99 99 99 99 99 ---------------------------------------- ------------------- ,transcriber's ,note3 ,inconsistent hyphenation in the original document has been preserved4 ,mathematical equations and variables are marked with ,math3 to reduce confusion between underscores used for italics and underscores used to indicate subscripts4 ,subscripts are indicated with underscores1 with the subscripted character marked with 's1 i4e43 xt ,greek letters have been transliterated and marked with 's1 i4e43 alpha ,obvious typographical errors have been corrected4 ,for a complete list1 please see the end of this document4 ---------------------------------------- ------------------- 99 99 99 99 99 ,,bertrand ,,russell ,,mysticism ,,and ,,logic ,,and ,,other ,,essays ,,london ,,george ,,allen ,,unwin ,,ltd ,,ruskin ,,house ,,museum ,,street ,,mysticism ,,and ,,logic ,,and ,,other ,,essays ,,by ,,bertrand ,,russell ,the ,,abc of ,relativity ,the ,analysis of ,matter ,human ,society in ,ethics and ,politics ,the ,impact of ,science on ,society ,new ,hopes for a ,changing ,world ,authority and the ,individual ,human ,knowledge ,history of ,western ,philosophy ,the ,principles of ,mathematics ,introduction to ,mathematical ,philosophy ,the ,analysis of ,mind ,our ,knowledge of the ,external ,world ,an ,outline of ,philosophy ,the ,philosophy of ,leibniz ,an ,inquiry into ,meaning and ,truth ,logic and ,knowledge ,the ,problems of ,philosophy ,principia ,mathematica ,common ,sense and ,nuclear ,warfare ,why ,i am ,not a ,christian ,portraits from ,memory ,my ,philosophical ,development ,unpopular ,essays ,power ,in ,praise of ,idleness ,the ,conquest of ,happiness ,sceptical ,essays ,the ,scientific ,outlook ,marriage and ,morals ,education and the ,social ,order ,on ,education ,freedom and ,organization ,principles of ,social ,reconstruction ,roads to ,freedom ,practice and ,theory of ,bolshevism ,satan in ,the ,suburbs ,nightmares of ,eminent ,persons ,first published as ,philosophical ,essays ,october #aiaj ,second ,edition as ,mysticism and ,logic ,december #aiag ,third ,impression ,april #aiah ,fourth ,impression ,february #aiai ,fifth ,impression ,october #aiba ,sixth ,impression ,august #aibe ,seventh ,impression ,january #aicb ,eighth ,impression #aidi ,ninth ,impression #aiej ,tenth ,impression #aiea ,eleventh ,impression #aiei ,this book is copyright under the ,berne ,convention4 ,apart from any fair dealing for the purpose of private study1 research1 criticism or review1 as permitted under the ,copyright ,act1 #aief1 no portion may be reproduced by any process without written permission4 ,enquiry should be made to the publisher4 ,,printed ,,in ,,great ,,britain by ,taylor ,garnett ,evans ,co4 ,ltd41 ,watford1 ,herts4 ,,preface ,the following essays have been written and published at various times1 and my thanks are due to the previous publishers for the permission to reprint them4 ,the essay on ,mysticism and ,logic appeared in the ,hibbert ,journal for ,july1 #aiad4 ,the ,place of ,science in a ,liberal ,education appeared in two numbers of ,the ,new ,statesman1 ,may #bd and #ca1 #aiac4 ,the ,free ,man's ,worship and ,the ,study of ,mathematics were included in a former collection 7now out of print71 ,philosophical ,essays1 also published by ,messrs4 ,longmans1 ,green ,co4 ,both were written in #aijb2 the first appeared originally in the ,independent ,review for #aijc1 the second in the ,new ,quarterly1 ,november1 #aijg4 ,in theoretical ,ethics1 the position advocated in ,the ,free ,man's ,worship is not quite identical with that which ,i hold now3 ,i feel less convinced than ,i did then of the objectivity of good and evil4 ,but the general attitude towards life which is suggested in that essay still seems to me1 in the main1 the one which must be adopted in times of stress and difficulty by those who have no dogmatic religious beliefs1 if inward defeat is to be avoided4 ,the essay on ,mathematics and the ,metaphysicians was written in #aija1 and appeared in an ,american magazine1 ,the ,international ,monthly1 under the title ,recent ,work in the ,philosophy of ,mathematics4 ,some points in this essay require modification in view of later work4 ,these are indicated in footnotes4 ,its tone is partly explained by the fact that the editor begged me to make the article as romantic as possible4 ,all the above essays are entirely popular1 but those that follow are somewhat more technical4 ,on ,scientific ,method in ,philosophy was the ,herbert ,spencer lecture at ,oxford in #aiad1 and was published by the ,clarendon ,press1 which has kindly allowed me to include it in this collection4 ,the ,ultimate ,constituents of ,matter was an address to the ,manchester ,philosophical ,society1 early in #aiae1 and was published in the ,monist in ,july of that year4 ,the essay on ,the ,relation of ,sense-data to ,physics was written in ,january1 #aiad1 and first appeared in ,no4 #d of that year's volume of ,scientia1 an ,international ,review of ,scientific ,synthesis1 edited by ,m4 ,eugenio ,rignano1 published monthly by ,messrs4 ,williams and ,norgate1 ,london1 ,nicola ,zanichelli1 ,bologna1 and ,flix ,alcan1 ,paris4 ,the essay ,on the ,notion of ,cause was the presidential address to the ,aristotelian ,society in ,november1 #aiab1 and was published in their ,proceedings for #aiab-ac4 ,knowledge by ,acquaintance and ,knowledge by ,description was also a paper read before the ,aristotelian ,society1 and published in their ,proceedings for #aiaj-aa4 ,,london1 ,september1 #aiag ,,contents ,chapter ,page ,i4 ,mysticism and ,logic #a ,,ii4 ,the ,place of ,science in a ,liberal ,education #cc ,,iii4 ,a ,free ,man's ,worship #df ,,iv4 ,the ,study of ,mathematics #eh ,v4 ,mathematics and the ,metaphysicians #gd ,,vi4 ,on ,scientific ,method in ,philosophy #ig ,,vii4 ,the ,ultimate ,constituents of ,matter #abe ,,viii4 ,the ,relation of ,sense-data to ,physics #ade ,,ix4 ,on the ,notion of ,cause #ahj ,x4 ,knowledge by ,acquaintance and ,knowledge by ,description #bji ,,mysticism ,,and ,,logic ,,and ,,other ,,essays ,i ,,mysticism ,,and ,,logic ,metaphysics1 or the attempt to conceive the world as a whole by means of thought1 has been developed1 from the first1 by the union and conflict of two very different human impulses1 the one urging men towards mysticism1 the other urging them towards science4 ,some men have achieved greatness through one of these impulses alone1 others through the other alone3 in ,hume1 for example1 the scientific impulse reigns quite unchecked1 while in ,blake a strong hostility to science co-exists with profound mystic insight4 ,but the greatest men who have been philosophers have felt the need both of science and of mysticism3 the attempt to harmonise the two was what made their life1 and what always must1 for all its arduous uncertainty1 make philosophy1 to some minds1 a greater thing than either science or religion4 ,before attempting an explicit characterisation of the scientific and the mystical impulses1 ,i will illustrate them by examples from two philosophers whose greatness lies in the very intimate blending which they achieved4 ,the two philosophers ,i mean are ,heraclitus and ,plato4 ,heraclitus1 as every one knows1 was a believer in universal flux3 time builds and destroys all things4 ,from the few fragments that remain1 it is not easy to discover how he arrived at his opinions1 but there are some sayings that strongly suggest scientific observation as the source4 ,the things that can be seen1 heard1 and learned1 he says1 are what ,i prize the most4 ,this is the language of the empiricist1 to whom observation is the sole guarantee of truth4 ,the sun is new every day1 is another fragment2 and this opinion1 in spite of its paradoxical character1 is obviously inspired by scientific reflection1 and no doubt seemed to him to obviate the difficulty of understanding how the sun can work its way underground from west to east during the night4 ,actual observation must also have suggested to him his central doctrine1 that ,fire is the one permanent substance1 of which all visible things are passing phases4 ,in combustion we see things change utterly1 while their flame and heat rise up into the air and vanish4 ,this world1 which is the same for all1 he says1 no one of gods or men has made2 but it was ever1 is now1 and ever shall be1 an ever-living ,fire1 with measures kindling1 and measures going out4 ,the transformations of ,fire are1 first of all1 sea2 and half of the sea is earth1 half whirlwind4 ,this theory1 though no longer one which science can accept1 is nevertheless scientific in spirit4 ,science1 too1 might have inspired the famous saying to which ,plato alludes3 ,you cannot step twice into the same rivers2 for fresh waters are ever flowing in upon you4 ,but we find also another statement among the extant fragments3 ,we step and do not step into the same rivers2 we are and are not4 ,the comparison of this statement1 which is mystical1 with the one quoted by ,plato1 which is scientific1 shows how intimately the two tendencies are blended in the system of ,heraclitus4 ,mysticism is1 in essence1 little more than a certain intensity and depth of feeling in regard to what is believed about the universe2 and this kind of feeling leads ,heraclitus1 on the basis of his science1 to strangely poignant sayings concerning life and the world1 such as3 ,time is a child playing draughts1 the kingly power is a child's4 ,it is poetic imagination1 not science1 which presents ,time as despotic lord of the world1 with all the irresponsible frivolity of a child4 ,it is mysticism1 too1 which leads ,heraclitus to assert the identity of opposites3 ,good and ill are one1 he says2 and again3 ,to ,god all things are fair and good and right1 but men hold some things wrong and some right4 ,much of mysticism underlies the ethics of ,heraclitus4 ,it is true that a scientific determinism alone might have inspired the statement3 ,man's character is his fate2 but only a mystic would have said3 ,every beast is driven to the pasture with blows2 and again3 ,it is hard to fight with one's heart's desire4 ,whatever it wishes to get1 it purchases at the cost of soul2 and again3 ,wisdom is one thing4 ,it is to know the thought by which all things are steered through all things4#a ,examples might be multiplied1 but those that have been given are enough to show the character of the man3 the facts of science1 as they appeared to him1 fed the flame in his soul1 and in its light he saw into the depths of the world by the reflection of his own dancing swiftly penetrating fire4 ,in such a nature we see the true union of the mystic and the man of science--the highest eminence1 as ,i think1 that it is possible to achieve in the world of thought4 ,in ,plato1 the same twofold impulse exists1 though the mystic impulse is distinctly the stronger of the two1 and secures ultimate victory whenever the conflict is sharp4 ,his description of the cave is the classical statement of belief in a knowledge and reality truer and more real than that of the senses3 ,imagine#b a number of men living in an underground cavernous chamber1 with an entrance open to the light1 extending along the entire length of the cavern1 in which they have been confined1 from their childhood1 with their legs and necks so shackled that they are obliged to sit still and look straight forwards1 because their chains render it impossible for them to turn their heads round3 and imagine a bright fire burning some way off1 above and behind them1 and an elevated roadway passing between the fire and the prisoners1 with a low wall built along it1 like the screens which conjurors put up in front of their audience1 and above which they exhibit their wonders4 ,i have it1 he replied4 ,also figure to yourself a number of persons walking behind this wall1 and carrying with them statues of men1 and images of other animals1 wrought in wood and stone and all kinds of materials1 together with various other articles1 which overtop the wall2 and1 as you might expect1 let some of the passers-by be talking1 and others silent4 ,you are describing a strange scene1 and strange prisoners4 ,they resemble us1 ,i replied4 ,now consider what would happen if the course of nature brought them a release from their fetters1 and a remedy for their foolishness1 in the following manner4 ,let us suppose that one of them has been released1 and compelled suddenly to stand up1 and turn his neck round and walk with open eyes towards the light2 and let us suppose that he goes through all these actions with pain1 and that the dazzling splendour renders him incapable of discerning those objects of which he used formerly to see the shadows4 ,what answer should you expect him to make1 if some one were to tell him that in those days he was watching foolish phantoms1 but that now he is somewhat nearer to reality1 and is turned towards things more real1 and sees more correctly2 above all1 if he were to point out to him the several objects that are passing by1 and question him1 and compel him to answer what they are8 ,should you not expect him to be puzzled1 and to regard his old visions as truer than the objects now forced upon his notice8 ,yes1 much truer4444 ,hence1 ,i suppose1 habit will be necessary to enable him to perceive objects in that upper world4 ,at first he will be most successful in distinguishing shadows2 then he will discern the reflections of men and other things in water1 and afterwards the realities2 and after this he will raise his eyes to encounter the light of the moon and stars1 finding it less difficult to study the heavenly bodies and the heaven itself by night1 than the sun and the sun's light by day4 ,doubtless4 ,last of all1 ,i imagine1 he will be able to observe and contemplate the nature of the sun1 not as it appears in water or on alien ground1 but as it is in itself in its own territory4 ,of course4 ,his next step will be to draw the conclusion1 that the sun is the author of the seasons and the years1 and the guardian of all things in the visible world1 and in a manner the cause of all those things which he and his companions used to see4 ,obviously1 this will be his next step4444 ,now this imaginary case1 my dear ,glancon1 you must apply in all its parts to our former statements1 by comparing the region which the eye reveals to the prison house1 and the light of the fire therein to the power of the sun3 and if1 by the upward ascent and the contemplation of the upper world1 you understand the mounting of the soul into the intellectual region1 you will hit the tendency of my own surmises1 since you desire to be told what they are2 though1 indeed1 ,god only knows whether they are correct4 ,but1 be that as it may1 the view which ,i take of the subject is to the following effect4 ,in the world of knowledge1 the essential ,form of ,good is the limit of our enquiries1 and can barely be perceived2 but1 when perceived1 we cannot help concluding that it is in every case the source of all that is bright and beautiful1--in the visible world giving birth to light and its master1 and in the intellectual world dispensing1 immediately and with full authority1 truth and reason2--and that whosoever would act wisely1 either in private or in public1 must set this ,form of ,good before his eyes4 ,but in this passage1 as throughout most of ,plato's teaching1 there is an identification of the good with the truly real1 which became embodied in the philosophical tradition1 and is still largely operative in our own day4 ,in thus allowing a legislative function to the good1 ,plato produced a divorce between philosophy and science1 from which1 in my opinion1 both have suffered ever since and are still suffering4 ,the man of science1 whatever his hopes may be1 must lay them aside while he studies nature2 and the philosopher1 if he is to achieve truth1 must do the same4 ,ethical considerations can only legitimately appear when the truth has been ascertained3 they can and should appear as determining our feeling towards the truth1 and our manner of ordering our lives in view of the truth1 but not as themselves dictating what the truth is to be4 ,there are passages in ,plato--among those which illustrate the scientific side of his mind--where he seems clearly aware of this4 ,the most noteworthy is the one in which ,socrates1 as a young man1 is explaining the theory of ideas to ,parmenides4 ,after ,socrates has explained that there is an idea of the good1 but not of such things as hair and mud and dirt1 ,parmenides advises him not to despise even the meanest things1 and this advice shows the genuine scientific temper4 ,it is with this impartial temper that the mystic's apparent insight into a higher reality and a hidden good has to be combined if philosophy is to realise its greatest possibilities4 ,and it is failure in this respect that has made so much of idealistic philosophy thin1 lifeless1 and insubstantial4 ,it is only in marriage with the world that our ideals can bear fruit3 divorced from it1 they remain barren4 ,but marriage with the world is not to be achieved by an ideal which shrinks from fact1 or demands in advance that the world shall conform to its desires4 ,parmenides himself is the source of a peculiarly interesting strain of mysticism which pervades ,plato's thought--the mysticism which may be called logical because it is embodied in theories on logic4 ,this form of mysticism1 which appears1 so far as the ,west is concerned1 to have originated with ,parmenides1 dominates the reasonings of all the great mystical metaphysicians from his day to that of ,hegel and his modern disciples4 ,reality1 he says1 is uncreated1 indestructible1 unchanging1 indivisible2 it is immovable in the bonds of mighty chains1 without beginning and without end2 since coming into being and passing away have been driven afar1 and true belief has cast them away4 ,the fundamental principle of his inquiry is stated in a sentence which would not be out of place in ,hegel3 ,thou canst not know what is not--that is impossible--nor utter it2 for it is the same thing that can be thought and that can be4 ,and again3 ,it needs must be that what can be thought and spoken of is2 for it is possible for it to be1 and it is not possible for what is nothing to be4 ,the impossibility of change follows from this principle2 for what is past can be spoken of1 and therefore1 by the principle1 still is4 ,mystical philosophy1 in all ages and in all parts of the world1 is characterised by certain beliefs which are illustrated by the doctrines we have been considering4 ,there is1 first1 the belief in insight as against discursive analytic knowledge3 the belief in a way of wisdom1 sudden1 penetrating1 coercive1 which is contrasted with the slow and fallible study of outward appearance by a science relying wholly upon the senses4 ,all who are capable of absorption in an inward passion must have experienced at times the strange feeling of unreality in common objects1 the loss of contact with daily things1 in which the solidity of the outer world is lost1 and the soul seems1 in utter loneliness1 to bring forth1 out of its own depths1 the mad dance of fantastic phantoms which have hitherto appeared as independently real and living4 ,this is the negative side of the mystic's initiation3 the doubt concerning common knowledge1 preparing the way for the reception of what seems a higher wisdom4 ,many men to whom this negative experience is familiar do not pass beyond it1 but for the mystic it is merely the gateway to an ampler world4 ,the mystic insight begins with the sense of a mystery unveiled1 of a hidden wisdom now suddenly become certain beyond the possibility of a doubt4 ,the sense of certainty and revelation comes earlier than any definite belief4 ,the definite beliefs at which mystics arrive are the result of reflection upon the inarticulate experience gained in the moment of insight4 ,often1 beliefs which have no real connection with this moment become subsequently attracted into the central nucleus2 thus in addition to the convictions which all mystics share1 we find1 in many of them1 other convictions of a more local and temporary character1 which no doubt become amalgamated with what was essentially mystical in virtue of their subjective certainty4 ,we may ignore such inessential accretions1 and confine ourselves to the beliefs which all mystics share4 ,the first and most direct outcome of the moment of illumination is belief in the possibility of a way of knowledge which may be called revelation or insight or intuition1 as contrasted with sense1 reason1 and analysis1 which are regarded as blind guides leading to the morass of illusion4 ,closely connected with this belief is the conception of a ,reality behind the world of appearance and utterly different from it4 ,this ,reality is regarded with an admiration often amounting to worship2 it is felt to be always and everywhere close at hand1 thinly veiled by the shows of sense1 ready1 for the receptive mind1 to shine in its glory even through the apparent folly and wickedness of ,man4 ,the poet1 the artist1 and the lover are seekers after that glory3 the haunting beauty that they pursue is the faint reflection of its sun4 ,but the mystic lives in the full light of the vision3 what others dimly seek he knows1 with a knowledge beside which all other knowledge is ignorance4 ,the second characteristic of mysticism is its belief in unity1 and its refusal to admit opposition or division anywhere4 ,we found ,heraclitus saying good and ill are one2 and again he says1 the way up and the way down is one and the same4 ,the same attitude appears in the simultaneous assertion of contradictory propositions1 such as3 ,we step and do not step into the same rivers2 we are and are not4 ,the assertion of ,parmenides1 that reality is one and indivisible1 comes from the same impulse towards unity4 ,in ,plato1 this impulse is less prominent1 being held in check by his theory of ideas2 but it reappears1 so far as his logic permits1 in the doctrine of the primacy of the ,good4 ,a third mark of almost all mystical metaphysics is the denial of the reality of ,time4 ,this is an outcome of the denial of division2 if all is one1 the distinction of past and future must be illusory4 ,we have seen this doctrine prominent in ,parmenides2 and among moderns it is fundamental in the systems of ,spinoza and ,hegel4 ,the last of the doctrines of mysticism which we have to consider is its belief that all evil is mere appearance1 an illusion produced by the divisions and oppositions of the analytic intellect4 ,mysticism does not maintain that such things as cruelty1 for example1 are good1 but it denies that they are real3 they belong to that lower world of phantoms from which we are to be liberated by the insight of the vision4 ,sometimes--for example in ,hegel1 and at least verbally in ,spinoza--not only evil1 but good also1 is regarded as illusory1 though nevertheless the emotional attitude towards what is held to be ,reality is such as would naturally be associated with the belief that ,reality is good4 ,what is1 in all cases1 ethically characteristic of mysticism is absence of indignation or protest1 acceptance with joy1 disbelief in the ultimate truth of the division into two hostile camps1 the good and the bad4 ,this attitude is a direct outcome of the nature of the mystical experience3 with its sense of unity is associated a feeling of infinite peace4 ,indeed it may be suspected that the feeling of peace produces1 as feelings do in dreams1 the whole system of associated beliefs which make up the body of mystic doctrine4 ,but this is a difficult question1 and one on which it cannot be hoped that mankind will reach agreement4 ,four questions thus arise in considering the truth or falsehood of mysticism1 namely3 ,i4 ,are there two ways of knowing1 which may be called respectively reason and intuition8 ,and if so1 is either to be preferred to the other8 ,,ii4 ,is all plurality and division illusory8 ,,iii4 ,is time unreal8 ,,iv4 ,what kind of reality belongs to good and evil8 ,on all four of these questions1 while fully developed mysticism seems to me mistaken1 ,i yet believe that1 by sufficient restraint1 there is an element of wisdom to be learned from the mystical way of feeling1 which does not seem to be attainable in any other manner4 ,if this is the truth1 mysticism is to be commended as an attitude towards life1 not as a creed about the world4 ,the meta-physical creed1 ,i shall maintain1 is a mistaken outcome of the emotion1 although this emotion1 as colouring and informing all other thoughts and feelings1 is the inspirer of whatever is best in ,man4 ,even the cautious and patient investigation of truth by science1 which seems the very antithesis of the mystic's swift certainty1 may be fostered and nourished by that very spirit of reverence in which mysticism lives and moves4 ,i4 ,,reason ,,and ,,intuition#c ,of the reality or unreality of the mystic's world ,i know nothing4 ,i have no wish to deny it1 nor even to declare that the insight which reveals it is not a genuine insight4 ,what ,i do wish to maintain--and it is here that the scientific attitude becomes imperative--is that insight1 untested and unsupported1 is an insufficient guarantee of truth1 in spite of the fact that much of the most important truth is first suggested by its means4 ,it is common to speak of an opposition between instinct and reason2 in the eighteenth century1 the opposition was drawn in favour of reason1 but under the influence of ,rousseau and the romantic movement instinct was given the preference1 first by those who rebelled against artificial forms of government and thought1 and then1 as the purely rationalistic defence of traditional theology became increasingly difficult1 by all who felt in science a menace to creeds which they associated with a spiritual outlook on life and the world4 ,bergson1 under the name of intuition1 has raised instinct to the position of sole arbiter of metaphysical truth4 ,but in fact the opposition of instinct and reason is mainly illusory4 ,instinct1 intuition1 or insight is what first leads to the beliefs which subsequent reason confirms or confutes2 but the confirmation1 where it is possible1 consists1 in the last analysis1 of agreement with other beliefs no less instinctive4 ,reason is a harmonising1 controlling force rather than a creative one4 ,even in the most purely logical realm1 it is insight that first arrives at what is new4 ,where instinct and reason do sometimes conflict is in regard to single beliefs1 held instinctively1 and held with such determination that no degree of inconsistency with other beliefs leads to their abandonment4 ,instinct1 like all human faculties1 is liable to error4 ,those in whom reason is weak are often unwilling to admit this as regards themselves1 though all admit it in regard to others4 ,where instinct is least liable to error is in practical matters as to which right judgment is a help to survival3 friendship and hostility in others1 for instance1 are often felt with extraordinary discrimination through very careful disguises4 ,but even in such matters a wrong impression may be given by reserve or flattery2 and in matters less directly practical1 such as philosophy deals with1 very strong instinctive beliefs are sometimes wholly mistaken1 as we may come to know through their perceived inconsistency with other equally strong beliefs4 ,it is such considerations that necessitate the harmonising mediation of reason1 which tests our beliefs by their mutual compatibility1 and examines1 in doubtful cases1 the possible sources of error on the one side and on the other4 ,in this there is no opposition to instinct as a whole1 but only to blind reliance upon some one interesting aspect of instinct to the exclusion of other more commonplace but not less trustworthy aspects4 ,it is such one-sidedness1 not instinct itself1 that reason aims at correcting4 ,these more or less trite maxims may be illustrated by application to ,bergson's advocacy of intuition as against intellect4 ,there are1 he says1 two profoundly different ways of knowing a thing4 ,the first implies that we move round the object3 the second that we enter into it4 ,the first depends on the point of view at which we are placed and on the symbols by which we express ourselves4 ,the second neither depends on a point of view nor relies on any symbol4 ,the first kind of knowledge may be said to stop at the relative2 the second1 in those cases where it is possible1 to attain the absolute4#d ,the second of these1 which is intuition1 is1 he says1 the kind of intellectual sympathy by which one places oneself within an object in order to coincide with what is unique in it and therefore inexpressible 7p4 #f74 ,in illustration1 he mentions self-knowledge3 there is one reality1 at least1 which we all seize from within1 by intuition and not by simple analysis4 ,it is our own personality in its flowing through time--our self which endures 7p4 #h74 ,the rest of ,bergson's philosophy consists in reporting1 through the imperfect medium of words1 the knowledge gained by intuition1 and the consequent complete condemnation of all the pretended knowledge derived from science and common sense4 ,this procedure1 since it takes sides in a conflict of instinctive beliefs1 stands in need of justification by proving the greater trustworthiness of the beliefs on one side than of those on the other4 ,bergson attempts this justification in two ways1 first by explaining that intellect is a purely practical faculty to secure biological success1 secondly by mentioning remarkable feats of instinct in animals and by pointing out characteristics of the world which1 though intuition can apprehend them1 are baffling to intellect as he interprets it4 ,of ,bergson's theory that intellect is a purely practical faculty1 developed in the struggle for survival1 and not a source of true beliefs1 we may say1 first1 that it is only through intellect that we know of the struggle for survival and of the biological ancestry of man3 if the intellect is misleading1 the whole of this merely inferred history is presumably untrue4 ,if1 on the other hand1 we agree with him in thinking that evolution took place as ,darwin believed1 then it is not only intellect1 but all our faculties1 that have been developed under the stress of practical utility4 ,intuition is seen at its best where it is directly useful1 for example in regard to other people's characters and dispositions4 ,bergson apparently holds that capacity for this kind of knowledge is less explicable by the struggle for existence than1 for example1 capacity for pure mathematics4 ,yet the savage deceived by false friendship is likely to pay for his mistake with his life2 whereas even in the most civilised societies men are not put to death for mathematical incompetence4 ,all the most striking of his instances of intuition in animals have a very direct survival value4 ,the fact is1 of course1 that both intuition and intellect have been developed because they are useful1 and that1 speaking broadly1 they are useful when they give truth and become harmful when they give falsehood4 ,intellect1 in civilised man1 like artistic capacity1 has occasionally been developed beyond the point where it is useful to the individual2 intuition1 on the other hand1 seems on the whole to diminish as civilisation increases4 ,it is greater1 as a rule1 in children than in adults1 in the uneducated than in the educated4 ,probably in dogs it exceeds anything to be found in human beings4 ,but those who see in these facts a recommendation of intuition ought to return to running wild in the woods1 dyeing themselves with woad and living on hips and haws4 ,let us next examine whether intuition possesses any such infallibility as ,bergson claims for it4 ,the best instance of it1 according to him1 is our acquaintance with ourselves2 yet self-knowledge is proverbially rare and difficult4 ,most men1 for example1 have in their nature meannesses1 vanities1 and envies of which they are quite unconscious1 though even their best friends can perceive them without any difficulty4 ,it is true that intuition has a convincingness which is lacking to intellect3 while it is present1 it is almost impossible to doubt its truth4 ,but if it should appear1 on examination1 to be at least as fallible as intellect1 its greater subjective certainty becomes a demerit1 making it only the more irresistibly deceptive4 ,apart from self-knowledge1 one of the most notable examples of intuition is the knowledge people believe themselves to possess of those with whom they are in love3 the wall between different personalities seems to become transparent1 and people think they see into another soul as into their own4 ,yet deception in such cases is constantly practised with success2 and even where there is no intentional deception1 experience gradually proves1 as a rule1 that the supposed insight was illusory1 and that the slower more groping methods of the intellect are in the long run more reliable4 ,bergson maintains that intellect can only deal with things in so far as they resemble what has been experienced in the past1 while intuition has the power of apprehending the uniqueness and novelty that always belong to each fresh moment4 ,that there is something unique and new at every moment1 is certainly true2 it is also true that this cannot be fully expressed by means of intellectual concepts4 ,only direct acquaintance can give knowledge of what is unique and new4 ,but direct acquaintance of this kind is given fully in sensation1 and does not require1 so far as ,i can see1 any special faculty of intuition for its apprehension4 ,it is neither intellect nor intuition1 but sensation1 that supplies new data2 but when the data are new in any remarkable manner1 intellect is much more capable of dealing with them than intuition would be4 ,the hen with a brood of ducklings no doubt has intuition which seems to place her inside them1 and not merely to know them analytically2 but when the ducklings take to the water1 the whole apparent intuition is seen to be illusory1 and the hen is left helpless on the shore4 ,intuition1 in fact1 is an aspect and development of instinct1 and1 like all instinct1 is admirable in those customary surroundings which have moulded the habits of the animal in question1 but totally incompetent as soon as the surroundings are changed in a way which demands some non-habitual mode of action4 ,the theoretical understanding of the world1 which is the aim of philosophy1 is not a matter of great practical importance to animals1 or to savages1 or even to most civilised men4 ,it is hardly to be supposed1 therefore1 that the rapid1 rough and ready methods of instinct or intuition will find in this field a favourable ground for their application4 ,it is the older kinds of activity1 which bring out our kinship with remote generations of animal and semi-human ancestors1 that show intuition at its best4 ,in such matters as self-preservation and love1 intuition will act sometimes 7though not always7 with a swiftness and precision which are astonishing to the critical intellect4 ,but philosophy is not one of the pursuits which illustrate our affinity with the past3 it is a highly refined1 highly civilised pursuit1 demanding1 for its success1 a certain liberation from the life of instinct1 and even1 at times1 a certain aloofness from all mundane hopes and fears4 ,it is not in philosophy1 therefore1 that we can hope to see intuition at its best4 ,on the contrary1 since the true objects of philosophy1 and the habit of thought demanded for their apprehension1 are strange1 unusual1 and remote1 it is here1 more almost than anywhere else1 that intellect proves superior to intuition1 and that quick unanalysed convictions are least deserving of uncritical acceptance4 ,in advocating the scientific restraint and balance1 as against the self-assertion of a confident reliance upon intuition1 we are only urging1 in the sphere of knowledge1 that largeness of contemplation1 that impersonal disinterestedness1 and that freedom from practical preoccupations which have been inculcated by all the great religions of the world4 ,thus our conclusion1 however it may conflict with the explicit beliefs of many mystics1 is1 in essence1 not contrary to the spirit which inspires those beliefs1 but rather the outcome of this very spirit as applied in the realm of thought4 ,,ii4 ,,unity ,,and ,,plurality ,one of the most convincing aspects of the mystic illumination is the apparent revelation of the oneness of all things1 giving rise to pantheism in religion and to monism in philosophy4 ,an elaborate logic1 beginning with ,parmenides1 and culminating in ,hegel and his followers1 has been gradually developed1 to prove that the universe is one indivisible ,whole1 and that what seem to be its parts1 if considered as substantial and self-existing1 are mere illusion4 ,the conception of a ,reality quite other than the world of appearance1 a reality one1 indivisible1 and unchanging1 was introduced into ,western philosophy by ,parmenides1 not1 nominally at least1 for mystical or religious reasons1 but on the basis of a logical argument as to the impossibility of not-being1 and most subsequent metaphysical systems are the outcome of this fundamental idea4 ,the logic used in defence of mysticism seems to be faulty as logic1 and open to technical criticisms1 which ,i have explained elsewhere4 ,i shall not here repeat these criticisms1 since they are lengthy and difficult1 but shall instead attempt an analysis of the state of mind from which mystical logic has arisen4 ,belief in a reality quite different from what appears to the senses arises with irresistible force in certain moods1 which are the source of most mysticism1 and of most metaphysics4 ,while such a mood is dominant1 the need of logic is not felt1 and accordingly the more thoroughgoing mystics do not employ logic1 but appeal directly to the immediate deliverance of their insight4 ,but such fully developed mysticism is rare in the ,west4 ,when the intensity of emotional conviction subsides1 a man who is in the habit of reasoning will search for logical grounds in favour of the belief which he finds in himself4 ,but since the belief already exists1 he will be very hospitable to any ground that suggests itself4 ,the paradoxes apparently proved by his logic are really the paradoxes of mysticism1 and are the goal which he feels his logic must reach if it is to be in accordance with insight4 ,the resulting logic has rendered most philosophers incapable of giving any account of the world of science and daily life4 ,if they had been anxious to give such an account1 they would probably have discovered the errors of their logic2 but most of them were less anxious to understand the world of science and daily life than to convict it of unreality in the interests of a super-sensible real world4 ,it is in this way that logic has been pursued by those of the great philosophers who were mystics4 ,but since they usually took for granted the supposed insight of the mystic emotion1 their logical doctrines were presented with a certain dryness1 and were believed by their disciples to be quite independent of the sudden illumination from which they sprang4 ,nevertheless their origin clung to them1 and they remained--to borrow a useful word from ,mr4 ,santayana--malicious in regard to the world of science and common sense4 ,it is only so that we can account for the complacency with which philosophers have accepted the inconsistency of their doctrines with all the common and scientific facts which seem best established and most worthy of belief4 ,the logic of mysticism shows1 as is natural1 the defects which are inherent in anything malicious4 ,the impulse to logic1 not felt while the mystic mood is dominant1 reasserts itself as the mood fades1 but with a desire to retain the vanishing insight1 or at least to prove that it was insight1 and that what seems to contradict it is illusion4 ,the logic which thus arises is not quite disinterested or candid1 and is inspired by a certain hatred of the daily world to which it is to be applied4 ,such an attitude naturally does not tend to the best results4 ,everyone knows that to read an author simply in order to refute him is not the way to understand him2 and to read the book of ,nature with a conviction that it is all illusion is just as unlikely to lead to understanding4 ,if our logic is to find the common world intelligible1 it must not be hostile1 but must be inspired by a genuine acceptance such as is not usually to be found among metaphysicians4 ,,iii4 ,,time ,the unreality of time is a cardinal doctrine of many metaphysical systems1 often nominally based1 as already by ,parmenides1 upon logical arguments1 but originally derived1 at any rate in the founders of new systems1 from the certainty which is born in the moment of mystic insight4 ,as a ,persian ,sufi poet says3 ,past and future are what veil ,god from our sight4 ,burn up both of them with fire6 ,how long ,wilt thou be partitioned by these segments as a reed8#e ,the belief that what is ultimately real must be immutable is a very common one3 it gave rise to the metaphysical notion of substance1 and finds1 even now1 a wholly illegitimate satisfaction in such scientific doctrines as the conservation of energy and mass4 ,it is difficult to disentangle the truth and the error in this view4 ,the arguments for the contention that time is unreal and that the world of sense is illusory must1 ,i think1 be regarded as fallacious4 ,nevertheless there is some sense--easier to feel than to state--in which time is an unimportant and superficial characteristic of reality4 ,past and future must be acknowledged to be as real as the present1 and a certain emancipation from slavery to time is essential to philosophic thought4 ,the importance of time is rather practical than theoretical1 rather in relation to our desires than in relation to truth4 ,a truer image of the world1 ,i think1 is obtained by picturing things as entering into the stream of time from an eternal world outside1 than from a view which regards time as the devouring tyrant of all that is4 ,both in thought and in feeling1 even though time be real1 to realise the unimportance of time is the gate of wisdom4 ,that this is the case may be seen at once by asking ourselves why our feelings towards the past are so different from our feelings towards the future4 ,the reason for this difference is wholly practical3 our wishes can affect the future but not the past1 the future is to some extent subject to our power1 while the past is unalterably fixed4 ,but every future will some day be past3 if we see the past truly now1 it must1 when it was still future1 have been just what we now see it to be1 and what is now future must be just what we shall see it to be when it has become past4 ,the felt difference of quality between past and future1 therefore1 is not an intrinsic difference1 but only a difference in relation to us3 to impartial contemplation1 it ceases to exist4 ,and impartiality of contemplation is1 in the intellectual sphere1 that very same virtue of disinterestedness which1 in the sphere of action1 appears as justice and unselfishness4 ,whoever wishes to see the world truly1 to rise in thought above the tyranny of practical desires1 must learn to overcome the difference of attitude towards past and future1 and to survey the whole stream of time in one comprehensive vision4 ,the kind of way in which1 as it seems to me1 time ought not to enter into our theoretic philosophical thought1 may be illustrated by the philosophy which has become associated with the idea of evolution1 and which is exemplified by ,nietzsche1 pragmatism1 and ,bergson4 ,this philosophy1 on the basis of the development which has led from the lowest forms of life up to man1 sees in progress the fundamental law of the universe1 and thus admits the difference between earlier and later into the very citadel of its contemplative outlook4 ,with its past and future history of the world1 conjectural as it is1 ,i do not wish to quarrel4 ,but ,i think that1 in the intoxication of a quick success1 much that is required for a true understanding of the universe has been forgotten4 ,something of ,hellenism1 something1 too1 of ,oriental resignation1 must be combined with its hurrying ,western self-assertion before it can emerge from the ardour of youth into the mature wisdom of manhood4 ,in spite of its appeals to science1 the true scientific philosophy1 ,i think1 is something more arduous and more aloof1 appealing to less mundane hopes1 and requiring a severer discipline for its successful practice4 ,darwin's ,origin of ,species persuaded the world that the difference between different species of animals and plants is not the fixed immutable difference that it appears to be4 ,the doctrine of natural kinds1 which had rendered classification easy and definite1 which was enshrined in the ,aristotelian tradition1 and protected by its supposed necessity for orthodox dogma1 was suddenly swept away for ever out of the biological world4 ,the difference between man and the lower animals1 which to our human conceit appears enormous1 was shown to be a gradual achievement1 involving intermediate being who could not with certainty be placed either within or without the human family4 ,the sun and the planets had already been shown by ,laplace to be very probably derived from a primitive more or less undifferentiated nebula4 ,thus the old fixed landmarks became wavering and indistinct1 and all sharp outlines were blurred4 ,things and species lost their boundaries1 and none could say where they began or where they ended4 ,but if human conceit was staggered for a moment by its kinship with the ape1 it soon found a way to reassert itself1 and that way is the philosophy of evolution4 ,a process which led from the amoeba to ,man appeared to the philosophers to be obviously a progress--though whether the amoeba would agree with this opinion is not known4 ,hence the cycle of changes which science had shown to be the probable history of the past was welcomed as revealing a law of development towards good in the universe--an evolution or unfolding of an idea slowly embodying itself in the actual4 ,but such a view1 though it might satisfy ,spencer and those whom we may call ,hegelian evolutionists1 could not be accepted as adequate by the more whole-hearted votaries of change4 ,an ideal to which the world continuously approaches is1 to these minds1 too dead and static to be inspiring4 ,not only the aspiration1 but the ideal too1 must change and develop with the course of evolution3 there must be no fixed goal1 but a continual fashioning of fresh needs by the impulse which is life and which alone gives unity to the process4 ,life1 in this philosophy1 is a continuous stream1 in which all divisions are artificial and unreal4 ,separate things1 beginnings and endings1 are mere convenient fictions3 there is only smooth unbroken transition4 ,the beliefs of to-day may count as true to-day1 if they carry us along the stream2 but to-morrow they will be false1 and must be replaced by new beliefs to meet the new situation4 ,all our thinking consists of convenient fictions1 imaginary congealings of the stream3 reality flows on in spite of all our fictions1 and though it can be lived1 it cannot be conceived in thought4 ,somehow1 without explicit statement1 the assurance is slipped in that the future1 though we cannot foresee it1 will be better than the past or the present3 the reader is like the child which expects a sweet because it has been told to open its mouth and shut its eyes4 ,logic1 mathematics1 physics disappear in this philosophy1 because they are too static2 what is real is no impulse and movement towards a goal which1 like the rainbow1 recedes as we advance1 and makes every place different when it reaches it from what it appeared to be at a distance4 ,i do not propose to enter upon a technical examination of this philosophy4 ,i wish only to maintain that the motives and interests which inspire it are so exclusively practical1 and the problems with which it deals are so special1 that it can hardly be regarded as touching any of the questions that1 to my mind1 constitute genuine philosophy4 ,the predominant interest of evolutionism is in the question of human destiny1 or at least of the destiny of ,life4 ,it is more interested in morality and happiness than in knowledge for its own sake4 ,it must be admitted that the same may be said of many other philosophies1 and that a desire for the kind of knowledge which philosophy can give is very rare4 ,but if philosophy is to attain truth1 it is necessary first and foremost that philosophers should acquire the disinterested intellectual curiosity which characterises the genuine man of science4 ,knowledge concerning the future--which is the kind of knowledge that must be sought if we are to know about human destiny--is possible within certain narrow limits4 ,it is impossible to say how much the limits may be enlarged with the progress of science4 ,but what is evident is that any proposition about the future belongs by its subject-matter to some particular science1 and is to be ascertained1 if at all1 by the methods of that science4 ,philosophy is not a short cut to the same kind of results as those of the other sciences3 if it is to be a genuine study1 it must have a province of its own1 and aim at results which the other sciences can neither prove nor disprove4 ,evolutionism1 in basing itself upon the notion of progress1 which is change from the worse to the better1 allows the notion of time1 as it seems to me1 to become its tyrant rather than its servant1 and thereby loses that impartiality of contemplation which is the source of all that is best in philosophic thought and feeling4 ,metaphysicians1 as we saw1 have frequently denied altogether the reality of time4 ,i do not wish to do this2 ,i wish only to preserve the mental outlook which inspired the denial1 the attitude which1 in thought1 regards the past as having the same reality as the present and the same importance as the future4 ,in so far1 says ,spinoza1#f as the mind conceives a thing according to the dictate of reason1 it will be equally affected whether the idea is that of a future1 past1 or present thing4 ,it is this conceiving according to the dictate of reason that ,i find lacking in the philosophy which is based on evolution4 ,,iv4 ,,good ,,and ,,evil ,mysticism maintains that all evil is illusory1 and sometimes maintains the same view as regards good1 but more often holds that all ,reality is good4 ,both views are to be found in ,heraclitus3 ,good and ill are one1 he says1 but again1 ,to ,god all things are fair and good and right1 but men hold some things wrong and some right4 ,a similar twofold position is to be found in ,spinoza1 but he uses the word perfection when he means to speak of the good that is not merely human4 ,by reality and perfection ,i mean the same thing1 he says2#g but elsewhere we find the definition3 ,by good ,i shall mean that which we certainly know to be useful to us4#h ,thus perfection belongs to ,reality in its own nature1 but goodness is relative to ourselves and our needs1 and disappears in an impartial survey4 ,some such distinction1 ,i think1 is necessary in order to understand the ethical outlook of mysticism3 there is a lower mundane kind of good and evil1 which divides the world of appearance into what seem to be conflicting parts2 but there is also a higher1 mystical kind of good1 which belongs to ,reality and is not opposed by any correlative kind of evil4 ,it is difficult to give a logically tenable account of this position without recognising that good and evil are subjective1 that what is good is merely that towards which we have one kind of feeling1 and what is evil is merely that towards which we have another kind of feeling4 ,in our active life1 where we have to exercise choice1 and to prefer this to that of two possible acts1 it is necessary to have a distinction of good and evil1 or at least of better and worse4 ,but this distinction1 like everything pertaining to action1 belongs to what mysticism regards as the world of illusion1 if only because it is essentially concerned with time4 ,in our contemplative life1 where action is not called for1 it is possible to be impartial1 and to overcome the ethical dualism which action requires4 ,so long as we remain merely impartial1 we may be content to say that both the good and the evil of action are illusions4 ,but if1 as we must do if we have the mystic vision1 we find the whole world worthy of love and worship1 if we see ,the earth1 and every common sight4444 ,apparell'd in celestial light1 we shall say that there is a higher good than that of action1 and that this higher good belongs to the whole world as it is in reality4 ,in this way the twofold attitude and the apparent vacillation of mysticism are explained and justified4 ,the possibility of this universal love and joy in all that exists is of supreme importance for the conduct and happiness of life1 and gives inestimable value to the mystic emotion1 apart from any creeds which may be built upon it4 ,but if we are not to be led into false beliefs1 it is necessary to realise exactly what the mystic emotion reveals4 ,it reveals a possibility of human nature--a possibility of a nobler1 happier1 freer life than any that can be otherwise achieved4 ,but it does not reveal anything about the non-human1 or about the nature of the universe in general4 ,good and bad1 and even the higher good that mysticism finds everywhere1 are the reflections of our own emotions on other things1 not part of the substance of things as they are in themselves4 ,and therefore an impartial contemplation1 freed from all pre-occupation with ,self1 will not judge things good or bad1 although it is very easily combined with that feeling of universal love which leads the mystic to say that the whole world is good4 ,the philosophy of evolution1 through the notion of progress1 is bound up with the ethical dualism of the worse and the better1 and is thus shut out1 not only from the kind of survey which discards good and evil altogether from its view1 but also from the mystical belief in the goodness of everything4 ,in this way the distinction of good and evil1 like time1 becomes a tyrant in this philosophy1 and introduces into thought the restless selectiveness of action4 ,good and evil1 like time1 are1 it would seem1 not general or fundamental in the world of thought1 but late and highly specialised members of the intellectual hierarchy4 ,although1 as we saw1 mysticism can be interpreted so as to agree with the view that good and evil are not intellectually fundamental1 it must be admitted that here we are no longer in verbal agreement with most of the great philosophers and religious teachers of the past4 ,i believe1 however1 that the elimination of ethical considerations from philosophy is both scientifically necessary and--though this may seem a paradox--an ethical advance4 ,both these contentions must be briefly defended4 ,the hope of satisfaction to our more human desires--the hope of demonstrating that the world has this or that desirable ethical characteristic--is not one which1 so far as ,i can see1 a scientific philosophy can do anything whatever to satisfy4 ,the difference between a good world and a bad one is a difference in the particular characteristics of the particular things that exist in these worlds3 it is not a sufficiently abstract difference to come within the province of philosophy4 ,love and hate1 for example1 are ethical opposites1 but to philosophy they are closely analogous attitudes towards objects4 ,the general form and structure of those attitudes towards objects which constitute mental phenomena is a problem for philosophy1 but the difference between love and hate is not a difference of form or structure1 and therefore belongs rather to the special science of psychology than to philosophy4 ,thus the ethical interests which have often inspired philosophers must remain in the background3 some kind of ethical interest may inspire the whole study1 but none must obtrude in the detail or be expected in the special results which are sought4 ,if this view seems at first sight disappointing1 we may remind ourselves that a similar change has been found necessary in all the other sciences4 ,the physicist or chemist is not now required to prove the ethical importance of his ions or atoms2 the biologist is not expected to prove the utility of the plants or animals which he dissects4 ,in pre-scientific ages this was not the case4 ,astronomy1 for example1 was studied because men believed in astrology3 it was thought that the movements of the planets had the most direct and important bearing upon the lives of human beings4 ,presumably1 when this belief decayed and the disinterested study of astronomy began1 many who had found astrology absorbingly interesting decided that astronomy had too little human interest to be worthy of study4 ,physics1 as it appears in ,plato's ,timus for example1 is full of ethical notions3 it is an essential part of its purpose to show that the earth is worthy of admiration4 ,the modern physicist1 on the contrary1 though he has no wish to deny that the earth is admirable1 is not concerned1 as physicist1 with its ethical attributes3 he is merely concerned to find out facts1 not to consider whether they are good or bad4 ,in psychology1 the scientific attitude is even more recent and more difficult than in the physical sciences3 it is natural to consider that human nature is either good or bad1 and to suppose that the difference between good and bad1 so all-important in practice1 must be important in theory also4 ,it is only during the last century that an ethically neutral psychology has grown up2 and here too1 ethical neutrality has been essential to scientific success4 ,in philosophy1 hitherto1 ethical neutrality has been seldom sought and hardly ever achieved4 ,men have remembered their wishes1 and have judged philosophies in relation to their wishes4 ,driven from the particular sciences1 the belief that the notions of good and evil must afford a key to the understanding of the world has sought a refuge in philosophy4 ,but even from this last refuge1 if philosophy is not to remain a set of pleasing dreams1 this belief must be driven forth4 ,it is a commonplace that happiness is not best achieved by those who seek it directly2 and it would seem that the same is true of the good4 ,in thought1 at any rate1 those who forget good and evil and seek only to know the facts are more likely to achieve good than those who view the world through the distorting medium of their own desires4 ,we are thus brought back to our seeming paradox1 that a philosophy which does not seek to impose upon the world its own conceptions of good and evil is not only more likely to achieve truth1 but is also the outcome of a higher ethical standpoint than one which1 like evolutionism and most traditional systems1 is perpetually appraising the universe and seeking to find in it an embodiment of present ideals4 ,in religion1 and in every deeply serious view of the world and of human destiny1 there is an element of submission1 a realisation of the limits of human power1 which is somewhat lacking in the modern world1 with its quick material successes and its insolent belief in the boundless possibilities of progress4 ,he that loveth his life shall lose it2 and there is danger lest1 through a too confident love of life1 life itself should lose much of what gives it its highest worth4 ,the submission which religion inculcates in action is essentially the same in spirit as that which science teaches in thought2 and the ethical neutrality by which its victories have been achieved is the outcome of that submission4 ,the good which it concerns us to remember is the good which it lies in our power to create--the good in our own lives and in our attitude towards the world4 ,insistence on belief in an external realisation of the good is a form of self-assertion1 which1 while it cannot secure the external good which it desires1 can seriously impair the inward good which lies within our power1 and destroy that reverence towards fact which constitutes both what is valuable in humility and what is fruitful in the scientific temper4 ,human beings cannot1 of course1 wholly transcend human nature2 something subjective1 if only the interest that determines the direction of our attention1 must remain in all our thought4 ,but scientific philosophy comes nearer to objectivity than any other human pursuit1 and gives us1 therefore1 the closest constant and the most intimate relation with the outer world that it is possible to achieve4 ,to the primitive mind1 everything is either friendly or hostile2 but experience has shown that friendliness and hostility are not the conceptions by which the world is to be understood4 ,scientific philosophy thus represents1 though as yet only in a nascent condition1 a higher form of thought than any pre-scientific belief or imagination1 and1 like every approach to self-transcendence1 it brings with it a rich reward in increase of scope and breadth and comprehension4 ,evolutionism1 in spite of its appeals to particular scientific facts1 fails to be a truly scientific philosophy because of its slavery to time1 its ethical preoccupations1 and its predominant interest in our mundane concerns and destiny4 ,a truly scientific philosophy will be more humble1 more piecemeal1 more arduous1 offering less glitter of outward mirage to flatter fallacious hopes1 but more indifferent to fate1 and more capable of accepting the world without the tyrannous imposition of our human and temporary demands4 ,,footnotes3 #a ,all the above quotations are from ,burnet's ,early ,greek ,philosophy1 7#bnd ed41 #aijh71 pp4 #adf-aef4 #b ,republic1 #ead1 translated by ,davies and ,vaughan4 #c ,this section1 and also one or two pages in later sections1 have been printed in a course of ,lowell lectures ,on our knowledge of the external world1 published by the ,open ,court ,publishing ,company4 ,but ,i have left them here1 as this is the context for which they were originally written4 #d ,introduction to ,metaphysics1 p4 #a4 #e ,whinfield's translation of the ,masnavi 7,trbner1 #ahhg71 p4 #cd4 #f ,ethics1 ,bk4 ,,iv1 ,prop4 ,,lxii4 #g ,ib41 ,pt4 ,,iv1 ,df4 ,i4 #h ,ethics4 ,pt4 ,,ii4 ,df4 ,,vi4 ,,ii ,,the ,,place ,,of ,,science ,,in ,a ,,liberal ,,education ,i ,science1 to the ordinary reader of newspapers1 is represented by a varying selection of sensational triumphs1 such as wireless telegraphy and aeroplanes1 radio-activity and the marvels of modern alchemy4 ,it is not of this aspect of science that ,i wish to speak4 ,science1 in this aspect1 consists of detached up-to-date fragments1 interesting only until they are replaced by something newer and more up-to-date1 displaying nothing of the systems of patiently constructed knowledge out of which1 almost as a casual incident1 have come the practically useful results which interest the man in the street4 ,the increased command over the forces of nature which is derived from science is undoubtedly an amply sufficient reason for encouraging scientific research1 but this reason has been so often urged and is so easily appreciated that other reasons1 to my mind quite as important1 are apt to be overlooked4 ,it is with these other reasons1 especially with the intrinsic value of a scientific habit of mind in forming our outlook on the world1 that ,i shall be concerned in what follows4 ,the instance of wireless telegraphy will serve to illustrate the difference between the two points of view4 ,almost all the serious intellectual labour required for the possibility of this invention is due to three men--,faraday1 ,maxwell1 and ,hertz4 ,in alternating layers of experiment and theory these three men built up the modern theory of electromagnetism1 and demonstrated the identity of light with electromagnetic waves4 ,the system which they discovered is one of profound intellectual interest1 bringing together and unifying an endless variety of apparently detached phenomena1 and displaying a cumulative mental power which cannot but afford delight to every generous spirit4 ,the mechanical details which remained to be adjusted in order to utilise their discoveries for a practical system of telegraphy demanded1 no doubt1 very considerable ingenuity1 but had not that broad sweep and that universality which could give them intrinsic interest as an object of disinterested contemplation4 ,from the point of view of training the mind1 of giving that well-informed1 impersonal outlook which constitutes culture in the good sense of this much-misused word1 it seems to be generally held indisputable that a literary education is superior to one based on science4 ,even the warmest advocates of science are apt to rest their claims on the contention that culture ought to be sacrificed to utility4 ,those men of science who respect culture1 when they associate with men learned in the classics1 are apt to admit1 not merely politely1 but sincerely1 a certain inferiority on their side1 compensated doubtless by the services which science renders to humanity1 but none the less real4 ,and so long as this attitude exists among men of science1 it tends to verify itself3 the intrinsically valuable aspects of science tend to be sacrificed to the merely useful1 and little attempt is made to preserve that leisurely1 systematic survey by which the finer quality of mind is formed and nourished4 ,but even if there be1 in present fact1 any such inferiority as is supposed in the educational value of science1 this is1 ,i believe1 not the fault of science itself1 but the fault of the spirit in which science is taught4 ,if its full possibilities were realised by those who teach it1 ,i believe that its capacity of producing those habits of mind which constitute the highest mental excellence would be at least as great as that of literature1 and more particularly of ,greek and ,latin literature4 ,in saying this ,i have no wish whatever to disparage a classical education4 ,i have not myself enjoyed its benefits1 and my knowledge of ,greek and ,latin authors is derived almost wholly from translations4 ,but ,i am firmly persuaded that the ,greeks fully deserve all the admiration that is bestowed upon them1 and that it is a very great and serious loss to be unacquainted with their writings4 ,it is not by attacking them1 but by drawing attention to neglected excellences in science1 that ,i wish to conduct my argument4 ,one defect1 however1 does seem inherent in a purely classical education--namely1 a too exclusive emphasis on the past4 ,by the study of what is absolutely ended and can never be renewed1 a habit of criticism towards the present and the future is engendered4 ,the qualities in which the present excels are qualities to which the study of the past does not direct attention1 and to which1 therefore1 the student of ,greek civilisation may easily become blind4 ,in what is new and growing there is apt to be something crude1 insolent1 even a little vulgar1 which is shocking to the man of sensitive taste2 quivering from the rough contact1 he retires to the trim gardens of a polished past1 forgetting that they were reclaimed from the wilderness by men as rough and earth-soiled as those from whom he shrinks in his own day4 ,the habit of being unable to recognise merit until it is dead is too apt to be the result of a purely bookish life1 and a culture based wholly on the past will seldom be able to pierce through everyday surroundings to the essential splendour of contemporary things1 or to the hope of still greater splendour in the future4 ,my eyes saw not the men of old2 ,and now their age away has rolled4 ,i weep--to think ,i shall not see ,the heroes of posterity4 ,so says the ,chinese poet2 but such impartiality is rare in the more pugnacious atmosphere of the ,west1 where the champions of past and future fight a never-ending battle1 instead of combining to seek out the merits of both4 ,this consideration1 which militates not only against the exclusive study of the classics1 but against every form of culture which has become static1 traditional1 and academic1 leads inevitably to the fundamental question3 ,what is the true end of education8 ,but before attempting to answer this question it will be well to define the sense in which we are to use the word education4 ,for this purpose ,i shall distinguish the sense in which ,i mean to use it from two others1 both perfectly legitimate1 the one broader and the other narrower than the sense in which ,i mean to use the word4 ,in the broader sense1 education will include not only what we learn through instruction1 but all that we learn through personal experience--the formation of character through the education of life4 ,of this aspect of education1 vitally important as it is1 ,i will say nothing1 since its consideration would introduce topics quite foreign to the question with which we are concerned4 ,in the narrower sense1 education may be confined to instruction1 the imparting of definite information on various subjects1 because such information1 in and for itself1 is useful in daily life4 ,elementary education--reading1 writing1 and arithmetic--is almost wholly of this kind4 ,but instruction1 necessary as it is1 does not per se constitute education in the sense in which ,i wish to consider it4 ,education1 in the sense in which ,i mean it1 may be defined as the formation1 by means of instruction1 of certain mental habits and a certain outlook on life and the world4 ,it remains to ask ourselves1 what mental habits1 and what sort of outlook1 can be hoped for as the result of instruction8 ,when we have answered this question we can attempt to decide what science has to contribute to the formation of the habits and outlook which we desire4 ,our whole life is built about a certain number--not a very small number--of primary instincts and impulses4 ,only what is in some way connected with these instincts and impulses appears to us desirable or important2 there is no faculty1 whether reason or virtue or whatever it may be called1 that can take our active life and our hopes and fears outside the region controlled by these first movers of all desire4 ,each of them is like a queen-bee1 aided by a hive of workers gathering honey2 but when the queen is gone the workers languish and die1 and the cells remain empty of their expected sweetness4 ,so with each primary impulse in civilised man3 it is surrounded and protected by a busy swarm of attendant derivative desires1 which store up in its service whatever honey the surrounding world affords4 ,but if the queen-impulse dies1 the death-dealing influence1 though retarded a little by habit1 spreads slowly through all the subsidiary impulses1 and a whole tract of life becomes inexplicably colourless4 ,what was formerly full of zest1 and so obviously worth doing that it raised no questions1 has now grown dreary and purposeless3 with a sense of disillusion we inquire the meaning of life1 and decide1 perhaps1 that all is vanity4 ,the search for an outside meaning that can compel an inner response must always be disappointed3 all meaning must be at bottom related to our primary desires1 and when they are extinct no miracle can restore to the world the value which they reflected upon it4 ,the purpose of education1 therefore1 cannot be to create any primary impulse which is lacking in the uneducated2 the purpose can only be to enlarge the scope of those that human nature provides1 by increasing the number and variety of attendant thoughts1 and by showing where the most permanent satisfaction is to be found4 ,under the impulse of a ,calvinistic horror of the natural man1 this obvious truth has been too often misconceived in the training of the young2 nature has been falsely regarded as excluding all that is best in what is natural1 and the endeavour to teach virtue has led to the production of stunted and contorted hypocrites instead of full-grown human beings4 ,from such mistakes in education a better psychology or a kinder heart is beginning to preserve the present generation2 we need1 therefore1 waste no more words on the theory that the purpose of education is to thwart or eradicate nature4 ,but although nature must supply the initial force of desire1 nature is not1 in the civilised man1 the spasmodic1 fragmentary1 and yet violent set of impulses that it is in the savage4 ,each impulse has its constitutional ministry of thought and knowledge and reflection1 through which possible conflicts of impulses are foreseen1 and temporary impulses are controlled by the unifying impulse which may be called wisdom4 ,in this way education destroys the crudity of instinct1 and increases through knowledge the wealth and variety of the individual's contacts with the outside world1 making him no longer an isolated fighting unit1 but a citizen of the universe1 embracing distant countries1 remote regions of space1 and vast stretches of past and future within the circle of his interests4 ,it is this simultaneous softening in the insistence of desire and enlargement of its scope that is the chief moral end of education4 ,closely connected with this moral end is the more purely intellectual aim of education1 the endeavour to make us see and imagine the world in an objective manner1 as far as possible as it is in itself1 and not merely through the distorting medium of personal desire4 ,the complete attainment of such an objective view is no doubt an ideal1 indefinitely approachable1 but not actually and fully realisable4 ,education1 considered as a process of forming our mental habits and our outlook on the world1 is to be judged successful in proportion as its outcome approximates to this ideal2 in proportion1 that is to say1 as it gives us a true view of our place in society1 of the relation of the whole human society to its non-human environment1 and of the nature of the non-human world as it is in itself apart from our desires and interests4 ,if this standard is admitted1 we can return to the consideration of science1 inquiring how far science contributes to such an aim1 and whether it is in any respect superior to its rivals in educational practice4 ,,ii ,two opposite and at first sight conflicting merits belong to science as against literature and art4 ,the one1 which is not inherently necessary1 but is certainly true at the present day1 is hopefulness as to the future of human achievement1 and in particular as to the useful work that may be accomplished by any intelligent student4 ,this merit and the cheerful outlook which it engenders prevent what might otherwise be the depressing effect of another aspect of science1 to my mind also a merit1 and perhaps its greatest merit--,i mean the irrelevance of human passions and of the whole subjective apparatus where scientific truth is concerned4 ,each of these reasons for preferring the study of science requires some amplification4 ,let us begin with the first4 ,in the study of literature or art our attention is perpetually riveted upon the past3 the men of ,greece or of the ,renaissance did better than any men do now2 the triumphs of former ages1 so far from facilitating fresh triumphs in our own age1 actually increase the difficulty of fresh triumphs by rendering originality harder of attainment2 not only is artistic achievement not cumulative1 but it seems even to depend upon a certain freshness and navet of impulse and vision which civilisation tends to destroy4 ,hence comes1 to those who have been nourished on the literary and artistic productions of former ages1 a certain peevishness and undue fastidiousness towards the present1 from which there seems no escape except into the deliberate vandalism which ignores tradition and in the search after originality achieves only the eccentric4 ,but in such vandalism there is none of the simplicity and spontaneity out of which great art springs3 theory is still the canker in its core1 and insincerity destroys the advantages of a merely pretended ignorance4 ,the despair thus arising from an education which suggests no pre-eminent mental activity except that of artistic creation is wholly absent from an education which gives the knowledge of scientific method4 ,the discovery of scientific method1 except in pure mathematics1 is a thing of yesterday2 speaking broadly1 we may say that it dates from ,galileo4 ,yet already it has transformed the world1 and its success proceeds with ever-accelerating velocity4 ,in science men have discovered an activity of the very highest value in which they are no longer1 as in art1 dependent for progress upon the appearance of continually greater genius1 for in science the successors stand upon the shoulders of their predecessors2 where one man of supreme genius has invented a method1 a thousand lesser men can apply it4 ,no transcendent ability is required in order to make useful discoveries in science2 the edifice of science needs its masons1 bricklayers1 and common labourers as well as its foremen1 master-builders1 and architects4 ,in art nothing worth doing can be done without genius2 in science even a very moderate capacity can contribute to a supreme achievement4 ,in science the man of real genius is the man who invents a new method4 ,the notable discoveries are often made by his successors1 who can apply the method with fresh vigour1 unimpaired by the previous labour of perfecting it2 but the mental calibre of the thought required for their work1 however brilliant1 is not so great as that required by the first inventor of the method4 ,there are in science immense numbers of different methods1 appropriate to different classes of problems2 but over and above them all1 there is something not easily definable1 which may be called the method of science4 ,it was formerly customary to identify this with the inductive method1 and to associate it with the name of ,bacon4 ,but the true inductive method was not discovered by ,bacon1 and the true method of science is something which includes deduction as much as induction1 logic and mathematics as much as botany and geology4 ,i shall not attempt the difficult task of stating what the scientific method is1 but ,i will try to indicate the temper of mind out of which the scientific method grows1 which is the second of the two merits that were mentioned above as belonging to a scientific education4 ,the kernel of the scientific outlook is a thing so simple1 so obvious1 so seemingly trivial1 that the mention of it may almost excite derision4 ,the kernel of the scientific outlook is the refusal to regard our own desires1 tastes1 and interests as affording a key to the understanding of the world4 ,stated thus baldly1 this may seem no more than a trite truism4 ,but to remember it consistently in matters arousing our passionate partisanship is by no means easy1 especially where the available evidence is uncertain and inconclusive4 ,a few illustrations will make this clear4 ,aristotle1 ,i understand1 considered that the stars must move in circles because the circle is the most perfect curve4 ,in the absence of evidence to the contrary1 he allowed himself to decide a question of fact by an appeal to sthetico-moral considerations4 ,in such a case it is at once obvious to us that this appeal was unjustifiable4 ,we know now how to ascertain as a fact the way in which the heavenly bodies move1 and we know that they do not move in circles1 or even in accurate ellipses1 or in any other kind of simply describable curve4 ,this may be painful to a certain hankering after simplicity of pattern in the universe1 but we know that in astronomy such feelings are irrelevant4 ,easy as this knowledge seems now1 we owe it to the courage and insight of the first inventors of scientific method1 and more especially of ,galileo4 ,we may take as another illustration ,malthus's doctrine of population4 ,this illustration is all the better for the fact that his actual doctrine is now known to be largely erroneous4 ,it is not his conclusions that are valuable1 but the temper and method of his inquiry4 ,as everyone knows1 it was to him that ,darwin owed an essential part of his theory of natural selection1 and this was only possible because ,malthus's outlook was truly scientific4 ,his great merit lies in considering man not as the object of praise or blame1 but as a part of nature1 a thing with a certain characteristic behaviour from which certain consequences must follow4 ,if the behaviour is not quite what ,malthus supposed1 if the consequences are not quite what he inferred1 that may falsify his conclusions1 but does not impair the value of his method4 ,the objections which were made when his doctrine was new--that it was horrible and depressing1 that people ought not to act as he said they did1 and so on--were all such as implied an unscientific attitude of mind2 as against all of them1 his calm determination to treat man as a natural phenomenon marks an important advance over the reformers of the eighteenth century and the ,revolution4 ,under the influence of ,darwinism the scientific attitude towards man has now become fairly common1 and is to some people quite natural1 though to most it is still a difficult and artificial intellectual contortion4 ,there is however1 one study which is as yet almost wholly untouched by the scientific spirit--,i mean the study of philosophy4 ,philosophers and the public imagine that the scientific spirit must pervade pages that bristle with allusions to ions1 germ-plasms1 and the eyes of shell-fish4 ,but as the devil can quote ,scripture1 so the philosopher can quote science4 ,the scientific spirit is not an affair of quotation1 of externally acquired information1 any more than manners are an affair of the etiquette-book4 ,the scientific attitude of mind involves a sweeping away of all other desires in the interests of the desire to know--it involves suppression of hopes and fears1 loves and hates1 and the whole subjective emotional life1 until we become subdued to the material1 able to see it frankly1 without preconceptions1 without bias1 without any wish except to see it as it is1 and without any belief that what it is must be determined by some relation1 positive or negative1 to what we should like it to be1 or to what we can easily imagine it to be4 ,now in philosophy this attitude of mind has not as yet been achieved4 ,a certain self-absorption1 not personal1 but human1 has marked almost all attempts to conceive the universe as a whole4 ,mind1 or some aspect of it--thought or will or sentience--has been regarded as the pattern after which the universe is to be conceived1 for no better reason1 at bottom1 than that such a universe would not seem strange1 and would give us the cosy feeling that every place is like home4 ,to conceive the universe as essentially progressive or essentially deteriorating1 for example1 is to give to our hopes and fears a cosmic importance which may1 of course1 be justified1 but which we have as yet no reason to suppose justified4 ,until we have learnt to think of it in ethically neutral terms1 we have not arrived at a scientific attitude in philosophy2 and until we have arrived at such an attitude1 it is hardly to be hoped that philosophy will achieve any solid results4 ,i have spoken so far largely of the negative aspect of the scientific spirit1 but it is from the positive aspect that its value is derived4 ,the instinct of constructiveness1 which is one of the chief incentives to artistic creation1 can find in scientific systems a satisfaction more massive than any epic poem4 ,disinterested curiosity1 which is the source of almost all intellectual effort1 finds with astonished delight that science can unveil secrets which might well have seemed for ever undiscoverable4 ,the desire for a larger life and wider interests1 for an escape from private circumstances1 and even from the whole recurring human cycle of birth and death1 is fulfilled by the impersonal cosmic outlook of science as by nothing else4 ,to all these must be added1 as contributing to the happiness of the man of science1 the admiration of splendid achievement1 and the consciousness of inestimable utility to the human race4 ,a life devoted to science is therefore a happy life1 and its happiness is derived from the very best sources that are open to dwellers on this troubled and passionate planet4 ,,iii ,a ,,free ,,man',s ,,worship#i ,to ,dr4 ,faustus in his study ,mephistopheles told the history of the ,creation1 saying3 ,the endless praises of the choirs of angels had begun to grow wearisome2 for1 after all1 did he not deserve their praise8 ,had he not given them endless joy8 ,would it not be more amusing to obtain undeserved praise1 to be worshipped by beings whom he tortured8 ,he smiled inwardly1 and resolved that the great drama should be performed4 ,for countless ages the hot nebula whirled aimlessly through space4 ,at length it began to take shape1 the central mass threw off planets1 the planets cooled1 boiling seas and burning mountains heaved and tossed1 from black masses of cloud hot sheets of rain deluged the barely solid crust4 ,and now the first germ of life grew in the depths of the ocean1 and developed rapidly in the fructifying warmth into vast forest trees1 huge ferns springing from the damp mould1 sea monsters breeding1 fighting1 devouring1 and passing away4 ,and from the monsters1 as the play unfolded itself1 ,man was born1 with the power of thought1 the knowledge of good and evil1 and the cruel thirst for worship4 ,and ,man saw that all is passing in this mad1 monstrous world1 that all is struggling to snatch1 at any cost1 a few brief moments of life before ,death's inexorable decree4 ,and ,man said3 ',there is a hidden purpose1 could we but fathom it1 and the purpose is good2 for we must reverence something1 and in the visible world there is nothing worthy of reverence4' ,and ,man stood aside from the struggle1 resolving that ,god intended harmony to come out of chaos by human efforts4 ,and when he followed the instincts which ,god had transmitted to him from his ancestry of beasts of prey1 he called it ,sin1 and asked ,god to forgive him4 ,but he doubted whether he could be justly forgiven1 until he invented a divine ,plan by which ,god's wrath was to have been appeased4 ,and seeing the present was bad1 he made it yet worse1 that thereby the future might be better4 ,and he gave ,god thanks for the strength that enabled him to forgo even the joys that were possible4 ,and ,god smiled2 and when he saw that ,man had become perfect in renunciation and worship1 he sent another sun through the sky1 which crashed into ,man's sun2 and all returned again to nebula4 ',yes1' he murmured1 'it was a good play2 ,i will have it performed again4' ,such1 in outline1 but even more purposeless1 more void of meaning1 is the world which ,science presents for our belief4 ,amid such a world1 if anywhere1 our ideals henceforward must find a home4 ,that ,man is the product of causes which had no prevision of the end they were achieving2 that his origin1 his growth1 his hopes and fears1 his loves and his beliefs1 are but the outcome of accidental collocations of atoms2 that no fire1 no heroism1 no intensity of thought and feeling1 can preserve an individual life beyond the grave2 that all the labours of the ages1 all the devotion1 all the inspiration1 all the noonday brightness of human genius1 are destined to extinction in the vast death of the solar system1 and that the whole temple of ,man's achievement must inevitably be buried beneath the dbris of a universe in ruins--all these things1 if not quite beyond dispute1 are yet so nearly certain1 that no philosophy which rejects them can hope to stand4 ,only within the scaffolding of these truths1 only on the firm foundation of unyielding despair1 can the soul's habitation henceforth be safely built4 ,how1 in such an alien and inhuman world1 can so powerless a creature as ,man preserve his aspirations untarnished8 ,a strange mystery it is that ,nature1 omnipotent but blind1 in the revolutions of her secular hurryings through the abysses of space1 has brought forth at last a child1 subject still to her power1 but gifted with sight1 with knowledge of good and evil1 with the capacity of judging all the works of his unthinking ,mother4 ,in spite of ,death1 the mark and seal of the parental control1 ,man is yet free1 during his brief years1 to examine1 to criticise1 to know1 and in imagination to create4 ,to him alone1 in the world with which he is acquainted1 this freedom belongs2 and in this lies his superiority to the resistless forces that control his outward life4 ,the savage1 like ourselves1 feels the oppression of his impotence before the powers of ,nature2 but having in himself nothing that he respects more than ,power1 he is willing to prostrate himself before his gods1 without inquiring whether they are worthy of his worship4 ,pathetic and very terrible is the long history of cruelty and torture1 of degradation and human sacrifice1 endured in the hope of placating the jealous gods3 surely1 the trembling believer thinks1 when what is most precious has been freely given1 their lust for blood must be appeased1 and more will not be required4 ,the religion of ,moloch--as such creeds may be generically called--is in essence the cringing submission of the slave1 who dare not1 even in his heart1 allow the thought that his master deserves no adulation4 ,since the independence of ideals is not yet acknowledged1 ,power may be freely worshipped1 and receive an unlimited respect1 despite its wanton infliction of pain4 ,but gradually1 as morality grows bolder1 the claim of the ideal world begins to be felt2 and worship1 if it is not to cease1 must be given to gods of another kind than those created by the savage4 ,some1 though they feel the demands of the ideal1 will still consciously reject them1 still urging that naked ,power is worthy of worship4 ,such is the attitude inculcated in ,god's answer to ,job out of the whirlwind3 the divine power and knowledge are paraded1 but of the divine goodness there is no hint4 ,such also is the attitude of those who1 in our own day1 base their morality upon the struggle for survival1 maintaining that the survivors are necessarily the fittest4 ,but others1 not content with an answer so repugnant to the moral sense1 will adopt the position which we have become accustomed to regard as specially religious1 maintaining that1 in some hidden manner1 the world of fact is really harmonious with the world of ideals4 ,thus ,man creates ,god1 all-powerful and all-good1 the mystic unity of what is and what should be4 ,but the world of fact1 after all1 is not good2 and1 in submitting our judgment to it1 there is an element of slavishness from which our thoughts must be purged4 ,for in all things it is well to exalt the dignity of ,man1 by freeing him as far as possible from the tyranny of non-human ,power4 ,when we have realised that ,power is largely bad1 that man1 with his knowledge of good and evil1 is but a helpless atom in a world which has no such knowledge1 the choice is again presented to us3 ,shall we worship ,force1 or shall we worship ,goodness8 ,shall our ,god exist and be evil1 or shall he be recognised as the creation of our own conscience8 ,the answer to this question is very momentous1 and affects profoundly our whole morality4 ,the worship of ,force1 to which ,carlyle and ,nietzsche and the creed of ,militarism have accustomed us1 is the result of failure to maintain our own ideals against a hostile universe3 it is itself a prostrate submission to evil1 a sacrifice of our best to ,moloch4 ,if strength indeed is to be respected1 let us respect rather the strength of those who refuse that false recognition of facts which fails to recognise that facts are often bad4 ,let us admit that1 in the world we know1 there are many things that would be better otherwise1 and that the ideals to which we do and must adhere are not realised in the realm of matter4 ,let us preserve our respect for truth1 for beauty1 for the ideal of perfection which life does not permit us to attain1 though none of these things meet with the approval of the unconscious universe4 ,if ,power is bad1 as it seems to be1 let us reject it from our hearts4 ,in this lies ,man's true freedom3 in determination to worship only the ,god created by our own love of the good1 to respect only the heaven which inspires the insight of our best moments4 ,in action1 in desire1 we must submit perpetually to the tyranny of outside forces2 but in thought1 in aspiration1 we are free1 free from our fellow-men1 free from the petty planet on which our bodies impotently crawl1 free even1 while we live1 from the tyranny of death4 ,let us learn1 then1 that energy of faith which enables us to live constantly in the vision of the good2 and let us descend1 in action1 into the world of fact1 with that vision always before us4 ,when first the opposition of fact and ideal grows fully visible1 a spirit of fiery revolt1 of fierce hatred of the gods1 seems necessary to the assertion of freedom4 ,to defy with ,promethean constancy a hostile universe1 to keep its evil always in view1 always actively hated1 to refuse no pain that the malice of ,power can invent1 appears to be the duty of all who will not bow before the inevitable4 ,but indignation is still a bondage1 for it compels our thoughts to be occupied with an evil world2 and in the fierceness of desire from which rebellion springs there is a kind of self-assertion which it is necessary for the wise to overcome4 ,indignation is a submission of our thoughts1 but not of our desires2 the ,stoic freedom in which wisdom consists is found in the submission of our desires1 but not of our thoughts4 ,from the submission of our desires springs the virtue of resignation2 from the freedom of our thoughts springs the whole world of art and philosophy1 and the vision of beauty by which1 at last1 we half reconquer the reluctant world4 ,but the vision of beauty is possible only to unfettered contemplation1 to thoughts not weighted by the load of eager wishes2 and thus ,freedom comes only to those who no longer ask of life that it shall yield them any of those personal goods that are subject to the mutations of ,time4 ,although the necessity of renunciation is evidence of the existence of evil1 yet ,christianity1 in preaching it1 has shown a wisdom exceeding that of the ,promethean philosophy of rebellion4 ,it must be admitted that1 of the things we desire1 some1 though they prove impossible1 are yet real goods2 others1 however1 as ardently longed for1 do not form part of a fully purified ideal4 ,the belief that what must be renounced is bad1 though sometimes false1 is far less often false than untamed passion supposes2 and the creed of religion1 by providing a reason for proving that it is never false1 has been the means of purifying our hopes by the discovery of many austere truths4 ,but there is in resignation a further good element3 even real goods1 when they are unattainable1 ought not to be fretfully desired4 ,to every man comes1 sooner or later1 the great renunciation4 ,for the young1 there is nothing unattainable2 a good thing desired with the whole force of a passionate will1 and yet impossible1 is to them not credible4 ,yet1 by death1 by illness1 by poverty1 or by the voice of duty1 we must learn1 each one of us1 that the world was not made for us1 and that1 however beautiful may be the things we crave1 ,fate may nevertheless forbid them4 ,it is the part of courage1 when misfortune comes1 to bear without repining the ruin of our hopes1 to turn away our thoughts from vain regrets4 ,this degree of submission to ,power is not only just and right3 it is the very gate of wisdom4 ,but passive renunciation is not the whole of wisdom2 for not by renunciation alone can we build a temple for the worship of our own ideals4 ,haunting foreshadowings of the temple appear in the realm of imagination1 in music1 in architecture1 in the untroubled kingdom of reason1 and in the golden sunset magic of lyrics1 where beauty shines and glows1 remote from the touch of sorrow1 remote from the fear of change1 remote from the failures and disenchantments of the world of fact4 ,in the contemplation of these things the vision of heaven will shape itself in our hearts1 giving at once a touchstone to judge the world about us1 and an inspiration by which to fashion to our needs whatever is not incapable of serving as a stone in the sacred temple4 ,except for those rare spirits that are born without sin1 there is a cavern of darkness to be traversed before that temple can be entered4 ,the gate of the cavern is despair1 and its floor is paved with the gravestones of abandoned hopes4 ,there ,self must die2 there the eagerness1 the greed of untamed desire must be slain1 for only so can the soul be freed from the empire of ,fate4 ,but out of the cavern the ,gate of ,renunciation leads again to the daylight of wisdom1 by whose radiance a new insight1 a new joy1 a new tenderness1 shine forth to gladden the pilgrim's heart4 ,when1 without the bitterness of impotent rebellion1 we have learnt both to resign ourselves to the outward rule of ,fate and to recognise that the non-human world is unworthy of our worship1 it becomes possible at last so to transform and refashion the unconscious universe1 so to transmute it in the crucible of imagination1 that a new image of shining gold replaces the old idol of clay4 ,in all the multiform facts of the world--in the visual shapes of trees and mountains and clouds1 in the events of the life of man1 even in the very omnipotence of ,death--the insight of creative idealism can find the reflection of a beauty which its own thoughts first made4 ,in this way mind asserts its subtle mastery over the thoughtless forces of ,nature4 ,the more evil the material with which it deals1 the more thwarting to untrained desire1 the greater is its achievement in inducing the reluctant rock to yield up its hidden treasures1 the prouder its victory in compelling the opposing forces to swell the pageant of its triumph4 ,of all the arts1 ,tragedy is the proudest1 the most triumphant2 for it builds its shining citadel in the very centre of the enemy's country1 on the very summit of his highest mountain2 from its impregnable watchtowers1 his camps and arsenals1 his columns and forts1 are all revealed2 within its walls the free life continues1 while the legions of ,death and ,pain and ,despair1 and all the servile captains of tyrant ,fate1 afford the burghers of that dauntless city new spectacles of beauty4 ,happy those sacred ramparts1 thrice happy the dwellers on that all-seeing eminence4 ,honour to those brave warriors who1 through countless ages of warfare1 have preserved for us the priceless heritage of liberty1 and have kept undefiled by sacrilegious invaders the home of the unsubdued4 ,but the beauty of ,tragedy does but make visible a quality which1 in more or less obvious shapes1 is present always and everywhere in life4 ,in the spectacle of ,death1 in the endurance of intolerable pain1 and in the irrevocableness of a vanished past1 there is a sacredness1 an overpowering awe1 a feeling of the vastness1 the depth1 the inexhaustible mystery of existence1 in which1 as by some strange marriage of pain1 the sufferer is bound to the world by bonds of sorrow4 ,in these moments of insight1 we lose all eagerness of temporary desire1 all struggling and striving for petty ends1 all care for the little trivial things that1 to a superficial view1 make up the common life of day by day2 we see1 surrounding the narrow raft illumined by the flickering light of human comradeship1 the dark ocean on whose rolling waves we toss for a brief hour2 from the great night without1 a chill blast breaks in upon our refuge2 all the loneliness of humanity amid hostile forces is concentrated upon the individual soul1 which must struggle alone1 with what of courage it can command1 against the whole weight of a universe that cares nothing for its hopes and fears4 ,victory1 in this struggle with the powers of darkness1 is the true baptism into the glorious company of heroes1 the true initiation into the overmastering beauty of human existence4 ,from that awful encounter of the soul with the outer world1 renunciation1 wisdom1 and charity are born2 and with their birth a new life begins4 ,to take into the inmost shrine of the soul the irresistible forces whose puppets we seem to be--,death and change1 the irrevocableness of the past1 and the powerlessness of man before the blind hurry of the universe from vanity to vanity--to feel these things and know them is to conquer them4 ,this is the reason why the ,past has such magical power4 ,the beauty of its motionless and silent pictures is like the enchanted purity of late autumn1 when the leaves1 though one breath would make them fall1 still glow against the sky in golden glory4 ,the ,past does not change or strive2 like ,duncan1 after life's fitful fever it sleeps well2 what was eager and grasping1 what was petty and transitory1 has faded away1 the things that were beautiful and eternal shine out of it like stars in the night4 ,its beauty1 to a soul not worthy of it1 is unendurable2 but to a soul which has conquered ,fate it is the key of religion4 ,the life of ,man1 viewed outwardly1 is but a small thing in comparison with the forces of ,nature4 ,the slave is doomed to worship ,time and ,fate and ,death1 because they are greater than anything he finds in himself1 and because all his thoughts are of things which they devour4 ,but1 great as they are1 to think of them greatly1 to feel their passionless splendour1 is greater still4 ,and such thought makes us free men2 we no longer bow before the inevitable in ,oriental subjection1 but we absorb it1 and make it a part of ourselves4 ,to abandon the struggle for private happiness1 to expel all eagerness of temporary desire1 to burn with passion for eternal things--this is emancipation1 and this is the free man's worship4 ,and this liberation is effected by a contemplation of ,fate2 for ,fate itself is subdued by the mind which leaves nothing to be purged by the purifying fire of ,time4 ,united with his fellow-men by the strongest of all ties1 the tie of a common doom1 the free man finds that a new vision is with him always1 shedding over every daily task the light of love4 ,the life of ,man is a long march through the night1 surrounded by invisible foes1 tortured by weariness and pain1 towards a goal that few can hope to reach1 and where none may tarry long4 ,one by one1 as they march1 our comrades vanish from our sight1 seized by the silent orders of omnipotent ,death4 ,very brief is the time in which we can help them1 in which their happiness or misery is decided4 ,be it ours to shed sunshine on their path1 to lighten their sorrows by the balm of sympathy1 to give them the pure joy of a never-tiring affection1 to strengthen failing courage1 to instil faith in hours of despair4 ,let us not weigh in grudging scales their merits and demerits1 but let us think only of their need--of the sorrows1 the difficulties1 perhaps the blindnesses1 that make the misery of their lives2 let us remember that they are fellow-sufferers in the same darkness1 actors in the same tragedy with ourselves4 ,and so1 when their day is over1 when their good and their evil have become eternal by the immortality of the past1 be it ours to feel that1 where they suffered1 where they failed1 no deed of ours was the cause2 but wherever a spark of the divine fire kindled in their hearts1 we were ready with encouragement1 with sympathy1 with brave words in which high courage glowed4 ,brief and powerless is ,man's life2 on him and all his race the slow1 sure doom falls pitiless and dark4 ,blind to good and evil1 reckless of destruction1 omnipotent matter rolls on its relentless way2 for ,man1 condemned to-day to lose his dearest1 to-morrow himself to pass through the gate of darkness1 it remains only to cherish1 ere yet the blow falls1 the lofty thoughts that ennoble his little day2 disdaining the coward terrors of the slave of ,fate1 to worship at the shrine that his own hands have built2 undismayed by the empire of chance1 to preserve a mind free from the wanton tyranny that rules his outward life2 proudly defiant of the irresistible forces that tolerate1 for a moment1 his knowledge and his condemnation1 to sustain alone1 a weary but unyielding ,atlas1 the world that his own ideals have fashioned despite the trampling march of unconscious power4 ,,footnotes3 #i ,reprinted from the ,independent ,review1 ,december1 #aijc4 ,,iv ,,the ,,study ,,of ,,mathematics ,in regard to every form of human activity it is necessary that the question should be asked from time to time1 ,what is its purpose and ideal8 ,in what way does it contribute to the beauty of human existence8 ,as respects those pursuits which contribute only remotely1 by providing the mechanism of life1 it is well to be reminded that not the mere fact of living is to be desired1 but the art of living in the contemplation of great things4 ,still more in regard to those avocations which have no end outside themselves1 which are to be justified1 if at all1 as actually adding to the sum of the world's permanent possessions1 it is necessary to keep alive a knowledge of their aims1 a clear prefiguring vision of the temple in which creative imagination is to be embodied4 ,the fulfilment of this need1 in what concerns the studies forming the material upon which custom has decided to train the youthful mind1 is indeed sadly remote--so remote as to make the mere statement of such a claim appear preposterous4 ,great men1 fully alive to the beauty of the contemplations to whose service their lives are devoted1 desiring that others may share in their joys1 persuade mankind to impart to the successive generations the mechanical knowledge without which it is impossible to cross the threshold4 ,dry pedants possess themselves of the privilege of instilling this knowledge3 they forget that it is to serve but as a key to open the doors of the temple2 though they spend their lives on the steps leading up to those sacred doors1 they turn their backs upon the temple so resolutely that its very existence is forgotten1 and the eager youth1 who would press forward to be initiated to its domes and arches1 is bidden to turn back and count the steps4 ,mathematics1 perhaps more even than the study of ,greece and ,rome1 has suffered from this oblivion of its due place in civilisation4 ,although tradition has decreed that the great bulk of educated men shall know at least the elements of the subject1 the reasons for which the tradition arose are forgotten1 buried beneath a great rubbish-heap of pedantries and trivialities4 ,to those who inquire as to the purpose of mathematics1 the usual answer will be that it facilitates the making of machines1 the travelling from place to place1 and the victory over foreign nations1 whether in war or commerce4 ,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 mathematicians1 the reply1 it is true1 will probably be that mathematics trains the reasoning faculties4 ,yet the very men who make this reply are1 for the most part1 unwilling to abandon the teaching of definite fallacies1 known to be such1 and instinctively rejected by the unsophisticated mind of every intelligent learner4 ,and the reasoning faculty itself is generally conceived1 by those who urge its cultivation1 as merely a means for the avoidance of pitfalls and a help in the discovery of rules for the guidance of practical life4 ,all these are undeniably important achievements to the credit of mathematics2 yet it is none of these that entitles mathematics to a place in every liberal education4 ,plato1 we know1 regarded the contemplation of mathematical truths as worthy of the ,deity2 and ,plato realised1 more perhaps than any other single man1 what those elements are in human life which merit a place in heaven4 ,there is in mathematics1 he says1 something which is necessary and cannot be set aside 444 and1 if ,i mistake not1 of divine necessity2 for as to the human necessities of which the ,many talk in this connection1 nothing can be more ridiculous than such an application of the words4 ,cleinias4 ,and what are these necessities of knowledge1 ,stranger1 which are divine and not human8 ,athenian4 ,those things without some use or knowledge of which a man cannot become a ,god to the world1 nor a spirit1 nor yet a hero1 nor able earnestly to think and care for man 7,laws1 p4 #hah74aj ,such was ,plato's judgment of mathematics2 but the mathematicians do not read ,plato1 while those who read him know no mathematics1 and regard his opinion upon this question as merely a curious aberration4 ,mathematics1 rightly viewed1 possesses not only truth1 but supreme beauty--a beauty cold and austere1 like that of sculpture1 without appeal to any part of our weaker nature1 without the gorgeous trappings of painting or music1 yet sublimely pure1 and capable of a stern perfection such as only the greatest art can show4 ,the true spirit of delight1 the exaltation1 the sense of being more than man1 which is the touchstone of the highest excellence1 is to be found in mathematics as surely as in poetry4 ,what is best in mathematics deserves not merely to be learnt as a task1 but to be assimilated as a part of daily thought1 and brought again and again before the mind with ever-renewed encouragement4 ,real life is1 to most men1 a long second-best1 a perpetual compromise between the ideal and the possible2 but the world of pure reason knows no compromise1 no practical limitations1 no barrier to the creative activity embodying in splendid edifices the passionate aspiration after the perfect from which all great work springs4 ,remote from human passions1 remote even from the pitiful facts of nature1 the generations have gradually created an ordered cosmos1 where pure thought can dwell as in its natural home1 and where one1 at least1 of our nobler impulses can escape from the dreary exile of the actual world4 ,so little1 however1 have mathematicians aimed at beauty1 that hardly anything in their work has had this conscious purpose4 ,much1 owing to irrepressible instincts1 which were better than avowed beliefs1 has been moulded by an unconscious taste2 but much also has been spoilt by false notions of what was fitting4 ,the characteristic excellence of mathematics is only to be found where the reasoning is rigidly logical3 the rules of logic are to mathematics what those of structure are to architecture4 ,in the most beautiful work1 a chain of argument is presented in which every link is important on its own account1 in which there is an air of ease and lucidity throughout1 and the premises achieve more than would have been thought possible1 by means which appear natural and inevitable4 ,literature embodies what is general in particular circumstances whose universal significance shines through their individual dress2 but mathematics endeavours to present whatever is most general in its purity1 without any irrelevant trappings4 ,how should the teaching of mathematics be conducted so as to communicate to the learner as much as possible of this high ideal8 ,here experience must1 in a great measure1 be our guide2 but some maxims may result from our consideration of the ultimate purpose to be achieved4 ,one of the chief ends served by mathematics1 when rightly taught1 is to awaken the learner's belief in reason1 his confidence in the truth of what has been demonstrated1 and in the value of demonstration4 ,this purpose is not served by existing instruction2 but it is easy to see ways in which it might be served4 ,at present1 in what concerns arithmetic1 the boy or girl is given a set of rules1 which present themselves as neither true nor false1 but as merely the will of the teacher1 the way in which1 for some unfathomable reason1 the teacher prefers to have the game played4 ,to some degree1 in a study of such definite practical utility1 this is no doubt unavoidable2 but as soon as possible1 the reasons of rules should be set forth by whatever means most readily appeal to the childish mind4 ,in geometry1 instead of the tedious apparatus of fallacious proofs for obvious truisms which constitutes the beginning of ,euclid1 the learner should be allowed at first to assume the truth of everything obvious1 and should be instructed in the demonstrations of theorems which are at once startling and easily verifiable by actual drawing1 such as those in which it is shown that three or more lines meet in a point4 ,in this way belief is generated2 it is seen that reasoning may lead to startling conclusions1 which nevertheless the facts will verify2 and thus the instinctive distrust of whatever is abstract or rational is gradually overcome4 ,where theorems are difficult1 they should be first taught as exercises in geometrical drawing1 until the figure has become thoroughly familiar2 it will then be an agreeable advance to be taught the logical connections of the various lines or circles that occur4 ,it is desirable also that the figure illustrating a theorem should be drawn in all possible cases and shapes1 that so the abstract relations with which geometry is concerned may of themselves emerge as the residue of similarity amid such great apparent diversity4 ,in this way the abstract demonstrations should form but a small part of the instruction1 and should be given when1 by familiarity with concrete illustrations1 they have come to be felt as the natural embodiment of visible fact4 ,in this early stage proofs should not be given with pedantic fullness2 definitely fallacious methods1 such as that of superposition1 should be rigidly excluded from the first1 but where1 without such methods1 the proof would be very difficult1 the result should be rendered acceptable by arguments and illustrations which are explicitly contrasted with demonstrations4 ,in the beginning of algebra1 even the most intelligent child finds1 as a rule1 very great difficulty4 ,the use of letters is a mystery1 which seems to have no purpose except mystification4 ,it is almost impossible1 at first1 not to think that every letter stands for some particular number1 if only the teacher would reveal what number it stands for4 ,the fact is1 that in algebra the mind is first taught to consider general truths1 truths which are not asserted to hold only of this or that particular thing1 but of any one of a whole group of things4 ,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 resides2 and ability to deal with the general as such is one of the gifts that a mathematical education should bestow4 ,but how little1 as a rule1 is the teacher of algebra able to explain the chasm which divides it from arithmetic1 and how little is the learner assisted in his groping efforts at comprehension6 ,usually the method that has been adopted in arithmetic is continued3 rules are set forth1 with no adequate explanation of their grounds2 the pupil learns to use the rules blindly1 and presently1 when he is able to obtain the answer that the teacher desires1 he feels that he has mastered the difficulties of the subject4 ,but of inner comprehension of the processes employed he has probably acquired almost nothing4 ,when algebra has been learnt1 all goes smoothly until we reach those studies in which the notion of infinity is employed--the infinitesimal calculus and the whole of higher mathematics4 ,the solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our own age has to boast4 ,since the beginnings of ,greek thought these difficulties have been known2 in every age the finest intellects have vainly endeavoured to answer the apparently unanswerable questions that had been asked by ,zeno the ,eleatic4 ,at last ,georg ,cantor has found the answer1 and has conquered for the intellect a new and vast province which had been given over to ,chaos and old ,night4 ,it was assumed as self-evident1 until ,cantor and ,dedekind established the opposite1 that if1 from any collection of things1 some were taken away1 the number of things left must always be less than the original number of things4 ,this assumption1 as a matter of fact1 holds only of finite collections2 and the rejection of it1 where the infinite is concerned1 has been shown to remove all the difficulties that had hitherto baffled human reason in this matter1 and to render possible the creation of an exact science of the infinite4 ,this stupendous fact ought to produce a revolution in the higher teaching of mathematics2 it has itself added immeasurably to the educational value of the subject1 and it has at last given the means of treating with logical precision many studies which1 until lately1 were wrapped in fallacy and obscurity4 ,by those who were educated on the old lines1 the new work is considered to be appallingly difficult1 abstruse1 and obscure2 and it must be confessed that the discoverer1 as is so often the case1 has hardly himself emerged from the mists which the light of his intellect is dispelling4 ,but inherently1 the new doctrine of the infinite1 to all candid and inquiring minds1 has facilitated the mastery of higher mathematics2 for hitherto1 it has been necessary to learn1 by a long process of sophistication1 to give assent to arguments which1 on first acquaintance1 were rightly judged to be confused and erroneous4 ,so far from producing a fearless belief in reason1 a bold rejection of whatever failed to fulfil the strictest requirements of logic1 a mathematical training1 during the past two centuries1 encouraged the belief that many things1 which a rigid inquiry would reject as fallacious1 must yet be accepted because they work in what the mathematician calls practice4 ,by this means1 a timid1 compromising spirit1 or else a sacerdotal belief in mysteries not intelligible to the profane1 has been bred where reason alone should have ruled4 ,all this it is now time to sweep away2 let those who wish to penetrate into the arcana of mathematics be taught at once the true theory in all its logical purity1 and in the concatenation established by the very essence of the entities concerned4 ,if we are considering mathematics as an end in itself1 and not as a technical training for engineers1 it is very desirable to preserve the purity and strictness of its reasoning4 ,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 deduced4 ,they should be taught--what the theory of infinity very aptly illustrates--that many propositions seem self-evident to the untrained mind which1 nevertheless1 a nearer scrutiny shows to be false4 ,by this means they will be led to a sceptical inquiry into first principles1 an examination of the foundations upon which the whole edifice of reasoning is built1 or1 to take perhaps a more fitting metaphor1 the great trunk from which the spreading branches spring4 ,at this stage1 it is well to study afresh the elementary portions of mathematics1 asking no longer merely whether a given proposition is true1 but also how it grows out of the central principles of logic4 ,questions of this nature can now be answered with a precision and certainty which were formerly quite impossible2 and in the chains of reasoning that the answer requires the unity of all mathematical studies at last unfolds itself4 ,in the great majority of mathematical text-books there is a total lack of unity in method and of systematic development of a central theme4 ,propositions of very diverse kinds are proved by whatever means are thought most easily intelligible1 and much space is devoted to mere curiosities which in no way contribute to the main argument4 ,but in the greatest works1 unity and inevitability are felt as in the unfolding of a drama2 in the premisses a subject is proposed for consideration1 and in every subsequent step some definite advance is made towards mastery of its nature4 ,the love of system1 of interconnection1 which is perhaps the inmost essence of the intellectual impulse1 can find free play in mathematics as nowhere else4 ,the learner who feels this impulse must not be repelled by an array of meaningless examples or distracted by amusing oddities1 but must be encouraged to dwell upon central principles1 to become familiar with the structure of the various subjects which are put before him1 to travel easily over the steps of the more important deductions4 ,in this way a good tone of mind is cultivated1 and selective attention is taught to dwell by preference upon what is weighty and essential4 ,when the separate studies into which mathematics is divided have each been viewed as a logical whole1 as a natural growth from the propositions which constitute their principles1 the learner will be able to understand the fundamental science which unifies and systematises the whole of deductive reasoning4 ,this is symbolic logic--a study which1 though it owes its inception to ,aristotle1 is yet1 in its wider developments1 a product1 almost wholly1 of the nineteenth century1 and is indeed1 in the present day1 still growing with great rapidity4 ,the true method of discovery in symbolic logic1 and probably also the best method for introducing the study to a learner acquainted with other parts of mathematics1 is the analysis of actual examples of deductive reasoning1 with a view to the discovery of the principles employed4 ,these principles1 for the most part1 are so embedded in our ratiocinative instincts1 that they are employed quite unconsciously1 and can be dragged to light only by much patient effort4 ,but when at last they have been found1 they are seen to be few in number1 and to be the sole source of everything in pure mathematics4 ,the discovery that all mathematics follows inevitably from a small collection of fundamental laws is one which immeasurably enhances the intellectual beauty of the whole2 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 revelation2 like a palace emerging from the autumn mist as the traveller ascends an ,italian hill-side1 the stately storeys of the mathematical edifice appear in their due order and proportion1 with a new perfection in every part4 ,until symbolic logic had acquired its present development1 the principles upon which mathematics depends were always supposed to be philosophical1 and discoverable only by the uncertain1 unprogressive methods hitherto employed by philosophers4 ,so long as this was thought1 mathematics seemed to be not autonomous1 but dependent upon a study which had quite other methods than its own4 ,moreover1 since the nature of the postulates from which arithmetic1 analysis1 and geometry are to be deduced was wrapped in all the traditional obscurities of metaphysical discussion1 the edifice built upon such dubious foundations began to be viewed as no better than a castle in the air4 ,in this respect1 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 obtained4 ,this satisfaction ought not to be refused to learners capable of enjoying it1 for it is of a kind to increase our respect for human powers and our knowledge of the beauties belonging to the abstract world4 ,philosophers have commonly held that the laws of logic1 which underlie mathematics1 are laws of thought1 laws regulating the operations of our minds4 ,by this opinion the true dignity of reason is very greatly lowered3 it ceases to be an investigation into the very heart and immutable essence of all things actual and possible1 becoming1 instead1 an inquiry into something more or less human and subject to our limitations4 ,the contemplation of what is non-human1 the discovery that our minds are capable of dealing with material not created by them1 above all1 the realisation that beauty belongs to the outer world as to the inner1 are the chief means of overcoming the terrible sense of impotence1 of weakness1 of exile amid hostile powers1 which is too apt to result from acknowledging the all-but omnipotence of alien forces4 ,to reconcile us1 by the exhibition of its awful beauty1 to the reign of ,fate--which is merely the literary personification of these forces--is the task of tragedy4 ,but mathematics takes us still further from what is human1 into the region of absolute necessity1 to which not only the actual world1 but every possible world1 must conform2 and even here it builds a habitation1 or rather finds a habitation eternally standing1 where our ideals are fully satisfied and our best hopes are not thwarted4 ,it is only when we thoroughly understand the entire independence of ourselves1 which belongs to this world that reason finds1 that we can adequately realise the profound importance of its beauty4 ,not only is mathematics independent of us and our thoughts1 but in another sense we and the whole universe of existing things are independent of mathematics4 ,the apprehension of this purely ideal character is indispensable1 if we are to understand rightly the place of mathematics as one among the arts4 ,it was formerly supposed that pure reason could decide1 in some respects1 as to the nature of the actual world3 geometry1 at least1 was thought to deal with the space in which we live4 ,but we now know that pure mathematics can never pronounce upon questions of actual existence3 the world of reason1 in a sense1 controls the world of fact1 but it is not at any point creative of fact1 and in the application of its results to the world in time and space1 its certainty and precision are lost among approximations and working hypotheses4 ,the objects considered by mathematicians have1 in the past1 been mainly of a kind suggested by phenomena2 but from such restrictions the abstract imagination should be wholly free4 ,a reciprocal liberty must thus be accorded3 reason cannot dictate to the world of facts1 but the facts cannot restrict reason's privilege of dealing with whatever objects its love of beauty may cause to seem worthy of consideration4 ,here1 as elsewhere1 we build up our own ideals out of the fragments to be found in the world2 and in the end it is hard to say whether the result is a creation or a discovery4 ,it is very desirable1 in instruction1 not merely to persuade the student of the accuracy of important theorems1 but to persuade him in the way which itself has1 of all possible ways1 the most beauty4 ,the true interest of a demonstration is not1 as traditional modes of exposition suggest1 concentrated wholly in the result2 where this does occur1 it must be viewed as a defect1 to be remedied1 if possible1 by so generalising the steps of the proof that each becomes important in and for itself4 ,an argument which serves only to prove a conclusion is like a story subordinated to some moral which it is meant to teach3 for sthetic perfection no part of the whole should be merely a means4 ,a certain practical spirit1 a desire for rapid progress1 for conquest of new realms1 is responsible for the undue emphasis upon results which prevails in mathematical instruction4 ,the better way is to propose some theme for consideration--in geometry1 a figure having important properties2 in analysis1 a function of which the study is illuminating1 and so on4 ,whenever proofs depend upon some only of the marks by which we define the object to be studied1 these marks should be isolated and investigated on their own account4 ,for it is a defect1 in an argument1 to employ more premisses than the conclusion demands3 what mathematicians call elegance results from employing only the essential principles in virtue of which the thesis is true4 ,it is a merit in ,euclid that he advances as far as he is able to go without employing the axiom of parallels--not1 as is often said1 because this axiom is inherently objectionable1 but because1 in mathematics1 every new axiom diminishes the generality of the resulting theorems1 and the greatest possible generality is before all things to be sought4 ,of the effects of mathematics outside its own sphere more has been written than on the subject of its own proper ideal4 ,the effect upon philosophy has1 in the past1 been most notable1 but most varied2 in the seventeenth century1 idealism and rationalism1 in the eighteenth1 materialism and sensationalism1 seemed equally its offspring4 ,of the effect which it is likely to have in the future it would be very rash to say much2 but in one respect a good result appears probable4 ,against that kind of scepticism which abandons the pursuit of ideals because the road is arduous and the goal not certainly attainable1 mathematics1 within its own sphere1 is a complete answer4 ,too often it is said that there is no absolute truth1 but only opinion and private judgment2 that each of us is conditioned1 in his view of the world1 by his own peculiarities1 his own taste and bias2 that there is no external kingdom of truth to which1 by patience and discipline1 we may at last obtain admittance1 but only truth for me1 for you1 for every separate person4 ,by this habit of mind one of the chief ends of human effort is denied1 and the supreme virtue of candour1 of fearless acknowledgment of what is1 disappears from our moral vision4 ,of such scepticism mathematics is a perpetual reproof2 for its edifice of truths stands unshakable and inexpungable to all the weapons of doubting cynicism4 ,the effects of mathematics upon practical life1 though they should not be regarded as the motive of our studies1 may be used to answer a doubt to which the solitary student must always be liable4 ,in a world so full of evil and suffering1 retirement into the cloister of contemplation1 to the enjoyment of delights which1 however noble1 must always be for the few only1 cannot but appear as a somewhat selfish refusal to share the burden imposed upon others by accidents in which justice plays no part4 ,have any of us the right1 we ask1 to withdraw from present evils1 to leave our fellow-men unaided1 while we live a life which1 though arduous and austere1 is yet plainly good in its own nature8 ,when these questions arise1 the true answer is1 no doubt1 that some must keep alive the sacred fire1 some must preserve1 in every generation1 the haunting vision which shadows forth the goal of so much striving4 ,but when1 as must sometimes occur1 this answer seems too cold1 when we are almost maddened by the spectacle of sorrows to which we bring no help1 then we may reflect that indirectly the mathematician often does more for human happiness than any of his more practically active contemporaries4 ,the history of science abundantly proves that a body of abstract propositions--even if1 as in the case of conic sections1 it remains two thousand years without effect upon daily life--may yet1 at any moment1 be used to cause a revolution in the habitual thoughts and occupations of every citizen4 ,the use of steam and electricity--to take striking instances--is rendered possible only by mathematics4 ,in the results of abstract thought the world possesses a capital of which the employment in enriching the common round has no hitherto discoverable limits4 ,nor does experience give any means of deciding what parts of mathematics will be found useful4 ,utility1 therefore1 can be only a consolation in moments of discouragement1 not a guide in directing our studies4 ,for the health of the moral life1 for ennobling the tone of an age or a nation1 the austerer virtues have a strange power1 exceeding the power of those not informed and purified by thought4 ,of these austerer virtues the love of truth is the chief1 and in mathematics1 more than elsewhere1 the love of truth may find encouragement for waning faith4 ,every great study is not only an end in itself1 but also a means of creating and sustaining a lofty habit of mind2 and this purpose should be kept always in view throughout the teaching and learning of mathematics4 ,,footnotes3 #aj ,this passage was pointed out to me by ,professor ,gilbert ,murray4 ,v ,,mathematics ,,and ,,the ,,metaphysicians ,the nineteenth century1 which prided itself upon the invention of steam and evolution1 might have derived a more legitimate title to fame from the discovery of pure mathematics4 ,this science1 like most others1 was baptised long before it was born2 and thus we find writers before the nineteenth century alluding to what they called pure mathematics4 ,but if they had been asked what this subject was1 they would only have been able to say that it consisted of ,arithmetic1 ,algebra1 ,geometry1 and so on4 ,as to what these studies had in common1 and as to what distinguished them from applied mathematics1 our ancestors were completely in the dark4 ,pure mathematics was discovered by ,boole1 in a work which he called the ,laws of ,thought 7#ahed74 ,this work abounds in asseverations that it is not mathematical1 the fact being that ,boole was too modest to suppose his book the first ever written on mathematics4 ,he was also mistaken in supposing that he was dealing with the laws of thought3 the question how people actually think was quite irrelevant to him1 and if his book had really contained the laws of thought1 it was curious that no one should ever have thought in such a way before4 ,his book was in fact concerned with formal logic1 and this is the same thing as mathematics4 ,pure mathematics consists entirely of assertions to the effect that1 if such and such a proposition is true of anything1 then such and such another proposition is true of that thing4 ,it is essential not to discuss whether the first proposition is really true1 and not to mention what the anything is1 of which it is supposed to be true4 ,both these points would belong to applied mathematics4 ,we start1 in pure mathematics1 from certain rules of inference1 by which we can infer that if one proposition is true1 then so is some other proposition4 ,these rules of inference constitute the major part of the principles of formal logic4 ,we then take any hypothesis that seems amusing1 and deduce its consequences4 ,if our hypothesis is about anything1 and not about some one or more particular things1 then our deductions constitute mathematics4 ,thus mathematics may be defined as the subject in which we never know what we are talking about1 nor whether what we are saying is true4 ,people who have been puzzled by the beginnings of mathematics will1 ,i hope1 find comfort in this definition1 and will probably agree that it is accurate4 ,as one of the chief triumphs of modern mathematics consists in having discovered what mathematics really is1 a few more words on this subject may not be amiss4 ,it is common to start any branch of mathematics--for instance1 ,geometry--with a certain number of primitive ideas1 supposed incapable of definition1 and a certain number of primitive propositions or axioms1 supposed incapable of proof4 ,now the fact is that1 though there are indefinables and indemonstrables in every branch of applied mathematics1 there are none in pure mathematics except such as belong to general logic4 ,logic1 broadly speaking1 is distinguished by the fact that its propositions can be put into a form in which they apply to anything whatever4 ,all pure mathematics--,arithmetic1 ,analysis1 and ,geometry--is built up by combinations of the primitive ideas of logic1 and its propositions are deduced from the general axioms of logic1 such as the syllogism and the other rules of inference4 ,and this is no longer a dream or an aspiration4 ,on the contrary1 over the greater and more difficult part of the domain of mathematics1 it has been already accomplished2 in the few remaining cases1 there is no special difficulty1 and it is now being rapidly achieved4 ,philosophers have disputed for ages whether such deduction was possible2 mathematicians have sat down and made the deduction4 ,for the philosophers there is now nothing left but graceful acknowledgments4 ,the subject of formal logic1 which has thus at last shown itself to be identical with mathematics1 was1 as every one knows1 invented by ,aristotle1 and formed the chief study 7other than theology7 of the ,middle ,ages4 ,but ,aristotle never got beyond the syllogism1 which is a very small part of the subject1 and the schoolmen never got beyond ,aristotle4 ,if any proof were required of our superiority to the medival doctors1 it might be found in this4 ,throughout the ,middle ,ages1 almost all the best intellects devoted themselves to formal logic1 whereas in the nineteenth century only an infinitesimal proportion of the world's thought went into this subject4 ,nevertheless1 in each decade since #ahej more has been done to advance the subject than in the whole period from ,aristotle to ,leibniz4 ,people have discovered how to make reasoning symbolic1 as it is in ,algebra1 so that deductions are effected by mathematical rules4 ,they have discovered many rules besides the syllogism1 and a new branch of logic1 called the ,logic of ,relatives1#aa has been invented to deal with topics that wholly surpassed the powers of the old logic1 though they form the chief contents of mathematics4 ,it is not easy for the lay mind to realise the importance of symbolism in discussing the foundations of mathematics1 and the explanation may perhaps seem strangely paradoxical4 ,the fact is that symbolism is useful because it makes things difficult4 7,this is not true of the advanced parts of mathematics1 but only of the beginnings47 ,what we wish to know is1 what can be deduced from what4 ,now1 in the beginnings1 everything is self-evident2 and it is very hard to see whether one self-evident proposition follows from another or not4 ,obviousness is always the enemy to correctness4 ,hence we invent some new and difficult symbolism1 in which nothing seems obvious4 ,then we set up certain rules for operating on the symbols1 and the whole thing becomes mechanical4 ,in this way we find out what must be taken as premiss and what can be demonstrated or defined4 ,for instance1 the whole of ,arithmetic and ,algebra has been shown to require three indefinable notions and five indemonstrable propositions4 ,but without a symbolism it would have been very hard to find this out4 ,it is so obvious that two and two are four1 that we can hardly make ourselves sufficiently sceptical to doubt whether it can be proved4 ,and the same holds in other cases where self-evident things are to be proved4 ,but the proof of self-evident propositions may seem1 to the uninitiated1 a somewhat frivolous occupation4 ,to this we might reply that it is often by no means self-evident that one obvious proposition follows from another obvious proposition2 so that we are really discovering new truths when we prove what is evident by a method which is not evident4 ,but a more interesting retort is1 that since people have tried to prove obvious propositions1 they have found that many of them are false4 ,self-evidence is often a mere will-o'-the-wisp1 which is sure to lead us astray if we take it as our guide4 ,for instance1 nothing is plainer than that a whole always has more terms than a part1 or that a number is increased by adding one to it4 ,but these propositions are now known to be usually false4 ,most numbers are infinite1 and if a number is infinite you may add ones to it as long as you like without disturbing it in the least4 ,one of the merits of a proof is that it instils a certain doubt as to the result proved2 and when what is obvious can be proved in some cases1 but not in others1 it becomes possible to suppose that in these other cases it is false4 ,the great master of the art of formal reasoning1 among the men of our own day1 is an ,italian1 ,professor ,peano1 of the ,university of ,turin4#ab ,he has reduced the greater part of mathematics 7and he or his followers will1 in time1 have reduced the whole7 to strict symbolic form1 in which there are no words at all4 ,in the ordinary mathematical books1 there are no doubt fewer words than most readers would wish4 ,still1 little phrases occur1 such as therefore1 let us assume1 consider1 or hence it follows4 ,all these1 however1 are a concession1 and are swept away by ,professor ,peano4 ,for instance1 if we wish to learn the whole of ,arithmetic1 ,algebra1 the ,calculus1 and indeed all that is usually called pure mathematics 7except ,geometry71 we must start with a dictionary of three words4 ,one symbol stands for zero1 another for number1 and a third for next after4 ,what these ideas mean1 it is necessary to know if you wish to become an arithmetician4 ,but after symbols have been invented for these three ideas1 not another word is required in the whole development4 ,all future symbols are symbolically explained by means of these three4 ,even these three can be explained by means of the notions of relation and class2 but this requires the ,logic of ,relations1 which ,professor ,peano has never taken up4 ,it must be admitted that what a mathematician has to know to begin with is not much4 ,there are at most a dozen notions out of which all the notions in all pure mathematics 7including ,geometry7 are compounded4 ,professor ,peano1 who is assisted by a very able school of young ,italian disciples1 has shown how this may be done2 and although the method which he has invented is capable of being carried a good deal further than he has carried it1 the honour of the pioneer must belong to him4 ,two hundred years ago1 ,leibniz foresaw the science which ,peano has perfected1 and endeavoured to create it4 ,he was prevented from succeeding by respect for the authority of ,aristotle1 whom he could not believe guilty of definite1 formal fallacies2 but the subject which he desired to create now exists1 in spite of the patronising contempt with which his schemes have been treated by all superior persons4 ,from this ,universal ,characteristic1 as he called it1 he hoped for a solution of all problems1 and an end to all disputes4 ,if controversies were to arise1 he says1 there would be no more need of disputation between two philosophers than between two accountants4 ,for it would suffice to take their pens in their hands1 to sit down to their desks1 and to say to each other 7with a friend as witness1 if they liked71 ',let us calculate4' ,this optimism has now appeared to be somewhat excessive2 there still are problems whose solution is doubtful1 and disputes which calculation cannot decide4 ,but over an enormous field of what was formerly controversial1 ,leibniz's dream has become sober fact4 ,in the whole philosophy of mathematics1 which used to be at least as full of doubt as any other part of philosophy1 order and certainty have replaced the confusion and hesitation which formerly reigned4 ,philosophers1 of course1 have not yet discovered this fact1 and continue to write on such subjects in the old way4 ,but mathematicians1 at least in ,italy1 have now the power of treating the principles of mathematics in an exact and masterly manner1 by means of which the certainty of mathematics extends also to mathematical philosophy4 ,hence many of the topics which used to be placed among the great mysteries--for example1 the natures of infinity1 of continuity1 of space1 time and motion--are now no longer in any degree open to doubt or discussion4 ,those who wish to know the nature of these things need only read the works of such men as ,peano or ,georg ,cantor2 they will there find exact and indubitable expositions of all these quondam mysteries4 ,in this capricious world1 nothing is more capricious than posthumous fame4 ,one of the most notable examples of posterity's lack of judgment is the ,eleatic ,zeno4 ,this man1 who may be regarded as the founder of the philosophy of infinity1 appears in ,plato's ,parmenides in the privileged position of instructor to ,socrates4 ,he invented four arguments1 all immeasurably subtle and profound1 to prove that motion is impossible1 that ,achilles can never overtake the tortoise1 and that an arrow in flight is really at rest4 ,after being refuted by ,aristotle1 and by every subsequent philosopher from that day to our own1 these arguments were reinstated1 and made the basis of a mathematical renaissance1 by a ,german professor1 who probably never dreamed of any connection between himself and ,zeno4 ,weierstrass1#ac by strictly banishing from mathematics the use of infinitesimals1 has at last shown that we live in an unchanging world1 and that the arrow in its flight is truly at rest4 ,zeno's only error lay in inferring 7if he did infer7 that1 because there is no such thing as a state of change1 therefore the world is in the same state at any one time as at any other4 ,this is a consequence which by no means follows2 and in this respect1 the ,german mathematician is more constructive than the ingenious ,greek4 ,weierstrass has been able1 by embodying his views in mathematics1 where familiarity with truth eliminates the vulgar prejudices of common sense1 to invest ,zeno's paradoxes with the respectable air of platitudes2 and if the result is less delightful to the lover of reason than ,zeno's bold defiance1 it is at any rate more calculated to appease the mass of academic mankind4 ,zeno was concerned1 as a matter of fact1 with three problems1 each presented by motion1 but each more abstract than motion1 and capable of a purely arithmetical treatment4 ,these are the problems of the infinitesimal1 the infinite1 and continuity4 ,to state clearly the difficulties involved1 was to accomplish perhaps the hardest part of the philosopher's task4 ,this was done by ,zeno4 ,from him to our own day1 the finest intellects of each generation in turn attacked the problems1 but achieved1 broadly speaking1 nothing4 ,in our own time1 however1 three men--,weierstrass1 ,dedekind1 and ,cantor--have not merely advanced the three problems1 but have completely solved them4 ,the solutions1 for those acquainted with mathematics1 are so clear as to leave no longer the slightest doubt or difficulty4 ,this achievement is probably the greatest of which our age has to boast2 and ,i know of no age 7except perhaps the golden age of ,greece7 which has a more convincing proof to offer of the transcendent genius of its great men4 ,of the three problems1 that of the infinitesimal was solved by ,weierstrass2 the solution of the other two was begun by ,dedekind1 and definitively accomplished by ,cantor4 ,the infinitesimal played formerly a great part in mathematics4 ,it was introduced by the ,greeks1 who regarded a circle as differing infinitesimally from a polygon with a very large number of very small equal sides4 ,it gradually grew in importance1 until1 when ,leibniz invented the ,infinitesimal ,calculus1 it seemed to become the fundamental notion of all higher mathematics4 ,carlyle tells1 in his ,frederick the ,great1 how ,leibniz used to discourse to ,queen ,sophia ,charlotte of ,prussia concerning the infinitely little1 and how she would reply that on that subject she needed no instruction--the behaviour of courtiers had made her thoroughly familiar with it4 ,but philosophers and mathematicians--who for the most part had less acquaintance with courts--continued to discuss this topic1 though without making any advance4 ,the ,calculus required continuity1 and continuity was supposed to require the infinitely little2 but nobody could discover what the infinitely little might be4 ,it was plainly not quite zero1 because a sufficiently large number of infinitesimals1 added together1 were seen to make up a finite whole4 ,but nobody could point out any fraction which was not zero1 and yet not finite4 ,thus there was a deadlock4 ,but at last ,weierstrass discovered that the infinitesimal was not needed at all1 and that everything could be accomplished without it4 ,thus there was no longer any need to suppose that there was such a thing4 ,nowadays1 therefore1 mathematicians are more dignified than ,leibniz3 instead of talking about the infinitely small1 they talk about the infinitely great--a subject which1 however appropriate to monarchs1 seems1 unfortunately1 to interest them even less than the infinitely little interested the monarchs to whom ,leibniz discoursed4 ,the banishment of the infinitesimal has all sorts of odd consequences1 to which one has to become gradually accustomed4 ,for example1 there is no such thing as the next moment4 ,the interval between one moment and the next would have to be infinitesimal1 since1 if we take two moments with a finite interval between them1 there are always other moments in the interval4 ,thus if there are to be no infinitesimals1 no two moments are quite consecutive1 but there are always other moments between any two4 ,hence there must be an infinite number of moments between any two2 because if there were a finite number one would be nearest the first of the two moments1 and therefore next to it4 ,this might be thought to be a difficulty2 but1 as a matter of fact1 it is here that the philosophy of the infinite comes in1 and makes all straight4 ,the same sort of thing happens in space4 ,if any piece of matter be cut in two1 and then each part be halved1 and so on1 the bits will become smaller and smaller1 and can theoretically be made as small as we please4 ,however small they may be1 they can still be cut up and made smaller still4 ,but they will always have some finite size1 however small they may be4 ,we never reach the infinitesimal in this way1 and no finite number of divisions will bring us to points4 ,nevertheless there are points1 only these are not to be reached by successive divisions4 ,here again1 the philosophy of the infinite shows us how this is possible1 and why points are not infinitesimal lengths4 ,as regards motion and change1 we get similarly curious results4 ,people used to think that when a thing changes1 it must be in a state of change1 and that when a thing moves1 it is in a state of motion4 ,this is now known to be a mistake4 ,when a body moves1 all that can be said is that it is in one place at one time and in another at another4 ,we must not say that it will be in a neighbouring place at the next instant1 since there is no next instant4 ,philosophers often tell us that when a body is in motion1 it changes its position within the instant4 ,to this view ,zeno long ago made the fatal retort that every body always is where it is2 but a retort so simple and brief was not of the kind to which philosophers are accustomed to give weight1 and they have continued down to our own day to repeat the same phrases which roused the ,eleatic's destructive ardour4 ,it was only recently that it became possible to explain motion in detail in accordance with ,zeno's platitude1 and in opposition to the philosopher's paradox4 ,we may now at last indulge the comfortable belief that a body in motion is just as truly where it is as a body at rest4 ,motion consists merely in the fact that bodies are sometimes in one place and sometimes in another1 and that they are at intermediate places at intermediate times4 ,only those who have waded through the quagmire of philosophic speculation on this subject can realise what a liberation from antique prejudices is involved in this simple and straightforward commonplace4 ,the philosophy of the infinitesimal1 as we have just seen1 is mainly negative4 ,people used to believe in it1 and now they have found out their mistake4 ,the philosophy of the infinite1 on the other hand1 is wholly positive4 ,it was formerly supposed that infinite numbers1 and the mathematical infinite generally1 were self-contradictory4 ,but as it was obvious that there were infinities--for example1 the number of numbers--the contradictions of infinity seemed unavoidable1 and philosophy seemed to have wandered into a cul-de-sac4 ,this difficulty led to ,kant's antinomies1 and hence1 more or less indirectly1 to much of ,hegel's dialectic method4 ,almost all current philosophy is upset by the fact 7of which very few philosophers are as yet aware7 that all the ancient and respectable contradictions in the notion of the infinite have been once for all disposed of4 ,the method by which this has been done is most interesting and instructive4 ,in the first place1 though people had talked glibly about infinity ever since the beginnings of ,greek thought1 nobody had ever thought of asking1 ,what is infinity8 ,if any philosopher had been asked for a definition of infinity1 he might have produced some unintelligible rigmarole1 but he would certainly not have been able to give a definition that had any meaning at all4 ,twenty years ago1 roughly speaking1 ,dedekind and ,cantor asked this question1 and1 what is more remarkable1 they answered it4 ,they found1 that is to say1 a perfectly precise definition of an infinite number or an infinite collection of things4 ,this was the first and perhaps the greatest step4 ,it then remained to examine the supposed contradictions in this notion4 ,here ,cantor proceeded in the only proper way4 ,he took pairs of contradictory propositions1 in which both sides of the contradiction would be usually regarded as demonstrable1 and he strictly examined the supposed proofs4 ,he found that all proofs adverse to infinity involved a certain principle1 at first sight obviously true1 but destructive1 in its consequences1 of almost all mathematics4 ,the proofs favourable to infinity1 on the other hand1 involved no principle that had evil consequences4 ,it thus appeared that common sense had allowed itself to be taken in by a specious maxim1 and that1 when once this maxim was rejected1 all went well4 ,the maxim in question is1 that if one collection is part of another1 the one which is a part has fewer terms than the one of which it is a part4 ,this maxim is true of finite numbers4 ,for example1 ,englishmen are only some among ,europeans1 and there are fewer ,englishmen than ,europeans4 ,but when we come to infinite numbers1 this is no longer true4 ,this breakdown of the maxim gives us the precise definition of infinity4 ,a collection of terms is infinite when it contains as parts other collections which have just as many terms as it has4 ,if you can take away some of the terms of a collection1 without diminishing the number of terms1 then there are an infinite number of terms in the collection4 ,for example1 there are just as many even numbers as there are numbers altogether1 since every number can be doubled4 ,this may be seen by putting odd and even numbers together in one row1 and even numbers alone in a row below3-- #a1 #b1 #c1 #d1 #e1 ad infinitum4 #b1 #d1 #f1 #h1 #aj1 ad infinitum4 ,there are obviously just as many numbers in the row below as in the row above1 because there is one below for each one above4 ,this property1 which was formerly thought to be a contradiction1 is now transformed into a harmless definition of infinity1 and shows1 in the above case1 that the number of finite numbers is infinite4 ,but the uninitiated may wonder how it is possible to deal with a number which cannot be counted4 ,it is impossible to count up all the numbers1 one by one1 because1 however many we may count1 there are always more to follow4 ,the fact is that counting is a very vulgar and elementary way of finding out how many terms there are in a collection4 ,and in any case1 counting gives us what mathematicians call the ordinal number of our terms2 that is to say1 it arranges our terms in an order or series1 and its result tells us what type of series results from this arrangement4 ,in other words1 it is impossible to count things without counting some first and others afterwards1 so that counting always has to do with order4 ,now when there are only a finite number of terms1 we can count them in any order we like2 but when there are an infinite number1 what corresponds to counting will give us quite different results according to the way in which we carry out the operation4 ,thus the ordinal number1 which results from what1 in a general sense may be called counting1 depends not only upon how many terms we have1 but also 7where the number of terms is infinite7 upon the way in which the terms are arranged4 ,the fundamental infinite numbers are not ordinal1 but are what is called cardinal4 ,they are not obtained by putting our terms in order and counting them1 but by a different method1 which tells us1 to begin with1 whether two collections have the same number of terms1 or1 if not1 which is the greater4#ad ,it does not tell us1 in the way in which counting does1 what number of terms a collection has2 but if we define a number as the number of terms in such and such a collection1 then this method enables us to discover whether some other collection that may be mentioned has more or fewer terms4 ,an illustration will show how this is done4 ,if there existed some country in which1 for one reason or another1 it was impossible to take a census1 but in which it was known that every man had a wife and every woman a husband1 then 7provided polygamy was not a national institution7 we should know1 without counting1 that there were exactly as many men as there were women in that country1 neither more nor less4 ,this method can be applied generally4 ,if there is some relation which1 like marriage1 connects the things in one collection each with one of the things in another collection1 and vice versa1 then the two collections have the same number of terms4 ,this was the way in which we found that there are as many even numbers as there are numbers4 ,every number can be doubled1 and every even number can be halved1 and each process gives just one number corresponding to the one that is doubled or halved4 ,and in this way we can find any number of collections each of which has just as many terms as there are finite numbers4 ,if every term of a collection can be hooked on to a number1 and all the finite numbers are used once1 and only once1 in the process1 then our collection must have just as many terms as there are finite numbers4 ,this is the general method by which the numbers of infinite collections are defined4 ,but it must not be supposed that all infinite numbers are equal4 ,on the contrary1 there are infinitely more infinite numbers than finite ones4 ,there are more ways of arranging the finite numbers in different types of series than there are finite numbers4 ,there are probably more points in space and more moments in time than there are finite numbers4 ,there are exactly as many fractions as whole numbers1 although there are an infinite number of fractions between any two whole numbers4 ,but there are more irrational numbers than there are whole numbers or fractions4 ,there are probably exactly as many points in space as there are irrational numbers1 and exactly as many points on a line a millionth of an inch long as in the whole of infinite space4 ,there is a greatest of all infinite numbers1 which is the number of things altogether1 of every sort and kind4 ,it is obvious that there cannot be a greater number than this1 because1 if everything has been taken1 there is nothing left to add4 ,cantor has a proof that there is no greatest number1 and if this proof were valid1 the contradictions of infinity would reappear in a sublimated form4 ,but in this one point1 the master has been guilty of a very subtle fallacy1 which ,i hope to explain in some future work4#ae ,we can now understand why ,zeno believed that ,achilles cannot overtake the tortoise and why as a matter of fact he can overtake it4 ,we shall see that all the people who disagreed with ,zeno had no right to do so1 because they all accepted premises from which his conclusion followed4 ,the argument is this3 ,let ,achilles and the tortoise start along a road at the same time1 the tortoise 7as is only fair7 being allowed a handicap4 ,let ,achilles go twice as fast as the tortoise1 or ten times or a hundred times as fast4 ,then he will never reach the tortoise4 ,for at every moment the tortoise is somewhere and ,achilles is somewhere2 and neither is ever twice in the same place while the race is going on4 ,thus the tortoise goes to just as many places as ,achilles does1 because each is in one place at one moment1 and in another at any other moment4 ,but if ,achilles were to catch up with the tortoise1 the places where the tortoise would have been would be only part of the places where ,achilles would have been4 ,here1 we must suppose1 ,zeno appealed to the maxim that the whole has more terms than the part4#af ,thus if ,achilles were to overtake the tortoise1 he would have been in more places than the tortoise2 but we saw that he must1 in any period1 be in exactly as many places as the tortoise4 ,hence we infer that he can never catch the tortoise4 ,this argument is strictly correct1 if we allow the axiom that the whole has more terms than the part4 ,as the conclusion is absurd1 the axiom must be rejected1 and then all goes well4 ,but there is no good word to be said for the philosophers of the past two thousand years and more1 who have all allowed the axiom and denied the conclusion4 ,the retention of this axiom leads to absolute contradictions1 while its rejection leads only to oddities4 ,some of these oddities1 it must be confessed1 are very odd4 ,one of them1 which ,i call the paradox of ,tristram ,shandy1 is the converse of the ,achilles1 and shows that the tortoise1 if you give him time1 will go just as far as ,achilles4 ,tristram ,shandy1 as we know1 employed two years in chronicling the first two days of his life1 and lamented that1 at this rate1 material would accumulate faster than he could deal with it1 so that1 as years went by1 he would be farther and farther from the end of his history4 ,now ,i maintain that1 if he had lived for ever1 and had not wearied of his task1 then1 even if his life had continued as event fully as it began1 no part of his biography would have remained unwritten4 ,for consider3 the hundredth day will be described in the hundredth year1 the thousandth in the thousandth year1 and so on4 ,whatever day we may choose as so far on that he cannot hope to reach it1 that day will be described in the corresponding year4 ,thus any day that may be mentioned will be written up sooner or later1 and therefore no part of the biography will remain permanently unwritten4 ,this paradoxical but perfectly true proposition depends upon the fact that the number of days in all time is no greater than the number of years4 ,thus on the subject of infinity it is impossible to avoid conclusions which at first sight appear paradoxical1 and this is the reason why so many philosophers have supposed that there were inherent contradictions in the infinite4 ,but a little practice enables one to grasp the true principles of ,cantor's doctrine1 and to acquire new and better instincts as to the true and the false4 ,the oddities then become no odder than the people at the antipodes1 who used to be thought impossible because they would find it so inconvenient to stand on their heads4 ,the solution of the problems concerning infinity has enabled ,cantor to solve also the problems of continuity4 ,of this1 as of infinity1 he has given a perfectly precise definition1 and has shown that there are no contradictions in the notion so defined4 ,but this subject is so technical that it is impossible to give any account of it here4 ,the notion of continuity depends upon that of order1 since continuity is merely a particular type of order4 ,mathematics has1 in modern times1 brought order into greater and greater prominence4 ,in former days1 it was supposed 7and philosophers are still apt to suppose7 that quantity was the fundamental notion of mathematics4 ,but nowadays1 quantity is banished altogether1 except from one little corner of ,geometry1 while order more and more reigns supreme4 ,the investigation of different kinds of series and their relations is now a very large part of mathematics1 and it has been found that this investigation can be conducted without any reference to quantity1 and1 for the most part1 without any reference to number4 ,all types of series are capable of formal definition1 and their properties can be deduced from the principles of symbolic logic by means of the ,algebra of ,relatives4 ,the notion of a limit1 which is fundamental in the greater part of higher mathematics1 used to be defined by means of quantity1 as a term to which the terms of some series approximate as nearly as we please4 ,but nowadays the limit is defined quite differently1 and the series which it limits may not approximate to it at all4 ,this improvement also is due to ,cantor1 and it is one which has revolutionised mathematics4 ,only order is now relevant to limits4 ,thus1 for instance1 the smallest of the infinite integers is the limit of the finite integers1 though all finite integers are at an infinite distance from it4 ,the study of different types of series is a general subject of which the study of ordinal numbers 7mentioned above7 is a special and very interesting branch4 ,but the unavoidable technicalities of this subject render it impossible to explain to any but professed mathematicians4 ,geometry1 like ,arithmetic1 has been subsumed1 in recent times1 under the general study of order4 ,it was formerly supposed that ,geometry was the study of the nature of the space in which we live1 and accordingly it was urged1 by those who held that what exists can only be known empirically1 that ,geometry should really be regarded as belonging to applied mathematics4 ,but it has gradually appeared1 by the increase of non-,euclidean systems1 that ,geometry throws no more light upon the nature of space than ,arithmetic throws upon the population of the ,united ,states4 ,geometry is a whole collection of deductive sciences based on a corresponding collection of sets of axioms4 ,one set of axioms is ,euclid's2 other equally good sets of axioms lead to other results4 ,whether ,euclid's axioms are true1 is a question as to which the pure mathematician is indifferent2 and1 what is more1 it is a question which it is theoretically impossible to answer with certainty in the affirmative4 ,it might possibly be shown1 by very careful measurements1 that ,euclid's axioms are false2 but no measurements could ever assure us 7owing to the errors of observation7 that they are exactly true4 ,thus the geometer leaves to the man of science to decide1 as best he may1 what axioms are most nearly true in the actual world4 ,the geometer takes any set of axioms that seem interesting1 and deduces their consequences4 ,what defines ,geometry1 in this sense1 is that the axioms must give rise to a series of more than one dimension4 ,and it is thus that ,geometry becomes a department in the study of order4 ,in ,geometry1 as in other parts of mathematics1 ,peano and his disciples have done work of the very greatest merit as regards principles4 ,formerly1 it was held by philosophers and mathematicians alike that the proofs in ,geometry depended on the figure2 nowadays1 this is known to be false4 ,in the best books there are no figures at all4 ,the reasoning proceeds by the strict rules of formal logic from a set of axioms laid down to begin with4 ,if a figure is used1 all sorts of things seem obviously to follow1 which no formal reasoning can prove from the explicit axioms1 and which1 as a matter of fact1 are only accepted because they are obvious4 ,by banishing the figure1 it becomes possible to discover all the axioms that are needed2 and in this way all sorts of possibilities1 which would have otherwise remained undetected1 are brought to light4 ,one great advance1 from the point of view of correctness1 has been made by introducing points as they are required1 and not starting1 as was formerly done1 by assuming the whole of space4 ,this method is due partly to ,peano1 partly to another ,italian named ,fano4 ,to those unaccustomed to it1 it has an air of somewhat wilful pedantry4 ,in this way1 we begin with the following axioms3 7#a7 ,there is a class of entities called points4 7#b7 ,there is at least one point4 7#c7 ,if a be a point1 there is at least one other point besides a4 ,then we bring in the straight line joining two points1 and begin again with 7#d71 namely1 on the straight line joining a and b1 there is at least one other point besides a and b4 7#e7 ,there is at least one point not on the line ab4 ,and so we go on1 till we have the means of obtaining as many points as we require4 ,but the word space1 as ,peano humorously remarks1 is one for which ,geometry has no use at all4 ,the rigid methods employed by modern geometers have deposed ,euclid from his pinnacle of correctness4 ,it was thought1 until recent times1 that1 as ,sir ,henry ,savile remarked in #afba1 there were only two blemishes in ,euclid1 the theory of parallels and the theory of proportion4 ,it is now known that these are almost the only points in which ,euclid is free from blemish4 ,countless errors are involved in his first eight propositions4 ,that is to say1 not only is it doubtful whether his axioms are true1 which is a comparatively trivial matter1 but it is certain that his propositions do not follow from the axioms which he enunciates4 ,a vastly greater number of axioms1 which ,euclid unconsciously employs1 are required for the proof of his propositions4 ,even in the first proposition of all1 where he constructs an equilateral triangle on a given base1 he uses two circles which are assumed to intersect4 ,but no explicit axiom assures us that they do so1 and in some kinds of spaces they do not always intersect4 ,it is quite doubtful whether our space belongs to one of these kinds or not4 ,thus ,euclid fails entirely to prove his point in the very first proposition4 ,as he is certainly not an easy author1 and is terribly long-winded1 he has no longer any but an historical interest4 ,under these circumstances1 it is nothing less than a scandal that he should still be taught to boys in ,england4#ag ,a book should have either intelligibility or correctness2 to combine the two is impossible1 but to lack both is to be unworthy of such a place as ,euclid has occupied in education4 ,the most remarkable result of modern methods in mathematics is the importance of symbolic logic and of rigid formalism4 ,mathematicians1 under the influence of ,weierstrass1 have shown in modern times a care for accuracy1 and an aversion to slipshod reasoning1 such as had not been known among them previously since the time of the ,greeks4 ,the great inventions of the seventeenth century--,analytical ,geometry and the ,infinitesimal ,calculus--were so fruitful in new results that mathematicians had neither time nor inclination to examine their foundations4 ,philosophers1 who should have taken up the task1 had too little mathematical ability to invent the new branches of mathematics which have now been found necessary for any adequate discussion4 ,thus mathematicians were only awakened from their dogmatic slumbers when ,weierstrass and his followers showed that many of their most cherished propositions are in general false4 ,macaulay1 contrasting the certainty of mathematics with the uncertainty of philosophy1 asks who ever heard of a reaction against ,taylor's theorem8 ,if he had lived now1 he himself might have heard of such a reaction1 for this is precisely one of the theorems which modern investigations have overthrown4 ,such rude shocks to mathematical faith have produced that love of formalism which appears1 to those who are ignorant of its motive1 to be mere outrageous pedantry4 ,the proof that all pure mathematics1 including ,geometry1 is nothing but formal logic1 is a fatal blow to the ,kantian philosophy4 ,kant1 rightly perceiving that ,euclid's propositions could not be deduced from ,euclid's axioms without the help of the figures1 invented a theory of knowledge to account for this fact2 and it accounted so successfully that1 when the fact is shown to be a mere defect in ,euclid1 and not a result of the nature of geometrical reasoning1 ,kant's theory also has to be abandoned4 ,the whole doctrine of a priori intuitions1 by which ,kant explained the possibility of pure mathematics1 is wholly inapplicable to mathematics in its present form4 ,the ,aristotelian doctrines of the schoolmen come nearer in spirit to the doctrines which modern mathematics inspire2 but the schoolmen were hampered by the fact that their formal logic was very defective1 and that the philosophical logic based upon the syllogism showed a corresponding narrowness4 ,what is now required is to give the greatest possible development to mathematical logic1 to allow to the full the importance of relations1 and then to found upon this secure basis a new philosophical logic1 which may hope to borrow some of the exactitude and certainty of its mathematical foundation4 ,if this can be successfully accomplished1 there is every reason to hope that the near future will be as great an epoch in pure philosophy as the immediate past has been in the principles of mathematics4 ,great triumphs inspire great hopes2 and pure thought may achieve1 within our generation1 such results as will place our time1 in this respect1 on a level with the greatest age of ,greece4#ah ,,footnotes3 #aa ,this subject is due in the main to ,mr4 ,c4,s4 ,peirce4 #ab ,i ought to have added ,frege1 but his writings were unknown to me when this article was written4 ,note added in #aiag4 #ac ,professor of ,mathematics in the ,university of ,berlin4 ,he died in #ahig4 #ad ,note added in #aiag4 ,although some infinite numbers are greater than some others1 it cannot be proved that of any two infinite numbers one must be the greater4 #ae ,cantor was not guilty of a fallacy on this point4 ,his proof that there is no greatest number is valid4 ,the solution of the puzzle is complicated and depends upon the theory of types1 which is explained in ,principia ,mathematica1 ,vol4 ,i 7,camb4 ,univ4 ,press1 #aiaj74 ,note added in #aiag4 #af ,this must not be regarded as a historically correct account of what ,zeno actually had in mind4 ,it is a new argument for his conclusion1 not the argument which influenced him4 ,on this point1 see e4g4 ,c4,d4 ,broad1 ,note on ,achilles and the ,tortoise1 ,mind1 ,n4,s41 ,vol4 ,,xxii1 pp4 #cah-ai4 ,much valuable work on the interpretation of ,zeno has been done since this article was written4 ,note added in #aiag4 #ag ,since the above was written1 he has ceased to be used as a textbook4 ,but ,i fear many of the books now used are so bad that the change is no great improvement4 ,note added in #aiag4 #ah ,the greatest age of ,greece was brought to an end by the ,peloponnesian ,war4 ,note added in #aiag4 ,,vi ,,on ,,scientific ,,method ,,in ,,philosophy ,when we try to ascertain the motives which have led men to the investigation of philosophical questions1 we find that1 broadly speaking1 they can be divided into two groups1 often antagonistic1 and leading to very divergent systems4 ,these two groups of motives are1 on the one hand1 those derived from religion and ethics1 and1 on the other hand1 those derived from science4 ,plato1 ,spinoza1 and ,hegel may be taken as typical of the philosophers whose interests are mainly religious and ethical1 while ,leibniz1 ,locke1 and ,hume may be taken as representatives of the scientific wing4 ,in ,aristotle1 ,descartes1 ,berkeley1 and ,kant we find both groups of motives strongly present4 ,herbert ,spencer1 in whose honour we are assembled to-day1 would naturally be classed among scientific philosophers3 it was mainly from science that he drew his data1 his formulation of problems1 and his conception of method4 ,but his strong religious sense is obvious in much of his writing1 and his ethical pre-occupations are what make him value the conception of evolution--that conception in which1 as a whole generation has believed1 science and morals are to be united in fruitful and indissoluble marriage4 ,it is my belief that the ethical and religious motives in spite of the splendidly imaginative systems to which they have given rise1 have been on the whole a hindrance to the progress of philosophy1 and ought now to be consciously thrust aside by those who wish to discover philosophical truth4 ,science1 originally1 was entangled in similar motives1 and was thereby hindered in its advances4 ,it is1 ,i maintain1 from science1 rather than from ethics and religion1 that philosophy should draw its inspiration4 ,but there are two different ways in which a philosophy may seek to base itself upon science4 ,it may emphasise the most general results of science1 and seek to give even greater generality and unity to these results4 ,or it may study the methods of science1 and seek to apply these methods1 with the necessary adaptations1 to its own peculiar province4 ,much philosophy inspired by science has gone astray through preoccupation with the results momentarily supposed to have been achieved4 ,it is not results1 but methods that can be transferred with profit from the sphere of the special sciences to the sphere of philosophy4 ,what ,i wish to bring to your notice is the possibility and importance of applying to philosophical problems certain broad principles of method which have been found successful in the study of scientific questions4 ,the opposition between a philosophy guided by scientific method and a philosophy dominated by religious and ethical ideas may be illustrated by two notions which are very prevalent in the works of philosophers1 namely the notion of the universe1 and the notion of good and evil4 ,a philosopher is expected to tell us something about the nature of the universe as a whole1 and to give grounds for either optimism or pessimism4 ,both these expectations seem to me mistaken4 ,i believe the conception of the universe to be1 as its etymology indicates1 a mere relic of pre-,copernican astronomy3 and ,i believe the question of optimism and pessimism to be one which the philosopher will regard as outside his scope1 except1 possibly1 to the extent of maintaining that it is insoluble4 ,in the days before ,copernicus1 the conception of the universe was defensible on scientific grounds3 the diurnal revolution of the heavenly bodies bound them together as all parts of one system1 of which the earth was the centre4 ,round this apparent scientific fact1 many human desires rallied3 the wish to believe ,man important in the scheme of things1 the theoretical desire for a comprehensive understanding of the ,whole1 the hope that the course of nature might be guided by some sympathy with our wishes4 ,in this way1 an ethically inspired system of metaphysics grew up1 whose anthropocentrism was apparently warranted by the geocentrism of astronomy4 ,when ,copernicus swept away the astronomical basis of this system of thought1 it had grown so familiar1 and had associated itself so intimately with men's aspirations1 that it survived with scarcely diminished force--survived even ,kant's ,copernican revolution1 and is still now the unconscious premiss of most metaphysical systems4 ,the oneness of the world is an almost undiscussed postulate of most metaphysics4 ,reality is not merely one and self-consistent1 but is a system of reciprocally determinate parts#ai--such a statement would pass almost unnoticed as a mere truism4 ,yet ,i believe that it embodies a failure to effect thoroughly the ,copernican revolution1 and that the apparent oneness of the world is merely the oneness of what is seen by a single spectator or apprehended by a single mind4 ,the ,critical ,philosophy1 although it intended to emphasise the subjective element in many apparent characteristics of the world1 yet1 by regarding the world in itself as unknowable1 so concentrated attention upon the subjective representation that its subjectivity was soon forgotten4 ,having recognised the categories as the work of the mind1 it was paralysed by its own recognition1 and abandoned in despair the attempt to undo the work of subjective falsification4 ,in part1 no doubt1 its despair was well founded1 but not1 ,i think1 in any absolute or ultimate sense4 ,still less was it a ground for rejoicing1 or for supposing that the nescience to which it ought to have given rise could be legitimately exchanged for a metaphysical dogmatism4 ,i ,as regards our present question1 namely1 the question of the unity of the world1 the right method1 as ,i think1 has been indicated by ,william ,james4#bj ,let us now turn our backs upon ineffable or unintelligible ways of accounting for the world's oneness1 and inquire whether1 instead of being a principle1 the 'oneness' affirmed may not merely be a name like 'substance' descriptive of the fact that certain specific and verifiable connections are found among the parts of the experiential flux4444 ,we can easily conceive of things that shall have no connection whatever with each other4 ,we may assume them to inhabit different times and spaces1 as the dreams of different persons do even now4 ,they may be so unlike and incommensurable1 and so inert towards one another1 as never to jostle or interfere4 ,even now there may actually be whole universes so disparate from ours that we who know ours have no means of perceiving that they exist4 ,we conceive their diversity1 however2 and by that fact the whole lot of them form what is known in logic as 'a universe of discourse4' ,to form a universe of discourse argues1 as this example shows1 no further kind of connexion4 ,the importance attached by certain monistic writers to the fact that any chaos may become a universe by merely being named1 is to me incomprehensible4 ,we are thus left with two kinds of unity in the experienced world2 the one what we may call the epistemological unity1 due merely to the fact that my experienced world is what one experience selects from the sum total of existence3 the other that tentative and partial unity exhibited in the prevalence of scientific laws in those portions of the world which science has hitherto mastered4 ,now a generalisation based upon either of these kinds of unity would be fallacious4 ,that the things which we experience have the common property of being experienced by us is a truism from which obviously nothing of importance can be deducible3 it is clearly fallacious to draw from the fact that whatever we experience is experienced the conclusion that therefore everything must be experienced4 ,the generalisation of the second kind of unity1 namely1 that derived from scientific laws1 would be equally fallacious1 though the fallacy is a trifle less elementary4 ,in order to explain it let us consider for a moment what is called the reign of law4 ,people often speak as though it were a remarkable fact that the physical world is subject to invariable laws4 ,in fact1 however1 it is not easy to see how such a world could fail to obey general laws4 ,taking any arbitrary set of points in space1 there is a function of the time corresponding to these points1 i4e4 expressing the motion of a particle which traverses these points3 this function may be regarded as a general law to which the behaviour of such a particle is subject4 ,taking all such functions for all the particles in the universe1 there will be theoretically some one formula embracing them all1 and this formula may be regarded as the single and supreme law of the spatio-temporal world4 ,thus what is surprising in physics is not the existence of general laws1 but their extreme simplicity4 ,it is not the uniformity of nature that should surprise us1 for1 by sufficient analytic ingenuity1 any conceivable course of nature might be shown to exhibit uniformity4 ,what should surprise us is the fact that the uniformity is simple enough for us to be able to discover it4 ,but it is just this characteristic of simplicity in the laws of nature hitherto discovered which it would be fallacious to generalise1 for it is obvious that simplicity has been a part cause of their discovery1 and can1 therefore1 give no ground for the supposition that other undiscovered laws are equally simple4 ,the fallacies to which these two kinds of unity have given rise suggest a caution as regards all use in philosophy of general results that science is supposed to have achieved4 ,in the first place1 in generalising these results beyond past experience1 it is necessary to examine very carefully whether there is not some reason making it more probable that these results should hold of all that has been experienced than that they should hold of things universally4 ,the sum total of what is experienced by mankind is a selection from the sum total of what exists1 and any general character exhibited by this selection may be due to the manner of selecting rather than to the general character of that from which experience selects4 ,in the second place1 the most general results of science are the least certain and the most liable to be upset by subsequent research4 ,in utilizing these results as the basis of a philosophy1 we sacrifice the most valuable and remarkable characteristic of scientific method1 namely1 that1 although almost everything in science is found sooner or later to require some correction1 yet this correction is almost always such as to leave untouched1 or only slightly modified1 the greater part of the results which have been deduced from the premiss subsequently discovered to be faulty4 ,the prudent man of science acquires a certain instinct as to the kind of uses which may be made of present scientific beliefs without incurring the danger of complete and utter refutation from the modifications likely to be introduced by subsequent discoveries4 ,unfortunately the use of scientific generalisations of a sweeping kind as the basis of philosophy is just that kind of use which an instinct of scientific caution would avoid1 since1 as a rule1 it would only lead to true results if the generalisation upon which it is based stood in no need of correction4 ,we may illustrate these general considerations by means of two examples1 namely1 the conservation of energy and the principle of evolution4 7#a7 ,let us begin with the conservation of energy1 or1 as ,herbert ,spencer used to call it1 the persistence of force4 ,he says3#ba ,before taking a first step in the rational interpretation of ,evolution1 it is needful to recognise1 not only the facts that ,matter is indestructible and ,motion continuous1 but also the fact that ,force persists4 ,an attempt to assign the causes of ,evolution would manifestly be absurd if that agency to which the metamorphosis in general and in detail is due1 could either come into existence or cease to exist4 ,the succession of phenomena would in such case be altogether arbitrary1 and deductive ,science impossible4 ,this paragraph illustrates the kind of way in which the philosopher is tempted to give an air of absoluteness and necessity to empirical generalisations1 of which only the approximate truth in the regions hitherto investigated can be guaranteed by the unaided methods of science4 ,it is very often said that the persistence of something or other is a necessary presupposition of all scientific investigation1 and this presupposition is then thought to be exemplified in some quantity which physics declares to be constant4 ,there are here1 as it seems to me1 three distinct errors4 ,first1 the detailed scientific investigation of nature does not presuppose any such general laws as its results are found to verify4 ,apart from particular observations1 science need presuppose nothing except the general principles of logic1 and these principles are not laws of nature1 for they are merely hypothetical1 and apply not only to the actual world but to whatever is possible4 ,the second error consists in the identification of a constant quantity with a persistent entity4 ,energy is a certain function of a physical system1 but is not a thing or substance persisting throughout the changes of the system4 ,the same is true of mass1 in spite of the fact that mass has often been defined as quantity of matter4 ,the whole conception of quantity1 involving1 as it does1 numerical measurement based largely upon conventions1 is far more artificial1 far more an embodiment of mathematical convenience1 than is commonly believed by those who philosophise on physics4 ,thus even if 7which ,i cannot for a moment admit7 the persistence of some entity were among the necessary postulates of science1 it would be a sheer error to infer from this the constancy of any physical quantity1 or the a priori necessity of any such constancy which may be empirically discovered4 ,in the third place1 it has become more and more evident with the progress of physics that large generalisations1 such as the conservation of energy or mass1 are far from certain and are very likely only approximate4 ,mass1 which used to be regarded as the most indubitable of physical quantities1 is now generally believed to vary according to velocity1 and to be1 in fact1 a vector quantity which at a given moment is different in different directions4 ,the detailed conclusions deduced from the supposed constancy of mass for such motions as used to be studied in physics will remain very nearly exact1 and therefore over the field of the older investigations very little modification of the older results is required4 ,but as soon as such a principle as the conservation of mass or of energy is erected into a universal a priori law1 the slightest failure in absolute exactness is fatal1 and the whole philosophic structure raised upon this foundation is necessarily ruined4 ,the prudent philosopher1 therefore1 though he may with advantage study the methods of physics1 will be very chary of basing anything upon what happen at the moment to be the most general results apparently obtained by those methods4 7#b7 ,the philosophy of evolution1 which was to be our second example1 illustrates the same tendency to hasty generalisation1 and also another sort1 namely1 the undue preoccupation with ethical notions4 ,there are two kinds of evolutionist philosophy1 of which both ,hegel and ,spencer represent the older and less radical kind1 while ,pragmatism and ,bergson represent the more modern and revolutionary variety4 ,but both these sorts of evolutionism have in common the emphasis on progress1 that is1 upon a continual change from the worse to the better1 or from the simpler to the more complex4 ,it would be unfair to attribute to ,hegel any scientific motive or foundation1 but all the other evolutionists1 including ,hegel's modern disciples1 have derived their impetus very largely from the history of biological development4 ,to a philosophy which derives a law of universal progress from this history there are two objections4 ,first1 that this history itself is concerned with a very small selection of facts confined to an infinitesimal fragment of space and time1 and even on scientific grounds probably not an average sample of events in the world at large4 ,for we know that decay as well as growth is a normal occurrence in the world4 ,an extra-terrestrial philosopher1 who had watched a single youth up to the age of twenty-one and had never come across any other human being1 might conclude that it is the nature of human beings to grow continually taller and wiser in an indefinite progress towards perfection2 and this generalisation would be just as well founded as the generalisation which evolutionists base upon the previous history of this planet4 ,apart1 however1 from this scientific objection to evolutionism1 there is another1 derived from the undue admixture of ethical notions in the very idea of progress from which evolutionism derives its charm4 ,organic life1 we are told1 has developed gradually from the protozoon to the philosopher1 and this development1 we are assured1 is indubitably an advance4 ,unfortunately it is the philosopher1 not the protozoon1 who gives us this assurance1 and we can have no security that the impartial outsider would agree with the philosopher's self-complacent assumption4 ,this point has been illustrated by the philosopher ,chuang ,tz7u in the following instructive anecdote3 ,the ,grand ,augur1 in his ceremonial robes1 approached the shambles and thus addressed the pigs3 ',how can you object to die8 ,i shall fatten you for three months4 ,i shall discipline myself for ten days and fast for three4 ,i shall strew fine grass1 and place you bodily upon a carved sacrificial dish4 ,does not this satisfy you8' ,then1 speaking from the pigs' point of view1 he continued3 ',it is better1 perhaps1 after all1 to live on bran and escape the shambles4444' ',but then1' added he1 speaking from his own point of view1 'to enjoy honour when alive one would readily die on a war-shield or in the headsman's basket4' ,so he rejected the pigs' point of view and adopted his own point of view4 ,in what sense1 then1 was he different from the pigs8 ,i much fear that the evolutionists too often resemble the ,grand ,augur and the pigs4 ,the ethical element which has been prominent in many of the most famous systems of philosophy is1 in my opinion1 one of the most serious obstacles to the victory of scientific method in the investigation of philosophical questions4 ,human ethical notions1 as ,chuang ,tz7u perceived1 are essentially anthropocentric1 and involve1 when used in metaphysics1 an attempt1 however veiled1 to legislate for the universe on the basis of the present desires of men4 ,in this way they interfere with that receptivity to fact which is the essence of the scientific attitude towards the world4 ,to regard ethical notions as a key to the understanding of the world is essentially pre-,copernican4 ,it is to make man1 with the hopes and ideals which he happens to have at the present moment1 the centre of the universe and the interpreter of its supposed aims and purposes4 ,ethical metaphysics is fundamentally an attempt1 however disguised1 to give legislative force to our own wishes4 ,this may1 of course1 be questioned1 but ,i think that it is confirmed by a consideration of the way in which ethical notions arise4 ,ethics is essentially a product of the gregarious instinct1 that is to say1 of the instinct to co-operate with those who are to form our own group against those who belong to other groups4 ,those who belong to our own group are good2 those who belong to hostile groups are wicked4 ,the ends which are pursued by our own group are desirable ends1 the ends pursued by hostile groups are nefarious4 ,the subjectivity of this situation is not apparent to the gregarious animal1 which feels that the general principles of justice are on the side of its own herd4 ,when the animal has arrived at the dignity of the metaphysician1 it invents ethics as the embodiment of its belief in the justice of its own herd4 ,so the ,grand ,augur invokes ethics as the justification of ,augurs in their conflicts with pigs4 ,but1 it may be said1 this view of ethics takes no account of such truly ethical notions as that of self-sacrifice4 ,this1 however1 would be a mistake4 ,the success of gregarious animals in the struggle for existence depends upon co-operation within the herd1 and co-operation requires sacrifice1 to some extent1 of what would otherwise be the interest of the individual4 ,hence arises a conflict of desires and instincts1 since both self-preservation and the preservation of the herd are biological ends to the individual4 ,ethics is in origin the art of recommending to others the sacrifices required for co-operation with oneself4 ,hence1 by reflexion1 it comes1 through the operation of social justice1 to recommend sacrifices by oneself1 but all ethics1 however refined1 remains more or less subjective4 ,even vegetarians do not hesitate1 for example1 to save the life of a man in a fever1 although in doing so they destroy the lives of many millions of microbes4 ,the view of the world taken by the philosophy derived from ethical notions is thus never impartial and therefore never fully scientific4 ,as compared with science1 it fails to achieve the imaginative liberation from self which is necessary to such understanding of the world as man can hope to achieve1 and the philosophy which it inspires is always more or less parochial1 more or less infected with the prejudices of a time and a place4 ,i do not deny the importance or value1 within its own sphere1 of the kind of philosophy which is inspired by ethical notions4 ,the ethical work of ,spinoza1 for example1 appears to me of the very highest significance1 but what is valuable in such work is not any metaphysical theory as to the nature of the world to which it may give rise1 nor indeed anything which can be proved or disproved by argument4 ,what is valuable is the indication of some new way of feeling towards life and the world1 some way of feeling by which our own existence can acquire more of the characteristics which we must deeply desire4 ,the value of such work1 however immeasurable it is1 belongs with practice and not with theory4 ,such theoretic importance as it may possess is only in relation to human nature1 not in relation to the world at large4 ,the scientific philosophy1 therefore1 which aims only at understanding the world and not directly at any other improvement of human life1 cannot take account of ethical notions without being turned aside from that submission to fact which is the essence of the scientific temper4 ,,ii ,if the notion of the universe and the notion of good and evil are extruded from scientific philosophy1 it may be asked what specific problems remain for the philosopher as opposed to the man of science8 ,it would be difficult to give a precise answer to this question1 but certain characteristics may be noted as distinguishing the province of philosophy from that of the special sciences4 ,in the first place a philosophical proposition must be general4 ,it must not deal specially with things on the surface of the earth1 or with the solar system1 or with any other portion of space and time4 ,it is this need of generality which has led to the belief that philosophy deals with the universe as a whole4 ,i do not believe that this belief is justified1 but ,i do believe that a philosophical proposition must be applicable to everything that exists or may exist4 ,it might be supposed that this admission would be scarcely distinguishable from the view which ,i wish to reject4 ,this1 however1 would be an error1 and an important one4 ,the traditional view would make the universe itself the subject of various predicates which could not be applied to any particular thing in the universe1 and the ascription of such peculiar predicates to the universe would be the special business of philosophy4 ,i maintain1 on the contrary1 that there are no propositions of which the universe is the subject2 in other words1 that there is no such thing as the universe4 ,what ,i do maintain is that there are general propositions which may be asserted of each individual thing1 such as the propositions of logic4 ,this does not involve that all the things there are form a whole which could be regarded as another thing and be made the subject of predicates4 ,it involves only the assertion that there are properties which belong to each separate thing1 not that there are properties belonging to the whole of things collectively4 ,the philosophy which ,i wish to advocate may be called logical atomism or absolute pluralism1 because1 while maintaining that there are many things1 it denies that there is a whole composed of those things4 ,we shall see1 therefore1 that philosophical propositions1 instead of being concerned with the whole of things collectively1 are concerned with all things distributively2 and not only must they be concerned with all things1 but they must be concerned with such properties of all things as do not depend upon the accidental nature of the things that there happen to be1 but are true of any possible world1 independently of such facts as can only be discovered by our senses4 ,this brings us to a second characteristic of philosophical propositions1 namely1 that they must be a priori4 ,a philosophical proposition must be such as can be neither proved nor disproved by empirical evidence4 ,too often we find in philosophical books arguments based upon the course of history1 or the convolutions of the brain1 or the eyes of shell-fish4 ,special and accidental facts of this kind are irrelevant to philosophy1 which must make only such assertions as would be equally true however the actual world were constituted4 ,we may sum up these two characteristics of philosophical propositions by saying that philosophy is the science of the possible4 ,but this statement unexplained is liable to be misleading1 since it may be thought that the possible is something other than the general1 whereas in fact the two are indistinguishable4 ,philosophy1 if what has been said is correct1 becomes indistinguishable from logic as that word has now come to be used4 ,the study of logic consists1 broadly speaking1 of two not very sharply distinguished portions4 ,on the one hand it is concerned with those general statements which can be made concerning everything without mentioning any one thing or predicate or relation1 such for example as if x is a member of the class alpha and every member of alpha is a member of beta1 then x is a member of the class beta1 whatever x1 alpha1 and beta may be4 ,on the other hand1 it is concerned with the analysis and enumeration of logical forms1 i4e4 with the kinds of propositions that may occur1 with the various types of facts1 and with the classification of the constituents of facts4 ,in this way logic provides an inventory of possibilities1 a repertory of abstractly tenable hypotheses4 ,it might be thought that such a study would be too vague and too general to be of any very great importance1 and that1 if its problems became at any point sufficiently definite1 they would be merged in the problems of some special science4 ,it appears1 however1 that this is not the case4 ,in some problems1 for example1 the analysis of space and time1 the nature of perception1 or the theory of judgment1 the discovery of the logical form of the facts involved is the hardest part of the work and the part whose performance has been most lacking hitherto4 ,it is chiefly for want of the right logical hypothesis that such problems have hitherto been treated in such an unsatisfactory manner1 and have given rise to those contradictions or antinomies in which the enemies of reason among philosophers have at all times delighted4 ,by concentrating attention upon the investigation of logical forms1 it becomes possible at last for philosophy to deal with its problems piecemeal1 and to obtain1 as the sciences do1 such partial and probably not wholly correct results as subsequent investigation can utilise even while it supplements and improves them4 ,most philosophies hitherto have been constructed all in one block1 in such a way that1 if they were not wholly correct1 they were wholly incorrect1 and could not be used as a basis for further investigations4 ,it is chiefly owing to this fact that philosophy1 unlike science1 has hitherto been unprogressive1 because each original philosopher has had to begin the work again from the beginning1 without being able to accept anything definite from the work of his predecessors4 ,a scientific philosophy such as ,i wish to recommend will be piecemeal and tentative like other sciences2 above all1 it will be able to invent hypotheses which1 even if they are not wholly true1 will yet remain fruitful after the necessary corrections have been made4 ,this possibility of successive approximations to the truth is1 more than anything else1 the source of the triumphs of science1 and to transfer this possibility to philosophy is to ensure a progress in method whose importance it would be almost impossible to exaggerate4 ,the essence of philosophy as thus conceived is analysis1 not synthesis4 ,to build up systems of the world1 like ,heine's ,german professor who knit together fragments of life and made an intelligible system out of them1 is not1 ,i believe1 any more feasible than the discovery of the philosopher's stone4 ,what is feasible is the understanding of general forms1 and the division of traditional problems into a number of separate and less baffling questions4 ,divide and conquer is the maxim of success here as elsewhere4 ,let us illustrate these somewhat general maxims by examining their application to the philosophy of space1 for it is only in application that the meaning or importance of a method can be understood4 ,suppose we are confronted with the problem of space as presented in ,kant's ,transcendental sthetic1 and suppose we wish to discover what are the elements of the problem and what hope there is of obtaining a solution of them4 ,it will soon appear that three entirely distinct problems1 belonging to different studies1 and requiring different methods for their solution1 have been confusedly combined in the supposed single problem with which ,kant is concerned4 ,there is a problem of logic1 a problem of physics1 and a problem of theory of knowledge4 ,of these three1 the problem of logic can be solved exactly and perfectly2 the problem of physics can probably be solved with as great a degree of certainty and as great an approach to exactness as can be hoped in an empirical region2 the problem of theory of knowledge1 however1 remains very obscure and very difficult to deal with4 ,let us see how these three problems arise4 7#a7 ,the logical problem has arisen through the suggestions of non-,euclidean geometry4 ,given a body of geometrical propositions1 it is not difficult to find a minimum statement of the axioms from which this body of propositions can be deduced4 ,it is also not difficult1 by dropping or altering some of these axioms1 to obtain a more general or a different geometry1 having1 from the point of view of pure mathematics1 the same logical coherence and the same title to respect as the more familiar ,euclidean geometry4 ,the ,euclidean geometry itself is true perhaps of actual space 7though this is doubtful71 but certainly of an infinite number of purely arithmetical systems1 each of which1 from the point of view of abstract logic1 has an equal and indefeasible right to be called a ,euclidean space4 ,thus space as an object of logical or mathematical study loses its uniqueness2 not only are there many kinds of spaces1 but there are an infinity of examples of each kind1 though it is difficult to find any kind of which the space of physics may be an example1 and it is impossible to find any kind of which the space of physics is certainly an example4 ,as an illustration of one possible logical system of geometry we may consider all relations of three terms which are analogous in certain formal respects to the relation between as it appears to be in actual space4 ,a space is then defined by means of one such three-term relation4 ,the points of the space are all the terms which have this relation to something or other1 and their order in the space in question is determined by this relation4 ,the points of one space are necessarily also points of other spaces1 since there are necessarily other three-term relations having those same points for their field4 ,the space in fact is not determined by the class of its points1 but by the ordering three-term relation4 ,when enough abstract logical properties of such relations have been enumerated to determine the resulting kind of geometry1 say1 for example1 ,euclidean geometry1 it becomes unnecessary for the pure geometer in his abstract capacity to distinguish between the various relations which have all these properties4 ,he considers the whole class of such relations1 not any single one among them4 ,thus in studying a given kind of geometry the pure mathematician is studying a certain class of relations defined by means of certain abstract logical properties which take the place of what used to be called axioms4 ,the nature of geometrical reasoning therefore is purely deductive and purely logical2 if any special epistemological peculiarities are to be found in geometry1 it must not be in the reasoning1 but in our knowledge concerning the axioms in some given space4 7#b7 ,the physical problem of space is both more interesting and more difficult than the logical problem4 ,the physical problem may be stated as follows3 to find in the physical world1 or to construct from physical materials1 a space of one of the kinds enumerated by the logical treatment of geometry4 ,this problem derives its difficulty from the attempt to accommodate to the roughness and vagueness of the real world some system possessing the logical clearness and exactitude of pure mathematics4 ,that this can be done with a certain degree of approximation is fairly evident ,if ,i see three people ,a1 ,b1 and ,c sitting in a row1 ,i become aware of the fact which may be expressed by saying that ,b is between ,a and ,c rather than that ,a is between ,b and ,c1 or ,c is between ,a and ,b4 ,this relation of between which is thus perceived to hold has some of the abstract logical properties of those three-term relations which1 we saw1 give rise to a geometry1 but its properties fail to be exact1 and are not1 as empirically given1 amenable to the kind of treatment at which geometry aims4 ,in abstract geometry we deal with points1 straight lines1 and planes2 but the three people ,a1 ,b1 and ,c whom ,i see sitting in a row are not exactly points1 nor is the row exactly a straight line4 ,nevertheless physics1 which formally assumes a space containing points1 straight lines1 and planes1 is found empirically to give results applicable to the sensible world4 ,it must therefore be possible to find an interpretation of the points1 straight lines1 and planes of physics in terms of physical data1 or at any rate in terms of data together with such hypothetical additions as seem least open to question4 ,since all data suffer from a lack of mathematical precision through being of a certain size and somewhat vague in outline1 it is plain that if such a notion as that of a point is to find any application to empirical material1 the point must be neither a datum nor a hypothetical addition to data1 but a construction by means of data with their hypothetical additions4 ,it is obvious that any hypothetical filling out of data is less dubious and unsatisfactory when the additions are closely analogous to data than when they are of a radically different sort4 ,to assume1 for example1 that objects which we see continue1 after we have turned away our eyes1 to be more or less analogous to what they were while we were looking1 is a less violent assumption than to assume that such objects are composed of an infinite number of mathematical points4 ,hence in the physical study of the geometry of physical space1 points must not be assumed ab initio as they are in the logical treatment of geometry1 but must be constructed as systems composed of data and hypothetical analogues of data4 ,we are thus led naturally to define a physical point as a certain class of those objects which are the ultimate constituents of the physical world4 ,it will be the class of all those objects which1 as one would naturally say1 contain the point4 ,to secure a definition giving this result1 without previously assuming that physical objects are composed of points1 is an agreeable problem in mathematical logic4 ,the solution of this problem and the perception of its importance are due to my friend ,dr4 ,whitehead4 ,the oddity of regarding a point as a class of physical entities wears off with familiarity1 and ought in any case not to be felt by those who maintain1 as practically every one does1 that points are mathematical fictions4 ,the word fiction is used glibly in such connexions by many men who seem not to feel the necessity of explaining how it can come about that a fiction can be so useful in the study of the actual world as the points of mathematical physics have been found to be4 ,by our definition1 which regards a point as a class of physical objects1 it is explained both how the use of points can lead to important physical results1 and how we can nevertheless avoid the assumption that points are themselves entities in the physical world4 ,many of the mathematically convenient properties of abstract logical spaces cannot be either known to belong or known not to belong to the space of physics4 ,such are all the properties connected with continuity4 ,for to know that actual space has these properties would require an infinite exactness of sense-perception4 ,if actual space is continuous1 there are nevertheless many possible non-continuous spaces which will be empirically indistinguishable from it2 and1 conversely1 actual space may be non-continuous and yet empirically indistinguishable from a possible continuous space4 ,continuity1 therefore1 though obtainable in the a priori region of arithmetic1 is not with certainty obtainable in the space or time of the physical world3 whether these are continuous or not would seem to be a question not only unanswered but for ever unanswerable4 ,from the point of view of philosophy1 however1 the discovery that a question is unanswerable is as complete an answer as any that could possibly be obtained4 ,and from the point of view of physics1 where no empirical means of distinction can be found1 there can be no empirical objection to the mathematically simplest assumption1 which is that of continuity4 ,the subject of the physical theory of space is a very large one1 hitherto little explored4 ,it is associated with a similar theory of time1 and both have been forced upon the attention of philosophically minded physicists by the discussions which have raged concerning the theory of relativity4 7#c7 ,the problem with which ,kant is concerned in the ,transcendental sthetic is primarily the epistemological problem3 ,how do we come to have knowledge of geometry a priori8 ,by the distinction between the logical and physical problems of geometry1 the bearing and scope of this question are greatly altered4 ,our knowledge of pure geometry is a priori but is wholly logical4 ,our knowledge of physical geometry is synthetic1 but is not a priori4 ,our knowledge of pure geometry is hypothetical1 and does not enable us to assert1 for example1 that the axiom of parallels is true in the physical world4 ,our knowledge of physical geometry1 while it does enable us to assert that this axiom is approximately verified1 does not1 owing to the inevitable inexactitude of observation1 enable us to assert that it is verified exactly4 ,thus1 with the separation which we have made between pure geometry and the geometry of physics1 the ,kantian problem collapses4 ,to the question1 ,how is synthetic a priori knowledge possible8 we can now reply1 at any rate so far as geometry is concerned1 ,it is not possible1 if synthetic means not deducible from logic alone4 ,our knowledge of geometry1 like the rest of our knowledge1 is derived partly from logic1 partly from sense1 and the peculiar position which in ,kant's day geometry appeared to occupy is seen now to be a delusion4 ,there are still some philosophers1 it is true1 who maintain that our knowledge that the axiom of parallels1 for example1 is true of actual space1 is not to be accounted for empirically1 but is as ,kant maintained derived from an a priori intuition4 ,this position is not logically refutable1 but ,i think it loses all plausibility as soon as we realise how complicated and derivative is the notion of physical space4 ,as we have seen1 the application of geometry to the physical world in no way demands that there should really be points and straight lines among physical entities4 ,the principle of economy1 therefore1 demands that we should abstain from assuming the existence of points and straight lines4 ,as soon1 however1 as we accept the view that points and straight lines are complicated constructions by means of classes of physical entities1 the hypothesis that we have an a priori intuition enabling us to know what happens to straight lines when they are produced indefinitely becomes extremely strained and harsh2 nor do ,i think that such an hypothesis would ever have arisen in the mind of a philosopher who had grasped the nature of physical space4 ,kant1 under the influence of ,newton1 adopted1 though with some vacillation1 the hypothesis of absolute space1 and this hypothesis1 though logically unobjectionable1 is removed by ,occam's razor1 since absolute space is an unnecessary entity in the explanation of the physical world4 ,although1 therefore1 we cannot refute the ,kantian theory of an a priori intuition1 we can remove its grounds one by one through an analysis of the problem4 ,thus1 here as in many other philosophical questions1 the analytic method1 while not capable of arriving at a demonstrative result1 is nevertheless capable of showing that all the positive grounds in favour of a certain theory are fallacious and that a less unnatural theory is capable of accounting for the facts4 ,another question by which the capacity of the analytic method can be shown is the question of realism4 ,both those who advocate and those who combat realism seem to me to be far from clear as to the nature of the problem which they are discussing4 ,if we ask3 ,are our objects of perception real and are they independent of the percipient8 it must be supposed that we attach some meaning to the words real and independent1 and yet1 if either side in the controversy of realism is asked to define these two words1 their answer is pretty sure to embody confusions such as logical analysis will reveal4 ,let us begin with the word real4 ,there certainly are objects of perception1 and therefore1 if the question whether these objects are real is to be a substantial question1 there must be in the world two sorts of objects1 namely1 the real and the unreal1 and yet the unreal is supposed to be essentially what there is not4 ,the question what properties must belong to an object in order to make it real is one to which an adequate answer is seldom if ever forthcoming4 ,there is of course the ,hegelian answer1 that the real is the self-consistent and that nothing is self-consistent except the ,whole2 but this answer1 true or false1 is not relevant in our present discussion1 which moves on a lower plane and is concerned with the status of objects of perception among other objects of equal fragmentariness4 ,objects of perception are contrasted1 in the discussions concerning realism1 rather with psychical states on the one hand and matter on the other hand than with the all-inclusive whole of things4 ,the question we have therefore to consider is the question as to what can be meant by assigning reality to some but not all of the entities that make up the world4 ,two elements1 ,i think1 make up what is felt rather than thought when the word reality is used in this sense4 ,a thing is real if it persists at times when it is not perceived2 or again1 a thing is real when it is correlated with other things in a way which experience has led us to expect4 ,it will be seen that reality in either of these senses is by no means necessary to a thing1 and that in fact there might be a whole world in which nothing was real in either of these senses4 ,it might turn out that the objects of perception failed of reality in one or both of these respects1 without its being in any way deducible that they are not parts of the external world with which physics deals4 ,similar remarks will apply to the word independent4 ,most of the associations of this word are bound up with ideas as to causation which it is not now possible to maintain4 ,a is independent of ,b when ,b is not an indispensable part of the cause of ,a4 ,but when it is recognised that causation is nothing more than correlation1 and that there are correlations of simultaneity as well as of succession1 it becomes evident that there is no uniqueness in a series of casual antecedents of a given event1 but that1 at any point where there is a correlation of simultaneity1 we can pass from one line of antecedents to another in order to obtain a new series of causal antecedents4 ,it will be necessary to specify the causal law according to which the antecedents are to be considered4 ,i received a letter the other day from a correspondent who had been puzzled by various philosophical questions4 ,after enumerating them he says3 ,these questions led me from ,bonn to ,strassburg1 where ,i found ,professor ,simmel4 ,now1 it would be absurd to deny that these questions caused his body to move from ,bonn to ,strassburg1 and yet it must be supposed that a set of purely mechanical antecedents could also be found which would account for this transfer of matter from one place to another4 ,owing to this plurality of causal series antecedent to a given event1 the notion of the cause becomes indefinite1 and the question of independence becomes correspondingly ambiguous4 ,thus1 instead of asking simply whether ,a is independent of ,b1 we ought to ask whether there is a series determined by such and such causal laws leading from ,b to ,a4 ,this point is important in connexion with the particular question of objects of perception4 ,it may be that no objects quite like those which we perceive ever exist unperceived2 in this case there will be a causal law according to which objects of perception are not independent of being perceived4 ,but even if this be the case1 it may nevertheless also happen that there are purely physical causal laws determining the occurrence of objects which are perceived by means of other objects which perhaps are not perceived4 ,in that case1 in regard to such causal laws objects of perception will be independent of being perceived4 ,thus the question whether objects of perception are independent of being perceived is1 as it stands1 indeterminate1 and the answer will be yes or no according to the method adopted of making it determinate4 ,i believe that this confusion has borne a very large part in prolonging the controversies on this subject1 which might well have seemed capable of remaining for ever undecided4 ,the view which ,i should wish to advocate is that objects of perception do not persist unchanged at times when they are not perceived1 although probably objects more or less resembling them do exist at such times2 that objects of perception are part1 and the only empirically knowable part1 of the actual subject-matter of physics1 and are themselves properly to be called physical2 that purely physical laws exist determining the character and duration of objects of perception without any reference to the fact that they are perceived2 and that in the establishment of such laws the propositions of physics do not presuppose any propositions of psychology or even the existence of mind4 ,i do not know whether realists would recognise such a view as realism4 ,all that ,i should claim for it is1 that it avoids difficulties which seem to me to beset both realism and idealism as hitherto advocated1 and that it avoids the appeal which they have made to ideas which logical analysis shows to be ambiguous4 ,a further defence and elaboration of the positions which ,i advocate1 but for which time is lacking now1 will be found indicated in my book on ,our ,knowledge of the ,external ,world4#bb ,the adoption of scientific method in philosophy1 if ,i am not mistaken1 compels us to abandon the hope of solving many of the more ambitious and humanly interesting problems of traditional philosophy4 ,some of these it relegates1 though with little expectation of a successful solution1 to special sciences1 others it shows to be such as our capacities are essentially incapable of solving4 ,but there remain a large number of the recognised problems of philosophy in regard to which the method advocated gives all those advantages of division into distinct questions1 of tentative1 partial1 and progressive advance1 and of appeal to principles with which1 independently of temperament1 all competent students must agree4 ,the failure of philosophy hitherto has been due in the main to haste and ambition3 patience and modesty1 here as in other sciences1 will open the road to solid and durable progress4 ,,footnotes3 #ai ,bosanquet1 ,logic1 ii1 p4 #baa4 #bj ,some ,problems of ,philosophy1 p #abd4 #ba ,first ,principles 7#ahfb71 ,part ,,ii1 beginning of chap4 viii4 #bb ,open ,court ,company1 #aiad4 ,,vii ,,the ,,ultimate ,,constituents ,,of ,,matter#bc ,i wish to discuss in this article no less a question than the ancient metaphysical query1 ,what is matter8 ,the question1 ,what is matter8 in so far as it concerns philosophy1 is1 ,i think1 already capable of an answer which in principle will be as complete as an answer can hope to be2 that is to say1 we can separate the problem into an essentially soluble and an essentially insoluble portion1 and we can now see how to solve the essentially soluble portion1 at least as regards its main outlines4 ,it is these outlines which ,i wish to suggest in the present article4 ,my main position1 which is realistic1 is1 ,i hope and believe1 not remote from that of ,professor ,alexander1 by whose writings on this subject ,i have profited greatly4#bd ,it is also in close accord with that of ,dr4 ,nunn4#be ,common sense is accustomed to the division of the world into mind and matter4 ,it is supposed by all who have never studied philosophy that the distinction between mind and matter is perfectly clear and easy1 that the two do not at any point overlap1 and that only a fool or a philosopher could be in doubt as to whether any given entity is mental or material4 ,this simple faith survives in ,descartes and in a somewhat modified form in ,spinoza1 but with ,leibniz it begins to disappear1 and from his day to our own almost every philosopher of note has criticised and rejected the dualism of common sense4 ,it is my intention in this article to defend this dualism2 but before defending it we must spend a few moments on the reasons which have prompted its rejection4 ,our knowledge of the material world is obtained by means of the senses1 of sight and touch and so on4 ,at first it is supposed that things are just as they seem1 but two opposite sophistications soon destroy this nave belief4 ,on the one hand the physicists cut up matter into molecules1 atoms1 corpuscles1 and as many more such subdivisions as their future needs may make them postulate1 and the units at which they arrive are uncommonly different from the visible1 tangible objects of daily life4 ,a unit of matter tends more and more to be something like an electromagnetic field filling all space1 though having its greatest intensity in a small region4 ,matter consisting of such elements is as remote from daily life as any metaphysical theory4 ,it differs from the theories of metaphysicians only in the fact that its practical efficacy proves that it contains some measure of truth and induces business men to invest money on the strength of it2 but1 in spite of its connection with the money market1 it remains a metaphysical theory none the less4 ,the second kind of sophistication to which the world of common sense has been subjected is derived from the psychologists and physiologists4 ,the physiologists point out that what we see depends upon the eye1 that what we hear depends upon the ear1 and that all our senses are liable to be affected by anything which affects the brain1 like alcohol or hasheesh4 ,psychologists point out how much of what we think we see is supplied by association or unconscious inference1 how much is mental interpretation1 and how doubtful is the residuum which can be regarded as crude datum4 ,from these facts it is argued by the psychologists that the notion of a datum passively received by the mind is a delusion1 and it is argued by the physiologists that even if a pure datum of sense could be obtained by the analysis of experience1 still this datum could not belong1 as common sense supposes1 to the outer world1 since its whole nature is conditioned by our nerves and sense organs1 changing as they change in ways which it is thought impossible to connect with any change in the matter supposed to be perceived4 ,this physiologist's argument is exposed to the rejoinder1 more specious than solid1 that our knowledge of the existence of the sense organs and nerves is obtained by that very process which the physiologist has been engaged in discrediting1 since the existence of the nerves and sense organs is only known through the evidence of the senses themselves4 ,this argument may prove that some reinterpretation of the results of physiology is necessary before they can acquire metaphysical validity4 ,but it does not upset the physiological argument in so far as this constitutes merely a reductio ad absurdum of nave realism4 ,these various lines of argument prove1 ,i think1 that some part of the beliefs of common sense must be abandoned4 ,they prove that1 if we take these beliefs as a whole1 we are forced into conclusions which are in part self-contradictory2 but such arguments cannot of themselves decide what portion of our common-sense beliefs is in need of correction4 ,common sense believes that what we see is physical1 outside the mind1 and continuing to exist if we shut our eyes or turn them in another direction4 ,i believe that common sense is right in regarding what we see as physical and 7in one of several possible senses7 outside the mind1 but is probably wrong in supposing that it continues to exist when we are no longer looking at it4 ,it seems to me that the whole discussion of matter has been obscured by two errors which support each other4 ,the first of these is the error that what we see1 or perceive through any of our other senses1 is subjective3 the second is the belief that what is physical must be persistent4 ,whatever physics may regard as the ultimate constituents of matter1 it always supposes these constituents to be indestructible4 ,since the immediate data of sense are not indestructible but in a state of perpetual flux1 it is argued that these data themselves cannot be among the ultimate constituents of matter4 ,i believe this to be a sheer mistake4 ,the persistent particles of mathematical physics ,i regard as logical constructions1 symbolic fictions enabling us to express compendiously very complicated assemblages of facts2 and1 on the other hand1 ,i believe that the actual data in sensation1 the immediate objects of sight or touch or hearing1 are extra-mental1 purely physical1 and among the ultimate constituents of matter4 ,my meaning in regard to the impermanence of physical entities may perhaps be made clearer by the use of ,bergson's favourite illustration of the cinematograph4 ,when ,i first read ,bergson's statement that the mathematician conceives the world after the analogy of a cinematograph1 ,i had never seen a cinematograph1 and my first visit to one was determined by the desire to verify ,bergson's statement1 which ,i found to be completely true1 at least so far as ,i am concerned4 ,when1 in a picture palace1 we see a man rolling down hill1 or running away from the police1 or falling into a river1 or doing any of those other things to which men in such places are addicted1 we know that there is not really only one man moving1 but a succession of films1 each with a different momentary man4 ,the illusion of persistence arises only through the approach to continuity in the series of momentary men4 ,now what ,i wish to suggest is that in this respect the cinema is a better metaphysician than common sense1 physics1 or philosophy4 ,the real man too1 ,i believe1 however the police may swear to his identity1 is really a series of momentary men1 each different one from the other1 and bound together1 not by a numerical identity1 but by continuity and certain intrinsic causal laws4 ,and what applies to men applies equally to tables and chairs1 the sun1 moon and stars4 ,each of these is to be regarded1 not as one single persistent entity1 but as a series of entities succeeding each other in time1 each lasting for a very brief period1 though probably not for a mere mathematical instant4 ,in saying this ,i am only urging the same kind of division in time as we are accustomed to acknowledge in the case of space4 ,a body which fills a cubic foot will be admitted to consist of many smaller bodies1 each occupying only a very tiny volume2 similarly a thing which persists for an hour is to be regarded as composed of many things of less duration4 ,a true theory of matter requires a division of things into time-corpuscles as well as into space-corpuscles4 ,the world may be conceived as consisting of a multitude of entities arranged in a certain pattern4 ,the entities which are arranged ,i shall call particulars4 ,the arrangement or pattern results from relations among particulars4 ,classes or series of particulars1 collected together on account of some property which makes it convenient to be able to speak of them as wholes1 are what ,i call logical constructions or symbolic fictions4 ,the particulars are to be conceived1 not on the analogy of bricks in a building1 but rather on the analogy of notes in a symphony4 ,the ultimate constituents of a symphony 7apart from relations7 are the notes1 each of which lasts only for a very short time4 ,we may collect together all the notes played by one instrument3 these may be regarded as the analogues of the successive particulars which common sense would regard as successive states of one thing4 ,but the thing ought to be regarded as no more real or substantial than1 for example1 the rle of the trombone4 ,as soon as things are conceived in this manner it will be found that the difficulties in the way of regarding immediate objects of sense as physical have largely disappeared4 ,when people ask1 ,is the object of sense mental or physical8 they seldom have any clear idea either what is meant by mental or physical1 or what criteria are to be applied for deciding whether a given entity belongs to one class or the other4 ,i do not know how to give a sharp definition of the word mental1 but something may be done by enumerating occurrences which are indubitably mental3 believing1 doubting1 wishing1 willing1 being pleased or pained1 are certainly mental occurrences2 so are what we may call experiences1 seeing1 hearing1 smelling1 perceiving generally4 ,but it does not follow from this that what is seen1 what is heard1 what is smelt1 what is perceived1 must be mental4 ,when ,i see a flash of lightning1 my seeing of it is mental1 but what ,i see1 although it is not quite the same as what anybody else sees at the same moment1 and although it seems very unlike what the physicist would describe as a flash of lightning1 is not mental4 ,i maintain1 in fact1 that if the physicist could describe truly and fully all that occurs in the physical world when there is a flash of lightning1 it would contain as a constituent what ,i see1 and also what is seen by anybody else who would commonly be said to see the same flash4 ,what ,i mean may perhaps be made plainer by saying that if my body could remain in exactly the same state in which it is1 although my mind had ceased to exist1 precisely that object which ,i now see when ,i see the flash would exist1 although of course ,i should not see it1 since my seeing is mental4 ,the principal reasons which have led people to reject this view have1 ,i think1 been two3 first1 that they did not adequately distinguish between my seeing and what ,i see2 secondly1 that the causal dependence of what ,i see upon my body has made people suppose that what ,i see cannot be outside me4 ,the first of these reasons need not detain us1 since the confusion only needs to be pointed out in order to be obviated2 but the second requires some discussion1 since it can only be answered by removing current misconceptions1 on the one hand as to the nature of space1 and on the other1 as to the meaning of causal dependence4 ,when people ask whether colours1 for example1 or other secondary qualities are inside or outside the mind1 they seem to suppose that their meaning must be clear1 and that it ought to be possible to say yes or no without any further discussion of the terms involved4 ,in fact1 however1 such terms as inside or outside are very ambiguous4 ,what is meant by asking whether this or that is in the mind8 ,the mind is not like a bag or a pie2 it does not occupy a certain region in space1 or1 if 7in a sense7 it does1 what is in that region is presumably part of the brain1 which would not be said to be in the mind4 ,when people say that sensible qualities are in the mind1 they do not mean spatially contained in in the sense in which the blackbirds were in the pie4 ,we might regard the mind as an assemblage of particulars1 namely1 what would be called states of mind1 which would belong together in virtue of some specific common quality4 ,the common quality of all states of mind would be the quality designated by the word mental2 and besides this we should have to suppose that each separate person's states of mind have some common characteristic distinguishing them from the states of mind of other people4 ,ignoring this latter point1 let us ask ourselves whether the quality designated by the word mental does1 as a matter of observation1 actually belong to objects of sense1 such as colours or noises4 ,i think any candid person must reply that1 however difficult it may be to know what we mean by mental1 it is not difficult to see that colours and noises are not mental in the sense of having that intrinsic peculiarity which belongs to beliefs and wishes and volitions1 but not to the physical world4 ,berkeley advances on this subject a plausible argument#bf which seems to me to rest upon an ambiguity in the word pain4 ,he argues that the realist supposes the heat which he feels in approaching a fire to be something outside his mind1 but that as he approaches nearer and nearer to the fire the sensation of heat passes imperceptibly into pain1 and that no one could regard pain as something outside the mind4 ,in reply to this argument1 it should be observed in the first place that the heat of which we are immediately aware is not in the fire but in our own body4 ,it is only by inference that the fire is judged to be the cause of the heat which we feel in our body4 ,in the second place 7and this is the more important point71 when we speak of pain we may mean one of two things3 we may mean the object of the sensation or other experience which has the quality of being painful1 or we may mean the quality of painfulness itself4 ,when a man says he has a pain in his great toe1 what he means is that he has a sensation associated with his great toe and having the quality of painfulness4 ,the sensation itself1 like every sensation1 consists in experiencing a sensible object1 and the experiencing has that quality of painfulness which only mental occurrences can have1 but which may belong to thoughts or desires1 as well as to sensations4 ,but in common language we speak of the sensible object experienced in a painful sensation as a pain1 and it is this way of speaking which causes the confusion upon which the plausibility of ,berkeley's argument depends4 ,it would be absurd to attribute the quality of painfulness to anything non-mental1 and hence it comes to be thought that what we call a pain in the toe must be mental4 ,in fact1 however1 it is not the sensible object in such a case which is painful1 but the sensation1 that is to say1 the experience of the sensible object4 ,as the heat which we experience from the fire grows greater1 the experience passes gradually from being pleasant to being painful1 but neither the pleasure nor the pain is a quality of the object experienced as opposed to the experience1 and it is therefore a fallacy to argue that this object must be mental on the ground that painfulness can only be attributed to what is mental4 ,if1 then1 when we say that something is in the mind we mean that it has a certain recognisable intrinsic characteristic such as belongs to thoughts and desires1 it must be maintained on grounds of immediate inspection that objects of sense are not in any mind4 ,a different meaning of in the mind is1 however1 to be inferred from the arguments advanced by those who regard sensible objects as being in the mind4 ,the arguments used are1 in the main1 such as would prove the causal dependence of objects of sense upon the percipient4 ,now the notion of causal dependence is very obscure and difficult1 much more so in fact than is generally realised by philosophers4 ,i shall return to this point in a moment4 ,for the present1 however1 accepting the notion of causal dependence without criticism1 ,i wish to urge that the dependence in question is rather upon our bodies than upon our minds4 ,the visual appearance of an object is altered if we shut one eye1 or squint1 or look previously at something dazzling2 but all these are bodily acts1 and the alterations which they effect are to be explained by physiology and optics1 not by psychology4#bg ,they are in fact of exactly the same kind as the alterations effected by spectacles or a microscope4 ,they belong therefore to the theory of the physical world1 and can have no bearing upon the question whether what we see is causally dependent upon the mind4 ,what they do tend to prove1 and what ,i for my part have no wish to deny1 is that what we see is causally dependent upon our body and is not1 as crude common sense would suppose1 something which would exist equally if our eyes and nerves and brain were absent1 any more than the visual appearance presented by an object seen through a microscope would remain if the microscope were removed4 ,so long as it is supposed that the physical world is composed of stable and more or less permanent constituents1 the fact that what we see is changed by changes in our body appears to afford reason for regarding what we see as not an ultimate constituent of matter4 ,but if it is recognised that the ultimate constituents of matter are as circumscribed in duration as in spatial extent1 the whole of this difficulty vanishes4 ,there remains1 however1 another difficulty1 connected with space4 ,when we look at the sun we wish to know something about the sun itself1 which is ninety-three million miles away2 but what we see is dependent upon our eyes1 and it is difficult to suppose that our eyes can affect what happens at a distance of ninety-three million miles4 ,physics tells us that certain electromagnetic waves start from the sun1 and reach our eyes after about eight minutes4 ,they there produce disturbances in the rods and cones1 thence in the optic nerve1 thence in the brain4 ,at the end of this purely physical series1 by some odd miracle1 comes the experience which we call seeing the sun1 and it is such experiences which form the whole and sole reason for our belief in the optic nerve1 the rods and cones1 the ninety-three million miles1 the electromagnetic waves1 and the sun itself4 ,it is this curious oppositeness of direction between the order of causation as affirmed by physics1 and the order of evidence as revealed by theory of knowledge1 that causes the most serious perplexities in regard to the nature of physical reality4 ,anything that invalidates our seeing1 as a source of knowledge concerning physical reality1 invalidates also the whole of physics and physiology4 ,and yet1 starting from a common-sense acceptance of our seeing1 physics has been led step by step to the construction of the causal chain in which our seeing is the last link1 and the immediate object which we see cannot be regarded as that initial cause which we believe to be ninety-three million miles away1 and which we are inclined to regard as the real sun4 ,i have stated this difficulty as forcibly as ,i can1 because ,i believe that it can only be answered by a radical analysis and reconstruction of all the conceptions upon whose employment it depends4 ,space1 time1 matter and cause1 are the chief of these conceptions4 ,let us begin with the conception of cause4 ,causal dependence1 as ,i observed a moment ago1 is a conception which it is very dangerous to accept at its face value4 ,there exists a notion that in regard to any event there is something which may be called the cause of that event--some one definite occurrence1 without which the event would have been impossible and with which it becomes necessary4 ,an event is supposed to be dependent upon its cause in some way which in it is not dependent upon other things4 ,thus men will urge that the mind is dependent upon the brain1 or1 with equal plausibility1 that the brain is dependent upon the mind4 ,it seems not improbable that if we had sufficient knowledge we could infer the state of a man's mind from the state of his brain1 or the state of his brain from the state of his mind4 ,so long as the usual conception of causal dependence is retained1 this state of affairs can be used by the materialist to urge that the state of our brain causes our thoughts1 and by the idealist to urge that our thoughts cause the state of our brain4 ,either contention is equally valid or equally invalid4 ,the fact seems to be that there are many correlations of the sort which may be called causal1 and that1 for example1 either a physical or a mental event can be predicted1 theoretically1 either from a sufficient number of physical antecedents or from a sufficient number of mental antecedents4 ,to speak of the cause of an event is therefore misleading4 ,any set of antecedents from which the event can theoretically be inferred by means of correlations might be called a cause of the event4 ,but to speak of the cause is to imply a uniqueness which does not exist4 ,the relevance of this to the experience which we call seeing the sun is obvious4 ,the fact that there exists a chain of antecedents which makes our seeing dependent upon the eyes and nerves and brain does not even tend to show that there is not another chain of antecedents in which the eyes and nerves and brain as physical things are ignored4 ,if we are to escape from the dilemma which seemed to arise out of the physiological causation of what we see when we say we see the sun1 we must find1 at least in theory1 a way of stating causal laws for the physical world1 in which the units are not material things1 such as the eyes and nerves and brain1 but momentary particulars of the same sort as our momentary visual object when we look at the sun4 ,the sun itself and the eyes and nerves and brain must be regarded as assemblages of momentary particulars4 ,instead of supposing1 as we naturally do when we start from an uncritical acceptance of the apparent dicta of physics1 that matter is what is really real in the physical world1 and that the immediate objects of sense are mere phantasms1 we must regard matter as a logical construction1 of which the constituents will be just such evanescent particulars as may1 when an observer happens to be present1 become data of sense to that observer4 ,what physics regards as the sun of eight minutes ago will be a whole assemblage of particulars1 existing at different times1 spreading out from a centre with the velocity of light1 and containing among their number all those visual data which are seen by people who are now looking at the sun4 ,thus the sun of eight minutes ago is a class of particulars1 and what ,i see when ,i now look at the sun is one member of this class4 ,the various particulars constituting this class will be correlated with each other by a certain continuity and certain intrinsic laws of variation as we pass outwards from the centre1 together with certain modifications correlated extrinsically with other particulars which are not members of this class4 ,it is these extrinsic modifications which represent the sort of facts that1 in our former account1 appeared as the influence of the eyes and nerves in modifying the appearance of the sun4#bh ,the prima facie difficulties in the way of this view are chiefly derived from an unduly conventional theory of space4 ,it might seem at first sight as if we had packed the world much fuller than it could possibly hold4 ,at every place between us and the sun1 we said1 there is to be a particular which is to be a member of the sun as it was a few minutes ago4 ,there will also1 of course1 have to be a particular which is a member of any planet or fixed star that may happen to be visible from that place4 ,at the place where ,i am1 there will be particulars which will be members severally of all the things ,i am now said to be perceiving4 ,thus throughout the world1 everywhere1 there will be an enormous number of particulars coexisting in the same place4 ,but these troubles result from contenting ourselves too readily with the merely three-dimensional space to which schoolmasters have accustomed us4 ,the space of the real world is a space of six dimensions1 and as soon as we realise this we see that there is plenty of room for all the particulars for which we want to find positions4 ,in order to realise this we have only to return for a moment from the polished space of physics to the rough and untidy space of our immediate sensible experience4 ,the space of one man's sensible objects is a three-dimensional space4 ,it does not appear probable that two men ever both perceive at the same time any one sensible object2 when they are said to see the same thing or hear the same noise1 there will always be some difference1 however slight1 between the actual shapes seen or the actual sounds heard4 ,if this is so1 and if1 as is generally assumed1 position in space is purely relative1 it follows that the space of one man's objects and the space of another man's objects have no place in common1 that they are in fact different spaces1 and not merely different parts of one space4 ,i mean by this that such immediate spatial relations as are perceived to hold between the different parts of the sensible space perceived by one man1 do not hold between parts of sensible spaces perceived by different men4 ,there are therefore a multitude of three-dimensional spaces in the world3 there are all those perceived by observers1 and presumably also those which are not perceived1 merely because no observer is suitably situated for perceiving them4 ,but although these spaces do not have to one another the same kind of spatial relations as obtain between the parts of one of them1 it is nevertheless possible to arrange these spaces themselves in a three-dimensional order4 ,this is done by means of the correlated particulars which we regard as members 7or aspects7 of one physical thing4 ,when a number of people are said to see the same object1 those who would be said to be near to the object see a particular occupying a larger part of their field of vision than is occupied by the corresponding particular seen by people who would be said to be farther from the thing4 ,by means of such considerations it is possible1 in ways which need not now be further specified1 to arrange all the different spaces in a three-dimensional series4 ,since each of the spaces is itself three-dimensional1 the whole world of particulars is thus arranged in a six-dimensional space1 that is to say1 six co-ordinates will be required to assign completely the position of any given particular1 namely1 three to assign its position in its own space and three more to assign the position of its space among the other spaces4 ,there are two ways of classifying particulars3 we may take together all those that belong to a given perspective1 or all those that are1 as common sense would say1 different aspects of the same thing4 ,for example1 if ,i am 7as is said7 seeing the sun1 what ,i see belongs to two assemblages3 7#a7 the assemblage of all my present objects of sense1 which is what ,i call a perspective2 7#b7 the assemblage of all the different particulars which would be called aspects of the sun of eight minutes ago--this assemblage is what ,i define as being the sun of eight minutes ago4 ,thus perspectives and things are merely two different ways of classifying particulars4 ,it is to be observed that there is no a priori necessity for particulars to be susceptible of this double classification4 ,there may be what might be called wild particulars1 not having the usual relations by which the classification is effected2 perhaps dreams and hallucinations are composed of particulars which are wild in this sense4 ,the exact definition of what is meant by a perspective is not quite easy4 ,so long as we confine ourselves to visible objects or to objects of touch we might define the perspective of a given particular as all particulars which have a simple 7direct7 spatial relation to the given particular4 ,between two patches of colour which ,i see now1 there is a direct spatial relation which ,i equally see4 ,but between patches of colour seen by different men there is only an indirect constructed spatial relation by means of the placing of things in physical space 7which is the same as the space composed of perspectives74 ,those particulars which have direct spatial relations to a given particular will belong to the same perspective4 ,but if1 for example1 the sounds which ,i hear are to belong to the same perspective with the patches of colour which ,i see1 there must be particulars which have no direct spatial relation and yet belong to the same perspective4 ,we cannot define a perspective as all the data of one percipient at one time1 because we wish to allow the possibility of perspectives which are not perceived by any one4 ,there will be need1 therefore1 in defining a perspective1 of some principle derived neither from psychology nor from space4 ,such a principle may be obtained from the consideration of time4 ,the one all-embracing time1 like the one all-embracing space1 is a construction2 there is no direct time-relation between particulars belonging to my perspective and particulars belonging to another man's4 ,on the other hand1 any two particulars of which ,i am aware are either simultaneous or successive1 and their simultaneity or successiveness is sometimes itself a datum to me4 ,we may therefore define the perspective to which a given particular belongs as all particulars simultaneous with the given particular1 where simultaneous is to be understood as a direct simple relation1 not the derivative constructed relation of physics4 ,it may be observed that the introduction of local time suggested by the principle of relativity has effected1 for purely scientific reasons1 much the same multiplication of times as we have just been advocating4 ,the sum-total of all the particulars that are 7directly7 either simultaneous with or before or after a given particular may be defined as the biography to which that particular belongs4 ,it will be observed that1 just as a perspective need not be actually perceived by any one1 so a biography need not be actually lived by any one4 ,those biographies that are lived by no one are called official4 ,the definition of a thing is effected by means of continuity and of correlations which have a certain differential independence of other things4 ,that is to say1 given a particular in one perspective1 there will usually in a neighbouring perspective be a very similar particular1 differing from the given particular1 to the first order of small quantities1 according to a law involving only the difference of position of the two perspectives in perspective space1 and not any of the other things in the universe4 ,it is this continuity and differential independence in the law of change as we pass from one perspective to another that defines the class of particulars which is to be called one thing4 ,broadly speaking1 we may say that the physicist finds it convenient to classify particulars into things1 while the psychologist finds it convenient to classify them into perspectives and biographies1 since one perspective may constitute the momentary data of one percipient1 and one biography may constitute the whole of the data of one percipient throughout his life4 ,we may now sum up our discussion4 ,our object has been to discover as far as possible the nature of the ultimate constituents of the physical world4 ,when ,i speak of the physical world1 ,i mean1 to begin with1 the world dealt with by physics4 ,it is obvious that physics is an empirical science1 giving us a certain amount of knowledge and based upon evidence obtained through the senses4 ,but partly through the development of physics itself1 partly through arguments derived from physiology1 psychology or metaphysics1 it has come to be thought that the immediate data of sense could not themselves form part of the ultimate constituents of the physical world1 but were in some sense mental1 in the mind1 or subjective4 ,the grounds for this view1 in so far as they depend upon physics1 can only be adequately dealt with by rather elaborate constructions depending upon symbolic logic1 showing that out of such materials as are provided by the senses it is possible to construct classes and series having the properties which physics assigns to matter4 ,since this argument is difficult and technical1 ,i have not embarked upon it in this article4 ,but in so far as the view that sense-data are mental rests upon physiology1 psychology1 or metaphysics1 ,i have tried to show that it rests upon confusions and prejudices--prejudices in favour of permanence in the ultimate constituents of matter1 and confusions derived from unduly simple notions as to space1 from the causal correlation of sense-data with sense-organs1 and from failure to distinguish between sense-data and sensations4 ,if what we have said on these subjects is valid1 the existence of sense-data is logically independent of the existence of mind1 and is causally dependent upon the body of the percipient rather than upon his mind4 ,the causal dependence upon the body of the percipient1 we found1 is a more complicated matter than it appears to be1 and1 like all causal dependence1 is apt to give rise to erroneous beliefs through misconceptions as to the nature of causal correlation4 ,if we have been right in our contentions1 sense-data are merely those among the ultimate constituents of the physical world1 of which we happen to be immediately aware2 they themselves are purely physical1 and all that is mental in connection with them is our awareness of them1 which is irrelevant to their nature and to their place in physics4 ,unduly simple notions as to space have been a great stumbling-block to realists4 ,when two men look at the same table1 it is supposed that what the one sees and what the other sees are in the same place4 ,since the shape and colour are not quite the same for the two men1 this raises a difficulty1 hastily solved1 or rather covered up1 by declaring what each sees to be purely subjective--though it would puzzle those who use this glib word to say what they mean by it4 ,the truth seems to be that space--and time also--is much more complicated than it would appear to be from the finished structure of physics1 and that the one all-embracing three-dimensional space is a logical construction1 obtained by means of correlations from a crude space of six dimensions4 ,the particulars occupying this six-dimensional space1 classified in one way1 form things1 from which with certain further manipulations we can obtain what physics can regard as matter2 classified in another way1 they form perspectives and biographies1 which may1 if a suitable percipient happens to exist1 form respectively the sense-data of a momentary or of a total experience4 ,it is only when physical things have been dissected into series of classes of particulars1 as we have done1 that the conflict between the point of view of physics and the point of view of psychology can be overcome4 ,this conflict1 if what has been said is not mistaken1 flows from different methods of classification1 and vanishes as soon as its source is discovered4 ,in favour of the theory which ,i have briefly outlined1 ,i do not claim that it is certainly true4 ,apart from the likelihood of mistakes1 much of it is avowedly hypothetical4 ,what ,i do claim for the theory is that it may be true1 and that this is more than can be said for any other theory except the closely analogous theory of ,leibniz4 ,the difficulties besetting realism1 the confusions obstructing any philosophical account of physics1 the dilemma resulting from discrediting sense-data1 which yet remain the sole source of our knowledge of the outer world--all these are avoided by the theory which ,i advocate4 ,this does not prove the theory to be true1 since probably many other theories might be invented which would have the same merits4 ,but it does prove that the theory has a better chance of being true than any of its present competitors1 and it suggests that what can be known with certainty is likely to be discoverable by taking our theory as a starting-point1 and gradually freeing it from all such assumptions as seem irrelevant1 unnecessary1 or unfounded4 ,on these grounds1 ,i recommend it to attention as a hypothesis and a basis for further work1 though not as itself a finished or adequate solution of the problem with which it deals4 ,,footnotes3 #bc ,an address delivered to the ,philosophical ,society of ,manchester in ,february1 #aiae4 ,reprinted from ,the ,monist1 ,july1 #aiae4 #bd ,cf4 especially ,samuel ,alexander1 ,the ,basis of ,realism1 ,british ,academy1 ,vol4 ,,vi4 #be ,are ,secondary ,qualities ,independent of ,perception8 ,proc4 ,arist4 ,soc41 #aiji-aj1 pp4 #aia-bah4 #bf ,first dialogue between ,hylas and ,philonous1 ,works 7,fraser's edition #aija74 ,i4 p4 #chd4 #bg ,this point has been well urged by the ,american realists4 #bh ,cf4 ,t4,p4 ,nunn1 ,are ,secondary ,qualities ,independent of ,perception8 ,proc4 ,arist4 ,soc41 #aiji-aiaj4 ,,viii ,,the ,,relation ,,of ,,sense-,,data ,,to ,,physics ,i4 ,,the ,,problem ,,stated ,physics is said to be an empirical science1 based upon observation and experiment4 ,it is supposed to be verifiable1 i4e4 capable of calculating beforehand results subsequently confirmed by observation and experiment4 ,what can we learn by observation and experiment8 ,nothing1 so far as physics is concerned1 except immediate data of sense3 certain patches of colour1 sounds1 tastes1 smells1 etc41 with certain spatio-temporal relations4 ,the supposed contents of the physical world are prima facie very different from these3 molecules have no colour1 atoms make no noise1 electrons have no taste1 and corpuscles do not even smell4 ,if such objects are to be verified1 it must be solely through their relation to sense-data3 they must have some kind of correlation with sense-data1 and must be verifiable through their correlation alone4 ,but how is the correlation itself ascertained8 ,a correlation can only be ascertained empirically by the correlated objects being constantly found together4 ,but in our case1 only one term of the correlation1 namely1 the sensible term1 is ever found3 the other term seems essentially incapable of being found4 ,therefore1 it would seem1 the correlation with objects of sense1 by which physics was to be verified1 is itself utterly and for ever unverifiable4 ,there are two ways of avoiding this result4 7#a7 ,we may say that we know some principle a priori1 without the need of empirical verification1 e4g4 that our sense-data have causes other than themselves1 and that something can be known about these causes by inference from their effects4 ,this way has been often adopted by philosophers4 ,it may be necessary to adopt this way to some extent1 but in so far as it is adopted physics ceases to be empirical or based upon experiment and observation alone4 ,therefore this way is to be avoided as much as possible4 7#b7 ,we may succeed in actually defining the objects of physics as functions of sense-data4 ,just in so far as physics leads to expectations1 this must be possible1 since we can only expect what can be experienced4 ,and in so far as the physical state of affairs is inferred from sense-data1 it must be capable of expression as a function of sense-data4 ,the problem of accomplishing this expression leads to much interesting logico-mathematical work4 ,in physics as commonly set forth1 sense-data appear as functions of physical objects3 when such-and-such waves impinge upon the eye1 we see such-and-such colours1 and so on4 ,but the waves are in fact inferred from the colours1 not vice versa4 ,physics cannot be regarded as validly based upon empirical data until the waves have been expressed as functions of the colours and other sense-data4 ,thus if physics is to be verifiable we are faced with the following problem3 ,physics exhibits sense-data as functions of physical objects1 but verification is only possible if physical objects can be exhibited as functions of sense-data4 ,we have therefore to solve the equations giving sense-data in terms of physical objects1 so as to make them instead give physical objects in terms of sense-data4 ,,ii4 ,,characteristics ,,of ,,sense-,,data ,when ,i speak of a sense-datum1 ,i do not mean the whole of what is given in sense at one time4 ,i mean rather such a part of the whole as might be singled out by attention3 particular patches of colour1 particular noises1 and so on4 ,there is some difficulty in deciding what is to be considered one sense-datum3 often attention causes divisions to appear where1 so far as can be discovered1 there were no divisions before4 ,an observed complex fact1 such as that this patch of red is to the left of that patch of blue1 is also to be regarded as a datum from our present point of view3 epistemologically1 it does not differ greatly from a simple sense-datum as regards its function in giving knowledge4 ,its logical structure is very different1 however1 from that of sense3 sense gives acquaintance with particulars1 and is thus a two-term relation in which the object can be named but not asserted1 and is inherently incapable of truth or falsehood1 whereas the observation of a complex fact1 which may be suitably called perception1 is not a two-term relation1 but involves the propositional form on the object-side1 and gives knowledge of a truth1 not mere acquaintance with a particular4 ,this logical difference1 important as it is1 is not very relevant to our present problem2 and it will be convenient to regard data of perception as included among sense-data for the purposes of this paper4 ,it is to be observed that the particulars which are constituents of a datum of perception are always sense-data in the strict sense4 ,concerning sense-data1 we know that they are there while they are data1 and this is the epistemological basis of all our knowledge of external particulars4 7,the meaning of the word external of course raises problems which will concern us later47 ,we do not know1 except by means of more or less precarious inferences1 whether the objects which are at one time sense-data continue to exist at times when they are not data4 ,sense-data at the times when they are data are all that we directly and primitively know of the external world2 hence in epistemology the fact that they are data is all-important4 ,but the fact that they are all that we directly know gives1 of course1 no presumption that they are all that there is4 ,if we could construct an impersonal metaphysic1 independent of the accidents of our knowledge and ignorance1 the privileged position of the actual data would probably disappear1 and they would probably appear as a rather haphazard selection from a mass of objects more or less like them4 ,in saying this1 ,i assume only that it is probable that there are particulars with which we are not acquainted4 ,thus the special importance of sense-data is in relation to epistemology1 not to metaphysics4 ,in this respect1 physics is to be reckoned as metaphysics3 it is impersonal1 and nominally pays no special attention to sense-data4 ,it is only when we ask how physics can be known that the importance of sense-data re-emerges4 ,,iii4 ,,sensibilia ,i shall give the name sensibilia to those objects which have the same metaphysical and physical status as sense-data1 without necessarily being data to any mind4 ,thus the relation of a sensibile to a sense-datum is like that of a man to a husband3 a man becomes a husband by entering into the relation of marriage1 and similarly a sensibile becomes a sense-datum by entering into the relation of acquaintance4 ,it is important to have both terms2 for we wish to discuss whether an object which is at one time a sense-datum can still exist at a time when it is not a sense-datum4 ,we cannot ask ,can sense-data exist without being given8 for that is like asking ,can husbands exist without being married8 ,we must ask ,can sensibilia exist without being given8 and also ,can a particular sensibile be at one time a sense-datum1 and at another not8 ,unless we have the word sensibile as well as the word sense-datum1 such questions are apt to entangle us in trivial logical puzzles4 ,it will be seen that all sense-data are sensibilia4 ,it is a metaphysical question whether all sensibilia are sense-data1 and an epistemological question whether there exist means of inferring sensibilia which are not data from those that are4 ,a few preliminary remarks1 to be amplified as we proceed1 will serve to elucidate the use which ,i propose to make of sensibilia4 ,i regard sense-data as not mental1 and as being1 in fact1 part of the actual subject-matter of physics4 ,there are arguments1 shortly to be examined1 for their subjectivity1 but these arguments seem to me only to prove physiological subjectivity1 i4e4 causal dependence on the sense-organs1 nerves1 and brain4 ,the appearance which a thing presents to us is causally dependent upon these1 in exactly the same way as it is dependent upon intervening fog or smoke or coloured glass4 ,both dependences are contained in the statement that the appearance which a piece of matter presents when viewed from a given place is a function not only of the piece of matter1 but also of the intervening medium4 7,the terms used in this statement--matter1 view from a given place1 appearance1 intervening medium--will all be defined in the course of the present paper47 ,we have not the means of ascertaining how things appear from places not surrounded by brain and nerves and sense-organs1 because we cannot leave the body2 but continuity makes it not unreasonable to suppose that they present some appearance at such places4 ,any such appearance would be included among sensibilia4 ,if--per impossibile--there were a complete human body with no mind inside it1 all those sensibilia would exist1 in relation to that body1 which would be sense-data if there were a mind in the body4 ,what the mind adds to sensibilia1 in fact1 is merely awareness3 everything else is physical or physiological4 ,,iv4 ,,sense-,,data ,,are ,,physical ,before discussing this question it will be well to define the sense in which the terms mental and physical are to be used4 ,the word physical1 in all preliminary discussions1 is to be understood as meaning what is dealt with by physics4 ,physics1 it is plain1 tells us something about some of the constituents of the actual world2 what these constituents are may be doubtful1 but it is they that are to be called physical1 whatever their nature may prove to be4 ,the definition of the term mental is more difficult1 and can only be satisfactorily given after many difficult controversies have been discussed and decided4 ,for present purposes therefore ,i must content myself with assuming a dogmatic answer to these controversies4 ,i shall call a particular mental when it is aware of something1 and ,i shall call a fact mental when it contains a mental particular as a constituent4 ,it will be seen that the mental and the physical are not necessarily mutually exclusive1 although ,i know of no reason to suppose that they overlap4 ,the doubt as to the correctness of our definition of the mental is of little importance in our present discussion4 ,for what ,i am concerned to maintain is that sense-data are physical1 and this being granted it is a matter of indifference in our present inquiry whether or not they are also mental4 ,although ,i do not hold1 with ,mach and ,james and the new realists1 that the difference between the mental and the physical is merely one of arrangement1 yet what ,i have to say in the present paper is compatible with their doctrine and might have been reached from their standpoint4 ,in discussions on sense-data1 two questions are commonly confused1 namely3 7#a7 ,do sensible objects persist when we are not sensible of them8 in other words1 do sensibilia which are data at a certain time sometimes continue to exist at times when they are not data8 ,and 7#b7 are sense-data mental or physical8 ,i propose to assert that sense-data are physical1 while yet maintaining that they probably never persist unchanged after ceasing to be data4 ,the view that they do not persist is often thought1 quite erroneously in my opinion1 to imply that they are mental2 and this has1 ,i believe1 been a potent source of confusion in regard to our present problem4 ,if there were1 as some have held1 a logical impossibility in sense-data persisting after ceasing to be data1 that certainly would tend to show that they were mental2 but if1 as ,i contend1 their non-persistence is merely a probable inference from empirically ascertained causal laws1 then it carries no such implication with it1 and we are quite free to treat them as part of the subject-matter of physics4 ,logically a sense-datum is an object1 a particular of which the subject is aware4 ,it does not contain the subject as a part1 as for example beliefs and volitions do4 ,the existence of the sense-datum is therefore not logically dependent upon that of the subject2 for the only way1 so far as ,i know1 in which the existence of ,a can be logically dependent upon the existence of ,b is when ,b is part of ,a4 ,there is therefore no a priori reason why a particular which is a sense-datum should not persist after it has ceased to be a datum1 nor why other similar particulars should not exist without ever being data4 ,the view that sense-data are mental is derived1 no doubt1 in part from their physiological subjectivity1 but in part also from a failure to distinguish between sense-data and sensations4 ,by a sensation ,i mean the fact consisting in the subject's awareness of the sense-datum4 ,thus a sensation is a complex of which the subject is a constituent and which therefore is mental4 ,the sense-datum1 on the other hand1 stands over against the subject as that external object of which in sensation the subject is aware4 ,it is true that the sense-datum is in many cases in the subject's body1 but the subject's body is as distinct from the subject as tables and chairs are1 and is in fact merely a part of the material world4 ,so soon1 therefore1 as sense-data are clearly distinguished from sensations1 and as their subjectivity is recognised to be physiological not psychical1 the chief obstacles in the way of regarding them as physical are removed4 ,v4 ,,sensibilia ,,and ,,things ,but if sensibilia are to be recognised as the ultimate constituents of the physical world1 a long and difficult journey is to be performed before we can arrive either at the thing of common sense or at the matter of physics4 ,the supposed impossibility of combining the different sense-data which are regarded as appearances of the same thing to different people has made it seem as though these sensibilia must be regarded as mere subjective phantasms4 ,a given table will present to one man a rectangular appearance1 while to another it appears to have two acute angles and two obtuse angles2 to one man it appears brown1 while to another1 towards whom it reflects the light1 it appears white and shiny4 ,it is said1 not wholly without plausibility1 that these different shapes and different colours cannot co-exist simultaneously in the same place1 and cannot therefore both be constituents of the physical world4 ,this argument ,i must confess appeared to me until recently to be irrefutable4 ,the contrary opinion has1 however1 been ably maintained by ,dr4 ,t4,p4 ,nunn in an article entitled3 ,are ,secondary ,qualities ,independent of ,perception8#bi ,the supposed impossibility derives its apparent force from the phrase3 in the same place1 and it is precisely in this phrase that its weakness lies4 ,the conception of space is too often treated in philosophy--even by those who on reflection would not defend such treatment--as though it were as given1 simple1 and unambiguous as ,kant1 in his psychological innocence1 supposed4 ,it is the unperceived ambiguity of the word place which1 as we shall shortly see1 has caused the difficulties to realists and given an undeserved advantage to their opponents4 ,two places of different kinds are involved in every sense-datum1 namely the place at which it appears and the place from which it appears4 ,these belong to different spaces1 although1 as we shall see1 it is possible1 with certain limitations1 to establish a correlation between them4 ,what we call the different appearances of the same thing to different observers are each in a space private to the observer concerned4 ,no place in the private world of one observer is identical with a place in the private world of another observer4 ,there is therefore no question of combining the different appearances in the one place2 and the fact that they cannot all exist in one place affords accordingly no ground whatever for questioning their physical reality4 ,the thing of common sense may in fact be identified with the whole class of its appearances--where1 however1 we must include among appearances not only those which are actual sense-data1 but also those sensibilia1 if any1 which1 on grounds of continuity and resemblance1 are to be regarded as belonging to the same system of appearances1 although there happen to be no observers to whom they are data4 ,an example may make this clearer4 ,suppose there are a number of people in a room1 all seeing1 as they say1 the same tables and chairs1 walls and pictures4 ,no two of these people have exactly the same sense-data1 yet there is sufficient similarity among their data to enable them to group together certain of these data as appearances of one thing to the several spectators1 and others as appearances of another thing4 ,besides the appearances which a given thing in the room presents to the actual spectators1 there are1 we may suppose1 other appearances which it would present to other possible spectators4 ,if a man were to sit down between two others1 the appearance which the room would present to him would be intermediate between the appearances which it presents to the two others3 and although this appearance would not exist as it is without the sense organs1 nerves and brain1 of the newly arrived spectator1 still it is not unnatural to suppose that1 from the position which he now occupies1 some appearance of the room existed before his arrival4 ,this supposition1 however1 need merely be noticed and not insisted upon4 ,since the thing cannot1 without indefensible partiality1 be identified with any single one of its appearances1 it came to be thought of as something distinct from all of them and underlying them4 ,but by the principle of ,occam's razor1 if the class of appearances will fulfil the purposes for the sake of which the thing was invented by the prehistoric metaphysicians to whom common sense is due1 economy demands that we should identify the thing with the class of its appearances4 ,it is not necessary to deny a substance or substratum underlying these appearances2 it is merely expedient to abstain from asserting this unnecessary entity4 ,our procedure here is precisely analogous to that which has swept away from the philosophy of mathematics the useless menagerie of metaphysical monsters with which it used to be infested4 ,,vi4 ,,constructions ,,versus ,,inferences ,before proceeding to analyse and explain the ambiguities of the word place1 a few general remarks on method are desirable4 ,the supreme maxim in scientific philosophising is this3 ,wherever possible1 logical constructions are to be substituted for inferred entities4 ,some examples of the substitution of construction for inference in the realm of mathematical philosophy may serve to elucidate the uses of this maxim4 ,take first the case of irrationals4 ,in old days1 irrationals were inferred as the supposed limits of series of rationals which had no rational limit2 but the objection to this procedure was that it left the existence of irrationals merely optative1 and for this reason the stricter methods of the present day no longer tolerate such a definition4 ,we now define an irrational number as a certain class of ratios1 thus constructing it logically by means of ratios1 instead of arriving at it by a doubtful inference from them4 ,take again the case of cardinal numbers4 ,two equally numerous collections appear to have something in common3 this something is supposed to be their cardinal number4 ,but so long as the cardinal number is inferred from the collections1 not constructed in terms of them1 its existence must remain in doubt1 unless in virtue of a metaphysical postulate ad hoc4 ,by defining the cardinal number of a given collection as the class of all equally numerous collections1 we avoid the necessity of this metaphysical postulate1 and thereby remove a needless element of doubt from the philosophy of arithmetic4 ,a similar method1 as ,i have shown elsewhere1 can be applied to classes themselves1 which need not be supposed to have any metaphysical reality1 but can be regarded as symbolically constructed fictions4 ,the method by which the construction proceeds is closely analogous in these and all similar cases4 ,given a set of propositions nominally dealing with the supposed inferred entities1 we observe the properties which are required of the supposed entities in order to make these propositions true4 ,by dint of a little logical ingenuity1 we then construct some logical function of less hypothetical entities which has the requisite properties4 ,this constructed function we substitute for the supposed inferred entities1 and thereby obtain a new and less doubtful interpretation of the body of propositions in question4 ,this method1 so fruitful in the philosophy of mathematics1 will be found equally applicable in the philosophy of physics1 where1 ,i do not doubt1 it would have been applied long ago but for the fact that all who have studied this subject hitherto have been completely ignorant of mathematical logic4 ,i myself cannot claim originality in the application of this method to physics1 since ,i owe the suggestion and the stimulus for its application entirely to my friend and collaborator ,dr4 ,whitehead1 who is engaged in applying it to the more mathematical portions of the region intermediate between sense-data and the points1 instants and particles of physics4 ,a complete application of the method which substitutes constructions for inferences would exhibit matter wholly in terms of sense-data1 and even1 we may add1 of the sense-data of a single person1 since the sense-data of others cannot be known without some element of inference4 ,this1 however1 must remain for the present an ideal1 to be approached as nearly as possible1 but to be reached1 if at all1 only after a long preliminary labour of which as yet we can only see the very beginning4 ,the inferences which are unavoidable can1 however1 be subjected to certain guiding principles4 ,in the first place they should always be made perfectly explicit1 and should be formulated in the most general manner possible4 ,in the second place the inferred entities should1 whenever this can be done1 be similar to those whose existence is given1 rather than1 like the ,kantian ,ding an sich1 something wholly remote from the data which nominally support the inference4 ,the inferred entities which ,i shall allow myself are of two kinds3 7a7 the sense-data of other people1 in favour of which there is the evidence of testimony1 resting ultimately upon the analogical argument in favour of minds other than my own2 7b7 the sensibilia which would appear from places where there happen to be no minds1 and which ,i suppose to be real although they are no one's data4 ,of these two classes of inferred entities1 the first will probably be allowed to pass unchallenged4 ,it would give me the greatest satisfaction to be able to dispense with it1 and thus establish physics upon a solipsistic basis2 but those--and ,i fear they are the majority--in whom the human affections are stronger than the desire for logical economy1 will1 no doubt1 not share my desire to render solipsism scientifically satisfactory4 ,the second class of inferred entities raises much more serious questions4 ,it may be thought monstrous to maintain that a thing can present any appearance at all in a place where no sense organs and nervous structure exist through which it could appear4 ,i do not myself feel the monstrosity2 nevertheless ,i should regard these supposed appearances only in the light of a hypothetical scaffolding1 to be used while the edifice of physics is being raised1 though possibly capable of being removed as soon as the edifice is completed4 ,these sensibilia which are not data to anyone are therefore to be taken rather as an illustrative hypothesis and as an aid in preliminary statement than as a dogmatic part of the philosophy of physics in its final form4 ,,vii4 ,,private ,,space ,,and ,,the ,,space ,,of ,,perspectives ,we have now to explain the ambiguity in the word place1 and how it comes that two places of different sorts are associated with every sense-datum1 namely the place at which it is and the place from which it is perceived4 ,the theory to be advocated is closely analogous to ,leibniz's monadology1 from which it differs chiefly in being less smooth and tidy4 ,the first fact to notice is that1 so far as can be discovered1 no sensibile is ever a datum to two people at once4 ,the things seen by two different people are often closely similar1 so similar that the same words can be used to denote them1 without which communication with others concerning sensible objects would be impossible4 ,but1 in spite of this similarity1 it would seem that some difference always arises from difference in the point of view4 ,thus each person1 so far as his sense-data are concerned1 lives in a private world4 ,this private world contains its own space1 or rather spaces1 for it would seem that only experience teaches us to correlate the space of sight with the space of touch and with the various other spaces of other senses4 ,this multiplicity of private spaces1 however1 though interesting to the psychologist1 is of no great importance in regard to our present problem1 since a merely solipsistic experience enables us to correlate them into the one private space which embraces all our own sense-data4 ,the place at which a sense-datum is1 is a place in private space4 ,this place therefore is different from any place in the private space of another percipient4 ,for if we assume1 as logical economy demands1 that all position is relative1 a place is only definable by the things in or around it1 and therefore the same place cannot occur in two private worlds which have no common constituent4 ,the question1 therefore1 of combining what we call different appearances of the same thing in the same place does not arise1 and the fact that a given object appears to different spectators to have different shapes and colours affords no argument against the physical reality of all these shapes and colours4 ,in addition to the private spaces belonging to the private worlds of different percipients1 there is1 however1 another space1 in which one whole private world counts as a point1 or at least as a spatial unit4 ,this might be described as the space of points of view1 since each private world may be regarded as the appearance which the universe presents from a certain point of view4 ,i prefer1 however1 to speak of it as the space of perspectives1 in order to obviate the suggestion that a private world is only real when someone views it4 ,and for the same reason1 when ,i wish to speak of a private world without assuming a percipient1 ,i shall call it a perspective4 ,we have now to explain how the different perspectives are ordered in one space4 ,this is effected by means of the correlated sensibilia which are regarded as the appearances1 in different perspectives1 of one and the same thing4 ,by moving1 and by testimony1 we discover that two different perspectives1 though they cannot both contain the same sensibilia1 may nevertheless contain very similar ones2 and the spatial order of a certain group of sensibilia in a private space of one perspective is found to be identical with1 or very similar to1 the spatial order of the correlated sensibilia in the private space of another perspective4 ,in this way one sensibile in one perspective is correlated with one sensibile in another4 ,such correlated sensibilia will be called appearances of one thing4 ,in ,leibniz's monadology1 since each monad mirrored the whole universe1 there was in each perspective a sensibile which was an appearance of each thing4 ,in our system of perspectives1 we make no such assumption of completeness4 ,a given thing will have appearances in some perspectives1 but presumably not in certain others4 ,the thing being defined as the class of its appearances1 if kappa is the class of perspectives in which a certain thing theta appears1 then theta is a member of the multiplicative class of kappa1 kappa being a class of mutually exclusive classes of sensibilia4 ,and similarly a perspective is a member of the multiplicative class of the things which appear in it4 ,the arrangement of perspectives in a space is effected by means of the differences between the appearances of a given thing in the various perspectives4 ,suppose1 say1 that a certain penny appears in a number of different perspectives2 in some it looks larger and in some smaller1 in some it looks circular1 in others it presents the appearance of an ellipse of varying eccentricity4 ,we may collect together all those perspectives in which the appearance of the penny is circular4 ,these we will place on one straight line1 ordering them in a series by the variations in the apparent size of the penny4 ,those perspectives in which the penny appears as a straight line of a certain thickness will similarly be placed upon a plane 7though in this case there will be many different perspectives in which the penny is of the same size2 when one arrangement is completed these will form a circle concentric with the penny71 and ordered as before by the apparent size of the penny4 ,by such means1 all those perspectives in which the penny presents a visual appearance can be arranged in a three-dimensional spatial order4 ,experience shows that the same spatial order of perspectives would have resulted if1 instead of the penny1 we had chosen any other thing which appeared in all the perspectives in question1 or any other method of utilising the differences between the appearances of the same things in different perspectives4 ,it is this empirical fact which has made it possible to construct the one all-embracing space of physics4 ,the space whose construction has just been explained1 and whose elements are whole perspectives1 will be called perspective-space4 ,,viii4 ,,the ,,placing ,,of ,,things ,,and ,,sensibilia ,,in ,,perspective ,,space ,the world which we have so far constructed is a world of six dimensions1 since it is a three-dimensional series of perspectives1 each of which is itself three-dimensional4 ,we have now to explain the correlation between the perspective space and the various private spaces contained within the various perspectives severally4 ,it is by means of this correlation that the one three-dimensional space of physics is constructed2 and it is because of the unconscious performance of this correlation that the distinction between perspective space and the percipient's private space has been blurred1 with disastrous results for the philosophy of physics4 ,let us revert to our penny3 the perspectives in which the penny appears larger are regarded as being nearer to the penny than those in which it appears smaller1 but as far as experience goes the apparent size of the penny will not grow beyond a certain limit1 namely1 that where 7as we say7 the penny is so near the eye that if it were any nearer it could not be seen4 ,by touch we may prolong the series until the penny touches the eye1 but no further4 ,if we have been travelling along a line of perspectives in the previously defined sense1 we may1 however1 by imagining the penny removed1 prolong the line of perspectives by means1 say1 of another penny2 and the same may be done with any other line of perspectives defined by means of the penny4 ,all these lines meet in a certain place1 that is1 in a certain perspective4 ,this perspective will be defined as the place where the penny is4 ,it is now evident in what sense two places in constructed physical space are associated with a given sensibile4 ,there is first the place which is the perspective of which the sensibile is a member4 ,this is the place from which the sensibile appears4 ,secondly there is the place where the thing is of which the sensibile is a member1 in other words an appearance2 this is the place at which the sensibile appears4 ,the sensibile which is a member of one perspective is correlated with another perspective1 namely1 that which is the place where the thing is of which the sensibile is an appearance4 ,to the psychologist the place from which is the more interesting1 and the sensibile accordingly appears to him subjective and where the percipient is4 ,to the physicist the place at which is the more interesting1 and the sensibile accordingly appears to him physical and external4 ,the causes1 limits and partial justification of each of these two apparently incompatible views are evident from the above duplicity of places associated with a given sensibile4 ,we have seen that we can assign to a physical thing a place in the perspective space4 ,in this way different parts of our body acquire positions in perspective space1 and therefore there is a meaning 7whether true or false need not much concern us7 in saying that the perspective to which our sense-data belong is inside our head4 ,since our mind is correlated with the perspective to which our sense-data belong1 we may regard this perspective as being the position of our mind in perspective space4 ,if1 therefore1 this perspective is1 in the above defined sense1 inside our head1 there is a good meaning for the statement that the mind is in the head4 ,we can now say of the various appearances of a given thing that some of them are nearer to the thing than others2 those are nearer which belong to perspectives that are nearer to the place where the thing is4 ,we can thus find a meaning1 true or false1 for the statement that more is to be learnt about a thing by examining it close to than by viewing it from a distance4 ,we can also find a meaning for the phrase the things which intervene between the subject and a thing of which an appearance is a datum to him4 ,one reason often alleged for the subjectivity of sense-data is that the appearance of a thing may change when we find it hard to suppose that the thing itself has changed--for example1 when the change is due to our shutting our eyes1 or to our screwing them up so as to make the thing look double4 ,if the thing is defined as the class of its appearances 7which is the definition adopted above71 there is of course necessarily some change in the thing whenever any one of its appearances changes4 ,nevertheless there is a very important distinction between two different ways in which the appearances may change4 ,if after looking at a thing ,i shut my eyes1 the appearance of my eyes changes in every perspective in which there is such an appearance1 whereas most of the appearances of the thing will remain unchanged4 ,we may say1 as a matter of definition1 that a thing changes when1 however near to the thing an appearance of it may be1 there are changes in appearances as near as1 or still nearer to1 the thing4 ,on the other hand we shall say that the change is in some other thing if all appearances of the thing which are at not more than a certain distance from the thing remain unchanged1 while only comparatively distant appearances of the thing are altered4 ,from this consideration we are naturally led to the consideration of matter1 which must be our next topic4 ,,ix4 ,,the ,,definition ,,of ,,matter ,we defined the physical thing as the class of its appearances1 but this can hardly be taken as a definition of matter4 ,we want to be able to express the fact that the appearance of a thing in a given perspective is causally affected by the matter between the thing and the perspective4 ,we have found a meaning for between a thing and a perspective4 ,but we want matter to be something other than the whole class of appearances of a thing1 in order to state the influence of matter on appearances4 ,we commonly assume that the information we get about a thing is more accurate when the thing is nearer4 ,far off1 we see it is a man2 then we see it is ,jones2 then we see he is smiling4 ,complete accuracy would only be attainable as a limit3 if the appearances of ,jones as we approach him tend towards a limit1 that limit may be taken to be what ,jones really is4 ,it is obvious that from the point of view of physics the appearances of a thing close to count more than the appearances far off4 ,we may therefore set up the following tentative definition3 ,the matter of a given thing is the limit of its appearances as their distance from the thing diminishes4 ,it seems probable that there is something in this definition1 but it is not quite satisfactory1 because empirically there is no such limit to be obtained from sense-data4 ,the definition will have to be eked out by constructions and definitions4 ,but probably it suggests the right direction in which to look4 ,we are now in a position to understand in outline the reverse journey from matter to sense-data which is performed by physics4 ,the appearance of a thing in a given perspective is a function of the matter composing the thing and of the intervening matter4 ,the appearance of a thing is altered by intervening smoke or mist1 by blue spectacles or by alterations in the sense-organs or nerves of the percipient 7which also must be reckoned as part of the intervening medium74 ,the nearer we approach to the thing1 the less its appearance is affected by the intervening matter4 ,as we travel further and further from the thing1 its appearances diverge more and more from their initial character2 and the causal laws of their divergence are to be stated in terms of the matter which lies between them and the thing4 ,since the appearances at very small distances are less affected by causes other than the thing itself1 we come to think that the limit towards which these appearances tend as the distance diminishes is what the thing really is1 as opposed to what it merely seems to be4 ,this1 together with its necessity for the statement of causal laws1 seems to be the source of the entirely erroneous feeling that matter is more real than sense-data4 ,consider for example the infinite divisibility of matter4 ,in looking at a given thing and approaching it1 one sense-datum will become several1 and each of these will again divide4 ,thus one appearance may represent many things1 and to this process there seems no end4 ,hence in the limit1 when we approach indefinitely near to the thing there will be an indefinite number of units of matter corresponding to what1 at a finite distance1 is only one appearance4 ,this is how infinite divisibility arises4 ,the whole causal efficacy of a thing resides in its matter4 ,this is in some sense an empirical fact1 but it would be hard to state it precisely1 because causal efficacy is difficult to define4 ,what can be known empirically about the matter of a thing is only approximate1 because we cannot get to know the appearances of the thing from very small distances1 and cannot accurately infer the limit of these appearances4 ,but it is inferred approximately by means of the appearances we can observe4 ,it then turns out that these appearances can be exhibited by physics as a function of the matter in our immediate neighbourhood2 e4g4 the visual appearance of a distant object is a function of the light-waves that reach the eyes4 ,this leads to confusions of thought1 but offers no real difficulty4 ,one appearance1 of a visible object for example1 is not sufficient to determine its other simultaneous appearances1 although it goes a certain distance towards determining them4 ,the determination of the hidden structure of a thing1 so far as it is possible at all1 can only be effected by means of elaborate dynamical inferences4 ,x4 ,,time#cj ,it seems that the one all-embracing time is a construction1 like the one all-embracing space4 ,physics itself has become conscious of this fact through the discussions connected with relativity4 ,between two perspectives which both belong to one person's experience1 there will be a direct time-relation of before and after4 ,this suggests a way of dividing history in the same sort of way as it is divided by different experiences1 but without introducing experience or anything mental3 we may define a biography as everything that is 7directly7 earlier or later than1 or simultaneous with1 a given sensibile4 ,this will give a series of perspectives1 which might all form parts of one person's experience1 though it is not necessary that all or any of them should actually do so4 ,by this means1 the history of the world is divided into a number of mutually exclusive biographies4 ,we have now to correlate the times in the different biographies4 ,the natural thing would be to say that the appearances of a given 7momentary7 thing in two different perspectives belonging to different biographies are to be taken as simultaneous2 but this is not convenient4 ,suppose ,a shouts to ,b1 and ,b replies as soon as he hears ,a's shout4 ,then between ,a's hearing of his own shout and his hearing of ,b's there is an interval2 thus if we made ,a's and ,b's hearing of the same shout exactly simultaneous with each other1 we should have events exactly simultaneous with a given event but not with each other4 ,to obviate this1 we assume a velocity of sound4 ,that is1 we assume that the time when ,b hears ,a's shout is half-way between the time when ,a hears his own shout and the time when he hears ,b's4 ,in this way the correlation is effected4 ,what has been said about sound applies of course equally to light4 ,the general principle is that the appearances1 in different perspectives1 which are to be grouped together as constituting what a certain thing is at a certain moment1 are not to be all regarded as being at that moment4 ,on the contrary they spread outward from the thing with various velocities according to the nature of the appearances4 ,since no direct means exist of correlating the time in one biography with the time in another1 this temporal grouping of the appearances belonging to a given thing at a given moment is in part conventional4 ,its motive is partly to secure the verification of such maxims as that events which are exactly simultaneous with the same event are exactly simultaneous with one another1 partly to secure convenience in the formulation of causal laws4 ,,xi4 ,,the ,,persistence ,,of ,,things ,,and ,,matter ,apart from any of the fluctuating hypotheses of physics1 three main problems arise in connecting the world of physics with the world of sense1 namely3 #a4 the construction of a single space2 #b4 the construction of a single time2 #c4 the construction of permanent things or matter4 ,we have already considered the first and second of these problems2 it remains to consider the third4 ,we have seen how correlated appearances in different perspectives are combined to form one thing at one moment in the all-embracing time of physics4 ,we have now to consider how appearances at different times are combined as belonging to one thing1 and how we arrive at the persistent matter of physics4 ,the assumption of permanent substance1 which technically underlies the procedure of physics1 cannot of course be regarded as metaphysically legitimate3 just as the one thing simultaneously seen by many people is a construction1 so the one thing seen at different times by the same or different people must be a construction1 being in fact nothing but a certain grouping of certain sensibilia4 ,we have seen that the momentary state of a thing is an assemblage of sensibilia1 in different perspectives1 not all simultaneous in the one constructed time1 but spreading out from the place where the thing is with velocities depending upon the nature of the sensibilia4 ,the time at which the thing is in this state is the lower limit of the times at which these appearances occur4 ,we have now to consider what leads us to speak of another set of appearances as belonging to the same thing at a different time4 ,for this purpose1 we may1 at least to begin with1 confine ourselves within a single biography4 ,if we can always say when two sensibilia in a given biography are appearances of one thing1 then1 since we have seen how to connect sensibilia in different biographies as appearances of the same momentary state of a thing1 we shall have all that is necessary for the complete construction of the history of a thing4 ,it is to be observed1 to begin with1 that the identity of a thing for common sense is not always correlated with the identity of matter for physics4 ,a human body is one persisting thing for common sense1 but for physics its matter is constantly changing4 ,we may say1 broadly1 that the common-sense conception is based upon continuity in appearances at the ordinary distances of sense-data1 while the physical conception is based upon the continuity of appearances at very small distances from the thing4 ,it is probable that the common-sense conception is not capable of complete precision4 ,let us therefore concentrate our attention upon the conception of the persistence of matter in physics4 ,the first characteristic of two appearances of the same piece of matter at different times is continuity4 ,the two appearances must be connected by a series of intermediaries1 which1 if time and space form compact series1 must themselves form a compact series4 ,the colour of the leaves is different in autumn from what it is in summer2 but we believe that the change occurs gradually1 and that1 if the colours are different at two given times1 there are intermediate times at which the colours are intermediate between those at the given times4 ,but there are two considerations that are important as regards continuity4 ,first1 it is largely hypothetical4 ,we do not observe any one thing continuously1 and it is merely a hypothesis to assume that1 while we are not observing it1 it passes through conditions intermediate between those in which it is perceived4 ,during uninterrupted observation1 it is true1 continuity is nearly verified2 but even here1 when motions are very rapid1 as in the case of explosions1 the continuity is not actually capable of direct verification4 ,thus we can only say that the sense-data are found to permit a hypothetical complement of sensibilia such as will preserve continuity1 and that therefore there may be such a complement4 ,since1 however1 we have already made such use of hypothetical sensibilia1 we will let this point pass1 and admit such sensibilia as are required to preserve continuity4 ,secondly1 continuity is not a sufficient criterion of material identity4 ,it is true that in many cases1 such as rocks1 mountains1 tables1 chairs1 etc41 where the appearances change slowly1 continuity is sufficient1 but in other cases1 such as the parts of an approximately homogeneous fluid1 it fails us utterly4 ,we can travel by sensibly continuous gradations from any one drop of the sea at any one time to any other drop at any other time4 ,we infer the motions of sea-water from the effects of the current1 but they cannot be inferred from direct sensible observation together with the assumption of continuity4 ,the characteristic required in addition to continuity is conformity with the laws of dynamics4 ,starting from what common sense regards as persistent things1 and making only such modifications as from time to time seem reasonable1 we arrive at assemblages of sensibilia which are found to obey certain simple laws1 namely those of dynamics4 ,by regarding sensibilia at different times as belonging to the same piece of matter1 we are able to define motion1 which presupposes the assumption or construction of something persisting throughout the time of the motion4 ,the motions which are regarded as occurring1 during a period in which all the sensibilia and the times of their appearance are given1 will be different according to the manner in which we combine sensibilia at different times as belonging to the same piece of matter4 ,thus even when the whole history of the world is given in every particular1 the question what motions take place is still to a certain extent arbitrary even after the assumption of continuity4 ,experience shows that it is possible to determine motions in such a way as to satisfy the laws of dynamics1 and that this determination1 roughly and on the whole1 is fairly in agreement with the common-sense opinions about persistent things4 ,this determination1 therefore1 is adopted1 and leads to a criterion by which we can determine1 sometimes practically1 sometimes only theoretically1 whether two appearances at different times are to be regarded as belonging to the same piece of matter4 ,the persistence of all matter throughout all time can1 ,i imagine1 be secured by definition4 ,to recommend this conclusion1 we must consider what it is that is proved by the empirical success of physics4 ,what is proved is that its hypotheses1 though unverifiable where they go beyond sense-data1 are at no point in contradiction with sense-data1 but1 on the contrary1 are ideally such as to render all sense-data calculable when a sufficient collection of sensibilia is given4 ,now physics has found it empirically possible to collect sense-data into series1 each series being regarded as belonging to one thing1 and behaving1 with regard to the laws of physics1 in a way in which series not belonging to one thing would in general not behave4 ,if it is to be unambiguous whether two appearances belong to the same thing or not1 there must be only one way of grouping appearances so that the resulting things obey the laws of physics4 ,it would be very difficult to prove that this is the case1 but for our present purposes we may let this point pass1 and assume that there is only one way4 ,thus we may lay down the following definition3 ,physical things are those series of appearances whose matter obeys the laws of physics4 ,that such series exist is an empirical fact1 which constitutes the verifiability of physics4 ,,xii4 ,,illusions1 ,,hallucinations1 ,,and ,,dreams ,it remains to ask how1 in our system1 we are to find a place for sense-data which apparently fail to have the usual connection with the world of physics4 ,such sense-data are of various kinds1 requiring somewhat different treatment4 ,but all are of the sort that would be called unreal1 and therefore1 before embarking upon the discussion1 certain logical remarks must be made upon the conceptions of reality and unreality4 ,mr4 ,a4 ,wolf#ca says3 ,the conception of mind as a system of transparent activities is1 ,i think1 also untenable because of its failure to account for the very possibility of dreams and hallucinations4 ,it seems impossible to realise how a bare1 transparent activity can be directed to what is not there1 to apprehend what is not given4 ,this statement is one which1 probably1 most people would endorse4 ,but it is open to two objections4 ,first it is difficult to see how an activity1 however un-transparent1 can be directed towards a nothing3 a term of a relation cannot be a mere nonentity4 ,secondly1 no reason is given1 and ,i am convinced that none can be given1 for the assertion that dream-objects are not there and not given4 ,let us take the second point first4 7#a7 ,the belief that dream-objects are not given comes1 ,i think1 from failure to distinguish1 as regards waking life1 between the sense-datum and the corresponding thing4 ,in dreams1 there is no such corresponding thing as the dreamer supposes2 if1 therefore1 the thing were given in waking life1 as e4g4 ,meinong maintains1#cb then there would be a difference in respect of givenness between dreams and waking life4 ,but if1 as we have maintained1 what is given is never the thing1 but merely one of the sensibilia which compose the thing1 then what we apprehend in a dream is just as much given as what we apprehend in waking life4 ,exactly the same argument applies as to the dream-objects being there4 ,they have their position in the private space of the perspective of the dreamer2 where they fail is in their correlation with other private spaces and therefore with perspective space4 ,but in the only sense in which there can be a datum1 they are there just as truly as any of the sense-data of waking life4 7#b7 ,the conception of illusion or unreality1 and the correlative conception of reality1 are generally used in a way which embodies profound logical confusions4 ,words that go in pairs1 such as real and unreal1 existent and non-existent1 valid and invalid1 etc41 are all derived from the one fundamental pair1 true and false4 ,now true and false are applicable only--except in derivative significations--to propositions4 ,thus wherever the above pairs can be significantly applied1 we must be dealing either with propositions or with such incomplete phrases as only acquire meaning when put into a context which1 with them1 forms a proposition4 ,thus such pairs of words can be applied to descriptions1#cc but not to proper names3 in other words1 they have no application whatever to data1 but only to entities or non-entities described in terms of data4 ,let us illustrate by the terms existence and non-existence4 ,given any datum x1 it is meaningless either to assert or to deny that x exists4 ,we might be tempted to say3 ,of course x exists1 for otherwise it could not be a datum4 ,but such a statement is really meaningless1 although it is significant and true to say ,my present sense-datum exists1 and it may also be true that x is my present sense-datum4 ,the inference from these two propositions to x exists is one which seems irresistible to people unaccustomed to logic2 yet the apparent proposition inferred is not merely false1 but strictly meaningless4 ,to say ,my present sense-datum exists is to say 7roughly73 ,there is an object of which 'my present sense-datum' is a description4 ,but we cannot say3 ,there is an object of which 'x' is a description1 because 'x' is 7in the case we are supposing7 a name1 not a description4 ,dr4 ,whitehead and ,i have explained this point fully elsewhere 7loc4 cit47 with the help of symbols1 without which it is hard to understand2 ,i shall not therefore here repeat the demonstration of the above propositions1 but shall proceed with their application to our present problem4 ,the fact that existence is only applicable to descriptions is concealed by the use of what are grammatically proper names in a way which really transforms them into descriptions4 ,it is1 for example1 a legitimate question whether ,homer existed2 but here ,homer means the author of the ,homeric poems1 and is a description4 ,similarly we may ask whether ,god exists2 but then ,god means the ,supreme ,being or the ens realissimum or whatever other description we may prefer4 ,if ,god were a proper name1 ,god would have to be a datum2 and then no question could arise as to ,his existence4 ,the distinction between existence and other predicates1 which ,kant obscurely felt1 is brought to light by the theory of descriptions1 and is seen to remove existence altogether from the fundamental notions of metaphysics4 ,what has been said about existence applies equally to reality1 which may1 in fact1 be taken as synonymous with existence4 ,concerning the immediate objects in illusions1 hallucinations1 and dreams1 it is meaningless to ask whether they exist or are real4 ,there they are1 and that ends the matter4 ,but we may legitimately inquire as to the existence or reality of things or other sensibilia inferred from such objects4 ,it is the unreality of these things and other sensibilia1 together with a failure to notice that they are not data1 which has led to the view that the objects of dreams are unreal4 ,we may now apply these considerations in detail to the stock arguments against realism1 though what is to be said will be mainly a repetition of what others have said before4 7#a7 ,we have first the variety of normal appearances1 supposed to be incompatible4 ,this is the case of the different shapes and colours which a given thing presents to different spectators4 ,locke's water which seems both hot and cold belongs to this class of cases4 ,our system of different perspectives fully accounts for these cases1 and shows that they afford no argument against realism4 7#b7 ,we have cases where the correlation between different senses is unusual4 ,the bent stick in water belongs here4 ,people say it looks bent but is straight3 this only means that it is straight to the touch1 though bent to sight4 ,there is no illusion1 but only a false inference1 if we think that the stick would feel bent to the touch4 ,the stick would look just as bent in a photograph1 and1 as ,mr4 ,gladstone used to say1 the photograph cannot lie4#cd ,the case of seeing double also belongs here1 though in this case the cause of the unusual correlation is physiological1 and would therefore not operate in a photograph4 ,it is a mistake to ask whether the thing is duplicated when we see it double4 ,the thing is a whole system of sensibilia1 and it is only those visual sensibilia which are data to the percipient that are duplicated4 ,the phenomenon has a purely physiological explanation2 indeed1 in view of our having two eyes1 it is in less need of explanation than the single visual sense-datum which we normally obtain from the things on which we focus4 7#c7 ,we come now to cases like dreams1 which may1 at the moment of dreaming1 contain nothing to arouse suspicion1 but are condemned on the ground of their supposed incompatibility with earlier and later data4 ,of course it often happens that dream-objects fail to behave in the accustomed manner3 heavy objects fly1 solid objects melt1 babies turn into pigs or undergo even greater changes4 ,but none of these unusual occurrences need happen in a dream1 and it is not on account of such occurrences that dream-objects are called unreal4 ,it is their lack of continuity with the dreamer's past and future that makes him1 when he wakes1 condemn them2 and it is their lack of correlation with other private worlds that makes others condemn them4 ,omitting the latter ground1 our reason for condemning them is that the things which we infer from them cannot be combined according to the laws of physics with the things inferred from waking sense-data4 ,this might be used to condemn the things inferred from the data of dreams4 ,dream-data are no doubt appearances of things1 but not of such things as the dreamer supposes4 ,i have no wish to combat psychological theories of dreams1 such as those of the psycho-analysts4 ,but there certainly are cases where 7whatever psychological causes may contribute7 the presence of physical causes also is very evident4 ,for instance1 a door banging may produce a dream of a naval engagement1 with images of battleships and sea and smoke4 ,the whole dream will be an appearance of the door banging1 but owing to the peculiar condition of the body 7especially the brain7 during sleep1 this appearance is not that expected to be produced by a door banging1 and thus the dreamer is led to entertain false beliefs4 ,but his sense-data are still physical1 and are such as a completed physics would include and calculate4 7#d7 ,the last class of illusions are those which cannot be discovered within one person's experience1 except through the discovery of discrepancies with the experiences of others4 ,dreams might conceivably belong to this class1 if they were jointed sufficiently neatly into waking life2 but the chief instances are recurrent sensory hallucinations of the kind that lead to insanity4 ,what makes the patient1 in such cases1 become what others call insane is the fact that1 within his own experience1 there is nothing to show that the hallucinatory sense-data do not have the usual kind of connection with sensibilia in other perspectives4 ,of course he may learn this through testimony1 but he probably finds it simpler to suppose that the testimony is untrue and that he is being wilfully deceived4 ,there is1 so far as ,i can see1 no theoretical criterion by which the patient can decide1 in such a case1 between the two equally satisfactory hypotheses of his madness and of his friends' mendacity4 ,from the above instances it would appear that abnormal sense-data1 of the kind which we regard as deceptive1 have intrinsically just the same status as any others1 but differ as regards their correlations or causal connections with other sensibilia and with things4 ,since the usual correlations and connections become part of our unreflective expectations1 and even seem1 except to the psychologist1 to form part of our data1 it comes to be thought1 mistakenly1 that in such cases the data are unreal1 whereas they are merely the causes of false inferences4 ,the fact that correlations and connections of unusual kinds occur adds to the difficulty of inferring things from sense and of expressing physics in terms of sense-data4 ,but the unusualness would seem to be always physically or physiologically explicable1 and therefore raises only a complication1 not a philosophical objection4 ,i conclude1 therefore1 that no valid objection exists to the view which regards sense-data as part of the actual substance of the physical world1 and that1 on the other hand1 this view is the only one which accounts for the empirical verifiability of physics4 ,in the present paper1 ,i have given only a rough preliminary sketch4 ,in particular1 the part played by time in the construction of the physical world is1 ,i think1 more fundamental than would appear from the above account4 ,i should hope that1 with further elaboration1 the part played by unperceived sensibilia could be indefinitely diminished1 probably by invoking the history of a thing to eke out the inferences derivable from its momentary appearance4 ,,footnotes3 #bi ,proc4 ,arist4 ,soc41 #aiji-aiaj1 pp4 #aia-bah4 #cj ,on this subject1 compare ,a ,theory of ,time and ,space1 by ,mr4 ,a4,a4 ,robb 7,camb4 ,univ4 ,press71 which first suggested to me the views advocated here1 though ,i have1 for present purposes1 omitted what is most interesting and novel in his theory4 ,mr4 ,robb has given a sketch of his theory in a pamphlet with the same title 7,heffer and ,sons1 ,cambridge1 #aiac74 #ca ,natural ,realism and ,present ,tendencies in ,philosophy1 ,proc4 ,arist4 ,soc41 #aijh-aiji1 p4 #afe4 #cb ,die ,erfahrungsgrundlagen unseres ,wissens1 p4 #bh4 #cc ,cf4 ,principia ,mathematica1 ,vol4 ,i1 99 #ad1 and ,introduction1 ,chap4 ,,iii4 ,for the definition of existence1 cf4 99 #ad4 #jb4 #cd ,cf4 ,edwin ,b4 ,holt1 ,the ,place of ,illusory ,experience in a ,realistic ,world4 ,the ,new ,realism1 p4 #cjc1 both on this point and as regards seeing double4 ,,ix ,,on ,,the ,,notion ,,of ,,cause ,in the following paper ,i wish1 first1 to maintain that the word cause is so inextricably bound up with misleading associations as to make its complete extrusion from the philosophical vocabulary desirable2 secondly1 to inquire what principle1 if any1 is employed in science in place of the supposed law of causality which philosophers imagine to be employed2 thirdly1 to exhibit certain confusions1 especially in regard to teleology and determinism1 which appear to me to be connected with erroneous notions as to causality4 ,all philosophers1 of every school1 imagine that causation is one of the fundamental axioms or postulates of science1 yet1 oddly enough1 in advanced sciences such as gravitational astronomy1 the word cause never occurs4 ,dr4 ,james ,ward1 in his ,naturalism and ,agnosticism1 makes this a ground of complaint against physics3 the business of those who wish to ascertain the ultimate truth about the world1 he apparently thinks1 should be the discovery of causes1 yet physics never even seeks them4 ,to me it seems that philosophy ought not to assume such legislative functions1 and that the reason why physics has ceased to look for causes is that1 in fact1 there are no such things4 ,the law of causality1 ,i believe1 like much that passes muster among philosophers1 is a relic of a bygone age1 surviving1 like the monarchy1 only because it is erroneously supposed to do no harm4 ,in order to find out what philosophers commonly understand by cause1 ,i consulted ,baldwin's ,dictionary1 and was rewarded beyond my expectations1 for ,i found the following three mutually incompatible definitions3-- ,,causality4 7#a7 ,the necessary connection of events in the time-series4444 ,,cause 7notion of74 ,whatever may be included in the thought or perception of a process as taking place in consequence of another process4444 ,,cause ,,and ,,effect4 7#a7 ,cause and effect 444 are correlative terms denoting any two distinguishable things1 phases1 or aspects of reality1 which are so related to each other that whenever the first ceases to exist the second comes into existence immediately after1 and whenever the second comes into existence the first has ceased to exist immediately before4 ,let us consider these three definitions in turn4 ,the first1 obviously1 is unintelligible without a definition of necessary4 ,under this head1 ,baldwin's ,dictionary gives the following3-- ,,necessary4 ,that is necessary which not only is true1 but would be true under all circumstances4 ,something more than brute compulsion is1 therefore1 involved in the conception2 there is a general law under which the thing takes place4 ,the notion of cause is so intimately connected with that of necessity that it will be no digression to linger over the above definition1 with a view to discovering1 if possible1 some meaning of which it is capable2 for1 as it stands1 it is very far from having any definite signification4 ,the first point to notice is that1 if any meaning is to be given to the phrase would be true under all circumstances1 the subject of it must be a propositional function1 not a proposition4#ce ,a proposition is simply true or false1 and that ends the matter3 there can be no question of circumstances4 ,charles ,i's head was cut off is just as true in summer as in winter1 on ,sundays as on ,mondays4 ,thus when it is worth saying that something would be true under all circumstances1 the something in question must be a propositional function1 i4e4 an expression containing a variable1 and becoming a proposition when a value is assigned to the variable2 the varying circumstances alluded to are then the different values of which the variable is capable4 ,thus if necessary means what is true under all circumstances1 then if x is a man1 x is mortal is necessary1 because it is true for any possible value of x4 ,thus we should be led to the following definition3-- ,,necessary is a predicate of a propositional function1 meaning that it is true for all possible values of its argument or arguments4 ,unfortunately1 however1 the definition in ,baldwin's ,dictionary says that what is necessary is not only true under all circumstances but is also true4 ,now these two are incompatible4 ,only propositions can be true1 and only propositional functions can be true under all circumstances4 ,hence the definition as it stands is nonsense4 ,what is meant seems to be this3 ,a proposition is necessary when it is a value of a propositional function which is true under all circumstances1 i4e4 for all values of its argument or arguments4 ,but if we adopt this definition1 the same proposition will be necessary or contingent according as we choose one or other of its terms as the argument to our propositional function4 ,for example1 if ,socrates is a man1 ,socrates is mortal1 is necessary if ,socrates is chosen as argument1 but not if man or mortal is chosen4 ,again1 if ,socrates is a man1 ,plato is mortal1 will be necessary if either ,socrates or man is chosen as argument1 but not if ,plato or mortal is chosen4 ,however1 this difficulty can be overcome by specifying the constituent which is to be regarded as argument1 and we thus arrive at the following definition3 ,a proposition is necessary with respect to a given constituent if it remains true when that constituent is altered in any way compatible with the proposition remaining significant4 ,we may now apply this definition to the definition of causality quoted above4 ,it is obvious that the argument must be the time at which the earlier event occurs4 ,thus an instance of causality will be such as3 ,if the event ,math3 e#a occurs at the time ,math3 t#a1 it will be followed by the event ,math3 e#b4 ,this proposition is intended to be necessary with respect to ,math3 t#a1 i4e4 to remain true however ,math3 t#a may be varied4 ,causality1 as a universal law1 will then be the following3 ,given any event ,math3 t#a1 there is an event ,math3 e#b such that1 whenever ,math3 t#a occurs1 ,math3 e#b occurs later4 ,but before this can be considered precise1 we must specify how much later ,math3 e#b is to occur4 ,thus the principle becomes3-- ,given any event ,math3 e#a1 there is an event ,math3 e#b and a time-interval tau such that1 whenever ,math3 e#a occurs1 ,math3 e#b follows after an interval tau4 ,i am not concerned as yet to consider whether this law is true or false4 ,for the present1 ,i am merely concerned to discover what the law of causality is supposed to be4 ,i pass1 therefore1 to the other definitions quoted above4 ,the second definition need not detain us long1 for two reasons4 ,first1 because it is psychological3 not the thought or perception of a process1 but the process itself1 must be what concerns us in considering causality4 ,secondly1 because it is circular3 in speaking of a process as taking place in consequence of another process1 it introduces the very notion of cause which was to be defined4 ,the third definition is by far the most precise2 indeed as regards clearness it leaves nothing to be desired4 ,but a great difficulty is caused by the temporal contiguity of cause and effect which the definition asserts4 ,no two instants are contiguous1 since the time-series is compact2 hence either the cause or the effect or both must1 if the definition is correct1 endure for a finite time2 indeed1 by the wording of the definition it is plain that both are assumed to endure for a finite time4 ,but then we are faced with a dilemma3 if the cause is a process involving change within itself1 we shall require 7if causality is universal7 causal relations between its earlier and later parts2 moreover1 it would seem that only the later parts can be relevant to the effect1 since the earlier parts are not contiguous to the effect1 and therefore 7by the definition7 cannot influence the effect4 ,thus we shall be led to diminish the duration of the cause without limit1 and however much we may diminish it1 there will still remain an earlier part which might be altered without altering the effect1 so that the true cause1 as defined1 will not have been reached1 for it will be observed that the definition excludes plurality of causes4 ,if1 on the other hand1 the cause is purely static1 involving no change within itself1 then1 in the first place1 no such cause is to be found in nature1 and in the second place1 it seems strange--too strange to be accepted1 in spite of bare logical possibility--that the cause1 after existing placidly for some time1 should suddenly explode into the effect1 when it might just as well have done so at any earlier time1 or have gone on unchanged without producing its effect4 ,this dilemma1 therefore1 is fatal to the view that cause and effect can be contiguous in time2 if there are causes and effects1 they must be separated by a finite time-interval tau1 as was assumed in the above interpretation of the first definition4 ,what is essentially the same statement of the law of causality as the one elicited above from the first of ,baldwin's definitions is given by other philosophers4 ,thus ,john ,stuart ,mill says3-- ,the ,law of ,causation1 the recognition of which is the main pillar of inductive science1 is but the familiar truth1 that invariability of succession is found by observation to obtain between every fact in nature and some other fact which has preceded it4#cf ,and ,bergson1 who has rightly perceived that the law as stated by philosophers is worthless1 nevertheless continues to suppose that it is used in science4 ,thus he says3-- ,now1 it is argued1 this law the law of causality means that every phenomenon is determined by its conditions1 or1 in other words1 that the same causes produce the same effects4#cg ,and again3-- ,we perceive physical phenomena1 and these phenomena obey laws4 ,this means3 7#a7 ,that phenomena a1 b1 c1 d1 previously perceived1 can occur again in the same shape2 7#b7 that a certain phenomenon ,p1 which appeared after the conditions a1 b1 c1 d1 and after these conditions only1 will not fail to recur as soon as the same conditions are again present4#ch ,a great part of ,bergson's attack on science rests on the assumption that it employs this principle4 ,in fact1 it employs no such principle1 but philosophers--even ,bergson--are too apt to take their views on science from each other1 not from science4 ,as to what the principle is1 there is a fair consensus among philosophers of different schools4 ,there are1 however1 a number of difficulties which at once arise4 ,i omit the question of plurality of causes for the present1 since other graver questions have to be considered4 ,two of these1 which are forced on our attention by the above statement of the law1 are the following3-- 7#a7 ,what is meant by an event8 7#b7 ,how long may the time-interval be between cause and effect8 7#a7 ,an event1 in the statement of the law1 is obviously intended to be something that is likely to recur since otherwise the law becomes trivial4 ,it follows that an event is not a particular1 but some universal of which there may be many instances4 ,it follows also that an event must be something short of the whole state of the universe1 since it is highly improbable that this will recur4 ,what is meant by an event is something like striking a match1 or dropping a penny into the slot of an automatic machine4 ,if such an event is to recur1 it must not be defined too narrowly3 we must not state with what degree of force the match is to be struck1 nor what is to be the temperature of the penny4 ,for if such considerations were relevant1 our event would occur at most once1 and the law would cease to give information4 ,an event1 then1 is a universal defined sufficiently widely to admit of many particular occurrences in time being instances of it4 7#b7 ,the next question concerns the time-interval4 ,philosophers1 no doubt1 think of cause and effect as contiguous in time1 but this1 for reasons already given1 is impossible4 ,hence1 since there are no infinitesimal time-intervals1 there must be some finite lapse of time tau between cause and effect4 ,this1 however1 at once raises insuperable difficulties4 ,however short we make the interval tau1 something may happen during this interval which prevents the expected result4 ,i put my penny in the slot1 but before ,i can draw out my ticket there is an earthquake which upsets the machine and my calculations4 ,in order to be sure of the expected effect1 we must know that there is nothing in the environment to interfere with it4 ,but this means that the supposed cause is not1 by itself1 adequate to insure the effect4 ,and as soon as we include the environment1 the probability of repetition is diminished1 until at last1 when the whole environment is included1 the probability of repetition becomes almost nil4 ,in spite of these difficulties1 it must1 of course1 be admitted that many fairly dependable regularities of sequence occur in daily life4 ,it is these regularities that have suggested the supposed law of causality2 where they are found to fail1 it is thought that a better formulation could have been found which would have never failed4 ,i am far from denying that there may be such sequences which in fact never do fail4 ,it may be that there will never be an exception to the rule that when a stone of more than a certain mass1 moving with more than a certain velocity1 comes in contact with a pane of glass of less than a certain thickness1 the glass breaks4 ,i also do not deny that the observation of such regularities1 even when they are not without exceptions1 is useful in the infancy of a science3 the observation that unsupported bodies in air usually fall was a stage on the way to the law of gravitation4 ,what ,i deny is that science assumes the existence of invariable uniformities of sequence of this kind1 or that it aims at discovering them4 ,all such uniformities1 as we saw1 depend upon a certain vagueness in the definition of the events4 ,that bodies fall is a vague qualitative statement2 science wishes to know how fast they fall4 ,this depends upon the shape of the bodies and the density of the air4 ,it is true that there is more nearly uniformity when they fall in a vacuum2 so far as ,galileo could observe1 the uniformity is then complete4 ,but later it appeared that even there the latitude made a difference1 and the altitude4 ,theoretically1 the position of the sun and moon must make a difference4 ,in short1 every advance in a science takes us farther away from the crude uniformities which are first observed1 into greater differentiation of antecedent and consequent1 and into a continually wider circle of antecedents recognised as relevant4 ,the principle same cause1 same effect1 which philosophers imagine to be vital to science1 is therefore utterly otiose4 ,as soon as the antecedents have been given sufficiently fully to enable the consequent to be calculated with some exactitude1 the antecedents have become so complicated that it is very unlikely they will ever recur4 ,hence1 if this were the principle involved1 science would remain utterly sterile4 ,the importance of these considerations lies partly in the fact that they lead to a more correct account of scientific procedure1 partly in the fact that they remove the analogy with human volition which makes the conception of cause such a fruitful source of fallacies4 ,the latter point will become clearer by the help of some illustrations4 ,for this purpose ,i shall consider a few maxims which have played a great part in the history of philosophy4 7#a7 ,cause and effect must more or less resemble each other4 ,this principle was prominent in the philosophy of occasionalism1 and is still by no means extinct4 ,it is still often thought1 for example1 that mind could not have grown up in a universe which previously contained nothing mental1 and one ground for this belief is that matter is too dissimilar from mind to have been able to cause it4 ,or1 more particularly1 what are termed the nobler parts of our nature are supposed to be inexplicable1 unless the universe always contained something at least equally noble which could cause them4 ,all such views seem to depend upon assuming some unduly simplified law of causality2 for1 in any legitimate sense of cause and effect1 science seems to show that they are usually very widely dissimilar1 the cause being1 in fact1 two states of the whole universe1 and the effect some particular event4 7#b7 ,cause is analogous to volition1 since there must be an intelligible nexus between cause and effect4 ,this maxim is1 ,i think1 often unconsciously in the imaginations of philosophers who would reject it when explicitly stated4 ,it is probably operative in the view we have just been considering1 that mind could not have resulted from a purely material world4 ,i do not profess to know what is meant by intelligible2 it seems to mean familiar to imagination4 ,nothing is less intelligible1 in any other sense1 than the connection between an act of will and its fulfilment4 ,but obviously the sort of nexus desired between cause and effect is such as could only hold between the events which the supposed law of causality contemplates2 the laws which replace causality in such a science as physics leave no room for any two events between which a nexus could be sought4 7#c7 ,the cause compels the effect in some sense in which the effect does not compel the cause4 ,this belief seems largely operative in the dislike of determinism2 but1 as a matter of fact1 it is connected with our second maxim1 and falls as soon as that is abandoned4 ,we may define compulsion as follows3 ,any set of circumstances is said to compel ,a when ,a desires to do something which the circumstances prevent1 or to abstain from something which the circumstances cause4 ,this presupposes that some meaning has been found for the word cause--a point to which ,i shall return later4 ,what ,i want to make clear at present is that compulsion is a very complex notion1 involving thwarted desire4 ,so long as a person does what he wishes to do1 there is no compulsion1 however much his wishes may be calculable by the help of earlier events4 ,and where desire does not come in1 there can be no question of compulsion4 ,hence it is1 in general1 misleading to regard the cause as compelling the effect4 ,a vaguer form of the same maxim substitutes the word determine for the word compel2 we are told that the cause determines the effect in a sense in which the effect does not determine the cause4 ,it is not quite clear what is meant by determining2 the only precise sense1 so far as ,i know1 is that of a function or one-many relation4 ,if we admit plurality of causes1 but not of effects1 that is1 if we suppose that1 given the cause1 the effect must be such and such1 but1 given the effect1 the cause may have been one of many alternatives1 then we may say that the cause determines the effect1 but not the effect the cause4 ,plurality of causes1 however1 results only from conceiving the effect vaguely and narrowly and the cause precisely and widely4 ,many antecedents may cause a man's death1 because his death is vague and narrow4 ,but if we adopt the opposite course1 taking as the cause the drinking of a dose of arsenic1 and as the effect the whole state of the world five minutes later1 we shall have plurality of effects instead of plurality of causes4 ,thus the supposed lack of symmetry between cause and effect is illusory4 7#d7 ,a cause cannot operate when it has ceased to exist1 because what has ceased to exist is nothing4 ,this is a common maxim1 and a still more common unexpressed prejudice4 ,it has1 ,i fancy1 a good deal to do with the attractiveness of ,bergson's dure3 since the past has effects now1 it must still exist in some sense4 ,the mistake in this maxim consists in the supposition that causes operate at all4 ,a volition operates when what it wills takes place2 but nothing can operate except a volition4 ,the belief that causes operate results from assimilating them1 consciously or unconsciously1 to volitions4 ,we have already seen that1 if there are causes at all1 they must be separated by a finite interval of time from their effects1 and thus cause their effects after they have ceased to exist4 ,it may be objected to the above definition of a volition operating that it only operates when it causes what it wills1 not when it merely happens to be followed by what it wills4 ,this certainly represents the usual view of what is meant by a volition operating1 but as it involves the very view of causation which we are engaged in combating1 it is not open to us as a definition4 ,we may say that a volition operates when there is some law in virtue of which a similar volition in rather similar circumstances will usually be followed by what it wills4 ,but this is a vague conception1 and introduces ideas which we have not yet considered4 ,what is chiefly important to notice is that the usual notion of operating is not open to us if we reject1 as ,i contend that we should1 the usual notion of causation4 7#e7 ,a cause cannot operate except where it is4 ,this maxim is very widespread2 it was urged against ,newton1 and has remained a source of prejudice against action at a distance4 ,in philosophy it has led to a denial of transient action1 and thence to monism or ,leibnizian monadism4 ,like the analogous maxim concerning temporal contiguity1 it rests upon the assumption that causes operate1 i4e4 that they are in some obscure way analogous to volitions4 ,and1 as in the case of temporal contiguity1 the inferences drawn from this maxim are wholly groundless4 ,i return now to the question1 ,what law or laws can be found to take the place of the supposed law of causality8 ,first1 without passing beyond such uniformities of sequence as are contemplated by the traditional law1 we may admit that1 if any such sequence has been observed in a great many cases1 and has never been found to fail1 there is an inductive probability that it will be found to hold in future cases4 ,if stones have hitherto been found to break windows1 it is probable that they will continue to do so4 ,this1 of course1 assumes the inductive principle1 of which the truth may reasonably be questioned2 but as this principle is not our present concern1 ,i shall in this discussion treat it as indubitable4 ,we may then say1 in the case of any such frequently observed sequence1 that the earlier event is the cause and the later event the effect4 ,several considerations1 however1 make such special sequences very different from the traditional relation of cause and effect4 ,in the first place1 the sequence1 in any hitherto unobserved instance1 is no more than probable1 whereas the relation of cause and effect was supposed to be necessary4 ,i do not mean by this merely that we are not sure of having discovered a true case of cause and effect2 ,i mean that1 even when we have a case of cause and effect in our present sense1 all that is meant is that on grounds of observation1 it is probable that when one occurs the other will also occur4 ,thus in our present sense1 ,a may be the cause of ,b even if there actually are cases where ,b does not follow ,a4 ,striking a match will be the cause of its igniting1 in spite of the fact that some matches are damp and fail to ignite4 ,in the second place1 it will not be assumed that every event has some antecedent which is its cause in this sense2 we shall only believe in causal sequences where we find them1 without any presumption that they always are to be found4 ,in the third place1 any case of sufficiently frequent sequence will be causal in our present sense2 for example1 we shall not refuse to say that night is the cause of day4 ,our repugnance to saying this arises from the ease with which we can imagine the sequence to fail1 but owing to the fact that cause and effect must be separated by a finite interval of time1 any such sequence might fail through the interposition of other circumstances in the interval4 ,mill1 discussing this instance of night and day1 says3-- ,it is necessary to our using the word cause1 that we should believe not only that the antecedent always has been followed by the consequent1 but that as long as the present constitution of things endures1 it always will be so4#ci ,in this sense1 we shall have to give up the hope of finding causal laws such as ,mill contemplated2 any causal sequence which we have observed may at any moment be falsified without a falsification of any laws of the kind that the more advanced sciences aim at establishing4 ,in the fourth place1 such laws of probable sequence1 though useful in daily life and in the infancy of a science1 tend to be displaced by quite different laws as soon as a science is successful4 ,the law of gravitation will illustrate what occurs in any advanced science4 ,in the motions of mutually gravitating bodies1 there is nothing that can be called a cause1 and nothing that can be called an effect2 there is merely a formula4 ,certain differential equations can be found1 which hold at every instant for every particle of the system1 and which1 given the configuration and velocities at one instant1 or the configurations at two instants1 render the configuration at any other earlier or later instant theoretically calculable4 ,that is to say1 the configuration at any instant is a function of that instant and the configurations at two given instants4 ,this statement holds throughout physics1 and not only in the special case of gravitation4 ,but there is nothing that could be properly called cause and nothing that could be properly called effect in such a system4 ,no doubt the reason why the old law of causality has so long continued to pervade the books of philosophers is simply that the idea of a function is unfamiliar to most of them1 and therefore they seek an unduly simplified statement4 ,there is no question of repetitions of the same cause producing the same effect2 it is not in any sameness of causes and effects that the constancy of scientific law consists1 but in sameness of relations4 ,and even sameness of relations is too simple a phrase2 sameness of differential equations is the only correct phrase4 ,it is impossible to state this accurately in non-mathematical language2 the nearest approach would be as follows3 ,there is a constant relation between the state of the universe at any instant and the rate of change in the rate at which any part of the universe is changing at that instant1 and this relation is many-one1 i4e4 such that the rate of change in the rate of change is determinate when the state of the universe is given4 ,if the law of causality is to be something actually discoverable in the practice of science1 the above proposition has a better right to the name than any law of causality to be found in the books of philosophers4 ,in regard to the above principle1 several observations must be made-- 7#a7 ,no one can pretend that the above principle is a priori or self-evident or a necessity of thought4 ,nor is it1 in any sense1 a premiss of science3 it is an empirical generalisation from a number of laws which are themselves empirical generalisations4 7#b7 ,the law makes no difference between past and future3 the future determines the past in exactly the same sense in which the past determines the future4 ,the word determine1 here1 has a purely logical significance3 a certain number of variables determine another variable if that other variable is a function of them4 7#c7 ,the law will not be empirically verifiable unless the course of events within some sufficiently small volume will be approximately the same in any two states of the universe which only differ in regard to what is at a considerable distance from the small volume in question4 ,for example1 motions of planets in the solar system must be approximately the same however the fixed stars may be distributed1 provided that all the fixed stars are very much farther from the sun than the planets are4 ,if gravitation varied directly as the distance1 so that the most remote stars made the most difference to the motions of the planets1 the world might be just as regular and just as much subject to mathematical laws as it is at present1 but we could never discover the fact4 7#d7 ,although the old law of causality is not assumed by science1 something which we may call the uniformity of nature is assumed1 or rather is accepted on inductive grounds4 ,the uniformity of nature does not assert the trivial principle same cause1 same effect1 but the principle of the permanence of laws4 ,that is to say1 when a law exhibiting1 e4g4 an acceleration as a function of the configuration has been found to hold throughout the observable past1 it is expected that it will continue to hold in the future1 or that1 if it does not itself hold1 there is some other law1 agreeing with the supposed law as regards the past1 which will hold for the future4 ,the ground of this principle is simply the inductive ground that it has been found to be true in very many instances2 hence the principle cannot be considered certain1 but only probable to a degree which cannot be accurately estimated4 ,the uniformity of nature1 in the above sense1 although it is assumed in the practice of science1 must not1 in its generality1 be regarded as a kind of major premiss1 without which all scientific reasoning would be in error4 ,the assumption that all laws of nature are permanent has1 of course1 less probability than the assumption that this or that particular law is permanent2 and the assumption that a particular law is permanent for all time has less probability than the assumption that it will be valid up to such and such a date4 ,science1 in any given case1 will assume what the case requires1 but no more4 ,in constructing the ,nautical ,almanac for #aiae it will assume that the law of gravitation will remain true up to the end of that year2 but it will make no assumption as to #aiaf until it comes to the next volume of the almanac4 ,this procedure is1 of course1 dictated by the fact that the uniformity of nature is not known a priori1 but is an empirical generalisation1 like all men are mortal4 ,in all such cases1 it is better to argue immediately from the given particular instances to the new instance1 than to argue by way of a major premiss2 the conclusion is only probable in either case1 but acquires a higher probability by the former method than by the latter4 ,in all science we have to distinguish two sorts of laws3 first1 those that are empirically verifiable but probably only approximate2 secondly1 those that are not verifiable1 but may be exact4 ,the law of gravitation1 for example1 in its applications to the solar system1 is only empirically verifiable when it is assumed that matter outside the solar system may be ignored for such purposes2 we believe this to be only approximately true1 but we cannot empirically verify the law of universal gravitation which we believe to be exact4 ,this point is very important in connection with what we may call relatively isolated systems4 ,these may be defined as follows3-- ,a system relatively isolated during a given period is one which1 within some assignable margin of error1 will behave in the same way throughout that period1 however the rest of the universe may be constituted4 ,a system may be called practically isolated during a given period if1 although there might be states of the rest of the universe which would produce more than the assigned margin of error1 there is reason to believe that such states do not in fact occur4 ,strictly speaking1 we ought to specify the respect in which the system is relatively isolated4 ,for example1 the earth is relatively isolated as regards falling bodies1 but not as regards tides2 it is practically isolated as regards economic phenomena1 although1 if ,jevons' sunspot theory of commercial crises had been true1 it would not have been even practically isolated in this respect4 ,it will be observed that we cannot prove in advance that a system is isolated4 ,this will be inferred from the observed fact that approximate uniformities can be stated for this system alone4 ,if the complete laws for the whole universe were known1 the isolation of a system could be deduced from them2 assuming1 for example1 the law of universal gravitation1 the practical isolation of the solar system in this respect can be deduced by the help of the fact that there is very little matter in its neighbourhood4 ,but it should be observed that isolated systems are only important as providing a possibility of discovering scientific laws2 they have no theoretical importance in the finished structure of a science4 ,the case where one event ,a is said to cause another event ,b1 which philosophers take as fundamental1 is really only the most simplified instance of a practically isolated system4 ,it may happen that1 as a result of general scientific laws1 whenever ,a occurs throughout a certain period1 it is followed by ,b2 in that case1 ,a and ,b form a system which is practically isolated throughout that period4 ,it is1 however1 to be regarded as a piece of good fortune if this occurs2 it will always be due to special circumstances1 and would not have been true if the rest of the universe had been different though subject to the same laws4 ,the essential function which causality has been supposed to perform is the possibility of inferring the future from the past1 or1 more generally1 events at any time from events at certain assigned times4 ,any system in which such inference is possible may be called a deterministic system4 ,we may define a deterministic system as follows3-- ,a system is said to be deterministic when1 given certain data1 ,math3 e#a1 e#b1 4441 en1 at times t#a1 t#b1 4441 tn respectively1 concerning this system1 if ,math3 ,et is the state of the system at any time t1 there is a functional relation of the form ,math3 ,et f 7e#a1 t#a1 e#b1 t#b1 4441 en1 tn1 t74 7,a7 ,the system will be deterministic throughout a given period if t1 in the above formula1 may be any time within that period1 though outside that period the formula may be no longer true4 ,if the universe1 as a whole1 is such a system1 determinism is true of the universe2 if not1 not4 ,a system which is part of a deterministic system ,i shall call determined2 one which is not part of any such system ,i shall call capricious4 ,the events ,math3 e#a1 e#b1 4441 en ,i shall call determinants of the system4 ,it is to be observed that a system which has one set of determinants will in general have many4 ,in the case of the motions of the planets1 for example1 the configurations of the solar system at any two given times will be determinants4 ,we may take another illustration from the hypothesis of psycho-physical parallelism4 ,let us assume1 for the purposes of this illustration1 that to a given state of brain a given state of mind always corresponds1 and vice versa1 i4e4 that there is a one-one relation between them1 so that each is a function of the other4 ,we may also assume1 what is practically certain1 that to a given state of a certain brain a given state of the whole material universe corresponds1 since it is highly improbable that a given brain is ever twice in exactly the same state4 ,hence there will be a one-one relation between the state of a given person's mind and the state of the whole material universe4 ,it follows that1 if n states of the material universe are determinants of the material universe1 then n states of a given man's mind are determinants of the whole material and mental universe--assuming1 that is to say1 that psycho-physical parallelism is true4 ,the above illustration is important in connection with a certain confusion which seems to have beset those who have philosophised on the relation of mind and matter4 ,it is often thought that1 if the state of the mind is determinate when the state of the brain is given1 and if the material world forms a deterministic system1 then mind is subject to matter in some sense in which matter is not subject to mind4 ,but if the state of the brain is also determinate when the state of the mind is given1 it must be exactly as true to regard matter as subject to mind as it would be to regard mind as subject to matter4 ,we could1 theoretically1 work out the history of mind without ever mentioning matter1 and then1 at the end1 deduce that matter must meanwhile have gone through the corresponding history4 ,it is true that if the relation of brain to mind were many-one1 not one-one1 there would be a one-sided dependence of mind on brain1 while conversely1 if the relation were one-many1 as ,bergson supposes1 there would be a one-aided dependence of brain on mind4 ,but the dependence involved is1 in any case1 only logical2 it does not mean that we shall be compelled to do things we desire not to do1 which is what people instinctively imagine it to mean4 ,as another illustration we may take the case of mechanism and teleology4 ,a system may be defined as mechanical when it has a set of determinants that are purely material1 such as the positions of certain pieces of matter at certain times4 ,it is an open question whether the world of mind and matter1 as we know it1 is a mechanical system or not2 let us suppose1 for the sake of argument1 that it is a mechanical system4 ,this supposition--so ,i contend--throws no light whatever on the question whether the universe is or is not a teleological system4 ,it is difficult to define accurately what is meant by a teleological system1 but the argument is not much affected by the particular definition we adopt4 ,broadly1 a teleological system is one in which purposes are realised1 i4e4 in which certain desires--those that are deeper or nobler or more fundamental or more universal or what not--are followed by their realisation4 ,now the fact--if it be a fact--that the universe is mechanical has no bearing whatever on the question whether it is teleological in the above sense4 ,there might be a mechanical system in which all wishes were realised1 and there might be one in which all wishes were thwarted4 ,the question whether1 or how far1 our actual world is teleological1 cannot1 therefore1 be settled by proving that it is mechanical1 and the desire that it should be teleological is no ground for wishing it to be not mechanical4 ,there is1 in all these questions1 a very great difficulty in avoiding confusion between what we can infer and what is in fact determined4 ,let us consider1 for a moment1 the various senses in which the future may be determined4 ,there is one sense--and a very important one--in which it is determined quite independently of scientific laws1 namely1 the sense that it will be what it will be4 ,we all regard the past as determined simply by the fact that it has happened2 but for the accident that memory works backward and not forward1 we should regard the future as equally determined by the fact that it will happen4 ,but1 we are told1 you cannot alter the past1 while you can to some extent alter the future4 ,this view seems to me to rest upon just those errors in regard to causation which it has been my object to remove4 ,you cannot make the past other than it was--true1 but this is a mere application of the law of contradiction4 ,if you already know what the past was1 obviously it is useless to wish it different4 ,but also you cannot make the future other than it will be2 this again is an application of the law of contradiction4 ,and if you happen to know the future--e4g4 in the case of a forthcoming eclipse--it is just as useless to wish it different as to wish the past different4 ,but1 it will be rejoined1 our wishes can cause the future1 sometimes1 to be different from what it would be if they did not exist1 and they can have no such effect upon the past4 ,this1 again1 is a mere tautology4 ,an effect being defined as something subsequent to its cause1 obviously we can have no effect upon the past4 ,but that does not mean that the past would not have been different if our present wishes had been different4 ,obviously1 our present wishes are conditioned by the past1 and therefore could not have been different unless the past had been different2 therefore1 if our present wishes were different1 the past would be different4 ,of course1 the past cannot be different from what it was1 but no more can our present wishes be different from what they are2 this again is merely the law of contradiction4 ,the facts seem to be merely 7#a7 that wishing generally depends upon ignorance1 and is therefore commoner in regard to the future than in regard to the past2 7#b7 that where a wish concerns the future1 it and its realisation very often form a practically independent system1 i4e4 many wishes regarding the future are realised4 ,but there seems no doubt that the main difference in our feelings arises from the accidental fact that the past but not the future can be known by memory4 ,although the sense of determined in which the future is determined by the mere fact that it will be what it will be is sufficient 7at least so it seems to me7 to refute some opponents of determinism1 notably ,m4 ,bergson and the pragmatists1 yet it is not what most people have in mind when they speak of the future as determined4 ,what they have in mind is a formula by means of which the future can be exhibited1 and at least theoretically calculated1 as a function of the past4 ,but at this point we meet with a great difficulty1 which besets what has been said above about deterministic systems1 as well as what is said by others4 ,if formul of any degree of complexity1 however great1 are admitted1 it would seem that any system1 whose state at a given moment is a function of certain measurable quantities1 must be a deterministic system4 ,let us consider1 in illustration1 a single material particle1 whose co-ordinates at time t are ,math3 xt1 yt1 zt4 ,then1 however1 the particle moves1 there must be1 theoretically1 functions ,math3 f#a1 f#b1 f#c1 such that ,math3 xt ft7t71 yt f#b7t71 zt f#c7t74 ,it follows that1 theoretically1 the whole state of the material universe at time t must be capable of being exhibited as a function of t4 ,hence our universe will be deterministic in the sense defined above4 ,but if this be true1 no information is conveyed about the universe in stating that it is deterministic4 ,it is true that the formul involved may be of strictly infinite complexity1 and therefore not practically capable of being written down or apprehended4 ,but except from the point of view of our knowledge1 this might seem to be a detail3 in itself1 if the above considerations are sound1 the material universe must be deterministic1 must be subject to laws4 ,this1 however1 is plainly not what was intended4 ,the difference between this view and the view intended may be seen as follows4 ,given some formula which fits the facts hitherto--say the law of gravitation--there will be an infinite number of other formul1 not empirically distinguishable from it in the past1 but diverging from it more and more in the future4 ,hence1 even assuming that there are persistent laws1 we shall have no reason for assuming that the law of the inverse square will hold in future2 it may be some other hitherto indistinguishable law that will hold4 ,we cannot say that every law which has held hitherto must hold in the future1 because past facts which obey one law will also obey others1 hitherto indistinguishable but diverging in future4 ,hence there must1 at every moment1 be laws hitherto unbroken which are now broken for the first time4 ,what science does1 in fact1 is to select the simplest formula that will fit the facts4 ,but this1 quite obviously1 is merely a methodological precept1 not a law of ,nature4 ,if the simplest formula ceases1 after a time1 to be applicable1 the simplest formula that remains applicable is selected1 and science has no sense that an axiom has been falsified4 ,we are thus left with the brute fact that1 in many departments of science1 quite simple laws have hitherto been found to hold4 ,this fact cannot be regarded as having any a priori ground1 nor can it be used to support inductively the opinion that the same laws will continue2 for at every moment laws hitherto true are being falsified1 though in the advanced sciences these laws are less simple than those that have remained true4 ,moreover it would be fallacious to argue inductively from the state of the advanced sciences to the future state of the others1 for it may well be that the advanced sciences are advanced simply because1 hitherto1 their subject-matter has obeyed simple and easily ascertainable laws1 while the subject-matter of other sciences has not done so4 ,the difficulty we have been considering seems to be met partly1 if not wholly1 by the principle that the time must not enter explicitly into our formul4 ,all mechanical laws exhibit acceleration as a function of configuration1 not of configuration and time jointly2 and this principle of the irrelevance of the time may be extended to all scientific laws4 ,in fact we might interpret the uniformity of nature as meaning just this1 that no scientific law involves the time as an argument1 unless1 of course1 it is given in an integrated form1 in which case lapse of time1 though not absolute time1 may appear in our formul4 ,whether this consideration suffices to overcome our difficulty completely1 ,i do not know2 but in any case it does much to diminish it4 ,it will serve to illustrate what has been said if we apply it to the question of free will4 7#a7 ,determinism in regard to the will is the doctrine that our volitions belong to some deterministic system1 i4e4 are determined in the sense defined above4 ,whether this doctrine is true or false1 is a mere question of fact2 no a priori considerations 7if our previous discussions have been correct7 can exist on either side4 ,on the one hand1 there is no a priori category of causality1 but merely certain observed uniformities4 ,as a matter of fact1 there are observed uniformities in regard to volitions2 thus there is some empirical evidence that volitions are determined4 ,but it would be very rash to maintain that the evidence is overwhelming1 and it is quite possible that some volitions1 as well as some other things1 are not determined1 except in the sense in which we found that everything must be determined4 7#b7 ,but1 on the other hand1 the subjective sense of freedom1 sometimes alleged against determinism1 has no bearing on the question whatever4 ,the view that it has a bearing rests upon the belief that causes compel their effects1 or that nature enforces obedience to its laws as governments do4 ,these are mere anthropomorphic superstitions1 due to assimilation of causes with volitions and of natural laws with human edicts4 ,we feel that our will is not compelled1 but that only means that it is not other than we choose it to be4 ,it is one of the demerits of the traditional theory of causality that it has created an artificial opposition between determinism and the freedom of which we are introspectively conscious4 7#c7 ,besides the general question whether volitions are determined1 there is the further question whether they are mechanically determined1 i4e4 whether they are part of what was above defined as a mechanical system4 ,this is the question whether they form part of a system with purely material determinants1 i4e4 whether there are laws which1 given certain material data1 make all volitions functions of those data4 ,here again1 there is empirical evidence up to a point1 but it is not conclusive in regard to all volitions4 ,it is important to observe1 however that even if volitions are part of a mechanical system1 this by no means implies any supremacy of matter over mind4 ,it may well be that the same system which is susceptible of material determinants is also susceptible of mental determinants2 thus a mechanical system may be determined by sets of volitions1 as well as by sets of material facts4 ,it would seem1 therefore1 that the reasons which make people dislike the view that volitions are mechanically determined are fallacious4 7#d7 ,the notion of necessity1 which is often associated with determinism1 is a confused notion not legitimately deducible from determinism4 ,three meanings are commonly confounded when necessity is spoken of3-- 7alpha7 ,an action is necessary when it will be performed however much the agent may wish to do otherwise4 ,determinism does not imply that actions are necessary in this sense4 7beta7 ,a propositional function is necessary when all its values are true4 ,this sense is not relevant to our present discussion4 7gamma7 ,a proposition is necessary with respect to a given constituent when it is the value1 with that constituent as argument1 of a necessary propositional function1 in other words1 when it remains true however that constituent may be varied4 ,in this sense1 in a deterministic system1 the connection of a volition with its determinants is necessary1 if the time at which the determinants occur be taken as the constituent to be varied1 the time-interval between the determinants and the volition being kept constant4 ,but this sense of necessity is purely logical1 and has no emotional importance4 ,we may now sum up our discussion of causality4 ,we found first that the law of causality1 as usually stated by philosophers1 is false1 and is not employed in science4 ,we then considered the nature of scientific laws1 and found that1 instead of stating that one event ,a is always followed by another event ,b1 they stated functional relations between certain events at certain times1 which we called determinants1 and other events at earlier or later times or at the same time4 ,we were unable to find any a priori category involved3 the existence of scientific laws appeared as a purely empirical fact1 not necessarily universal1 except in a trivial and scientifically useless form4 ,we found that a system with one set of determinants may very likely have other sets of a quite different kind1 that1 for example1 a mechanically determined system may also be teleologically or volitionally determined4 ,finally we considered the problem of free will3 here we found that the reasons for supposing volitions to be determined are strong but not conclusive1 and we decided that even if volitions are mechanically determined1 that is no reason for denying freedom in the sense revealed by introspection1 or for supposing that mechanical events are not determined by volitions4 ,the problem of free will versus determinism is therefore1 if we were right1 mainly illusory1 but in part not yet capable of being decisively solved4 ,,footnotes3 #ce ,a propositional function is an expression containing a variable1 or undetermined constituent1 and becoming a proposition as soon as a definite value is assigned to the variable4 ,examples are3 ,a is ,a1 x is a number4 ,the variable is called the argument of the function4 #cf ,logic1 ,bk4 ,,iii1 ,chap4 ,v1 #b4 #cg ,time and ,free ,will1 p4 #aii4 #ch ,time and ,free ,will4 p4 #bjb4 #ci ,loc4 cit41 #f ,x ,,knowledge ,,by ,,acquaintance ,,and ,,knowledge ,,by ,,description ,the object of the following paper is to consider what it is that we know in cases where we know propositions about the so-and-so without knowing who or what the so-and-so is4 ,for example1 ,i know that the candidate who gets most votes will be elected1 though ,i do not know who is the candidate who will get most votes4 ,the problem ,i wish to consider is3 ,what do we know in these cases1 where the subject is merely described8 ,i have considered this problem elsewhere#dj from a purely logical point of view2 but in what follows ,i wish to consider the question in relation to theory of knowledge as well as in relation to logic1 and in view of the above-mentioned logical discussions1 ,i shall in this paper make the logical portion as brief as possible4 ,in order to make clear the antithesis between acquaintance and description1 ,i shall first of all try to explain what ,i mean by acquaintance4 ,i say that ,i am acquainted with an object when ,i have a direct cognitive relation to that object1 i4e4 when ,i am directly aware of the object itself4 ,when ,i speak of a cognitive relation here1 ,i do not mean the sort of relation which constitutes judgment1 but the sort which constitutes presentation4 ,in fact1 ,i think the relation of subject and object which ,i call acquaintance is simply the converse of the relation of object and subject which constitutes presentation4 ,that is1 to say that ,s has acquaintance with ,o is essentially the same thing as to say that ,o is presented to ,s4 ,but the associations and natural extensions of the word acquaintance are different from those of the word presentation4 ,to begin with1 as in most cognitive words1 it is natural to say that ,i am acquainted with an object even at moments when it is not actually before my mind1 provided it has been before my mind1 and will be again whenever occasion arises4 ,this is the same sense in which ,i am said to know that #bbd even when ,i am thinking of something else4 ,in the second place1 the word acquaintance is designed to emphasise1 more than the word presentation1 the relational character of the fact with which we are concerned4 ,there is1 to my mind1 a danger that1 in speaking of presentation1 we may so emphasise the object as to lose sight of the subject4 ,the result of this is either to lead to the view that there is no subject1 whence we arrive at materialism2 or to lead to the view that what is presented is part of the subject1 whence we arrive at idealism1 and should arrive at solipsism but for the most desperate contortions4 ,now ,i wish to preserve the dualism of subject and object in my terminology1 because this dualism seems to me a fundamental fact concerning cognition4 ,hence ,i prefer the word acquaintance because it emphasises the need of a subject which is acquainted4 ,when we ask what are the kinds of objects with which we are acquainted1 the first and most obvious example is sense-data4 ,when ,i see a colour or hear a noise1 ,i have direct acquaintance with the colour or the noise4 ,the sense-datum with which ,i am acquainted in these cases is generally1 if not always1 complex4 ,this is particularly obvious in the case of sight4 ,i do not mean1 of course1 merely that the supposed physical object is complex1 but that the direct sensible object is complex and contains parts with spatial relations4 ,whether it is possible to be aware of a complex without being aware of its constituents is not an easy question1 but on the whole it would seem that there is no reason why it should not be possible4 ,this question arises in an acute form in connection with self-consciousness1 which we must now briefly consider4 ,in introspection1 we seem to be immediately aware of varying complexes1 consisting of objects in various cognitive and conative relations to ourselves4 ,when ,i see the sun1 it often happens that ,i am aware of my seeing the sun1 in addition to being aware of the sun2 and when ,i desire food1 it often happens that ,i am aware of my desire for food4 ,but it is hard to discover any state of mind in which ,i am aware of myself alone1 as opposed to a complex of which ,i am a constituent4 ,the question of the nature of self-consciousness is too large and too slightly connected with our subject1 to be argued at length here4 ,it is difficult1 but probably not impossible1 to account for plain facts if we assume that we do not have acquaintance with ourselves4 ,it is plain that we are not only acquainted with the complex ,self-acquainted-with-,a1 but we also know the proposition ,i am acquainted with ,a4 ,now here the complex has been analysed1 and if ,i does not stand for something which is a direct object of acquaintance1 we shall have to suppose that ,i is something known by description4 ,if we wished to maintain the view that there is no acquaintance with ,self1 we might argue as follows3 ,we are acquainted with acquaintance1 and we know that it is a relation4 ,also we are acquainted with a complex in which we perceive that acquaintance is the relating relation4 ,hence we know that this complex must have a constituent which is that which is acquainted1 i4e4 must have a subject-term as well as an object-term4 ,this subject-term we define as ,i4 ,thus ,i means the subject-term in awarenesses of which ,i am aware4 ,but as a definition this cannot be regarded as a happy effort4 ,it would seem necessary1 therefore1 either to suppose that ,i am acquainted with myself1 and that ,i1 therefore1 requires no definition1 being merely the proper name of a certain object1 or to find some other analysis of self-consciousness4 ,thus self-consciousness cannot be regarded as throwing light on the question whether we can know a complex without knowing its constituents4 ,this question1 however1 is not important for our present purposes1 and ,i shall therefore not discuss it further4 ,the awarenesses we have considered so far have all been awarenesses of particular existents1 and might all in a large sense be called sense-data4 ,for1 from the point of view of theory of knowledge1 introspective knowledge is exactly on a level with knowledge derived from sight or hearing4 ,but1 in addition to awareness of the above kind of objects1 which may be called awareness of particulars2 we have also 7though not quite in the same sense7 what may be called awareness of universals4 ,awareness of universals is called conceiving1 and a universal of which we are aware is called a concept4 ,not only are we aware of particular yellows1 but if we have seen a sufficient number of yellows and have sufficient intelligence1 we are aware of the universal yellow2 this universal is the subject in such judgments as yellow differs from blue or yellow resembles blue less than green does4 ,and the universal yellow is the predicate in such judgments as this is yellow1 where this is a particular sense-datum4 ,and universal relations1 too1 are objects of awarenesses2 up and down1 before and after1 resemblance1 desire1 awareness itself1 and so on1 would seem to be all of them objects of which we can be aware4 ,in regard to relations1 it might be urged that we are never aware of the universal relation itself1 but only of complexes in which it is a constituent4 ,for example1 it may be said that we do not know directly such a relation as before1 though we understand such a proposition as this is before that1 and may be directly aware of such a complex as this being before that4 ,this view1 however1 is difficult to reconcile with the fact that we often know propositions in which the relation is the subject1 or in which the relata are not definite given objects1 but anything4 ,for example1 we know that if one thing is before another1 and the other before a third1 then the first is before the third2 and here the things concerned are not definite things1 but anything4 ,it is hard to see how we could know such a fact about before unless we were acquainted with before1 and not merely with actual particular cases of one given object being before another given object4 ,and more directly3 ,a judgment such as this is before that1 where this judgment is derived from awareness of a complex1 constitutes an analysis1 and we should not understand the analysis if we were not acquainted with the meaning of the terms employed4 ,thus we must suppose that we are acquainted with the meaning of before1 and not merely with instances of it4 ,there are thus at least two sorts of objects of which we are aware1 namely1 particulars and universals4 ,among particulars ,i include all existents1 and all complexes of which one or more constituents are existents1 such as this-before-that1 this-above-that1 the-yellowness-of-this4 ,among universals ,i include all objects of which no particular is a constituent4 ,thus the disjunction universal-particular includes all objects4 ,we might also call it the disjunction abstract-concrete4 ,it is not quite parallel with the opposition concept-percept1 because things remembered or imagined belong with particulars1 but can hardly be called percepts4 7,on the other hand1 universals with which we are acquainted may be identified with concepts47 ,it will be seen that among the objects with which we are acquainted are not included physical objects 7as opposed to sense-data71 nor other people's minds4 ,these things are known to us by what ,i call knowledge by description1 which we must now consider4 ,by a description ,i mean any phrase of the form a so-and-so or the so-and-so4 ,a phrase of the form a so-and-so ,i shall call an ambiguous description2 a phrase of the form the so-and-so 7in the singular7 ,i shall call a definite description4 ,thus a man is an ambiguous description1 and the man with the iron mask is a definite description4 ,there are various problems connected with ambiguous descriptions1 but ,i pass them by1 since they do not directly concern the matter ,i wish to discuss4 ,what ,i wish to discuss is the nature of our knowledge concerning objects in cases where we know that there is an object answering to a definite description1 though we are not acquainted with any such object4 ,this is a matter which is concerned exclusively with definite descriptions4 ,i shall1 therefore1 in the sequel1 speak simply of descriptions when ,i mean definite descriptions4 ,thus a description will mean any phrase of the form the so-and-so in the singular4 ,i shall say that an object is known by description when we know that it is the so-and-so1 i4e4 when we know that there is one object1 and no more1 having a certain property2 and it will generally be implied that we do not have knowledge of the same object by acquaintance4 ,we know that the man with the iron mask existed1 and many propositions are known about him2 but we do not know who he was4 ,we know that the candidate who gets most votes will be elected1 and in this case we are very likely also acquainted 7in the only sense in which one can be acquainted with some one else7 with the man who is1 in fact1 the candidate who will get most votes1 but we do not know which of the candidates he is1 i4e4 we do not know any proposition of the form ,a is the candidate who will get most votes where ,a is one of the candidates by name4 ,we shall say that we have merely descriptive knowledge of the so-and-so when1 although we know that the so-and-so exists1 and although we may possibly be acquainted with the object which is1 in fact1 the so-and-so1 yet we do not know any proposition a is the so-and-so1 where a is something with which we are acquainted4 ,when we say the so-and-so exists1 we mean that there is just one object which is the so-and-so4 ,the proposition a is the so-and-so means that a has the property so-and-so1 and nothing else has4 ,sir ,joseph ,larmor is the ,unionist candidate means ,sir ,joseph ,larmor is a ,unionist candidate1 and no one else is4 ,the ,unionist candidate exists means some one is a ,unionist candidate1 and no one else is4 ,thus1 when we are acquainted with an object which we know to be the so-and-so1 we know that the so-and-so exists but we may know that the so-and-so exists when we are not acquainted with any object which we know to be the so-and-so1 and even when we are not acquainted with any object which1 in fact1 is the so-and-so4 ,common words1 even proper names1 are usually really descriptions4 ,that is to say1 the thought in the mind of a person using a proper name correctly can generally only be expressed explicitly if we replace the proper name by a description4 ,moreover1 the description required to express the thought will vary for different people1 or for the same person at different times4 ,the only thing constant 7so long as the name is rightly used7 is the object to which the name applies4 ,but so long as this remains constant1 the particular description involved usually makes no difference to the truth or falsehood of the proposition in which the name appears4 ,let us take some illustrations4 ,suppose some statement made about ,bismarck4 ,assuming that there is such a thing as direct acquaintance with oneself1 ,bismarck himself might have used his name directly to designate the particular person with whom he was acquainted4 ,in this case1 if he made a judgment about himself1 he himself might be a constituent of the judgment4 ,here the proper name has the direct use which it always wishes to have1 as simply standing for a certain object1 and not for a description of the object4 ,but if a person who knew ,bismarck made a judgment about him1 the case is different4 ,what this person was acquainted with were certain sense-data which he connected 7rightly1 we will suppose7 with ,bismarck's body4 ,his body as a physical object1 and still more his mind1 were only known as the body and the mind connected with these sense-data4 ,that is1 they were known by description4 ,it is1 of course1 very much a matter of chance which characteristics of a man's appearance will come into a friend's mind when he thinks of him2 thus the description actually in the friend's mind is accidental4 ,the essential point is that he knows that the various descriptions all apply to the same entity1 in spite of not being acquainted with the entity in question4 ,when we1 who did not know ,bismarck1 make a judgment about him1 the description in our minds will probably be some more or less vague mass of historical knowledge--far more1 in most cases1 than is required to identify him4 ,but1 for the sake of illustration1 let us assume that we think of him as the first ,chancellor of the ,german ,empire4 ,here all the words are abstract except ,german4 ,the word ,german will again have different meanings for different people4 ,to some it will recall travels in ,germany1 to some the look of ,germany on the map1 and so on4 ,but if we are to obtain a description which we know to be applicable1 we shall be compelled1 at some point1 to bring in a reference to a particular with which we are acquainted4 ,such reference is involved in any mention of past1 present1 and future 7as opposed to definite dates71 or of here and there1 or of what others have told us4 ,thus it would seem that1 in some way or other1 a description known to be applicable to a particular must involve some reference to a particular with which we are acquainted1 if our knowledge about the thing described is not to be merely what follows logically from the description4 ,for example1 the most long-lived of men is a description which must apply to some man1 but we can make no judgments concerning this man which involve knowledge about him beyond what the description gives4 ,if1 however1 we say1 the first ,chancellor of the ,german ,empire was an astute diplomatist1 we can only be assured of the truth of our judgment in virtue of something with which we are acquainted--usually a testimony heard or read4 ,considered psychologically1 apart from the information we convey to others1 apart from the fact about the actual ,bismarck1 which gives importance to our judgment1 the thought we really have contains the one or more particulars involved1 and otherwise consists wholly of concepts4 ,all names of places--,london1 ,england1 ,europe1 the earth1 the ,solar ,system--similarly involve1 when used1 descriptions which start from some one or more particulars with which we are acquainted4 ,i suspect that even the ,universe1 as considered by metaphysics1 involves such a connection with particulars4 ,in logic1 on the contrary1 where we are concerned not merely with what does exist1 but with whatever might or could exist or be1 no reference to actual particulars is involved4 ,it would seem that1 when we make a statement about something only known by description1 we often intend to make our statement1 not in the form involving the description1 but about the actual thing described4 ,that is to say1 when we say anything about ,bismarck1 we should like1 if we could1 to make the judgment which ,bismarck alone can make1 namely1 the judgment of which he himself is a constituent4 ,in this we are necessarily defeated1 since the actual ,bismarck is unknown to us4 ,but we know that there is an object ,b called ,bismarck1 and that ,b was an astute diplomatist4 ,we can thus describe the proposition we should like to affirm1 namely1 ,b was an astute diplomatist1 where ,b is the object which was ,bismarck4 ,what enables us to communicate in spite of the varying descriptions we employ is that we know there is a true proposition concerning the actual ,bismarck1 and that1 however we may vary the description 7so long as the description is correct71 the proposition described is still the same4 ,this proposition1 which is described and is known to be true1 is what interests us2 but we are not acquainted with the proposition itself1 and do not know it1 though we know it is true4 ,it will be seen that there are various stages in the removal from acquaintance with particulars3 there is ,bismarck to people who knew him1 ,bismarck to those who only know of him through history1 the man with the iron mask1 the longest-lived of men4 ,these are progressively further removed from acquaintance with particulars1 and there is a similar hierarchy in the region of universals4 ,many universals1 like many particulars1 are only known to us by description4 ,but here1 as in the case of particulars1 knowledge concerning what is known by description is ultimately reducible to knowledge concerning what is known by acquaintance4 ,the fundamental epistemological principle in the analysis of propositions containing descriptions is this3 ,every proposition which we can understand must be composed wholly of constituents with which we are acquainted4 ,from what has been said already1 it will be plain why ,i advocate this principle1 and how ,i propose to meet the case of propositions which at first sight contravene it4 ,let us begin with the reasons for supposing the principle true4 ,the chief reason for supposing the principle true is that it seems scarcely possible to believe that we can make a judgment or entertain a supposition without knowing what it is that we are judging or supposing about4 ,if we make a judgment about 7say7 ,julius ,csar1 it is plain that the actual person who was ,julius ,csar is not a constituent of the judgment4 ,but before going further1 it may be well to explain what ,i mean when ,i say that this or that is a constituent of a judgment1 or of a proposition which we understand4 ,to begin with judgments3 a judgment1 as an occurrence1 ,i take to be a relation of a mind to several entities1 namely1 the entities which compose what is judged4 ,if1 e4g4 ,i judge that ,a loves ,b1 the judgment as an event consists in the existence1 at a certain moment1 of a specific four-term relation1 called judging1 between me and ,a and love and ,b4 ,that is to say1 at the time when ,i judge1 there is a certain complex whose terms are myself and ,a and love and ,b1 and whose relating relation is judging4 ,my reasons for this view have been set forth elsewhere1#da and ,i shall not repeat them here4 ,assuming this view of judgment1 the constituents of the judgment are simply the constituents of the complex which is the judgment4 ,thus1 in the above case1 the constituents are myself and ,a and love and ,b and judging4 ,but myself and judging are constituents shared by all my judgments2 thus the distinctive constituents of the particular judgment in question are ,a and love and ,b4 ,coming now to what is meant by understanding a proposition1 ,i should say that there is another relation possible between me and ,a and love and ,b1 which is called my supposing that ,a loves ,b4#db ,when we can suppose that ,a loves ,b1 we understand the proposition ,a loves ,b4 ,thus we often understand a proposition in cases where we have not enough knowledge to make a judgment4 ,supposing1 like judging1 is a many-term relation1 of which a mind is one term4 ,the other terms of the relation are called the constituents of the proposition supposed4 ,thus the principle which ,i enunciated may be re-stated as follows3 ,whenever a relation of supposing or judging occurs1 the terms to which the supposing or judging mind is related by the relation of supposing or judging must be terms with which the mind in question is acquainted4 ,this is merely to say that we cannot make a judgment or a supposition without knowing what it is that we are making our judgment or supposition about4 ,it seems to me that the truth of this principle is evident as soon as the principle is understood2 ,i shall1 therefore1 in what follows1 assume the principle1 and use it as a guide in analysing judgments that contain descriptions4 ,returning now to ,julius ,csar1 ,i assume that it will be admitted that he himself is not a constituent of any judgment which ,i can make4 ,but at this point it is necessary to examine the view that judgments are composed of something called ideas1 and that it is the idea of ,julius ,csar that is a constituent of my judgment4 ,i believe the plausibility of this view rests upon a failure to form a right theory of descriptions4 ,we may mean by my idea of ,julius ,csar the things that ,i know about him1 e4g4 that he conquered ,gaul1 was assassinated on the ,ides of ,march1 and is a plague to schoolboys4 ,now ,i am admitting1 and indeed contending1 that in order to discover what is actually in my mind when ,i judge about ,julius ,csar1 we must substitute for the proper name a description made up of some of the things ,i know about him4 7,a description which will often serve to express my thought is the man whose name was ,julius ,csar4 ,for whatever else ,i may have forgotten about him1 it is plain that when ,i mention him ,i have not forgotten that that was his name47 ,but although ,i think the theory that judgments consist of ideas may have been suggested in some such way1 yet ,i think the theory itself is fundamentally mistaken4 ,the view seems to be that there is some mental existent which may be called the idea of something outside the mind of the person who has the idea1 and that1 since judgment is a mental event1 its constituents must be constituents of the mind of the person judging4 ,but in this view ideas become a veil between us and outside things--we never really1 in knowledge1 attain to the things we are supposed to be knowing about1 but only to the ideas of those things4 ,the relation of mind1 idea1 and object1 on this view1 is utterly obscure1 and1 so far as ,i can see1 nothing discoverable by inspection warrants the intrusion of the idea between the mind and the object4 ,i suspect that the view is fostered by the dislike of relations1 and that it is felt the mind could not know objects unless there were something in the mind which could be called the state of knowing the object4 ,such a view1 however1 leads at once to a vicious endless regress1 since the relation of idea to object will have to be explained by supposing that the idea itself has an idea of the object1 and so on ad infinitum4 ,i therefore see no reason to believe that1 when we are acquainted with an object1 there is in us something which can be called the idea of the object4 ,on the contrary1 ,i hold that acquaintance is wholly a relation1 not demanding any such constituent of the mind as is supposed by advocates of ideas4 ,this is1 of course1 a large question1 and one which would take us far from our subject if it were adequately discussed4 ,i therefore content myself with the above indications1 and with the corollary that1 in judging1 the actual objects concerning which we judge1 rather than any supposed purely mental entities1 are constituents of the complex which is the judgment4 ,when1 therefore1 ,i say that we must substitute for ,julius ,csar some description of ,julius ,csar1 in order to discover the meaning of a judgment nominally about him1 ,i am not saying that we must substitute an idea4 ,suppose our description is the man whose name was ,julius ,csar4 ,let our judgment be ,julius ,csar was assassinated4 ,then it becomes the man whose name was ,julius ,csar was assassinated4 ,here ,julius ,csar is a noise or shape with which we are acquainted1 and all the other constituents of the judgment 7neglecting the tense in was7 are concepts with which we are acquainted4 ,thus our judgment is wholly reduced to constituents with which we are acquainted1 but ,julius ,csar himself has ceased to be a constituent of our judgment4 ,this1 however1 requires a proviso1 to be further explained shortly1 namely that the man whose name was ,julius ,csar must not1 as a whole1 be a constituent of our judgment1 that is to say1 this phrase must not1 as a whole1 have a meaning which enters into the judgment4 ,any right analysis of the judgment1 therefore1 must break up this phrase1 and not treat it as a subordinate complex which is part of the judgment4 ,the judgment the man whose name was ,julius ,csar was assassinated may be interpreted as meaning one and only one man was called ,julius ,csar1 and that one was assassinated4 ,here it is plain that there is no constituent corresponding to the phrase the man whose name was ,julius ,csar4 ,thus there is no reason to regard this phrase as expressing a constituent of the judgment1 and we have seen that this phrase must be broken up if we are to be acquainted with all the constituents of the judgment4 ,this conclusion1 which we have reached from considerations concerned with the theory of knowledge1 is also forced upon us by logical considerations1 which must now be briefly reviewed4 ,it is common to distinguish two aspects1 meaning and denotation1 such phrases as the author of ,waverley4 ,the meaning will be a certain complex1 consisting 7at least7 of authorship and ,waverley with some relation2 the denotation will be ,scott4 ,similarly featherless bipeds will have a complex meaning1 containing as constituents the presence of two feet and the absence of feathers1 while its denotation will be the class of men4 ,thus when we say ,scott is the author of ,waverley or men are the same as featherless bipeds1 we are asserting an identity of denotation1 and this assertion is worth making because of the diversity of meaning4#dc ,i believe that the duality of meaning and denotation1 though capable of a true interpretation1 is misleading if taken as fundamental4 ,the denotation1 ,i believe1 is not a constituent of the proposition1 except in the case of proper names1 i4e4 of words which do not assign a property to an object1 but merely and solely name it4 ,and ,i should hold further that1 in this sense1 there are only two words which are strictly proper names of particulars1 namely1 ,i and this4#dd ,one reason for not believing the denotation to be a constituent of the proposition is that we may know the proposition even when we are not acquainted with the denotation4 ,the proposition the author of ,waverley is a novelist was known to people who did not know that the author of ,waverley denoted ,scott4 ,this reason has been already sufficiently emphasised4 ,a second reason is that propositions concerning the so-and-so are possible even when the so-and-so has no denotation4 ,take1 e4g4 the golden mountain does not exist or the round square is self-contradictory4 ,if we are to preserve the duality of meaning and denotation1 we have to say1 with ,meinong1 that there are such objects as the golden mountain and the round square1 although these objects do not have being4 ,we even have to admit that the existent round square is existent1 but does not exist4#de ,meinong does not regard this as a contradiction1 but ,i fail to see that it is not one4 ,indeed1 it seems to me evident that the judgment there is no such object as the round square does not presuppose that there is such an object4 ,if this is admitted1 however1 we are led to the conclusion that1 by parity of form1 no judgment concerning the so-and-so actually involves the so-and-so as a constituent4 ,miss ,jones#df contends that there is no difficulty in admitting contradictory predicates concerning such an object as the present ,king of ,france1 on the ground that this object is in itself contradictory4 ,now it might1 of course1 be argued that this object1 unlike the round square1 is not self-contradictory1 but merely non-existent4 ,this1 however1 would not go to the root of the matter4 ,the real objection to such an argument is that the law of contradiction ought not to be stated in the traditional form ,a is not both ,b and not ,b1 but in the form no proposition is both true and false4 ,the traditional form only applies to certain propositions1 namely1 to those which attribute a predicate to a subject4 ,when the law is stated of propositions1 instead of being stated concerning subjects and predicates1 it is at once evident that propositions about the present ,king of ,france or the round square can form no exception1 but are just as incapable of being both true and false as other propositions4 ,miss ,jones#dg argues that ,scott is the author of ,waverley asserts identity of denotation between ,scott and the author of ,waverley4 ,but there is some difficulty in choosing among alternative meanings of this contention4 ,in the first place1 it should be observed that the author of ,waverley is not a mere name1 like ,scott4 ,scott is merely a noise or shape conventionally used to designate a certain person2 it gives us no information about that person1 and has nothing that can be called meaning as opposed to denotation4 7,i neglect the fact1 considered above1 that even proper names1 as a rule1 really stand for descriptions47 ,but the author of ,waverley is not merely conventionally a name for ,scott2 the element of mere convention belongs here to the separate words1 the and author and of and ,waverley4 ,given what these words stand for1 the author of ,waverley is no longer arbitrary4 ,when it is said that ,scott is the author of ,waverley1 we are not stating that these are two names for one man1 as we should be if we said ,scott is ,sir ,walter4 ,a man's name is what he is called1 but however much ,scott had been called the author of ,waverley1 that would not have made him be the author2 it was necessary for him actually to write ,waverley1 which was a fact having nothing to do with names4 ,if1 then1 we are asserting identity of denotation1 we must not mean by denotation the mere relation of a name to the thing named4 ,in fact1 it would be nearer to the truth to say that the meaning of ,scott is the denotation of the author of ,waverley4 ,the relation of ,scott to ,scott is that ,scott means ,scott1 just as the relation of author to the concept which is so called is that author means this concept4 ,thus if we distinguish meaning and denotation in the author of ,waverley1 we shall have to say that ,scott has meaning but not denotation4 ,also when we say ,scott is the author of ,waverley1 the meaning of the author of ,waverley is relevant to our assertion4 ,for if the denotation alone were relevant1 any other phrase with the same denotation would give the same proposition4 ,thus ,scott is the author of ,marmion would be the same proposition as ,scott is the author of ,waverley4 ,but this is plainly not the case1 since from the first we learn that ,scott wrote ,marmion and from the second we learn that he wrote ,waverley1 but the first tells us nothing about ,waverley and the second nothing about ,marmion4 ,hence the meaning of the author of ,waverley1 as opposed to the denotation1 is certainly relevant to ,scott is the author of ,waverley4 ,we have thus agreed that the author of ,waverley is not a mere name1 and that its meaning is relevant in propositions in which it occurs4 ,thus if we are to say1 as ,miss ,jones does1 that ,scott is the author of ,waverley asserts an identity of denotation1 we must regard the denotation of the author of ,waverley as the denotation of what is meant by the author of ,waverley4 ,let us call the meaning of the author of ,waverley ,m4 ,thus ,m is what the author of ,waverley means4 ,then we are to suppose that ,scott is the author of ,waverley means ,scott is the denotation of ,m4 ,but here we are explaining our proposition by another of the same form1 and thus we have made no progress towards a real explanation4 ,the denotation of ,m1 like the author of ,waverley1 has both meaning and denotation1 on the theory we are examining4 ,if we call its meaning ,m'1 our proposition becomes ,scott is the denotation of ,m'4 ,but this leads at once to an endless regress4 ,thus the attempt to regard our proposition as asserting identity of denotation breaks down1 and it becomes imperative to find some other analysis4 ,when this analysis has been completed1 we shall be able to reinterpret the phrase identity of denotation1 which remains obscure so long as it is taken as fundamental4 ,the first point to observe is that1 in any proposition about the author of ,waverley1 provided ,scott is not explicitly mentioned1 the denotation itself1 i4e4 ,scott1 does not occur1 but only the concept of denotation1 which will be represented by a variable4 ,suppose we say the author of ,waverley was the author of ,marmion1 we are certainly not saying that both were ,scott--we may have forgotten that there was such a person as ,scott4 ,we are saying that there is some man who was the author of ,waverley and the author of ,marmion4 ,that is to say1 there is some one who wrote ,waverley and ,marmion1 and no one else wrote them4 ,thus the identity is that of a variable1 i4e4 of an indefinite subject1 some one4 ,this is why we can understand propositions about the author of ,waverley1 without knowing who he was4 ,when we say the author of ,waverley was a poet1 we mean one and only one man wrote ,waverley1 and he was a poet2 when we say the author of ,waverley was ,scott we mean one and only one man wrote ,waverley1 and he was ,scott4 ,here the identity is between a variable1 i4e4 an indeterminate subject 7he71 and ,scott2 the author of ,waverley has been analysed away1 and no longer appears as a constituent of the proposition4#dh ,the reason why it is imperative to analyse away the phrase the author of ,waverley may be stated as follows4 ,it is plain that when we say the author of ,waverley is the author of ,marmion1 the is expresses identity4 ,we have seen also that the common denotation1 namely ,scott1 is not a constituent of this proposition1 while the meanings 7if any7 of the author of ,waverley and the author of ,marmion are not identical4 ,we have seen also that1 in any sense in which the meaning of a word is a constituent of a proposition in whose verbal expression the word occurs1 ,scott means the actual man ,scott1 in the same sense 7so far as concerns our present discussion7 in which author means a certain universal4 ,thus1 if the author of ,waverley were a subordinate complex in the above proposition1 its meaning would have to be what was said to be identical with the meaning of the author of ,marmion4 ,this is plainly not the case2 and the only escape is to say that the author of ,waverley does not1 by itself1 have a meaning1 though phrases of which it is part do have a meaning4 ,that is1 in a right analysis of the above proposition1 the author of ,waverley must disappear4 ,this is effected when the above proposition is analysed as meaning3 ,some one wrote ,waverley and no one else did1 and that some one also wrote ,marmion and no one else did4 ,this may be more simply expressed by saying that the propositional function x wrote ,waverley and ,marmion1 and no one else did is capable of truth1 i4e4 some value of x makes it true1 but no other value does4 ,thus the true subject of our judgment is a propositional function1 i4e4 a complex containing an undetermined constituent1 and becoming a proposition as soon as this constituent is determined4 ,we may now define the denotation of a phrase4 ,if we know that the proposition a is the so-and-so is true1 i4e4 that a is so-and-so and nothing else is1 we call a the denotation of the phrase the so-and-so4 ,a very great many of the propositions we naturally make about the so-and-so will remain true or remain false if we substitute a for the so-and-so1 where a is the denotation of the so-and-so4 ,such propositions will also remain true or remain false if we substitute for the so-and-so any other phrase having the same denotation4 ,hence1 as practical men1 we become interested in the denotation more than in the description1 since the denotation decides as to the truth or falsehood of so many statements in which the description occurs4 ,moreover1 as we saw earlier in considering the relations of description and acquaintance1 we often wish to reach the denotation1 and are only hindered by lack of acquaintance3 in such cases the description is merely the means we employ to get as near as possible to the denotation4 ,hence it naturally comes to be supposed that the denotation is part of the proposition in which the description occurs4 ,but we have seen1 both on logical and on epistemological grounds1 that this is an error4 ,the actual object 7if any7 which is the denotation is not 7unless it is explicitly mentioned7 a constituent of propositions in which descriptions occur2 and this is the reason why1 in order to understand such propositions1 we need acquaintance with the constituents of the description1 but do not need acquaintance with its denotation4 ,the first result of analysis1 when applied to propositions whose grammatical subject is the so-and-so1 is to substitute a variable as subject2 i4e4 we obtain a proposition of the form3 ,there is something which alone is so-and-so1 and that something is such-and-such4 ,the further analysis of propositions concerning the so-and-so is thus merged in the problem of the nature of the variable1 i4e4 of the meanings of some1 any1 and all4 ,this is a difficult problem1 concerning which ,i do not intend to say anything at present4 ,to sum up our whole discussion4 ,we began by distinguishing two sorts of knowledge of objects1 namely1 knowledge by acquaintance and knowledge by description4 ,of these it is only the former that brings the object itself before the mind4 ,we have acquaintance with sense-data1 with many universals1 and possibly with ourselves1 but not with physical objects or other minds4 ,we have descriptive knowledge of an object when we know that it is the object having some property or properties with which we are acquainted2 that is to say1 when we know that the property or properties in question belong to one object and no more1 we are said to have knowledge of that one object by description1 whether or not we are acquainted with the object4 ,our knowledge of physical objects and of other minds is only knowledge by description1 the descriptions involved being usually such as involve sense-data4 ,all propositions intelligible to us1 whether or not they primarily concern things only known to us by description1 are composed wholly of constituents with which we are acquainted1 for a constituent with which we are not acquainted is unintelligible to us4 ,a judgment1 we found1 is not composed of mental constituents called ideas1 but consists of an occurrence whose constituents are a mind#di and certain objects1 particulars or universals4 7,one at least must be a universal47 ,when a judgment is rightly analysed1 the objects which are constituents of it must all be objects with which the mind which is a constituent of it is acquainted4 ,this conclusion forces us to analyse descriptive phrases occurring in propositions1 and to say that the objects denoted by such phrases are not constituents of judgments in which such phrases occur 7unless these objects are explicitly mentioned74 ,this leads us to the view 7recommended also on purely logical grounds7 that when we say the author of ,marmion was the author of ,waverley1 ,scott himself is not a constituent of our judgment1 and that the judgment cannot be explained by saying that it affirms identity of denotation with diversity of meaning4 ,it also1 plainly1 does not assert identity of meaning4 ,such judgments1 therefore1 can only be analysed by breaking up the descriptive phrases1 introducing a variable1 and making propositional functions the ultimate subjects4 ,in fact1 the so-and-so is such-and-such will mean that x is so-and-so and nothing else is1 and x is such-and-such is capable of truth4 ,the analysis of such judgments involves many fresh problems1 but the discussion of these problems is not undertaken in the present paper4 ,,footnotes3 #dj ,see references later4 #da ,philosophical ,essays1 ,the ,nature of ,truth4 ,i have been persuaded by ,mr4 ,wittgenstein that this theory is somewhat unduly simple1 but the modification which ,i believe it to require does not affect the above argument #aiag4 #db ,cf4 ,meinong1 ,ueber ,annahmen1 passim4 ,i formerly supposed1 contrary to ,meinong's view1 that the relationship of supposing might be merely that of presentation4 ,in this view ,i now think ,i was mistaken1 and ,meinong is right4 ,but my present view depends upon the theory that both in judgment and in assumption there is no single ,objective1 but the several constituents of the judgment or assumption are in a many-term relation to the mind4 #dc ,this view has been recently advocated by ,miss ,e4,e4,c4 ,jones4 ,a ,new ,law of ,thought and its ,implications1 ,mind1 ,january1 #aiaa4 #dd ,i should now exclude ,i from proper names in the strict sense1 and retain only this #aiag4 #de ,meinong1 ,ueber ,annahmen1 #bnd ed41 ,leipzig1 #aiaj1 p4 #ada4 #df ,mind1 ,july1 #aiaj1 p4 #chj4 #dg ,mind1 ,july1 #aiaj1 p4 #cgi4 #dh ,the theory which ,i am advocating is set forth fully1 with the logical grounds in its favour1 in ,principia ,mathematica1 ,vol4 ,i4 ,introduction1 ,chap4 ,,iii2 also1 less fully1 in ,mind1 ,october1 #aije4 #di ,i use this phrase merely to denote the something psychological which enters into judgment1 without intending to prejudge the question as to what this something is4 ,,index ,achilles and the tortoise1 #hj ff1 #hi ff ,acquaintance1 the relation of1 #bji ff ,alexander1 #abe ,american ,realists1 the1 #acd ,aristotle1 #db1 #gf1 #ig ,bacon1 #da ,bergson1 #ad ff1 #bb1 #aje1 #abh1 #ahe ff1 #bjc ,berkeley1 #ig1 #acb ,blake1 #a ,bosanquet1 #ii ,broad1 #hi n ,calculus1 the1 #hb ,cantor1 ,georg1 #fd1 #ha ff1 #he1 #ia ,carlyle1 #ej1 #hb ,cause1 the conception of1 #ace n1 #ahj ff ,christianity and renunciation1 #ea ,chuang ,tz7u1 #ajf ,construction of permanent things and matter1 #afi ff ,constructions1 logical1 #aee ff ,darwin1 #ae1 #bc1 #dc ,dedekind1 #fd1 #ha ff1 #he ,descartes1 #ig1 #abf ,descriptions1 #age1 #bad ff ,education1 #cg ff ,euclid1 #fb1 #ib1 #id ,evolutionism1 #bc ff1 #bh ,fano1 #ic ,faraday1 #cd ,free will1 #bje ff ,frege1 #gh n ,galileo1 #db ,gladstone1 #agg ,good and evil1 #bf ff ,hegel1 #h1 #aj1 #ah1 #he1 #ig1 #aje ff ,heine1 #aac ,heraclitus1 #a ff1 #aj ,hertz1 #cd ,holt1 #agg n ,hume1 #a1 #ig ,infinite1 the mathematical1 #hd ff ,james1 ,william1 #ajj ,jones1 ,miss ,e4,e4,c41 #bbd n1 #bbe ,judgment1 #bai ff ,kant1 #he1 #if1 #ig1 #ii1 #aah ff ,knowledge by acquaintance1 #bji ff2 by description1 #bad ff ,laplace1 #bc ,leibniz1 #gf1 #gi1 #hb ff1 #ig1 #abf1 #add1 #afj ,locke1 #ig ,logic1 the laws of1 #fh ff ,macaulay and ,taylor's theorem1 #ie ,malthus1 #dc ,mathematics1 #eh ff2 and the ,metaphysicians1 #gd ff2 and logic1 #ge ff2 and the infinitesimal1 #hb ff ,matter1 the nature of1 #abe ff2 definition of1 #afd ff ,maxwell1 #cd ,meaning and denotation1 #bbc ff ,meinong1 #agd1 #bbj n1 #bbe ,militarism1 #ej ,mill1 #ahe1 #aic ff ,mysticism and logic1 #a ff ,necessity1 the notion of1 #bjg ff ,nietzsche1 #bb1 #ej ,nunn1 #abe1 #acg n1 #aec ,parmenides1 #g ff1 #ah1 #ba ,particulars1 awareness of1 #baj ff ,peano1 #gh ff1 #ic ff ,perspectives1 #aci ff2 the space of1 #aeh ff ,philosophy and logic1 #aaa ,physics1 sense-data and1 #ade ff ,pierce1 #gf n ,plato1 #a ff1 #aj1 #cj1 #fj1 #ig ,pragmatism1 #bb1 #aje ,realism and the analytic method1 #abj ff ,reason and intuition1 #ab ff ,relatives1 the logic of1 #gf ,robb1 #afg n ,santayana1 #bj ,sense-data1 #adg1 #baj ff2 and physics1 #ade ff ,sensibilia1 #adh ff ,space1 #ach ff2 private1 #aeh ff2 the logical problem1 #aad ff2 the problem in physics1 #aae ff2 the epistemological problem1 #aah ff ,systems1 deterministic1 #aii2 practically isolated1 #aih2 relatively isolated1 #aig2 mechanical1 #bja ,time1 #aj1 #ba ff1 #ada ff1 #afg ff ,tristram ,shandy1 the paradox of1 #ij ff ,unity and ,plurality1 #ah ff ,universals1 awareness of1 #bab ff ,ward1 #ahj ,weierstrass1 #hj1 #hb1 #ie ,whitehead1 #aag1 #aeg1 #age ,wolf1 #agc ,zeno the ,eleatic1 #fd1 #hj1 #hd1 #hi ff ,illustration ,,george ,,allen ,,unwin ,,ltd ,london3 #dj ,museum ,street1 ,w4,c4 #a ,auckland3 #bd ,wyndham ,street ,bombay3 #ae ,graham ,road1 ,ballard ,estate1 ,bombay #a ,calcutta3 #ag ,chittaranjan ,avenue1 ,calcutta #ac ,cape ,town3 #aji ,long ,street ,karachi3 ,metherson's ,estate1 ,wood ,street1 ,karachi #b ,new ,delhi3 #ac-ad ,ajmeri ,gate ,extension1 ,new ,delhi #a ,so ,paulo3 ,avenida #i de ,julho #aach--;,ap4 #ea ,singapore1 ,south ,east ,asia and ,far ,east1 #cf;c1 ,prinsep ,street ,sydney1 ,n4,s4,w43 ,bradbury ,house1 #ee ,york ,street ,toronto3 #ia ,wellington ,street ,west 99 99 99 99 99 ---------------------------------------- ------------------- ,typographical errors corrected in text3 ,page #aaa3 charateristic replaced with characteristic ,page #ga3 inexpugnable replaced with inexpungable ---------------------------------------- ------------------- 99 99 99 99 99