veracity that we should bear the hypothesis in mind and allow to it whatever influence over our emotions and actions corresponds to the degree of its probability we will next examine the argument that in doubtful cases the precept we must know the truth should lead us to believe one hypothesis at a venture since if we believe neither we certainly do not know the truth this argument rests upon an ambiguity in the word no at first sight it might be thought that if we believe what is in fact true we must have knowledge but this is not the sense in which the word is commonly used suppose to take a trivial instance that a man believed that the late prime minister's name began with a b but believed this because he thought Mr. Balfour was the late prime minister what he believes is in fact true yet no one would say that he knew that the late prime minister's name began with a b in this case the true belief is based upon a false reason but the case is similar when the true belief is based upon no reason except indeed in the case of immediate data such as the facts of perception thus if in the case of an option which we have no rational means of deciding we believe one alternative at a venture we cannot be said to know even if by good luck we have chosen the alternative which in fact is true in such cases we cannot know the truth though we may by chance believe it hence the precept we must know the truth which James invokes is irrelevant to the issue the usual antithesis of belief and disbelief what is known and what is unknown are not adequate to meet the situation the true precept of veracity which includes both the pursuit of truth and the avoidance of error is this we ought to give every proposition which we consider as nearly as possible that degree of credence which is warranted by the probability it acquires from the evidence known to us the further questions what propositions to consider and how much trouble to take to acquire knowledge of the evidence depend of course upon our circumstances and the importance of the issue but to go about the world believing everything the hope that thereby we shall believe as much truth as possible is like practicing polygamy in the hope that among so many we shall find someone who will make us happy another interesting point to observe in James's doctrine is the immense multiplicity of differing beliefs which it simultaneously justifies in different people this arises from the condition that the option must be what he calls a living option that is it must be one in which either alternative seems to us possible quote if I say to you be a theosophist or be a Muhammadian it is probably a dead option because for you neither hypothesis is likely to be alive but if I say be an agnostic it is otherwise trained as you are each hypothesis makes some appeal however small to your belief end of quote he points out that to different people different options are living it follows that the beliefs which on his principles different men ought to adopt are different since the three conditions for adopting a belief without evidence are that the option should be living, forced and momentous one gathers perhaps wrongly from his instances that a Frenchman ought to believe in Catholicism an American in the Monroe doctrine and an Arab in the muddy he wrote before the battle of Amdurman it seems odd that in view of this outcome he should maintain that acceptance of his doctrine would diminish persecution for an essential part of each of the above three creeds is that people who think otherwise must be taught their place to sum up our criticism of the will to believe it ignores the distinction between believing and entertaining a hypothesis and wrongly assumes that if we do not completely believe a hypothesis we must either completely disbelieve it or wholly suspend judgment hence it is able to represent the option either accept this truth or go without it as one from which there is no escape whereas all experiment both in science and in daily life implies a state of mind which accepts neither alternative he assumes that we may be said to know a truth when we believe it at a venture without reasons and that therefore in order to maximize our knowledge we have only to maximize our beliefs and his doctrines lead to the conclusion that different people ought to have incompatible beliefs these objections we shall find may also be urged against full-fledged pragmatism but we must now approach somewhat more difficult topics than those which have concerned us hitherto since pragmatism cannot be understood without examining its doctrine as to the nature of truth to this doctrine therefore we will now turn our attention the pragmatic theory of truth takes credit to itself rightly as we think for due consideration of error most theories as to the nature of truth have tacitly assumed to begin with that all our beliefs are true and have arrived at results incompatible with the existence of error they have then had to add a post script explaining that what we call error is really partial truth if we think it is Tuesday when it is really Wednesday we are at least right in thinking that it is a day of the week if we think America was discovered in 1066 we are at least right in thinking that something happened in that year if we think Charles the first died in his bed we are at least so far right that in view of the many people who do die in their beds he probably had the potentiality of dying in his bed and so on Dr. Schiller rightly points to the Theotetus as showing the difficulties to which knowledge is reduced by neglecting to take due account of error from the beginning and among more recent books Mr. Joachim's The Nature of Truth is used to point the same moral Pragmatism then emphasizes from the start the fact that some of our beliefs turn out to be mistaken and that the proper business of a theory of truth and falsehood are distinguished this might seem to those not sophisticated by philosophy to be an obvious truism but in fact philosophy has always regarded it as its business to prove as far as possible that everything is true rather than to distinguish between truth and falsehood similarly in ethics philosophers have not sought to distinguish between the good and the bad so much as to prove that everything is good if little truth has been attained in philosophy the reason is chiefly that few philosophers have wished to attain truth whether pragmatists are superior in this respect we shall not venture to pronounce but at any rate the peculiarity of their bias makes them willing to admit facts which other philosophers find inconvenient and among such facts is the prevalence of error in order to discover the difference between truth and falsehood pragmatism sets about a socratic inductive inquiry as to the things we call true and false these words to begin with are applied to beliefs and are applied only when a question has arisen in the ordinary facts of perception we do not ask questions until we have become philosophers we do not apply either of the words true and false to such unquestioned matters but when once the question has arisen concerning some actual belief is it a true or false belief how do we in fact decide the question the answer of pragmatism is that if the belief furthers the purpose which led us to ask the question it is regarded as true belief if it fails to further the purpose it is regarded as a false belief this therefore according to pragmatism is the meaning of the words true and false true means furthering the purpose which led to the question or more explicitly when in pursuing any purpose a belief is entertained which is relevant to the purpose the belief is true if it furthers the achievement of the purpose and false if it does not do so footnote 1 confer Schiller studies in humanism page 154 end of footnote 1 a few quotations will serve to amplify and elucidate the above brief statement after explaining recent changes in the methodology of science james says quote writing now on the front of this wave of scientific logic messes Schiller and Dewey appear with their pragmatist account of what truth everywhere signifies everywhere these teachers say truth in our ideas and beliefs means the same thing that it means in science it means they say nothing but this that ideas which themselves are but parts of our experience become true just in so far as they help us to get into satisfactory relations with other parts of our experience end of quote footnote 2 pragmatism pages 57 58 footnote 2 again quote I am well aware how odd it must seem to some of you to hear me say that an idea is true so long as to believe it is profitable to our lives that is good for as much as it profits you will gladly admit but is it not a strange misuse of the word truth you will say to call ideas also true for this reason you touch here upon the very central point of messers shillers deweys and my own doctrine of truth let me now say only this that truth is one species of good and not as is usually supposed a category distinct from good and coordinate with it the true is the name of whatever proves itself to be good in the way of belief and good too for definite assignable reasons end of quote footnote 3 pragmatism pages 75 76 end of footnote 3 the sixth of william james' lectures on pragmatism is concerned wholly with the notion of truth he begins by ascending to the dictionary which means the agreement of our ideas with reality but as he justly discovers this definition does not take us very far unless we know what we mean by agreement and what we mean by reality the pragmatist holds that different sorts of agreement and different sorts of reality are concerned in different cases the popular notion that a true idea must copy its reality holds good he says of sensible things but goes wrong as soon as we come to abstractions the idea of the elasticity of a spring for example cannot according to him be a copy of reality presumably on the ground that an elasticity is not an actually existing thing the question is then what sort of agreement with reality is possible in such cases quote the great assumption of the intellectual lists he says is that truth means essentially an inert static relation end of quote an intellectual list by the way is anyone who is not a pragmatist he proceeds quote pragmatism on the other hand asks its usual question grant an idea or belief to be true it says what concrete difference will its being true make in anyone's actual life how will the truth be realized what experiences will be different from those which would obtain if the belief were false what in short is the truth's cash in experiential terms the moment pragmatism asks this question it sees the answer true ideas are those that we can assimilate validate corroborate and verify false ideas are those that we cannot the truth of an idea is not a stagnant property inherent in it truth happens to an idea it becomes true is made true by events its verity is in fact an event a process the process namely of its verifying itself its verification its validity is the process of its validation end of quote footnote 1 see the same source pages 200, 201 end of footnote 1 recurring to the definition of truth as agreement with reality james sums up by distinguishing 3 kinds of reality 1 concrete facts 2 abstract kinds of things and relations perceived intuitively between them end of quote 3 agreement he defines as follows quote see in the widest sense with a reality can only mean to be guided either straight up to it or into its surroundings or to be put into such working touch with it as to handle either it or something connected with it better than if we disagreed end of quote page 212 2 further quotations will complete the material understanding james's account of truth quote the true to put it very briefly is only the expedient in the way of our thinking just as the right is only the expedient in the way of our behaving expedient in almost any fashion and expedient in the long run and on the whole of course end of quote page 222 quote our account of truth is an account of truths in the plural of processes of leading realized in Revis and having only this quality in common that they pay end of quote page 218 before proceeding further it will be as well to clear up a misunderstanding from which the pragmatists themselves appear not to be exempt when it is said that truth is one species of good it is natural to suppose that ethical considerations are involved in that logic will become dependent upon ethics this view is in fact adopted in Dr. Schiller's essay footnote 1 the first essay in his humanism end of footnote 1 the ethical basis of metaphysics but a closer examination shows that pragmatists mean by the word good whatever satisfies desire footnote 2 Schiller studies in humanism page 152 quote good and bad also in their wider and primary sense have reference to purpose good is what conduces to bad what thwarts a purpose end of quote end of footnote 2 so far as we know they have nowhere justified this use of the word but that is not our present concern what concerns us at present is to observe that in virtue of this definition only psychological considerations are relevant where to judge from the language psychological considerations might seem to be involved in order to judge whether a belief is true it is only necessary to discover whether it tends to the satisfaction of desire footnote 3 Schiller studies in humanism page 154 quote in all actual knowing the question whether an assertion is true or false is decided uniformly and very simply it is decided that is by its consequences by its bearing on the interest which prompted to the assertion by its relation to the purpose which put the question to add to this that the consequences must be good is superfluous for if and so far as an assertion satisfies or forwards the purpose of the inquiry which it owes its being it is so far true if and so far as it thwarts or baffles it it is unworkable unserviceable, false end of quote end of footnote 3 the nature of the desire to be satisfied is only relevant in so far as it may involve conflict with other desires thus psychology is paramount not only over logic and the theory of knowledge but also over ethics in order to discover what is good we have only to inquire how people are to get what they want and true beliefs are those which help in this process this is the pragmatist theory of truth and its consequences as might be supposed before considering the metaphysic which Dr. Schiller has deduced from the pragmatist theory of truth let us examine the grounds upon which that theory is based most philosophies are determined by their initial questions and by the facts which habitually fill the imagination of the philosopher the initial question of pragmatism is what characteristics of beliefs do in fact lead men to regard some as true others as false to answer this question so pragmatism assumes will give us the meaning of truth and falsehood the facts which fill the imaginations of pragmatists are psychical facts where others might think of the starry heavens pragmatists think of the perception of the starry heavens where others might think of God pragmatists think of the belief in God and so on in discussing the sciences they never think like scientific specialists about the facts upon which scientific theories are based they think about the theories themselves thus their initial question and their habitual imaginative background psychological in order to arrive at an external world they have to prove that the belief in an external world has the marks which according to them distinguish a true belief hence they infer that there is an external world and a similar process is necessary as regards all other facts which transcend the ego one of the approaches to pragmatism is through the consideration of induction and scientific method the old inductive philosophy as exemplified in mill's logic conceived the nature and scope of induction far too narrowly and pragmatism deserves credit for having remedied this defect induction that cannot give complete certainty underlies all the sciences even pure mathematics in any science we have a collection of facts bound together as far as possible by general laws the facts appear in the formal exposition as deductions from the laws this at least holds for the most advanced sciences such as mathematics and physics but in reality the laws are inductions from facts we cannot say that this or that fact proves this or that law the whole body of facts proves or rather renders probable the whole body of laws it might be thought that in an experimentum crucis a single fact establishes a single law but this is only the case as long as the other laws of the science are taken for granted if other facts should lead us to doubt the other laws the interpretation of our experimentum crucis might be wholly changed thus the justification of a science is that it fits all the known facts and that no alternative system of hypothesis is known which fits the facts equally well we may therefore say truly that scientific theories are adopted simply because they work that is because their consequences are satisfactory thus it would appear as though a right analysis of scientific induction let us straight to the pragmatist test of truth certain objections to this conclusion however at once suggest themselves in the first place scientific induction assumes certain data the facts with which our theories have to agree that the heavenly bodies have the apparent positions in the sky which we perceive them to have is not proved by astronomy but it is assumed as the datum upon which astronomy proceeds it would seem therefore that there are truths of fact which are prior to the whole inductive procedure and that these truths of fact must be true in some other sense than that the consequences of supposing them true are satisfactory to this argument pragmatists reply that what really is fact is neither true nor false but prior to the whole antithesis truth and falsehood quote day follows day and its contents are simply added the new contents themselves are not true but simply come and are truth is what we say about them and when we say that they have come truth is satisfied by the plain additive formula end of quote footnote one pragmatism page 62 end of footnote one pragmatists contend therefore that the mere recognition of facts is the simplest case of the application of their formula if all truth were of this simple nature pragmatist doctrine would be unnecessary though there would be nothing to show that it was false but the truths which do not consist in the mere recognition of facts cannot according to pragmatism be explained in this simple way hence we are forced to adopt a theory of truth not derived from the exclusive consideration of this simplest case for the moment let us allow this answer to pass we shall return to the subject of facts in connection with Dr. Schiller's doctrine of the making of reality a more serious objection to the argument from the procedure of the sciences is derived from the ambiguity of the conception of working what science requires of a working hypothesis is that it shall work theoretically that is that all its verifiable consequences shall be true and non false the law of gravitation enables us to calculate the motions of the heavenly bodies so far as these motions can be observed they are found to agree with our calculations it is true that the heavenly bodies have such and such apparent positions at such and such times and the law of gravitation agrees with this truth this is what we mean when we say that the law works we do not mean that it gives us emotional satisfaction that it satisfies our aspirations that it is a help in navigation or that it facilitates a virtuous life any or all of these may be true but they are irrelevant if they were all false we should still say that the law works because it agrees with observed facts thus the kind of working which science desiderates is a very different thing from the kind which pragmatism considers to be the essence of truth to this as to our previous objection pragmatists reply that the truth concerned is a particular species of truth and that scientific working is a particular species of their general conception of working our purpose they say and asking the question to which the law of gravitation is an answer is to be able to calculate the motions of the heavenly bodies the law of gravitation furthers this purpose and is therefore true in the pragmatic sense this answer shows that the procedure of science so far has not been shown to contradict pragmatism but it does not show that the procedure of science positively supports pragmatism where as in science our purpose is to discover truth an answer which furthers our purpose will be true but from this truism it cannot be inferred as pragmatists pretend that if we had some quite different purpose an answer which furthered it would still have been true another objection to the argument of some working hypothesis is that by men of science these are explicitly contrasted with established truths unhypothesis as experience shows may explain all known relevant facts admirably and yet may at any moment be rendered inadequate by new facts for this reason prudent men give only a very provisional assent of working hypothesis thus the cases from which pragmatism endeavors to discover the nature of truth are the very cases in which we have least assurance that truth is present at all this is certainly a curious and not very hopeful mode of procedure it may be said however that what leads us to feel doubtful about a working hypothesis is merely that it has not yet been shown to work over a sufficiently wide field the more it works the more we believe in it but to this again it may be rejoined that the more it works the less probability is there that any other hypothesis would also work to pursue this topic however would require a discussion of the laws of probability this is not the place from what has been said it results that the utmost that pragmatism can derive from science is that the scientific conception of working is not incompatible with the pragmatist conception since the scientific working may be regarded as a species of the pragmatic working it is however a species whose differential adds just those elements which other philosophies declare to be necessary to truth while pragmatism declares them to be unnecessary the essential novelty of pragmatism is that it admits as a ground of belief any kind of satisfaction to be derived from entertaining the belief not merely the theoretic satisfaction which is sought by science for this contention no support whatever is to be found in science let us see whether any support is to be found elsewhere end of first half