E THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES Ex Lihris SIR MICHAEL SADLER ACQUIRED 1948 WITH THE HELP OF ALUMNI OF THE SCHOOL OF EDUCATION I PliitmHhin's UlaiuialB for (txiuj)crs Edited nv OSCAR BROWNING, M.A., Principal of the Cambridge University Day Training College AND S. S. F. FLETCHER, B.A., Ph.D., Master of Method in the Cambridge University Day Training College THE LOGICAL BASES OF EDUCATION ^^^^m. THE LOGICAL BASES OF EDUCATION J. WELTON, M.A. PROFESSOR OF EDUCATION IN" THE YORKSHIRE COLLEGE, VICTORIA UNIVERSITY AUTHOR OF ''A MANUAL OF LOGIC, "ETC. Eonlion MACMILLAN AND CO., Limited NEW YORK : THE MACMILLAN COMPANY 1S99 Ail rights reserved Richard Clay and Sons, Limited, london and bvngav. Li 7/46 PREFACE The aim of this book is to set forth the rational bases of all true educational work. It is believed that such bases can only be found in those modern developments of logical theory which have marked the latter half of this century. Hence, but little of the traditional formal logic will be found in the book. As a mental discipline I believe that formal logic has considerable value, but it seems to me certain that we cannot find foundations for modern education in a logical theory developed under a conception of knowledge very different from that of the present day. After the whole of the present book was planned, and much of it written, I I'ead in an interesting ** Review of Educational Currents of Thought in 1895 in Central Europe," published in the Rejwrt of the Commissioner of Education, 1896-7, issued by the Central Bureau of Education in the United States of America, a passage which so exactly ex- vi PREFACE presses the conception under which I was writing, that I venture to quote it : " Logic . . . aims at the development of a view by which the world of phenomena can be actually understood and the truth found. It endeavours to prove that by proper percep- tion, consideration, and comparative observation, by an arrangement and adjustment under definitions (con- sequently by critical judgment and conclusion), and by convincing argument and reliable development of a scientific system (by means of continued and strict induction, deduction, and classification) science originates, and a proper view of the world can be gained and made perceptible. " Such a logic will show how the growing human being must be directed so that the physical and psychical germs of possibilities of a later develop- ment within him may grow towards perfection, and that his whole earthly existence may present the realization of ethical and aesthetic ideals. It there- fore points out the course to be pursued by individual training, and outlines the duties of social education, which, in its ultimate aims, is more definitely defined by ethics. It is the duty of the teacher, therefore, to see that upon the foundation of the original work of the expounders of this science, a logic be prepared in which all useless ballast from formal logic ... is omitted, and a scientific methodology (induction, de- duction, &c.), be founded on the basis of the qualities PREFACE vii and laws of human thought which have been made objects of perception by psychology. Vpon the basis of such a logic alone can pedagogy establish the laws of intellectual education and found a pedagogical methodology" (vol. i., p. 133). My experience with the students of the Depart- ment for the Training of Teachers at the Yorkshire College for the last eight years has convinced me that such a treatment of logic appeals to them as both helpful and interesting, especially if its reality is brought home by the analysis of actual specimens of human reasoning such as are given as Exercises at the end of this book. In such a work as this it would be pedantic to attempt to mention all the logicians from whose writings I have derived inspiration and suggestion, but I cannot refrain from expressing my special obligations to Dr. Bosanquet, Dr. Bradley, and Mr. Hobhouse. My thanks are due to Mr. W. P. Welpton, Lecturer on Education at the York Training Col- lege, for his kindness in reading certain portions of the book in manuscript and the whole of it in proof, and suggesting various improvements. J. W. Leeds, June, 1899. TABLE OF CONTENTS CHAPTER I GENERAL NATURE OF KXOWLEDOE PAGE § 1. Education and Knowledge 1 § 2. Knowledge and Truth 1 § 3. Knowledge and Superstition 2 § 4. Knowledge and Belief 4 § 5. Savage Philosophy 7 § 6. Explanation of the World as a Sum of Things. . 9 § 7. Explanation of the World by Laws 11 Factors of Change 12 Necessity and Universality of Law .... 14 Atoms and Energy 15 § 8. Explanation of the World as Sj'stem 16 § 9. Nature of Reality and of Knowledge 19 The Test of Truth 23 §10. The World as Mental Construction 24 CHAPTER II POSTri.ATE.S OF KNOWLEDGE § 1. The Factors of Knowledge 27 § 2. Postulates of Knowledge 28 § 3. The Postulates at the Stage of Sense-perception . 29 Identity 20 Contradiction 29 Excluded Middle 30 Sufficient Reason 31 X CONTENTS FAOE § 4. The Postulates at the Stage of Law 31 Causation 33 ' Every Event has a Cause ' 34 ' Same Cause, same Eifect ' 34 ' Same Effect, same Cause ' 34 ' Cause and Efifect equal in Enei'gy ' . . . 36 Causation and Sequence in Time 36 § 5. The Postulates at the Stage of System 38 Final Causes 39 CHAPTER III KNOWLEDGE AND LANGUAGE § 1. Ideas and Knowledge 42 § 2. Ideas and Reality 42 § 3. Ideas and Images 43 Thought and Imagination 43 § 4. Development of Ideas 45 § 5. Ideas and Language 45 § 6. Language and Communication of Knowledge . , 4(3 § 7. Verbal Language 46 Writing 47 § 8. Language and Learning 48 § 9. Spoken and Written Language 49 §10. Meaning and Context 50 Specific and General Meanings of Words . . 53 §11. Ambiguities of Language 55 Ambiguities in Individual Words 55 Ambiguities in Construction 60 CHAPTER IV KNOWLEDGE AND LOGIC § 1. Nature of Logic 62 § 2. Nature of Judgment 63 § 3. Judgments and Logic 63 CONTENTS xi PAGE § 4. Abstract Nature of Thouglit 64 § 5. Form and Matter 65 § 6. Logic is Abstract and Formal 66 § 7. Function of Logic 67 § 8. Value of Logic 68 CHAPTER V NATURE OF JUDGMENT § 1. Judgment and Proposition 69 § 2. Judgment and Truth 70 § 3. Judgment and Experience 72 § 4. Judgment is an Act of both Analysis and Sj-nthesis 73 § 5. Subject and Predicate 75 § 6. Copula 77 § 7. Relative Prominence of Analysis and Synthesis in Judgments 78 § 8. Summary 78 CHAPTER VI TYPES OF JUDGMENT § 1. Main Tj^pes of Judgment 80 § 2. Development of Judgment 81 Impersonal Judgments 81 Demonstrative Judgments 82 Judgments of Particular Relation .... 82 Historical Singular Judgments 83 Enumerative Judgments 83 Search for the Universal Judgment .... 84 The Generic Judgment 85 The Hypothetical Judgment 85 Reciprocal Universal Judgments 88 The Disjunctive Judgment 88 § 3. Negation 91 xii CONTENTS PAGE § 4. Quality and Quantity in Categorical Judgments . 94 § 5. Quality and Quantity in Hypothetical and Dis- junctive Judgments 96 CHAPTER VII FORMAL RELATIONS OF PROPOSITIONS § 1. The Four-fold Scheme of Propositions 97 § 2. Distribution of Terms 98 § 3. Conversion 99 § 4. Modes of Opposition 101 Subalternation 101 Contradiction 102 Contrariety 102 Sub-contrariety 10.3 Summary of Opposition 103 CHAPTER VIII THE METHOD OF KNOWLEDGE § 1. Truth and Evidence 104 § 2. Nature of Method 104 § 3. Development of Doctrine of Method 105 Aristotle 105 Mediaeval Logic 105 Bacon 106 Newton 107 Mill 107 Modern Logic 108 § 4. Method and Thought 108 § 5. Method and Facts 109 §6. Inferential Character of Method 110 § 7. Characteristics of Methodical Thought Ill Purpose Ill Definite Starting-point 112 §8. Fallacies incidental to Method 112 Petitio Princijni 112 Ignoratio Elenchi 114 CONTENTS xiii PAGE § 9. Essence of Methodical Process 116 §10. Nature of Inference 116 Inference and Sj'stem 117 Inference and Previous Knowledge .... 118 Inference and Universals 119 §11. Deductive and Inductive Inference 119 §12. Analj-sis and Sj'nthesis 121 §13. Analytic and Synthetic Methods 122 CHAPTER IX DEDUCTIVE INFERENCE § 1. Kinds of Deductive Inference 123 SYLLOGISM § 2. Nature of Syllogism 124 Distributed Middle Term 124 Conclusion warranted by Premises .... 127 Validity of Syllogism 128 Minor Rules of Syllogism 129 § 3. Forms of Syllogism 129 § 4. Hypothetical Syllogisms 130 CONSTRUCTION § 5. Nature of Construction 132 § 6. Types of Construction 133 Arithmetical Constructions 133 Geometrical Constructions 135 § 7. Inductive Aspect of Construction 135 CHAPTER X OUTLINE OF INDUCTIVE METHOD § 1. Meaning of 'Induction' 136 §2. General Method of Induction 137 § 3. Direct and Indirect Testing of Hypotheses ... 138 xiv CONTENTS CHAPTER XI OBSERVATION PAGE § 1. Importance of Observation 140 § 2. Liability of Observation to Error 140 § 3. Depemlence of Observation on Previous Knowledge 141 § 4. Observation and Inference 142 Selection 142 Recognition 143 Distinction between ' Observation ' and ' Inference ' 147 § 5. Observation and Prejudice 149 § 6. Observation and Scientific Instruments 150 § 7. Experiment 150 CHAPTER XII TESTIMONY § 1. Necessity of Testimony 153 § 2. Reception of Testimony 154 § 3. Tests of Testimony 155 Good Faith 156 Accuracy 158 § 4. Anonymous Testimony 160 § 5. Corroboration of Testimony 1G2 Tradition 163 Independent Corroboration 164 § 6. Inference from' Absence of Testimony 164 CHAPTER XIII HYPOTHESES § 1. Nature of Hypotheses 166 § 2. Origin of Hypotheses 167 § 3. Hypotheses and Facts 16S Danger of Bias 170 CONTENTS XV PAOE § 4. Testing of Hj-potheses 171 § 5. Descriptive and Working Hypotheses 172 § 6. Permissible Hj-potheses 173 S 7. Crucial Instances 174 CHAPTER XIV DIRECT DEVELOPMENT OF HYPOTHESES § 1. Accidental Coincidences and Necessary Connexions 177 § 2. Empirical Generalization and Enumerative In- duction 178 § 3. Analogy 180 § 4. Nature of Direct Methods in Induction 184 § 5. Method of Agreement 188 § 6. Method of Exclusions 191 § 7. Method of Diflterence 192 § 8. Method of Concomitant Variations 195 § 9. Method of Residues 200 §10. Example of Use of Methods : Colour of Animals . 200 CHAPTER XV INDIRECT VERIFICATIOX OF HYPOTHESES § 1. Relation of Indirect to Direct Methods 204 § 2. Initial Use of Indirect Method 205 Circumstantial Evidence 206 § 3. The Indirect Method in History 207 § 4. The Indirect Method in Geology and Biology . . 208 § 5. Establishment of the Theorj- of Gravitation . . . 213 Empirical Laws of Falling Bodies 213 Empirical Laws of Planetary Motion , . . 214 Gravitation applied to Moon 215 Gravitation extended to Planetary Motion 216 Gravitation extended to all Particles of Matter 217 xvi CONTENTS CHAPTER XVI DEFINITION, CLASSIFICATION, AND EXPLANATION PAGE § 1. Aim of Methods of Knowledge 220 g 2. Development of Definition 221 § 3. Nature of Definition 223 S 4. Definition and other Modes of Stating Meaning . 226 g 5. Limits of Definition 229 Meaning of Proper Names 230 § 6. Rules of Definition 231 § 7. Nature of Classification 234 § 8. Rules of Classification 235 § 9. Classification and Definition 235 Classification and Partition 237 §10. Disjunctive Classification 238 §11. Subsumptive Classification 238 §12. Provisional Character of Classification and Defini- tion 241 §13. Classification and Explanation 242 §14. Limits of ^Explanation 244 §15. Logical Explanation and Familiarization .... 244 CHAPTER XVII LOGIC AND EDUCATION § 1. General Relation of Logic to Education . . , . . 246 § 2. Education Relative to Society 249 § 3. Method and Self-Activity 252 Method not Mechanical 253 § 4. Educational Method Relative to Current Concep- tion of Knowledge 255 Heuristic Methods 255 § 5. Method of Science and Method of Education . . 257 § 6. Maxims of Method 261 EXERCISES IN INFERENCE 266 INDEX 281 THE LOGICAL BASES OF EDUCATION. CHAPTER I GENKHAL XATUKE OF KNOWKKDGE § 1. — Bacon begins one of the best-known of his Education essays with the words: "'What is truth?' said knowledge, jesting Pihite ; and would not stay for an answer." Whether or not this is a Hbel on the Roman pro- curator, it certainly represents a mental attitude which cannot be adopted by the educator. One of the main parts of his work is teaching. And teaching has a two-fold aspect — on the one hand it regards the pupil, and on the other it regards the subject taught. Between these two it tries to estaljlish the I'elation we call knowledge. The aim of teaching is, then, to lead the pupil to attain knowledge, and to develop in him the power of using and extending that knowledge. ^ 2. — Now, if we ask ourselves Avhat wc mean by KnnwicdRe ' knowledge ' we can find no other answer than that '""^ T»utli- E n 2 THE LOGICAL BASES OF EDUCATION chap. it is that part of human thought which is true. And human thought is true just so far as it agrees with the actual facts of the world. All knowledge is, then, a grasp of truth. Not indeed of the whole truth : that we do not know, and never shall know. For the whole truth is the totality of reality or existence ; in other words, the universe. As this is infinite it can never be grasped by the finite human intelligence. But, as generations succeed each other, knowledge advances. Taking each new position as a fresh starting point, man uses the knowledge he has acquired as a key to unlock fresh mysteries. What was so wonderful to our foi'efathers that it could only be accounted for by the assumption of supernatural agency is regarded by us as common- place. Thus the bounds of superstition are con- tinually contracted. For superstition has play only where knowledge is absent and fancy takes its place. As Mr. Clodd remarks, " magic rules the life of the savage," ^ whilst the life of civilized man tends to become more and more completely ruled by a rational conception of law and system. Knowledge J^ 3. — The thought of the modern civilized European supoisti- is then, especially at first sight, very different from tion. ^^^.j^j- Qf ^j-^g savage. But this must not blind us to the fact that there is continuity between them ; that the former has been evolved slowly and with difficulty from the latter. " The low intellectual environment of man's barbaric past was constant in his history for thousands of years."" It was only when man began to think and enquire, as well as to feel and fancy, that knowledge began to take the place of belief in magic, in charms, in fairies, and in all the other apparatus by which savage man attempts to explain 1 Tom Til Tot, p. 54. 2 ciocUl, ojj. cit., p. 106. I GENERAL NATURE OF KNOWLEDGE 3 the phenomena he sees about him. For modern Europe this birth of thought took place in Greece less than three thousand years ago. Since then there has been gradual advance, not however without lung periods of stagnation, and even of retrogression. We need not go back very far to find superstition governing most of the life of the majority of English- men. King James I. believed firmly in magic, and in his book on Doenionology, he speaks of the " devil teaching how to make pictures of wax or clay, that by roasting thereof the persons that they bear the name of may be continually melted or dried away by sickness." And James was " the British Solomon." Indeed, we need not leave our own day to find many examples of the truth that whenever knowledge is absent superstition reigns. The thorough-going con- ception of the universality of natural law exists amongst comparatively few even in our own day. " Scratch the epiderm of the civilized man, and the barbarian is found in the derm " says Mr. Clodd with undeni- able truth. "In proof of which," he goes on, "there are more people who believe in Zadkiel's Vox Stellarum than in the Nautical A Imanac ; and rare are the households where the Book of Breams and Fortune- 2'eller are not to be found in the kitchen." ^ And again : " As many a stable-door and mainmast testify, the nailing of horse shoes to ' keep off the pixies,' and, conversely, to bring luck to farmer and sailor, thrives to this day." - Many other examples are given by Mr. Clodd in the very interesting book from which we have quoted, and doubtless, every reader will Ije able to furnisli additional instances. IJut enough has Ijeen said to illustrate the point that the outcome of ignorance is superstition. Now, it should ])o noted that superstitions have ' Op. fit., p. 97. - IbaL, I). :U. u -1 4 THK LUCICAL BASES OF EDUCATION ohap. llu'ir ui-igin mainly in nuurs feelings and emotions, and especially in the emotion of fear, for the unknown genei'ally inspires terror in a mind that has little or no conception of natural law. But superstitions ai'e not merely mental errors, they have a practical bearing, for, in so far as they are believed, they determine conduct. Further, what has been said has made it evident that the only cure for superstition is increased know- ledge. And this has a deep interest for the educator ; for, to again quote Mr. Clodd, " the art of life largely consists in that control of the emotions, and that diversion of them into wholesome channels, which the intellect, braced with the latest knowledge and with freedom in the application of it, can alone eflfect." 1 Kiiuwiedgc s ^ — -jjjy above remarks have brought into and Belief. - . . . 1 • 1 1 n prominence several important points which we shall do well to consider. In the first place we see that all belief is not knowledge. Belief is unquestioning acceptance by the mind. But the savage believes as firmly in various forms of magic as the civilized man does in the law of gravitation. And his beliefs influence his actions. " The Basuto avoids the river- bank, lest, as his shadow falls on the water, a crocodile may seize it, and harm the owner .... the Arabs believe that if a hyena treads on a shadow, it deprives the man of the power of speech." - Now it may seem strange that such beliefs have been able to survive for so many generations the continual contradictions they must have received from experi- ence. Indeed, this would be inexplicable were it not for another piece of experience — the fact of the marked conservatism which human nature shows with regard to its beliefs. Prejudice is an enormous 1 Olj. at., p. lU'J. - Ibid., pp. 79—80. I GENERAL NATURE OF KNOWLEDGE 5 foi-ce in human life, and not less potent is that mental inertia which makes it hard for men to strike out a new line of thought for themselves. '• Tt is not error," wrote Turgot, " which opposes the pro- gress of truth ; it is indolence, obstinacy, the spirit of routine, everything that favours inaction." ^ It is only when this mental indolence is overcome, when the spirit of enquiry is roused, that men l^egin to ask why they believe this or that, and according to the answer to retain or reject the belief. This leads us to see both the difference and the connexion between l^elief and knowledge. So far as the mental state of any individual is concerned, Ijelief and knowledge are so far alike that both are states of full assurance of the truth of the matter in question. liut the}' differ in this — that in the case of knowledge alone this assurance can be shown to be justified by evidence other than itself. For ex- ample a savage believes that an earthquake is the mark of the anger of some supernatural being with those who suffer its effects, but he can luring forward no evidence outside the earthquake itself to support his belief. On the other hand, the modern scientific man can show by unimpeachaljle evidence that the earthquake is the result of natural laws and is itself an expression of the orderly working of the universe. In thus relating the earthcjuake to other physical events he has replaced what was mere belief by knowleflge. There is a further and most important distinction. Jjelief is always an individual act. An}' numljer of persons may, indeed, agree in believing the same thing, and this we loosely call " sharing a belief " or " holding a common faith." But the belief is not common if we use our words strictly. What is ' (Quoted by Mr. Clodd, op. cit,, p. 108, G THE LOGICAL BASES OF EDUCATION chap. common is the object of belief : each man beUeves for liimself, each man feels his own full assurance. And this assurance he cannot communicate to another. The utmost he can do is to influence the mind of him whom he wishes to convert so as to incline him to accept the same object of belief. Belief is then, in its very essence, particular ; that is, it is the state of some one individual mind. Know- ledge, on the other hand, is universal ; that is, it is common to any number of minds. This is because knowledge is, as has been ah^eady said, a grasp of truth, or, as we may put it in other words, an insight into some portion of reality. It follows that knowledge is not dependent on any one individual mind, for neither the belief nor the thought of any individual can alter an element of the real world. It is true that knowledge is increased by the work of individual minds. But once a piece of knowledge is arrived at it can be com- municated to others and made common property. This is so because the evidence which establishes every piece of knowledge can be made clear. Of course, when a piece of knowledge is grasped by an individual mind, it is believed, and it becomes part of the contents of that mind ; the act of knowing is thus individual. But whilst belief is nothing beyond the act of believing, knowledge is not the mere act of knowing. For nothing is knowledge which is not based on evidence sufficient to prove it, that is, which is not shown to be part of the order of the world. Any mind which can appreciate this evidence is forced to accept the piece of knowledge which is thus substantiated. Hence, all knowledge is in its very essence universal in its nature ; for all minds which can understand it must accept it as something not merely believed but I GENERAL NATURE OF KNOWLEDGE 7 as actually proved, and thei'efore known to be true. This fact that all knowledge is of the truth, whilst belief is frequently of the false, leads us to see that the general conditions of knowledge are independent of in- di\ndual beliefs. Men have, indeed, often believed they possessed knowledge when future advances have shown that their supposed knowledge was imperfect or even false. Such a mistake is easily understood vfhen it is borne in mind that to the individual both knowledge and belief are states of full assurance ; that all knowledge is belief, though all belief is not knowledge. It is easy, then, for a man to deceive himself as to the extent to which his beliefs ai'e really supported by sufficient evidence, and especially so since even his power to appreciate the weight of evidence is partly dependent on the amount of his knowledge. He may, then, easily confuse considera- tions which appeal to his prejudices and agree with his Ijeliefs with true evidence which appeals only to his reason. Such considerations help us to see that whenever what is not true has been mistaken for knowledge the reason has been that the real condi- tions of knowing have been departed from. When these conditions are really fulfilled, knowledge results. It will be our task in this book to examine the nature of these conditions. § 5 — A second point bi'ought out by the compari- .Say.ige son of the thought of savages with that of civilized ' "*°^ ^ ' man is that at all times man tries to find some explanation of the world in which he lives. At every moment of his life he is brought into contact with objects and phenomena over which his wishes and feelings and thoughts have no control. The storm comes and sweeps away his hut, the sun rises and sets, the moon waxes and wanes, the clouds gather and 8 THE LOGI(L\L BASES OF EDUCATION chap. disappoiir. Ov ;iy;ain, liis own actions frequently liavo results which he neither forsees nor desires. He eats a new beriy and is ill. He steps on-a stone in clinihino; a hill ; it gives Avay under him, he falls and is injured. Even consequences which he can foresee, in many cases he cannot prevent. He fails to find water and suffers thirst ; he is overtaken by the prairie fire and is burnt. Thus even at the lowest stage of development man cannot help finding himself in the midst of a world of which he forms a part, but which exists independ- ently of him. But the savage has not in the strict sense of the word begun to think. He is too fully occupied in keeping himself alive to concern himself with anything whicli has not a direct personal bearing. Especially must he be continually on guard against agencies that may work him ill. He is always finding new sources of evil to himself, and he is inclined to suspect the unknown. Savage man thus never looks at his world as a whole. For him it consists of isolated things and events which have a bearing — generally evil— on his own life and his own comfort. The most obvious explanation which occurs to him is to attribute to all things those powers of life which he himself possesses. Every thing is alive, or is at least the abode of a living spirit, generally of a malignant nature. Hence arises that general belief in magic which marks all races of savages. So, too, savage man has not learnt to distinguish between idealities and symbols. Nothing is con- nected with a man more uniformly than his shadow ; hence it is believed that a man may be injured by doing to his shadow what would injure the man if done to himself. Similarly a man's name is believed to be an integral part of himself, and it is a t GENERAL NATURE OF KNOWLEDGE 9 universal l)elief amongst savages that if an enemy knows a man's name he has him in his power. Consequently, in many tribes the real names are kept secret and ever}' individual is known by a nickname. Tliese few examples warn us against expecting to find any consistency in the philosophy of the savage. He attempts to explain his world not as a whole but piece by piece. He has hardly indeed begun even to ask himself what these separate ol)jects of his experience are ; of their real properties he is profoundly ignorant. Still, he has begun to see, though most diml}', that there are relations between things. It is true that the only relations he founds his attempts at explanation upon are those of striking, but often very superficial, resemblance. Yet it is in this vague and fragmentary recognition of relations that science has its root. ^ G. — As man begins slowly to emerge from Exiiiana- savagery less and le.ss of his time and energy is workl as"' occupied with the mere preservation of his life. 80 i}.v"'"Y'^ he begins to find time to feel curiosity about those things which do not immediately affect him, and even about the world as a whole. But the influence of the traditional beliefs remains strong. He still regards himself as the centre of the universe, the being for whose benefit sun, moon, stars and earth were made. Consistently with this he still thinks of 'things' — i.e. material objects which can affect him through his senses — as independent pieces of reality whose nature is not affected by the relations in which they stand to each other. In other words, he regards the world as a sum of things whose relations with each other are accidental. From this point of view 'things' are units of exist- ence which can be re-arranged in any way, like a set 10 THR LOGICAL BASES OF EDUCATION chap. of ninepins or a group of billiard balls, without altering their nature. Within such a philosophy there is still abundant i-ooni for magic and supernatural agencies. For whilst the relations between things are regarded as indifferent and variable in any way without affecting the nature of the things related, it is obvious that those relations will not be carefully investigated, and the analogy of a living agent will still be con- tinually called in to explain occurrences which are not understood. So fairies and witches remain part of the machinery of the world, and means must be taken to guard against their evil influence. Hence the survival of the use of charms, which is still extremely common amongst the majority of the people of Western Europe. " Many a fragment of cabalistic writing is cherished and concealed about their persons by the rustics of Western Europe as safeguards against black magic." ^ Again, so long as the relations of things are not regarded as important to the constitution of reality, and so remain unstudied, relations of striking like- ness will continue to exercise undue influence over man's attempts at explanation. Thus, " doctors in the seventeenth century... with... perchance unconscious humour, gave their patients pulverized mummy to prolong their years. ' Mummie,' says Sir Thomas Browne, ' is become merchandise. Mizraim cures wounds, and Pharaoh is sold for balsams.' " ^ Even in the present day " in Suffolk and other parts of these islands, a common remedy for warts is to secretly pierce a snail or ' dodman ' with a gooseberry- bush thorn, rub the snail on the wart, and then bury it, so that, as it decays, the wart may wither ^ Clofkl, op. rif., pp. 214—215. 3 Ibid., pp. 62—63. Laws. I GENERAL NATURE OF KNOWLEDGE 11 awa}'." ^ This is quite on a level with the action of the Cheroki Indians when " to ensure a fine voice, they boil crickets and drink the liquor." - § 7. — Insufficient as is the explanation of the Expiana- world which sees in it only a sum of things which world by may enter into any relations with each other without affecting their own nature, it yet satisfied the mind of man till a few centuries ago. It was only with the liirth of modern physical science that men really began to appreciate the importance of relations in the constitution of the woi-ld. But the old view of the independence of things still remains the philosophy of all the uneducated — that is, of all young children and of the great majority of adults. And it is from that view the educator must start in leading his pupils to a truer conception of the world. In this respect, as in so many others, the child epitomizes the evolution of the race. It may be said, then, that modern science began with the discovery that the nature of things is affected by their relations. And this discovery was the necessary result of a deeper study of things themselves. Even to a superficial observation it was evident that many things change according to the relations in which they are placed. The clouds are scattered Ijy the wind, the snow melts in the sun. With other things, indeed, the case seemed different, and in nothing was stability more apparent than in " the everlasting hills." But closer i))>servatiou showed that even these changed contin- uously. Kain and frost, torrent and glacier were always at work, and tlieir effects could be seen by the careful watcher. Thus, the idea that change is the characteristic of all things, and not a mere accident to some, began to take firmer and firmer hold of men's ' Op. rit., p. G-J. - Jhid, 12 'n\K L()(!ICAL r.ASKS OF EDUCATION chap. minds, though doubtless it was long before the stage was reached wliieh is expressed in Tennyson's Hnes, " Tlie liills are sliaflows and they flow From form to form and nothing stands ; They melt like mist, tlie solid lands, Like clouds tliey shape tiiemselves and go ! " ^ Factors of J^m change implies an agency which causes the i.inge. ^.j^j^j-^gp Either tliis agency is to be found in the nature of the thing itself, in some other thing in active relation to it, or in a combination of the two. Now, the agency of things from without is in many cases obvious. Trees and land are washed away by a torrent, smiling fields and prosperous cities are over- whelmed by a volcanic eruption, fire burns and water drowns. Hence, agency from without has seemed to some a sufficient explanation of all change. In this too we find the survival of the older belief, though under a new aspect. The older belief regarded things as essentially stable, and all change as accidental and exceptional to the general order. When change was observed it was attributed to external agency. The newer view was in opposition to this in regarding change as the normal state, but it agreed with it in attributing all change to outside agency, though the agency sought was that of material things instead of that of supernatural beings and unknown powers. Such a view, however, cannot survive deeper critical examination. External influences are soon seen not to be the only determining factors. An acorn and a grain of corn may be planted side by side and exposed to the same influences of soil and weather, but the one will deAelop into an ear of corn and the other into an oak tree. It is true that 1 In Jilemoriam, exxiii. I GENERAL NATURE OF KNOWLEDGE 13 neither will develop at all apart from appropriate conditions of soil aud climate, and so their develop- ment is determined by those external conditions. But it is equally clear that, given the conditions, the development which actually takes place is determined by the thing's own nature. And this nature is the essence of the thing itself. Grains of corn buried with the Pharaohs for thousands of years have been sown, and have borne fruit. External conditions are, then, contributing factors in development, but they alone do not determine the nature of that develop- ment. In the animal world the same thing is yet more manifest. An animal is much more independent of external conditions than is a plant, for by changing his locality he may seek conditions which suit him. To the extent to which he can do this he determines liis conditions rather than is determined by them. Doubtless the latter factor in his life is not absent, and in the course of ages may profoundly modify his constitution. But the mere influence of surround- ings will not account for the whole of animal life. In the highest degree of all is this self-determina- tion seen in man, who, by the exercise of his reason and will, can modify his environment in all kinds of waj-s. Wliat a man does and becomes is, of course, influenced by circumstances external to himself, and that often in a very great degree. But his conduct and life are not aljsolutely determined by those circumstances, but are regulated by the mans own nature. Even in the inorganic world the same thing is seen. Soil is wasluid away by a torrent, but both th(; extent and the mode of th(! denudation is detei'- rnined by the nature of tlie soil itself as well as by the character of the torrent. Many solids melt 14 THE LOGICAL BASES OF EDUCATION chap. when exposed to heat ; but whilst wax Hquefies at 65° C, lead remains solid till 335° C. is reached, and iron only leaves the solid state at a temperature of 1200° C. Throughout then, it is seen that all change in any object whatever is determined both from within and from without. The extent and time of the change are mainly determined by action from with- out, but its character is, at any rate partially, determined by the inner nature of the thing. XeccHsity It is Only when this is fully grasped that the versaiity Conception arises that every change which takes of Law. place is necessary. And Ijy ' necessary ' is meant that given such a thing under such conditions, such a change must take place. This is the conception of the universality of law which marks modern scientific thought. We are apt to under-estimate the scope of this principle. As Professor Huxley put it : " Even thoughtful men usually receive with surprise the suggestion, that the form of the curl of every wave that bi'eaks, wind-driven, on the sea-shore, and the direction of every particle of foam that flies before the gale, are the exact effects of definite causes ; and as such must be capable of being determined, de- ductively, from the laws of motion and the properties of air and water." ^ Such an example shows how limited our knowledge really is. It is mainly under the pressure of some practical interest that men strive to extend their knowledge. And so it is only about a few classes of things and events that men consider it worth their while to think accurately — that is, to think trul}', or to know. But accurate thought is scientific thought. We are apt to suppose that nothing belongs to science except those few phenomena about which men do try to think ^ Hume, p. 122. 1 GENERAL NATURE OF KNOWLEDGE 15 accurately. But the scope of science is the scope of the possibility of knowledge. As the late Professor Clifford said : " Scientific thought does not mean thought about scientific subjects with long names. There are no scientific subjects. The subject of science is the human universe ; that is to say, every- thing, which is, or has been, or may be related to man." ^ The scientific conception of the universality of law |^^"g^^^"'^ is, then, an attempt to explain everything which happens in the universe by the relations involved. If these are made clear, then, assuming that the nature of the ' things ' related remains constant, any change is so far accounted for that it is shown to be consistent with what is already known of the action of thing on thing. But modern physics goes further and tries to explain the nature of the ' things ' of ordinary life — the animal, the plant, the rock, the water — on the same principle. It seeks " the final constituents of the physical world in countless atoms, invisible from their minuteness, persistent in their duration, and unchangeable in their properties. These atoms .... produce by the variety of their positions and motions the different kinds of natural products and their change- ful development." "^ The atom, then, is assumed to have no positive quality of its own to produce change — it simply persists unchanged as a centre of the action and reaction of forces. Change is thus the result of energy ; it is only a rearrangement of the forces centred round the atom. Hence, the ultimate reality of the universe is found in energy, and this mechanical explanation of the world assumes its most developed fcjrm in the doctrine of the con- ' Eftfityii, p. 86. - Lotze, MiiroroamuH, vol, i, pj). '.M-'.Vl. 16 THE LOGICAL BASKS OF EDUCATION chav. servation of energy. This theory is certainly simple, but, as an ultimate and complete explanation of reality, it is inadequate. It does not fully explain the whole of the phenomena of the inorganic world, whilst it is quite unable to deal with the phenomena of life, especially with those of development. Rxi.iaiia- i^ 8. — But even were this not the case, the Worid^jw "^ mechanical theory does not give an ultimate resting- Systcm. place for thought. For it looks upon everything which exists as dependent on its relations to some- thing else. Now, if a phenomenon A is explained as due to the combination of B and C in a customary relation X, yet B, C, and X equally need explanation, and so with the factors which compose their causes. Thus we are driven into a series of explanations by relations which can never come to an end. Again, we must remember that when we speak of an event or a change, we are arbitrarily separating in thought one little piece of the world process which is not so separate in reality. As Macli puts it : " There is no cause nor effect in nature ; nature has but an individual existence ; nature simply is." ^ By nature here is meant the universe as a whole. That cannot be explained l)y its relations to anything else, for there is nothing else. This leads us to pass from the scientific to the philosophic stage of interpreta- tion. The essence of this is that it regards the universe as a system whose changes are due to its own inherent activity. But the only self-originating activity we can conceive is that of thought and will ; that is, of rational will. We are then compelled, if we push our search for explanation as far as it will go, to find in the universe the expression of the rational activity of an Absolute Being who includes all existence. Here, however, we have stepped beyond ^ Scieiice of Mechanics, p. -483. I GENERAL NATURE OF KNOWLEDGE 17 the bounds of science into philosophy. As Dr. INIerz says : " Science will not teach us to understand nature and life .... it is the philosophical or religious problem." ^ But it is only when the inter- mediate or scientific stage has been passed through, and this ultimate stage reached, that education can be said to have accomplished its work. A conception of the necessai'y order of development such as we are sketching, is, therefore, a part of the essential equipment of the educator. The idea of system is partially recognized in the scientific view. For according to it the universe is no longer looked upon as a sum of independent units, as in the interpretation of sense-perception, but as composed of parts in essential relation to each other. The philosophic view simply completes this idea of system and makes it the basis of all interpretation, and in doing so it takes up into itself what is true in each of the preceding modes of interpretation. It will be well, then, to consider briefly what is really meant by a ' system.' Let us do this by taking a piece of machinery, say a watch, as an illustration. The watch consists of various wheels, springs, and other ' works ' ; but these do not constitute a watch unless they are arranged in a certain definite way. The watch is, therefore, not merely the complete sum of its parts ; there is no watch unless those parts are in certain relations to each other. Further, the mean- ing of each part depends on those relations ; for its meaning is the share it plays in that work of measur- ing time for which the watch exists. But this share it is only able to perform through the action upon it of the other parts of the watch. A knowledge of its relations to those other parts will, then, enable us to ' Hiatory of European Thonnht in (he Nineteenth Ctnturu, vol. i., p. .S83. 18 THE LOGICAL BASES OF EDUCATION chap. undei'stand how the part in question does its work. An insight into ^vhy that work is done involves however, a knowledge of the purpose for which the whole watch exists and of the relation of the activity of this part to the total activity by which that purpose is carried out. A complete comprehension, then, of any one part of such a system involves a knowledge of the relations of that part to every other part, and to the whole. Of course, these relations are of very diiferent degrees of directness. But in a system there is no break, and therefore every part is connected, directly or indirectly, with every other part. Complete know- ledge of any one part would include knowledge of all its relations — direct and indirect — and would, consequently, be knowledge of the whole. Of a small and artificial system like that of a watch such complete knowledge is attainable, but the wider and more complex a system is, the more difficult it becomes to reach such perfection of knowledge. Still the characteristic features of a system are the same, no matter what its extent and complexity. The scien- tific view then, by insisting on the essential part played by relations in the universe, begins to regard it as a system. The philosophical view by emphasiz- ing the essential i^elation of each part to the whole, that is, the purpose or function of each part with respect to the whole, as that in which alone com- plete explanation can be found, develops and com- pletes this conception. Of this system of the universe the total knowledge of mankind is very imperfect. Still more imperfect is the knowledge of each individual man, for meagre as is the total knowledge of the race it is yet so ex- tensive as compared with the limited capacities of each individual that no one can master more than a I GENERAL NATURE OF KNOWLEDGE 19 small portion of it. Hence we have specialists ; that is, the totality of the field of knowledge is divided up into sections, and each thinker confines his efforts to a more or less limited section. These sections, which we are accustomed somewhat loosely to regard and speak of as separate ' sciences,' are more or less fully organized systems in themselves, and the}' are in turn divided by us into smaller constituent systems. The conception of system, therefore, determines all man's attempts at organizing knowledge. We have a countless number of small systems, themselves constituents of larger systems, and so on till we reach the all-embracing system of the universe itself. And throughout all there is continuity of i-elation, so that even the smallest thing — a grain of dust or a passing whim — is in essential connexion with every other part and with the whole. As Tennyson beautifully says — " Flower in tlie crannied wall, I pluck j-ou out of the crannies, I hold vou here, root and all, in mj' hand, Little flower — but if I could understand Wliat you are, root and all, and all in all, I should know what God and man is." § 9. — But it may be asked " In what sense can Nature of this ultimate stage be called knowledge ? Is it not "fd oF rather a piece of philosophical imagination or of Knowledge, religious faith 1 " To answer this question we must investigate somewhat more fully the nature of knowledge. Knowledge, as has been said, is an insight into the nature of reality. In other words, the object of knowledge is always some portion of that real world of which we ourselves form a part. Now we are brought into contact with reality in every piece of sense-experience. We look, and what we c 2 20 THE LOGICAL BASES OF EDUCATION chap. see is independent of our wish ; we listen, and cannot determine what we shall hear ; we touch, but the surface touched is not influenced by our desires ; we taste and smell, but the resulting sensation is due to the object tasted or smelled. In a word, what we perceive is given us, is determined for us by the nature of the real world. Thus, reality con- strains us, and it is this constraining power which marks off reality from fancy. But reality is not simply what we experience through our senses here and now. We find the same constraint in memory. We can recall our past doings and experiences, and much as we may wish them difFei'ent from what they were, we cannot believe them different. They also are part of our reality. They form our real past, which is often as diffei'ent as possible from the past we like to fancy. This same constraint is not felt as regards the future. That, indeed, we can often anticipate, but we know the anticipation is only more or less probable, it is never absolutely certain as is the past. But neither present sense-experience nor memory of the past does more than put us in touch with reality. It gives us the material of knowledge, but not knowledge itself. Even in the simplest case, what is given to the senses has to be inter- preted by thought. I see a yellow sphere of two or three inches diameter and I recognize it as an orange, and acting on this recognition I attribute to it many qualities and relations other than those now present to my senses. I say it is juicy and the fruit of a tree which grows in a warm climate. This and much more the little yellow sphere means to me. But very little of this is directly given in experience. Some of the rest has been given in my past experience, some I have received on the testimony of others, I GENERAL NATURE OF KNOWLEDGE 21 some I have inferred. Or again, I wake in the morn- ing and see the ground covered with snow, whilst my memory tells me there was no snow there when I went to bed the night before. I feel no hesitation in saying the snow has fallen from the clouds during the night. But I do not know this by sense-ex- perience ; I infer it. No doubt the inference is based on past experiences, but it is itself neither an experience of the senses nor the memory of .such an experience. And, of course, even in explaining the white appearance which the ground presents to my sight as due to a covering of snow, I am going beyond sense-experience in the same way as in the case of the orange we have just considered. Further, sense-experience leaves many gaps which thought must fill up. For example, I left my house this morning and returned to it this afternoon. T quite expected to find it standing just where and how I had left it. But it had not been presented to my senses all day, nor had I received the testimony of another to whom it had been thus presented. Yet I feel no doubt that it continued to exist, for other- wise I must assume that it comes into being just as some one happens to look at it or touch it, and goes out of being immediately it ceases to be perceived. But this is unthinkable, for it contradicts the only possible explanation of reality. If the existence of things were dependent on their perception, then obviously they could not compel that perception. But this contradiction is, of course, made manifest by thought, not l)y the testimony of the senses indepen- dently of thought. Hence in every case we sec that sense impressions have to be interpreted by thought before they can have meaning for us, and without meaning they caiiuot enter into knowledge. Wlicn so inter- 22 THE LOGICAL BASES OF EDUCATION chap. preted we call them 'facts.' A 'fact' then is a thing or event interpreted by thought. And this interpretation is, speaking broadly, the harmonizing the present experience with experiences received in the past. Such interpretation may, no doubt, be wrong. The yellow sphere may be a skilful imitation of an orange, and not the fruit itself ; the whiteness of the ground may be due to hoar frost, and not to snow. In such cases, however, further investigation shows the mis- take by bringing to light something inconsistent with our suggested explanation. The mock orange con- tradicts past experiences of touch and taste ; we find appearances in the hoar frost which we do not find in snow, or some one who has been out all night assures us that no snow has fallen. Truth cannot contradict itself ; whenever, therefore, we find con- tradiction, we know that we have falsity. All thought must postulate this, for, without it, thought itself becomes impossible. Thus we do not hesitate to reject even personal testimony on the ground that it is inconsistent with the only explanation which will harmonize an enormous number of other experi- ences. For example, when " M. Louis de Rougemont " asserted that, whilst swimming in the sea ten miles from land, he could see the natives " putting out in their catamarans to help us," ^ we declined to accept the statement as true, on the ground that the rotundity of the earth would make the alleged fact impossible unless those savages were some sixty-six feet in height. No one thought of accepting the writer's statement as a disproof of the general theory of the shape of the earth, for to do so would have been to accept as a fact a contradiction to innumerable other facts as to whose reality there can be no doubt. ^ Wide World Magazine, Ot;tobei-, 1S98, p. 6. I GENERAL NATURE OF KNOWLEDGE 23 Of course, it not infrequently happens, as has already been said, that what is at one time regarded as true is found at a later period to be false. This always takes place when some previously un- known facts are discovered which are inconsistent with the accepted explanation. We continually have examples of this in our daily life, and the phrase " Ah, that throws a new light on the matter ! " indicates that the explanation which had hitherto been satisfactory to us, as harmonizing all tlie facts known, is now, by the knowledge of other facts inconsistent with it, found wanting. We must then seek a new explanation which will find a place for these new facts as well as for those formerly known. In the history of the world's thought probably the most striking example of this was the substitution of the theory that the sun is the centre of the planetary system for the theory that the earth holds that posi- tion. Here also it was the discovery of new facts which made the old theory untenable, though it had for centuries sufficed to harmonize all that was known of the motions of the heavenly bodies. It appears, then, that consistency with all other The Test knowledge is the test of truth, and it follows that, as " knowledge is always advancing, it is often impossible to say with absolute assurance that any particular item of our interpretation of the world is true. Further knowledge may, in many cases, necessitate a revision of such interpretations in the future as in the pa.st. As knowledge grows, liowever, the amount of fully established truth is gradually increased. An item of interpretation must be held to be absolutely estab- lished as true whenever it is the only possible explanation of the facts. If the ground is covered with snow, suow must have fallen from the clouds. 24 THE LOGICAL BASES OP EDUCATION chap. Similarly, the cissumption of the continuous existence of material objects independently of our perception of them is the only possible way of bringing con- sistency into our experience. Whenever, then, an explanation is ' necessary,' in the sense that to refuse to accept it would be to introduce contradiction into the thought and experience of mankind, that ex- planation is as much a part of knowledge as is the actual experience to which it gives meaning. It is in these considerations that we find the answer to the question with which we began this section. It is in this sense of necessary explanation that we hold the theory that the universe is a self-determined system — the expression of a rational activity which manifests itself in all the changes which are, or ever have been, or ever will be — to be a matter of knowledge. It is the only interpretation which can harmonize the thought and experiences of mankind, and give a firm basis to knowledge- Moreover, the very fact that we can interpret the world and give a meaning to what goes on in it proves that the world itself is rational. Rational thought could find no meaning in a world which was not itself the expression of rational thought, for nothing but the rational has meaning. Without this assumption, man's knowledge is an edifice without foundation. i:^ 10. — We see, then, that in every case, great as well as small, the material of knowledge is given us ^we cannot make reality other than it is. But, on the other hand, this material only becomes intelligible when it is interpreted by thought. It is thought which makes reality known to us. In this sense man may be said to construct his world. Indeed, each one of us constructs his own world, for each one of us comes into contact with reality in his own 1 GENERAL NATURE OF KNOWLEDGE 25 individual experiences, and interprets those ex- periences according to his own amount of knowledge. But no two of us have either exactly the same experiences or the same knowledge. Consequently, each one of us sees the world from a standpoint somewhat different from that of all others, and sees it through a different medium of personal knowledge. Yet there is common knowledge, for all knowledge is of the same reality, and though there are many minds yet there is only one kind of intelligence. These different individual constructions of reality in thought are well likened by Dr. Bosanquet to " drawings in perspective of the same building from different points of view. . . . Our separate worlds may be compared to such drawings : the things in them are identified by their relations and functions, so that we can understand eacli other, i.e. make identical references, though my drawing be taken from the east, and yours from the west." ^ It is, then, only by comparison of the construction of reality of one indi\'idual with that of another, and the consequent correction and enlargement of each by each, that we have that common knowledge which represents the totality of individual knowledges and which is the extent to which mankind has grasped truth. This is the universal knowledge of which the individual knowledge of each one of us is but an imperfect reflexion. It should 1)e noted tliat this common knowledge is not the product of any one generation. It is the result of the attempts of countless generations of men to understand more and more of the world — attempts l)rompted from the first by practical needs, and in addition, in more civilized days, by the simple love of knowledge for its own sake. Every individual enters ' Ednendals of Loyic, p. IS. 26 THE LOGICAL BASES OF EDUCATION ch. i into the heritage of the thought of the past, for he finds much interpretation current in the society into which he is born, and expressed in the language which he learns. Much of this knowledge he imbibes unconsciously, by imitation and by learning to use language, and much he receives by direct instruction from otliers. Thus, no individual takes up the task of trying to understand the world from the begin- ning ; he accepts much that has already been done. Were it not for this no growth of knowledge would be possible. This it is which makes the common knowledge of mankind an ever swelling flood, and enables man to read more and more fully the riddle of the universe. CHAPTER II POSTULATES OF KNOWLEDGE § 1. — We found in the last chapter that know- xhe ledge implies both a real world and intelligence Knowledge capable of understanding that world. But though we can distinguish these two factors of knowledge, they cannot be actually separated. Neither can exist without the other. We cannot have thought about nothing ; so thought cannot exist without the world. On the other hand, if any reality exists out of all relation to human consciousness, that reality does not exist for man. The world exists for each one of us just so far as he knows it, and no further. If we extend this thought, we are led to see that a reality which exists for no consciousness at all — Iniman or divine — is absolutely unthinkable, because it is devoid of meaning. We must not, therefore, think of man and of the rest of the universe as two separate orders of existence in no essential relation to each other. The universe is the whole of existence including man, and it is only because man is an integral part of the universe that he can enter into that relation to it which we call knowledge. 28 THE LOGICAL BASES OF EDUCATION chap. Postulates § 2. — This relation starts with the very beginning Kiuiwiedgc. oi experience. As Dr. Bosanquet puts it, " Experience may be said to begin with the certainity that ' there is somewhat.' " ^ The growth of knowledge is just the fuller and fuller understandingof that "somewhat." Now, this growth has been the work of many minds continued throughout long ages. Such co-operation in the increase of knowledge is only possible on the assumption that human intelligence always works fundamentally in the same way. Its products indeed differ, for they include all attempts to explain the universe, from that of the rudest savage to that of the most profound philosopher. But this difference is due to the different starting points made possible by the growth of knowledge itself, not to differences in the principles on which interpretation of experience proceeds. Such common principles can be found by analysing the process of acquiring knowledge. They are called the Postulates of Knoivleclge, because they az'e presupposed in all knowledge from the very beginning, and are the very life-blood of its growth. As knowledge grows these postulates get a wider and deeper meaning, but in their essential nature they are the same throughout. Of these Postulates of Knowledge four are of great importance. They have long been named the Principles of (1) Identity, (2) Contradiction, (3) Excluded Middle, (4) Sufficient Reason. As they are all operative together and each is more or less closely involved in each of the others, instead of examining them separately it will be convenient to discuss their combined scope at each of the three great stages of interpretation of the world brought out in the last chapter — that of sense-perception; that of law ; that of system. ^ Loijk, vol. ii, p. 206. II POSTULATES OF KNOWLEDGE 29 § 3. — The distinguishing mark of the stage of sense- The perception — which ma}-^ perhaps be called that of un- f t°the"^*^^ educated common sense — is that the common ' thintrs ' '^'^^se of 1-1 • 1 1 • 11- Sense-per- which man perceives by his senses ai-e the ultimate ception— forms of reality. Relations are regarded as indiffer- ent ; the things stand fast like " the everlasting hills," whilst relations form and scatter around them like the clouds, and with no more effect on their real nature. To this view, the world is a sum of separate and independent units, and the highest aim of knowledge is to classify and describe these correctly. Here the Principle of Identity is most prominent, identity. It asserts that the real nature of everything is constant. This does not deny difference or change. Indeed it is only amidst diversity that identity is ever known. Oak-trees differ in size, shape, position, and in many other ways, yet they have an identi- cal nature, shown in a general identity of life-histoiy. Time brings changes to all things more or less rapidly, and we learn what amount of change to expect, and refuse to recognize identity at all if that change is not there. If I see a child to-daj'^ whose appearance seems to me to coincide with that of a child I knew thirty years ago, that very resemblance will prevent me from believing that he is the same person. Identity, then, is always found amidst diversity. The Principle of Contradiction is essential to give Contradic- a full and precise meaning to that of Identity. It ''""' asserts that the same nature cannot have contra- dictory qualities, or, in other words, that a statement and its denial cannot both be true. Of course, the statement and its denial must both refer to the same piece of reality at the same time. Yesterday I could truly say, " I have a headache " ; to-day with equal truth I can deny the headache. But these two 30 THE LOGICAL BASES OF EDUCATION chap. statements are not contradictory, or in any way incompatible, for though both refer to "I," yet the " I " in the one case is the " I of yesterday " and in the other case the " I of to-day." Indeed the prin- ciple of Identity may be expressed by saying that " what is once true is always true " — for if the state- ment refers to anything which changes with time, it does so within definite time limitations. The time limits may be very narrow, as in the case just quoted, or they may be of considerable extent. When a statement concerns the essential nature of a thing, its time limits are coextensive with the existence of that thing. Thus the statement that " oaks spring from acorns " must be held as true for all oaks that ever have been or ever will be in the woi'ld. Here we see how the principles of Identity and Contra- diction complement each other : that of Identity says : oaks are always produced from acorns ; that of Con- tradiction denies that they can ever be produced in any other way, or that any other growth can spring from acorns. Excluded The Principle of Excluded Middle affirms that Maidh. qH\^qy r^ statement or its denial must be true, and thus completes the Principle of Contradiction, which says that one of them must be false. An important bearing of this is that when we prove a statement to be false we necessarily prove that its denial is true. Of course, this principle must be understood with the same strictness as those we have already discussed. It does not imply that we are always sure which of two contradictory statements is really true. In every case of doubt we are unable to decide this because we have not sufficient knowledge in some way of the matter in hand. We may be un- able by lifting them to determine which of two nearly equal weights is the heavier, yet one of them is POSTULATES OF KNOWLEDGE 31 the heavier, and a pair of scales may decide the question. The doubt is not in the things themselves, but in our interpretation of the effect they produce upon us. The Principle of Sufficient Reason afhrms that everything is capable of explanation. At the stage of knowledge we are now considering such explanation is always imperfect, and very often more or less fanciful. As we saw in the last chapter, savages — who are the most thoroughgoing representatives of this stage of thought — do seek explanation, but they seek it mainly in the activity of supposed super- natural beings. Indeed, as soon as men seriously seek an explanation for the events they see around them, they begin to pass into the next stage of thought. i< 4. — The characteristic of the second — or scientific — stage of interpretation is the attempt to explain everything in the world by its relations to other things. As has been already pointed out, modern physical science pushes this explanation of the things of sense-perception so far that it nearly explains them away altogether. It finds the ultimate reality in the relations to each other of simple and unchangeable atoms, and teaches that constancy in the nature of ' things ' is due to con- stancy in the relations between their constituent atoms. The principles of Identity, Contradiction, and Excluded Middle are, therefore, given a wider application. They apply now primarily to the relations of atoms, and only secondarily to the ' things ' constituted by such relations. Moreover, modern science insists on the truth that these 'things' are in relations to each other, and change with every alteration in such relations. The actual phenomena of the universe can, then, only be Sufficient Httisoit. The Postulates at the Stag of Law. 32 THE LOGICAL BASES OF EDUCATION chap. understood when relations of thing to thing are investigated. This emphasizes the Princijile of Siifjiclrnt Jieason, but also involves the other prin- ciples. For as similarity of the nature of things is explained by the assumption of similarity of relations ])etwe(Mi tha,, constituent atoms, so similarity of change is explained by assuming similarity in the relations of the things involved. We speak here of ' similarity ' rather than of identity, because, as has lieen already pointed out, identity is never found except amidst diversity, and ' similarity ' expresses this very combination, and is, therefore, the most appropriate term to apply to the actual events which take place in the universe. In all similar phenomena there is an element' of identity to which the simi- larity is due, and on the basis of which alone we can infer from one to the other. But this element of identity is by no means always on the sui'face ; in many cases, indeed, we have to assume its existence without being able to specify exactly either its nature or its extent. As Mill reminds us : " The course of nature, in truth, is not only uniform, it is also infinitely various. Some phenomena are alwa^^s seen to recur in the very same combinations in which we met with them at first ; others seem altogether capricious ; while some, which we had been accus- tomed to regard as bound down exclusively to a particular set of combinations, we unexpectedly find detached from some of the elements with which we had hitherto found them conjoined, and united to others of quite a contrary description." ^ To first experience, then, the world is chaotic, and, as we have seen, the savage so regards it. This is because he applies the Principle of Identity only to things, in the independent nature of which he seeks ^ Logic, vol. i, p. 359. II POSTULATES OF KNOWLEDGE 33 all explanation. " Man after man dies in the same way, but it never occurs to the savage that there is one constant and explicalile cause to account for all cases. Instead of that, he regards each successive death as an event wholly by itself — apparently un- expected — and only to be explained by some super- natural agency." ^ It is only when the importance of relations is recognized and the postulates of know- ledge applied to them, that the conception that underneath all the apparent confusion of phenomena there is an always present and essential uniformity begins to govern man's mode of interpreting his ex- periences. Then science begins, for man recognizes that upon him " is imposed the task of everyAvhere seeking out in the natural phenomena those elements that ai'e the same, and that amid all multiplicity are ever present." " When such elements are found, the work of science is done. " When once we have reached the point where we are every^vhere able to detect the same iew simple elements combining in the ordinary manner, then they appear to us as things that are familiar ; we are no longer surprised, there is nothing new or strange to us in the pheno- mena, we feel at home with them, they no longer perplex us, they are explained." ^ The explanation given by science, then, consists in causation. determining the conditions under which any change or event takes place. And the whole of these con ditions together are styled the Efficient Cause — or simply the cause — of the phenomenon in question. The Principle of Causation is, then, one aspect of that of Sufficient Reason. Its most general axiom is : (1) " Every event must have a cause." Then, in combination with the principle of Identity and its ' Lionel Decle, Three Yearn in Savage Africa, p. i312 - Mach, Science of Mechanics, p. 5. •' Ibid., pp. 5 — 6. P M THE LOGICAL BASES OF EDUCATION chap. ' Every Event has a Cause.' 'Same Cause, same Effect.' complementary pi'inciples, it assumes uniformity in causation in the axioms — (2) " The same cause always produces the same effect;" (3) "The same eflfect is always due to the same cause ; " (4) " Cause and effect are equal in amount of energy." As we have seen, the first of these three axioms is implied in all attempts to explain the world ; even the rudest savage assumes it. But the other three axioms are only operative when explanation is sought in relations. Then, as man's early seekings after knowledge are always motived by practical needs, the uniformity of causation appeals to him first in the light of the second axiom. He is interested more in what will result from certain conditions than in the inverse problem of what conditions will produce a given result. Hence, he studies causation mainly from the point of view of the cause. In other words, he analyses more or less cai^efully the conditions that will give a certain desired result, and he assumes that if the result comes in one case it will come in all, provided that he secures the same conditions. He applies the principle of Causation forwards. '.Same But the result obtained is often a very general one, cfuse.''"'^""'' and man's practical needs do not usually prompt him to analyse it carefully. Hence it often appears to superficial observation that the third axiom is not true, and that the same effect may be produced by different causes on different occasions. If this were so, the principle of Causation would be one-sided, for the principle of Identity would be only half applic- able to it. And, indeed, this was the common opinion till quite recently. Even the savage recog- nizes some uniformity of causation in cases in which his own activity in carrying out his own purposes plays an important part. He desires to kill his enemies or the animals he requires for food, and he II POSTULATES OF KNOWLEDGE 35 knows he can do this in a variety of ways. When he sees death which has not resulted from visible violence, he assumes that a similar destructive activity' is exercised by malignant spirits. Death, then, to his mind, obviously results from a variety of causes. Nor is the savage alone in this rough and ready way of interpreting events. Even so great a logician as Mill says : " It is not true that only one effect must be connected with only one cause, or assemblage of con- ditions . . . many causes may produce death." ^ But in speaking of "death" Mill shows that he has not applied the same searching analysis to the effect which he tells us is necessary to discover the cause. Every coroner's inquest is an attempt to perform such an analysis, and of necessity proceeds on the assumption that exactly the same kind of effect can have only one cause. There is no such thing as death in general ; every death is one particular kind of death, and in speaking of ' death ' as the effect of a bullet through the head or of swallowing arsenic, we are either using the word very loosely or we are picking out from the total effect the one factor which is of the greatest personal interest. A hole in the head is just as much part of the effect of the bullet in the first case as is the death, and similarly a particular condition of the organs of the body results from taking arsenic just as surely as does death. No doubt, at first sight it seems certain that the same effect is due now to one cause, now to another. " Thus friction, combustion, the liquefaction of a vapour, freezing, pressure, all produce heat. What could be more apparently disparate than these agen- cies ? Yet all of them alike involve the liberation of molecular motion in accordance with mechanical ' Lofjir, vol. i, p. ijO.j, D 2 M THE LOGICAL BASES OF EDUCATION chap. ' Cause and Effect equal in Knergv.' Causation and Sequence in Time. laws common to all the cases." ^ This oxample admirably brings out the difference between the popu- lar and the scientific views of causation. The former confines itself to the sphere of sense-percep- tion, and finds causation in the influence of one visible and tangible body upon another ; the latter seeks it in an analysis of the process which brings to light a persistent and identical nature changing in determinate ways under definite conditions. In all cases, such an analj^sis is a task of difficulty ; in many, it has not yet been accomplished. But the belief that, when such an analysis is found possible, it will always reveal an underlying identity, even amidst the greatest apparent diversity, is involved in the acceptance of the axiom that causation is uniform. As the third axiom was recognized later than the second, so the fourth can only be recognized when the third is accepted. It is a yet further application of the principle of Identity to that of Causation, and when stated in its most general form it becomes the doctrine of the conservation of energy — that the amount of energy in the world is not subject to either decrease or increase, but only to change in mode of expression. This is one of the latest con- ceptions of modern physical science, but we see in it only the further application of the same principles of interpretation which have been operative from the first in the development of knowledge. A consideration of these axioms of causation makes it evident that, in another respect, the common way of regarding causation is indefinite. We con- stantly look upon the cause as necessarily preceding the effect in time. Indeed, not infrequently mere succession in time is mistaken for a true causal con- nexion, as when the appearance of comets is held to ^ Hobhouse, The Theory of Knowledge, p. 366. 11 POSTULATES OF KNOWLEDGE 37 be the cause of a war or other calamity, which may follow shortly after. It can be easily shown, however, that the cause does not always precede the effect. A blot is the effect of letting a drop of ink fall on paper, but the blot does not follow the contact of ink with paper ; its appearance is simultaneous with that contact. So the height of the mercury in a barometer is the effect of the pressure of the atmos^Dhere, but it is simultaneous with that pressure. In other cases, the effect seems subsequent to the cause. A cricket ball is struck by a bat, and the motion of the ball is subsequent to the stroke which was its cause. But here again we want a deeper analysis of the process. The impulse given by the bat is communicated to the ball in the moment of impact, and not subsequently to that moment. Thus it is the accumulated effect which is subsequent to the original stroke, and furthei" analysis shows that we have a continuous transition of events each of which is at once cause and effect. Whether we say, then, that effect follows cause or is simultaneous with it depends upon how we are using the terms. This is admirably put by Whewell : " The instantaneous effect or change is simultaneous with the instantaneous force or cause by which it is produced. But if we consider a series of such instantaneous forces as a single aggregate cause, and the final condition as a permanent effect of this cause, the effect is subsequent to the cause. In this case, the cause is immediately succeeded by the effect. The cause acts in time : the effect goes on in time. The times occupied by the cause and by the effect succeed each other, the one ending at the point of time at which the other begins." ^ In brief, we nmst remember the continuity of ^ History of SckiUiJic Mean, vol. 1, pp. 197 — 198. 38 THE LOGICAL BASES OF EDUCATION chap. change iu the world, and the artificial character of what we single out as ' events.' As Mr. Hobhouse says : " No event ever begins or ends ; but a process goes on which passes gradually from one phase into another. We ticket prominent or clearly distinct phases with separate names, and speak of them as different events ; but we must remember that, though in one sense they are different, there is yet no barrier.''^ 'Cause' and 'Effect,' in the common use of the terms, are but separate names for artificially limited earlier and later phases in one continuous process. Causality is, then, a principle on which the human mind acts from the first. It is not gathered from sense- experience, for it is involved in all interpretation of such experience. " What causes produce what effects ; what is the cause of any particular event ; what will be the effect of any peculiar process ; these are points on which experience may enlighten us. . . . But that every event has some cause, experience cannot prove any more than she can disprove." ^ Nor can experience demonstrate that one cause is universally connected with one effect. But this is assumed in the statement of every scientific ' law,' for such laws assert that a causal relation which has been observed in a limited number of cases holds true throughout the universe, and this is, obviously, not a matter which can be either proved or disproved by observation. The establishment of such laws is the ideal of knowledge at this stage. The ^ 5.— We saw, however, in the last chapter, that a°till!'stege explanation by bringing a particular case under a df System, general law cannot be ultimate, and that we are driven by the necessities of thought to regard the ^ The Theory of Knowledge, p. 277. 2 Whewell, op. cit., p. 174. ri POSTULATES OF KNOWLEDGE 39 universe as one self-determined system. With this conception we have obviously a very considerable extension of the principles of interpretation beyond their application in the scientific stage. The universe itself, as well as its constituent parts, is now regarded as embodying those principles. It is thought under Identity as a continuous unity retain- ing its essential nature amidst all the infinite number of varied manifestations of that nature. Undei' Contradiction it is thought as essentially consistent ; as containing no contradictions. This is why we find contradiction always a proof of error, for this principle compels us to recognize that error cannot ultimately be made consistent. Under Excluded Middle we think of it as a system of mutually-detei'mined parts. Lastly, under Srifficieiit Reason we regard it as furnishing in the relations of part to part the first stage of explanation, and in the relation of parts to the whole an ultimate explanation. In discussing the scientific method of interpretation Final we saw that it is mechanical, that is, it explains one phenomenon by its relations to others according to mechanical laws. We have also seen that this explanation is not final. The conception of efficient cause which dominates scientific interpretation is supplemented in the philosophical stage by the con- ception of purpose. This is inherent in the con- ception of system. To revert to the illustration of the watch. The efficient cause of its marking the time is the relation of part to part. But that does not explain tchy the watch exists. This is found in the human purpose which it serves. The watch is planned and niarle by man just for that very object, and without it the watch would not exist. This conception of purpose — or Final Cause, as it is frc(juently called — is moiildiiij; more and more man's Causes. 40 THE LOGICAL BASES OF EDUCATION chap. interpretation of the world. Of course, the purpose is not always relative to man. It is so in the case of things like the watch, which he invents and makes to serve his own ends. But we have got beyond the stage of thought in which sun, moon, and stars were regarded as existing solely for the purpose of giving man light, and in which efforts were made to find a reason for the existence of everything by showing that it is of some use to man. Such an attempt was common enough even in the last centui'y, and perhaps reached its highest point of absurdity when the existence of noisome domestic insects was accounted for on the ground that such pests induced personal cleanliness. We now regard each form of existence as having its own purpose. Of course such purpose can only be known by beings endowed with minds. Man can aim at attaining a certain form of character, and even the lower animals are conscious of wants which they strive to satisfy. But the modern doctrine of evolution finds progression in the vegetable as well as in the animal world, and we may quite intelligibly speak of the purpose of the existence of oak-trees as the gradual attainment of the perfection of oak-tree life. Even in the inorganic woi'ld we must think of all change as the gradual attainment of some end, though we must not try to find that end in reference to the needs of men. In so far as any thing freely manifests its own nature it may be said to fulfil its purpose. Thus we think all change as having an object, though that object is often hidden from us. As Dr. Harris puts it : " In the view of evolution there is a goal towards which relatively lower orders are progressing, and the facts, forces, and laws are seen as parts of a great world-process which explains all. At this point science rises into n POSTULATES OF KNOWLEDGE 41 philosophy. . . . When science comes to study all objects in view of the principle of evolution, it has transcended the stage of mind whose highest object is to discover classes ; likewise the stage that makes law an ultimate. Besides efficient cause, which makes or produces some new state or condition, there is ' final cause ' or purpose — design or ' end and aim.' '' ^ ' Psychologic Foundations of Education, pp. 19 — 20. CHAPTER III KNOWLEDGE AND LANGUAGE Ideas and § 1. — We have Seen that all knowledge consists in now gc. (.Q),j.ggj^]^y interpreting or giving a meaning to ex- perience, and that such interpretation means the harmonizing this experience with others. Or we may put it in another way, and say that to give meaning to any piece of reality is to think it in its proper place in an appropriate system. But systems of reality exist in consciousness as mental construc- tions, or ideas. Hence, to give meaning is to think an experience under an idea already existing in consciousness. We may say, then, that experience as interpreted is made up of ideas, and that know- ledge consists of all those ideas which are true. Ideas and § 2. — But reality to each of us is only our Ueahty. experience as thus interpreted. Therefore, by ' ideas ' is meant the way in which the mind grasps reality. Every known piece of reality exists in consciousness as an idea. It is not merely 7'epresented in consciousness, as if the world of reality were separate and distinct from the world of knowledge. We must not, therefore, think that things in the eternal world impress copies of themselves upon our CH. Ill KNOWLEDGE AND LANGUAGE 43 minds, as a seal stamps impressions on wax, or as the image of an object is impressed on a photographic plate. It is true the x^etina of the eye does act very similarly to a photographic plate, but the eye is not the mind, and the retinal image is not itself in consciousness. § 3. — It is true also that we talk of the "eye of ideas and the mind," and that most people can call up more or ™*s*^^- less vivid and distinct mental images of absent objects. Images, however, are not ideas, but only symbols of ideas. Just as the shape and colour of an orange are symbols of all else that ' orange ' means to us when the orange is actually present to pei*- ception, so the visual image of an orange acts as a sign in exactly the same way. The idea is the meaning which the mind finds for the present ex- perience by referring it to other experiences, and any mental image that may come into the mind is only an example or illustration of that meaning. In many cases, indeed, such images do not corres- pond to the idea, and when present tend to obscure meaning and hinder understanding. " We can image some object that is acted upon by force — we can image it before it is acted upon and after it is acted upon. That is to say, we can image the results of the force, but not the force itself. We can think of force, but not image it." ^ To " have an idea " of anything is, then, to know its nature and meaning ; in other words, to think it, not to look at it either in reality or as represented in a mental image. DouVjtless, real thought is difficult, and many Thougiii persons are satisfied to suljstitutc for it panoramas inuigina- of mental pictures. This tendency is promoted by ^'•^"• " what we may call the Photographic writing which alone obtains at present. For a long while back, writers ^ Harris, Psychologic Foundations of Education, p. 40. 44 THE LOGICAL BASES OF EDUCATION chap. have desired to write only to our eyes, not to our thoughts. History now is as a picture-gallery, or as a puppet-show ; men with particular legs and par- ticular noses, street-processions, battle-scenes, — these — images — all images ! — mow and mop and grin on us from every canvas now. We are never asked to think — only to look — as into a peep-show, where, on the right, we see that, and on the left this ! " ^ It is true, as Dr. Stirling himself reminds us, that images "are always the beginning, and con- stitute the express conditions, of thought."^ Whilst an individual is in the first stage of thought — that of sense-perception — he will not have separated his meanings fi'om his images and his percepts. But unless we pass beyond this stage to that of the abstract idea, or meaning, " we never attain to mastery over ourselves, but float about a helpless prey to our own pictures." ^ This is so because all such pictures are of individual and particular things, and every particular exhibits qualities and relations of its own, which are not part of the meaning, and which obscure that meaning. For example, all who have worked problems in geometry know how easy it is to be misled by some accidental feature of the particular diagram we draw, or picture in our minds, to aid us in the solution. We desire, it may be, to establish some relation of triangles in general, and the particular triangle we draw has perhaps two of its angles equal, and we are apt to ti'eat this accidental relation as essential, and base our proof upon it. In contrast to the particular image, mean- ing is always universal ; that is, it is common to all pieces of experience which we think under the same idea. 1 Stirling, The Secret of Hegel, p. xlii. - Ibid., p. xliii. 3 Ihid. Ill KNOWLEDGE AND LANGUAGE 45 § 4.- — If we now ask how knowledge, oi' a system Doveiop- of meanings, develops in an individual mind we are "aeas." at once met by a theory once very connnonly ac- cepted but now proved to be tlioroughly false. According to this theory, the mind liegins with ideas of individual things, then, by comparison, classes them together, and so goes on to construct its world in a manner very similar to that in which a brick- layer builds a wall. Nothing could be farther from the truth. Modern psychology has thoroughly established that the mind begins with a vague apprehension of its experience as a whole, and then little by little divides this up, as this or that piece of experience secures its interest and special attention. As Dr. Bosanquet suggests, the process may be illus- trated by " the discernment of features in a distant landscape which prolonged attention even without optical assistance has the power to effect." ^ The process starts from the whole, not from the elements. Ideas of classes are formed out of wider and vaguer ideas as striking diflferences attract the attention. The first idea is of a vague " something," and from this by continual division more and more definite ideas of difiercnt forms of reality ax-e evolved. But at every stage tlie ideas reached are used to interpret fresh experiences which are gathered under them. Thus in the process of the development of know- ledge, analysis — or splitting up, and synthesis — or binding together, go hand in hand. § 5. — This process would be impossible without a ideas and system of signs by which, on the one hand, attention can be concentrated on one element in the complex whole of which experience at every moment consists, and on the other hand, the ideas, when once reached, can he represented symbolically in consciousness. ' Loyic, vol. i, p. 32. 4G THE LOGICAL BASES OF EDUCATION chap. Language andCommn- iiication of Knowledge. Verbal l^anguage. Any such system of signs is a language. Thus, even in the individual mind, knowledge could not develop without a language of some kind. § G. — Even easier is it to see the necessity of language when we con.sider the growth of know- ledge, not in an individual mind, but in the race. We have seen that this growth depends on com- munication of knowledge between men. But such communication implies a common language, or system of signs whose reference to reality is generally accepted and understood. This, in turn, implies that the signs are also instruments of individual thought : language as a means of communication rests upon language as a means of individual thought. § 7. — Of all systems of signs for thinking and communicating thought, words are by far the most convenient, because, owing to their conventional and artificial character, thoy can sustain a much more general and abstract meaning than can any other thought-symbols. Thus, as knowledge advances, language becomes more and more exclusively verbal. Savages convey much of their meaning by descriptive gestures, and some of the least developed in intelligence have so poor a language of words that they cannot understand each other in the dark, because the gestures which fill out their speech cannot be seen. But gestures have very similar disadvantages to mental pictures as symbols for thought. Like visual images they can only represent the outward and visible qualities, and these are frequently far from being the most important. Gestures are also frequently doubtful in their reference ; a flapping of the arms, for instance, may represent either a bird, or the act of flying. With a language wholly or mainly of gestures, then, knowledge could advance but a little way even on the stage of sense-perception. Hence, in KNOWLEDGE AND LANGUAGE 47 a system of conventional signs, capable of express- ing meaning with any required degree of definiteness, is essential to really developed thought. Speech, fulfils this requirement, and has the additional ad- vantages that it is easil}' produced, can be used as a means of communication in the dark as well as in the light, and between pei'sons at some distance from each other, an advantage which the modern applica- tions of electricity have enormously increased. Writing is, of course, only verbal language in writing. another form, but it pla5's a part in the development of knowledge which nothing else could have played, in that it extends the communication of knowledge to an indefinite extent, and renders possible contact of any one individual mind with many other minds both in the present and in the past. It is mainly by means of written language that the knowledge of the individual on the one hand contributes to the knowledge of the race, and on the other hand is checked and corrected by it. And such correction is necessary. For, as experience is interpreted bj' experience, and as the experiences of every individual differ from those of every other individual, it follows that vai'ious interpretations of the same piece of reality may be given by different persons. Were the interpretations of each person wholly dependent on his own narrow range of ex- perience, this would certainly be tlio ca.se to an appalling extent, and, of course only one at most of a set of incompatible interpretations can be true. Even now we find plenty of such variations ; every " difference of opinion " is a case in point. But when we can test our ideas by the experiences of innumerable other people, we are much more likely to reach the truth at last. Such testing goes on through- out life by means of both written and .spoken language. 48 THE LOGICAL BASES OF EDUCATION chap. Language >5 8. — When ca child learns his mother tongue, the Lcarnin?. wonls ho acquires ai^e from the first sii^ns of ideas, in lliat tlioy arc referred to certain pieces of reality. His ideas are doubtless extremely imperfect at first, hut the fact that the reference to reality is the same to him and to others, renders instruction possible. He may, for example, find himself ignorant of nearly everything concerning a certain flower which he has seen and the name of which he has learnt. But he can seek instruction from another person whose idea of that flower is full and accurate, and therefore very different from his own. And he can do this because, though the ideas are different, yet their reference to reality is the same. And that identity of reference is marked by the name, so that to utter the name indicates tvhat the child wants fuller information about as clearly as showing the actual flower would do. But such instruction is effectual only so far as the teacher uses words which have a clear meaning to the child, that is, which call up in his mind definite ideas. It is by combining these ideas that he is led to form a fuller and more accurate idea of the flower than he had at first. The same pi^ocess makes it possible to lead the child to form ideas of parts of reality he has never experienced. " We wish to describe quicksilver to a child. We say that it is something like this pew- ter in its brightness and the way it reflects the light ; it is even heavier than this lead ; it is liquid like water, so that I could pour it from one vessel to another. And we might further qualify each of these statements so as to render them more exact. Now, we may assume that all the words in which the quicksilver is described are significant to the child ; if they are not significant the description so far fails. At the end, if he have good powers of Ill KNOWLEDGE AND LANGUAGE 49 synthesis, he may combine these pai'ticular properties thus signified into the new idea we wish him to form. The word ' quicksilver ' then becomes significant to him." 1 It is in this way that we all gain knowledge in- directly, through the verbal testimon}^ of others to parts of reality which we have not oursehes experi- enced. It is evident, however, that such indirect knowledge must I'est ultimately upon that direct knowledge of reality which springs from our own experiences, and which alone can give meaning to the language by which indirect knowledge is com- municated. It is this which makes it all important that in early life, not only should the ideas which a child gains through careful examination and analysis of direct experience be as numerous, full, and exact as possible, but that they should be correctly associated with language. This is the foundation of that thorough command over language without which all good mental work is impossible, and which it is, therefore, one of the chief duties of the educator to develop in his pupils. 8 9. — Communication of thought and knowledge, spokeu aud 11 1 1 • i c T • 1 Written then, depends on the existence ot corresponding ideas Language in different minds. By "corresponding ideas" is meant ideas which refer to the same reality and give substantially the same meaning to it. The ideas of different people will hardly coincide more closely than this, owing to the differences of experience from which those ideas have sprung.- Now it is evident that if the ideas of the hearer or reader differ materially from those of the .speaker or writer, grave misunderstanding may arise. This may be a\oided in oral communication Vjy questioning on the one side ' Lloyd Morgan, Pnycholoyy for Teachers, p. 178. = Cf. p. 25. 50 THE LOGICAL BASES OF EDUCATION chap. 01' the other, on any point whose interpretation seems dovibtful. But writer and reader are much more at each other's mercy. On the one hand, the reader may bring a number of false preconceived ideas to. the interpretation of his author, or he may read carelessly and hurriedly. In both cases wrong meanings are attributed to the writer and the corrective of oral intercourse is absent. As Plato long ago said, " Speeches . . . when they have been once written down are tumbled about anywhere among those who may or may not understand them, and know not to whom they should reply, to whom not : and, if they are maltreated or abused, they have no parent to protect them ; and they cannot pr"otect or defend themselves." ^ On the other hand, the writer may have expressed himself obscurely, and the reader be unable to grasp his meaning, not from carelessness or poverty of ideas, but from being doubtful exactly what it is the author wishes to say. A question would lead to the solution of his difficulty, but if you question a printed page it " always gives one unvarying answer."'^ On the other side, it may be truly urged that the printed page has an advan- tage over tlie oral teacher in that it is always ready to be questioned, and bears the dulness or perversity of the scholar with a great deal more patience than the living teacher is apt to do. Moaning § 10.— The liability to misunderstanding is enor- Contoxt. iwously increased when speech is ambiguous. Am- biguity is possible because every word has its mean- ing partly determined by its context. As was pointed out in speaking of the development of ideas, we do not begin with ideas of separate things and weld them together, but we begin with a vague idea of a whole which we have to analyse. Now, 1 Phaedrm (Jowett's Translation), p. 275. ^ Ibid. in KNOWLEDGE AND LANGUAGE 51 language symbolizes ideas. "We must look for the beginnings of language, then, in actual speech, not in isolated words. Indeed, in early stages of language there is no division into words, either in speech or in writing. " It is always very late in the day before the seminal principles of speech are detected and explained. Indeed, the language which owed to them both birth and growth may have ceased to be a li^•ing tongue befoie these, the regulative elements of its formation, come to light and are embodied in written grannnar. That most elementary species of instruction which we familiarly tei-m the A, B, C, had no express or articulate existence in the minds or on the lips of men, until thousands of years after the invention and employment of language ; yet these, the vital constituents of all speech, were there from the beginning." ^ Knowledge of language, like knowledge of every other part of reality, works at first from the whole towards the elements. All portions of speech, then, depend for their full meaning upon the context in which they exist. For example, my idea (»f the relation of logic to education is expressed in this book as a whole, though even that total idea, as we may call it, owes its character to its relation to the rest of my mental life. How- ever, taking tliat as a sufficiently self-contained whole, it is evident that the full meaning of each cliapter involves the relation of the idea expressed by that chapter to the whole idea developed in the book. Similarly, the idea set forth in each para- graph depends for its full meaning upon its relation to the rest of the chapter ; the idea expressed by each sentence is relative to the paragraph of which it forms a part. With the sentence we have reached ' Ferrier, Imtitules oj Metaphynic, p. lo. E 2 62 THE LOGICAL BASES OF EDUCATION chap. the unit of tliought. It is true that the sentence is composed of words, and if we speaic or write it, the words have to appear separately. But in thought the sentence exists as one idea. We may write or say " The gi'ound is covered with snow," but that expresses a single and undivided fact of experience. We are so accustomed to the gram- matical treatment of language as composed of words, and to seeing single words defined in a dictionary, that wc are apt to overlook the truth that isolated words are, as Mr. Hobhouse well says, mere " dead fragments of language." ^ If we hear an isolated word, e.g., "Fire," we either regard it as an abbreviated sentence — that is, as intended to convey some information — or we are thrown into a state of mental perplexity as to what idea the speaker wishes to convey. It is related that a famous head-master once dumbfounded the whole of his sixth form by commencing a lesson with a question propounded in the single word ' Abraham 1 ' 8uch considerations make it clear that each word depends for much of its meaning on its context. For example, we speak of a hrir/ht day, or a Imght boy, but the force of " bright " is by no means identical in the two cases. The word, then, is relative in meaning to the sentence, and the sentence to the context in which it occurrs. Isolated sentences, like isolated words, do not occur in actual thought, though they have to be used for illustrative purposes in text-books on logic and grammar. But if we take such a sentence as " The fire is out " we see at once that its meaning is very different when it is spoken in reference to my study or to a row of warehouses. The same is true throughout : a sentence — despite the assertions of many grammar books — does not express a complete thought, but only ^ The Theory of Knowledgt, p. 1(J4. Ill KNOWLEDGE AND LANGUAGE 53 tlie smallest separable element in the ever-moving and living thought process. The exact meaning, then, in which sentences or words are used is determined by the general topic of thought. That is wliy no confusion is caused by the fact that some verbal signs have two or more distinct meanings, as, for instance, a ' page ' may be a boy or a piece of paper. No doubt ever arises in the use of such signs, though their existence makes punning possible. In fact, as they stand for distinct ideas, the}' are really distinct words, though they happen to have the same form. When we hear a lecture or read a book each portion receives much of its mean- ing from all that has gone before. Indeed, it is often impossible to understand the latter part unless the earlier has been grasped. Frequently, too, the meaning is shaded by our anticipation of what is coming. We see, then, tbat we can only full}- appreciate the meaning of words when we think of them as elements in sentences which are themselves elements in an organic whole or system of thought. Every word, then, as used in the expression of actual Specific and thought, has a specific meaning which varies according Meani'nss of to the context in which it occurs, that is, according to ^^''>^<^^- the system of thought it helps to express. .Still, these specific meanings have much in common. There is to every word a general meaning which is always present and forms the bond of connexion between the many occasional meanings, and this general meaning when explicitly stated we call the definition of the word. The nature of definition will be considered in a later chapter; ^ it is sufiicient to point out here that even when we have clearly grasped the true general meaning of a word, we never use the word in that general sense alone. Just as there is no such thing ' See Cliapter xvi. 54 THJO LOGICAL BASES OF EDUCATION chap. as a child in general corresponding to the general idea of child, but every embodiment of that general idea is a very individual little boy or girl, so eveiy time we use the word ' child ' in a real process of thought the general idea which corresponds to that word is modified by the nature of the particular thought. Our knowledge of general meaning, then, does not alter the fact that in actual use every word is modified in meaning by its context ; the general meaning is a kind of nucleus round which the occasional meanings wax and wane, but some such occasional meaning is always pi'esent. Even in scientific terms, where the genei'al mean- ing is not only most definite but most prominent, there is yet a slight occasional meaning. ' Oxygen ' has a quite fixed meaning, but when we think of oxygen we always do so in some particular connexion — for example, as combining with hydrogen to form water — and so the whole thought detei'mines the exact force of the word ' oxygen ' in the actual sentence. Scientific terms, however, are much less flexible than the words of ordinary speech. Fortunately they are generally so long and so ugly that there is little danger of their ever becoming constituents of ordinary discourse. We say fortunately, because it would be a great loss were language to decrease in flexibilit}'. The tendency, however, is naturally all the other wa}^ And it should be noted that this flexibility marks the meanings of all words. Even such a little word as ill differs in meaning in such sentences as " I am in trouble " and " I am in London ; " and the equally simple word and can be used conjunctively or adver- satively. Indeed, every word whatever is always a factor in exjDressing a certain idea and has its meaning modified according to the idea to be expressed. KNOWLEDGE AND LANGUAGE 55 § 1 1. — There ai-e enormous advantages in this flexi- Ambigaii- bility of meaning, for it makes it possible to express Language, an innumerable number of shades of meaning with a comparatively limited vocabulary. The English peasant expresses all his thoughts with a few hundred words, and it is computed that even Shakespeare made use of only some twenty thousand words ; yet what a wealth of thought and feeling he uttered with them ! But, like all other good things, the flexibility of meaning has also a grave disadvantage — the con- sequent liability of language to become ambiguous to which i-eference has already been made. Now ambiguity is at bottom indefiniteness in the reference to reality. Such indefiniteness may be due to un- certainty as to the sense in which a particular word is used or to faulty construction of a sentence. In the case of individual words the doubt may affect the general meaning. For with the course of time even general meanings may change, often by some one class of occasional meanings displacing all others, or by new occasional meanings being adopted. Such changes are continually going on in every living language, though the existence of written and printed literature enormously retards the process. At any one period it may be doubtful how far the change has gone. Such a question cannot be determined by etymology or by aj^peal to former usage. As Dr. Bosanquet says, " a word means what it is used to mean, not what it once meant." ' Sometimes the difficulty is increased by the older meaning lingering on in one special department of thought and knowledge. De Morgan gives a good example: "The word publication has gradually changed its meaning, except in the courts of law. It stood for communication to othcri^ without I'eference '. Lofjic, vol. i, p. 52. Ambigiii- ties ill Individual Words. 56 THE LOGICAL BASES OF EDUCATION chap. to tho mode of communication, or the number of recipients. Gradually, as printing became the easiest and most usual mode of publication, the word acquired its modern meaning ; if we say a man publishes his travels, we mean that he writes and prints a book descriptive of them. I suspect that many persons have come within the danger of the law, by not knowing that to write a letter which contains defamation, and to send it to another person to read, is publishing a lihcl ; that is, by imagining that they were safe from the consequences of publishing, so long as they did not print." ■* But when ambiguity arises from individual words it is generally due to doubt as to which of various current meanings is intended. Such instances of ambiguity ai^e especially common in the sciences which deal with man's life. These naturally have very few technical terms, but use the words of common speech with all their vast flexibility of meaning. The door is thus opened wide to misconceptions of meaning. A writer intends, to use a word — say such a term as ' money ' or ' value,' or * motive ' — in one sense, and is, it may be, careful to state his intention explicitly. But his reader may forget this limitation and read another sense into the word, and so misunderstand him. Indeed, words which are used in widely differing senses are a pitfall to the writer himself. He is liable when using such a term in one sense to make assertions or to draw inferences which are only justified when the term is used in another sense. For example, when ' money ' is said to be ' scarce ' in the money market, the meaning is that there is a scarcity of capital seeking investment. To infer from this that the coinage of gold and silver coins 1 Formal Logic, p. 243. in KNOWLEDGE AND LANGUAGE 57 should be increased is to be misled by the fact that in another meaning ' money ' is limited to such coin- age. But ' scarcity of money ' in the former sense is by no means the same thing as ' scarcity of money ' in the latter sense, and has no necessary connexion with it. Another ambiguous word is ' government.' Suppose we ai'e asked whether it is ever lawful to resist the gover-nment. Our answer must depend upon whether by ' government ' is meant the sj^stem of laws established in a nation or the bod}^ of men charged with carrying out those laws. It may liappen that the government in the latter sense is trying to subvert the government in the former sense. In that case, in whichever way a man acts, he resists the government in one of the two senses of the word, and what is loyalty from the one point of view is disloyalty from tlie other. ' Nature ' is another very ambiguous word, and particularly so when used in the attractive phrase, "education accoi-ding to nature." This has meant very different things with different writers. With Comenius it meant that educational method should be based on more or less fanciful analogies with processes in the physical world. For example : " The sun does not occupy itself with an}^ single object, animal, or tree ; but lights and warms the whole earth at once. ... In imitation of this there should only be one teacher in each school, or, at any rate, in each class." ^ Rousseau first made the phrase really fashionable. Witli him and his followers it meant that the educator sliould mainly look on, whilst the child follows his innate impulses. The perfecticm le. Misconception or doubt as to meaning arises even 60 THE LOGICAL BASES OF EDUCATION chap. Ambigui- more frequently from clumsily constructed sentences strucUon." than from doubt ^ 3. — Now, about every assertion the fundamental •Tudgmcnts questions to be asked are : What docs it mean 1 On what evidence is it based 1 Is it true ? On the answers which can be given to these questions in any particular L-ase depends the decision whether the judgment in (juestion is to be admitted as a piece of knowledge. It is not, however, with the meaning and truth of this or that particular judgment that logic is and Logic. 64 THE LOGICAL BASES OF EDUCATION chap. coucerned, but with the conditions of the validity of judgment in general. Whether those conditions are fulfilled in any particular case must be left for decision to that branch of science which enquires into the special subject-matter with which the judgment deals. Hence it is about judgments in general that logic asks the questions which the special sciences ask about particular judgments. Abstract g 4, — This makes it plain that logic is a very Thought, abstract science. All science, indeed, is abstract, for each science is the construction of reality from one special point of view. It is only by approaching reality now from this side, and now from that, that human thought can deal with it at all. " The mind, with all its powers, is incapable of grasping the whole even of the ' flower in the crannied wall.' ^ It deals with it first under this aspect, and then under that — as a thing of beauty, as suggestive of a Wordsworthian sonnet, as injurious to the structure of the wall, as a Composita, as consisting mainly of carbon, oxygen, hydrogen, and nitrogen in certain proportions, as decomposing so many cubic feet of carbonic acid per diem under the influence of sunlight. And whichever asj)ect we like to take we are pretty sure to leave out the rest. The sonnet would be deranged by a thought of the carbonic acid. And yet somehow all these aspects belong to the flower. The whole, which is the real, contains or presents them all and many more. And so we learn our first lesson about thought, that to grasp anything at all we must leave out the greater part of it. . . . We must admit that the mind never yet sifted out a grain of truth without letting twenty other grains slip past unnoticed." - 1 Cf. p. 19. - Hobhoiise, The Theory of Knoivhdge, pp. 6—7. IV KNOWLEDGE AND LOGIC 65 To know even the smallest piece of reality at all thoroughly, we have, then, to think it successively under a great number of general ideas, each of which includes under it a vast number of other particular facts. Every general idea is thus the expression of a relation binding together a vast number of individuals ; it is the universal identity which exists amidst the particular differences of the individual facts. Each general idea is also related to other general ideas dealing with similar aspects of reality, and thus we get those organized systems of knowledge which Ave call the ' sciences.' It is evident, then, that every fact may be considered from the point of view of many sciences, each of which deals with it from one side. This is just what is meant by saying the fact is concrete, and the science ahstract. The concrete means simply the embodiment of a number of general qualities or relations ; the abstract means simply the selection of one of those aspects and the exclusion of the others. § 5. — This distinction is closely connected with Form and that between yb?-m and matter. The simplest example ^^"®'- of ' form ' is the shape of a material object, say a statue, whilst tlie ' matter ' is the marble, bronze, or other matei'ial of which it is composed. Here we see at once that the form is the creation of man's mind ; it is that which gives artistic value to the statue, indeed, that which makes it a statue at all as dis- tinguished from a mere block of stone or metal. This, however, is only a first application of the terms. Further thought shows that the same distinction can be applied throughout. " There is no matter without form ... In a knife the matter is steel, the form is the shape of the blade. But the qualities of steel again depend, we must suppose, upon a certain char- acter and arrangement in its particles, and this is, as F 66 THE LOGICAL BASES OF EDUCATION chap. Bacon would have called it, the form of steel. But taken as purely relative, the distinction is good prima facie. Steel has its own form, but the knife has its form, and the matter steel can take many other forms besides that of a knife. Marble has its own form, its definable properties as marble (chemical and mechanical), but in a statue, marble is the matter, and the form is the shape given by the sculptor." ^ Similarly, we may say that a mathematical formula is the form, of which the particular examples which come under it are the matter. But just as there can be no matter without form, so there can be no form without matter. Nor is the form independent of the matter. Many forms which can be expressed in gold cannot exist in clay, in sand, or in water. The form each material can take is partly determined by its own nature, and is one way in which that nature is expressed. Logic is § 6. — The ' form ' then of any piece of reality con- '*^^d*F^r'^ 1 ^^^^^ °^ ^^^ general abstract qualities and relations which it exemplifies. Thus every science deals with one particular ' form,^ or kind of qualities and rela- tions, and the more general those qualities and rela- tions are the more emphatically 'formal' is the science. Thus, mathematics is one of the most formal and abstract of sciences, as it deals with an aspect of all things which can have quantity. But logic is yet more formal, as it deals with the form of all know- ledge, that is with those most general conditions which difterentiate knowledge from what is not knowledge. As each science neglects every aspect of reality but one, so logic neglects all aspects of actual knowledge except those which belong to it simply as knowledge, irrespective of the ideality which is known. It deals " not with the results of knowledge, but with the ' Bosanquet, Essentials of Logic, p. 43. IV KNOWLEDGE AND LOGIC 67 outline plan upon which these results ma}'^ ultimately be put together."^ Thus, logic has to find its subject matter, not in the external world of sense-experience, but in the world of thought. Its subject matter is, in a sense, not new. ; for in studying knowledge we are neces- sarily dealing with the same objects of knowledge with which we deal in other sciences. The difference is that in the other sciences we deal with these objects as they are in themselves and in relation to each other, whilst in logic we deal vvuth them merely as examples of how we know, that is, in a certain relation to our own minds. In this logic resembles psychology. But in logic the emphasis is laid on the knowledge, whilst in psychology it is laid on the mind. In other words, logic is concerned with the validity of the thought, psychology onl}'^ with the manner of its occurrence. § 7. — But though logic considers the validity of Function thought itisnot its function to teach men how to reason. " °^"^* " Men reasoned generation after generation long before they knew a single dialectical rule. . . . The principles of logic were operative in every ratiocina- tion, yet the reasoner was incognisant of their influence until Aristotle anatomized the process." - And nowadays men reason — and often reason well — who have never studied logic. Logic, in other words, does not lay down laws for thought, it does not .set itself up to decide what methods of investiga- tion will lead to truth. In the Middle Ages logic pretended to do this, with the result that during the centuries when men accepted its guidance, knowledge made scarcely any advance. The logician nowadays is more modest. He sees that his pi-ovince is to accept as valid all methods which lead to an increase ^ Hobhousc, op. cit., p. 10. ^ Ferrier, Inntituten of Mtluj>hyHic, p. 1"). 6S THi: LOOTCAL BASES OF EDUCATION cir. iv of knowledge, and to analyse them, so as to find out what is essential and what is accidental in them. Nor does he claim to dictate to the future. For just as sciences like botany and geology can speak with much more certainty of the form which development has taken up to the present than of the form it will take in the whole range of the future, so it is with logic. The logician can analyse the processes which have led to knowledge in the past, and are leading to knowledge in the present, but he must not attempt to limit the activity of thought by saying that those processes are the only ones which can ever lead to knowledge. Value of i5 8. — The purpose of logic is, then, to make Logic. clear and explicit the principles and the character of valid thought; of thought, that is, which attains knowledge. And in this is its value. The person who has not studied logic has generally never made clear to his own mind the conditions which deter- mine the accuracy of his inferences. Many a man " infers, but can give you a very poor account of the grounds of his inference. He may, even so, infer well, in which case he is a person of insight, tact, skill, wisdom, but not a reasoner, nor one who understands the logical connexion of things. The practical mark of such a person is the irregularity of his success in inference. He reasons well when he has great experience or some natural gift, but apart from that he flounders. A logical mind is slower but surer." ^ The study of logic aids in the cultivation of the logical mind, though it will not ensure its development. By making clear the principles on which correct thought proceeds, logic indirectly helps the production of correct thought, for those principles can be consciously accepted as guides. ' Hobhouse, op. ciL, pp. 237 — 238. CHAPTER V NATURE OF JUDGMENT ^ 1. — We have seen that every piece of know- Judgment ledge and of belief exists in the form of judgment proposition. or mental assertion, and further that about every judg- ment we should ask the three fundamental questions as to its meaning, its truth, and its justification.^ We have now to deal with the first of these questions in that general way in which alone logic is con- cerned with them. We have to enquire what is involved in the act of judgment as such, and what, consequently is implied by every judgment, no matter what the subject is with which it deals. In entering on this enquiry it must be borne in mind that it is judgment as a mental act, and not the proposition, or form of words in which it may be expressed, with which we are primarily con- cerned. We can only consider judgments when they are verbally expressed, but this expression is very often imperfect, and in such cases we must go behind the proposition to find the true judgment, and having found it we are at liberty to express it in anotlier verbal form if in that way we can state ' .Vee p. (ill 70 THE LOGICAL BASES OF EDUCATION chap. the real meaning more clearly. Logic, indeed, postu- lates that expression must be adapted to thought. Of course, Ave only know the judgments of others through the propositions in which they are pi'esented to us, but we can frequently see that the verbal presentation does not precisely coincide with the judgment it is intended to express. We have, then, to interpret the verbal expressions of other people's thought just as much as other pieces of our experience. Sometimes, no doubt, our inter- pretation is wrong, and then the judgment conveyed to our mind is different from that which existed in the mind of the speaker or writer from whom we received the proposition, and we have a case of mis- undei'standing. Having decided what judgment a given proposi- tion conveys, we must either accept it, reject it, or be in doubt about it. In the last case we do not our- selves judge at all ; we suspend judgment. But both when we accept and when we reject a proposi- tion offered us by another, we ourselves perform an act of judgment. In the one case we adopt the suggested judgment as our own ; in the other case in rejecting the suggested judgment we of necessity accept its contradictory ; if, for example, we reject the judgment that war is sometimes necessary we by that very rejection mentally affirm — i.e., we judge — that war is never necessary.^ Judgment § 2. — This has led us to one essential characteristic of judgment as a mental act ; it always claims to be true. It is impossible for any one to judge what he believes to be false. Any one judgment may of course be actually untrue ; but it cannot appear untrue to him who makes it at the moment when he makes it. A judgment, then, may be a truth or a 1 C/. p. 29-30. and Truth. V NATURE OF JUDGMENT 71 falsity, but it cannot be a falsehood. A proposition may, of course, be a falsehood, and it may even be a falsehood when it is true, for he who utters it may believe it to be false and so to him it is a falsehood. But this is an ethical and psychological consideration, not a logical one. Logically we are concerned, not with whether a person who makes a statement actually believes it, but with whether it is in reality true or false. The question of intention has no interest for logic, but only the question of actual truth or falsity ; and this is a question which apj^lies to every judg- ment and to every proposition. This claim to truth makes it clear that every sen- tence is not a proposition. A sentence may express a command, a wish, or a question. But to command or to wish a thing does not necessarily make it true or real — " If wishes were horses, beggars would ride." However, the command or the wish exists truly enough in the mind, though its accomplishment may never become a reality in the world of hard fact. Hence, every command or wish may be taken as an indirect expression of a judgment concerning the desires of him who makes it ; for instance, " Come here, John," is an indirect way of expressing the judgment "My wish (or intention) i that John should come here." Similarly, a question snot a judg- ment ; indeed it indicates the absence of the power of jud.ging in some particular about the matter with which the question deals. But indirectly it may be taken to express a judgment as to the mental state of the (juestioner — the judgment that he is ignorant and desires information on a certain point. Further, nothing but a judgment can be true or false. We say sometimes " Nothing can be truer than fact," but by fact we do not mean simply an occurrence in the external world but such an occurrence as and Ex perience 72 THE LOGICAL BASES OF EDUCATION chap. known ; i.e., as judged. The occurrence simply is ; it is the judgment about it which is true or false. Judgment § 3. — Whenever we judge, then, whether our judgment is original or whether it is the acceptance of a judgment offered us by another, we assert what we believe to be true. And such assertion is not arbitrary, it has behind it what seems to us a sufficient ground — a ground which would compel any other rational mind to make the same judgment. The question of when such ground is really sufficient will occuj)y us in future chapters : we only point out now that to judge without any grounds is impossible to a rational mind. Of necessity, the grounds for every judgment must be found in the apprehended nature of that with which the judgment is concerned. To say a judg- ment is true is to say it represents reality. But, as we have seen, reality exists for man only so far as it is known ; it exists for him in the form of judgment and in that form only.^ Ever}^ separate judgment is, then, an attempt — believed at the time to be a valid attempt — to mentally reconstruct reality, that is, to construct in our thought a system corresponding to actual existence. Every such attempt is occasioned by some expei'ience, for it is only in experience that reality is known. Every piece of experience must be interpreted, or made intelligible, before it can take its place in our system of knowledge. Such interpreta- tion harmonizes that experience with the system of knowledge already existing and derived from other experiences, either of ourselves or of others. But our systems of knowledge exist in the form of ideas.^ Interpretation of any experience is, then, the bringing it under some idea, that is, the seeing it as an example of the general nature or law which that 1 Cf. pp. 27, 63. - Cf. p. 42. NATURE OF JUDGMENT » idea embodies. It must not be forgotten, however, that the idea is itself a part of reality and is derived from the reality it more or less truly represents. Ideas are not made by the mind outside of experience and independently of reality. Their content is found by us in reality; but found by thought and not by the exercise of the senses of seeing, hear- ing, ifec. Experience is the rvhole of mental life, and includes our interpretation of what comes to us through the senses as well as those sense-impressions themselves. If we remember this, then we can truly say that all knowledge is experience, but if we make the very common mistake of limiting " experi- ence " to sense-impressions, then such a statement becomes absolutely absurd, for sense-impressions are not knowledge at all, but only the materials out of which the mind makes knowledge. Jlj 4. — In every judgment, then, we interpx'et some piece of experience by referring it to an idea derived from previous experiences. But the piece of experience we interpret is never the whole of our experience at the moment ; it is some element in that whole selected by attention. If I say, '.' This room is too warm," I am fixing attention not merely upon my space surroundings, but upon one aspect of those surroundings, and by so doing I am neglecting the rest. There are other aspects of the room besides its temperature to which I could attend, but I am led by my feelings, or by some purpose, to attend only to the wannth. The judgment is, then, an act of analysis, or of selection of some elements out of a totality to the neglect of the rest. In other words, the judgment actually made is only one of a large number of judgments which could be made about the room ; " warmth " is only one of the ideas under which it could be regarded. Every judgment, then. .Judgment is an act of l.oth Analj-sis and Synthesis. 74 THE LOGICAL BASES OF EDUCATION chap. is merely a partial interpretation of experience ; we can only master reality bit by bit.^ The judgment is an act of analysis in a further sense. The too high temperature is one experience which forces itself upon my attention. When attended to, it is resolved into the two ideas of the temperature of the room, and of excessive warmth as a quality of that temperature. It is the actual room-temperature which is experienced by the senses ; its effect on me is explained by bringing that tempera- ture under the idea of excessive warmth. So in every case. We see a bird flying, and the bird and its flight are one and the same experience, and the judgment which expresses that experience is one simple act of thought. But it is an act which analyses the experience into the two elements of bird and act of flying, and asserts that the latter is true of the former. This is, however, only one side of the truth. Each of the two parts into which a judgment analyses an experience has a meaning by itself, and these mean- ings are not identical with each other. We can think of birds in many other acts besides that of flying ; and we can think of flying as the movement of kites and arrows as well as of birds, or of other birds besides this particular individual. The judg- ment is an act of synthesis, or building up, as well as an act of analysis, or taking to pieces. The two general ideas of bird and flight are thought together and modify each other. Every judgment is, then, an act both of analysis and of synthesis. The fact that judgments can only be examined in the form of propositions tends, however, to cause the analytic aspect of the act to be overlooked. For the proposition is composed of words, each of 1 Gf. p. 64. V NATURE OF JUDGMENT 75 which is a separate element in that proposition, and these words must be both produced and received successively. Hence there arises a tendency to regard a judgment as a synthesis only. Because in the pro- position "The bird flies" the words " the bird" must be both uttered and heard before the word "flies," and because he who hears the statement must gather its meaning by putting together these two ideas, it is assumed that this is a suflicient account of the judgment. But it is not so. The judgment originated in the anal3'sis of an act of perception, and when it is communicated to another, it only becomes a judgment to him when the whole is grasped, so that the elements are no longer separate but are seen as connected in that whole, and, therefore, stand before the mind as the results of an analysis of that whole. It must be always borne in mind that the proposition or verbal statement is only instrumental to the judg- ment, and that in the latter the two essential parts, though they are distinguished, are not separated as are the words in a sentence. S 5. — We have, then, two essential parts in a Suijject and PrcdiCtitc judgment, and these are called the Subject and the Predicate. The same two terms are used in grammar, but the grammatical subject is not always the logical subject. By the latter is meant that part of the experience interpreted from which the thought starts ; and by the logical predicate is meant that further movement of thought which makes the experience more explicit. In isolated judgments it is frequently impossible to say with certainty what is the logical subject. Take the sentence "This is an orchid." This may be an answer to an enquiry as to which of certain plants is an orchid, when the subject would " an orchid," and the predicate would be the indication of a pai-ticular flower, this indication 76 THE LOGICAL BASES OF EDUCATION chap. being verbally represented by the word " this." But on the other hand the same sentence may be an answer to the question " What is this flower 1 " and in that case the " this " represents the subject, for it is the starting point of the thought, and " an orchid " is the predicate, for it is the further filling out of that thought. Similarly, the limits of the logical subject depend on what is already known. " If you say, ' He is going down to Yorkshire to-morrow by the 9'45 from King's Cross,' you divide 'he' as the grammatical subject froin the rest as predicate ; but the real transition in thought is from what we knew before to what the judgment tells us, and on this principle we might divide the judgment at any point, and should do so if we wish to represent the character of the advance, according to the interest which the statement satisfies — 'He,' or 'going,' or ' Yorkshire,' or ' the 9-45 ' or ' King's Cross,' may be the real predicate, the real addition to what we knew before." ^ This shows that the actual determination of subject and predicate in any case is psychological. There is always a logical subject and a logical predicate, but these are not fixed elements. " The content of the judgment is a complex of inter- connected elements, any one of which can stand as subject or as predicate to the rest." - It is evident, then, that the ' grammatical subject ' — that is, the nominative to the principal verb — cannot in any proposition be taken, without further enquiiy, as the logical subject. But yet, as speech should express thought with the greatest possible exactness, judg- ments are most adequately represented by propositions in which there is this coincidence, so that, as Dr. Bosanquet puts it : "I think that to ask whether the grammatical corresponds to the logical subject is ^ Hobhouse, The Theory of Knowledge, p. 156. - Ihid. V NATURE OF JUDGMENT 77 only to ask whether we have said what we meant to say.-i § 6. — We have, however, yet another element of CopuL the proposition to examine. Logic prefers to express judgments by propositions in which subject and predicate are separated by the verb ' is ' or ' are,' with or without the negative 'not.' Thus, the form " Gold is lustrous " would be preferred to the form "Gold glitters." This additional element in the expression of a judgment is called the Copula, and always consists of the present tense of the verb ' to be.' Now the word " copula" suggests the idea of a link joining two independent ideas ; and then the analytic aspect of the judgment is lost sight of. So fully is this sometimes done that IMr. Swinburne in his Picture Logic represents subject and predicate as two railway carriages, and the copula as the coupling chain attaching them to each other.^ " This," as Dr. Bosanquet remarks, "is an excellent type of the way in which we should not think of it."^ The copula is, indeed, not an independent element of the judgment at all, and its function in the proposition is only to indicate that the act of judgment has really taken place. " Benno Erdmann has strikingly expressed this point of view hy saying, that in the judgment, ' The dead ride fast,' the subject is 'the dead,' the predicate ' fast riding,' and the coj)ula ' the fast riding of the dead.'' '' * The copula is, then, a sign of judgment ; it is not a mere link joining two independent elements ; it does not add on to the subject a new idea which had previously no connexion with it, but it declares ^ Knowledge and Reality, p. 183. - Firfure Logic, p. 173. •' Es.t<'mifilv of Logic, p. 100 (note). ^ Bosanquet, ojj. cit., p. 100. 78 THE LOGICAL BASES OF EDUCATION chap. Summary. that subject and predicate are connected elements in one whole which the act of judgment has analysed. It is, therefore, a sign of both that analysis and synthesis which are aspects of every judgment. § 7. — Though every judgment is both an analysis and a synthesis, yet either of these aspects may be the more prominent. It all depends upon whether the thought starts from the whole, and proceeds to make explicit the I'elations of the parts within that whole, when the analytic aspect is the more promi- nent ; or whether it starts from the parts as distinct and proceeds to bring out their connexion with each other, thus constituting the whole, when the syn- thesis is the more apparent. Simple examples can be found in such judgments as 8 = 5 + 3 where the analysis is the more prominent ; and in 5 + 3 = 8 where the synthesis predominates. The fact is the same in each case, though the ways of approaching it are different ; and reality is not affected by the way we state it. This question, however, cannot be fully discussed at this stage ; all we would insist on now is that, as in each case both a whole and its connected parts enter into the judgment, and as they are distinguished but not separate in the act of judging, so in each case the judgment is both an analysis and a synthesis § 8. — If- now we sum up the results we have reached in this chapter, we may say : That judg- ment is coextensive with affirmation and denial ; that every judgment is a truth or falsity, but from its very nature claims to be true ; that truth means correct interpretation of the ideality given in experience ; that every judgment is a single act of thought, and is both analytic and synthetic, though one of these aspects may preponderate ; that the copula is not a link joining separate ideas, but is a sign that subject V NATURE OF JUDGMENT 79 and predicate have been distinguished as connected elements in a given whole ; that the distinction of subject and predicate is not a fixed one, but is relative to the actual work of thought in the judg- ment ; that the proposition should be as exact a verbal presentment of the judgment as possible. CHAPTER VI TYPES OP JUDGMENT Main Types § 1. — A COMPLETE enumeration of the forms of ment. ^ verbal statement in which judgments are expressed is obviously impossible, and even were it made it would be of rhetorical leather than of logical interest. But an enumeration of the main types of judgment is a much simpler matter, and, as was said in the last chapter, it is the judgment with which logic as a theory of knowledge is primarily concerned. Logic deals with the proposition only as expressive of a judgment, and is, therefore, justified in reducing the multitudinous forms of statement of ordinary speech to a few typical forms, so long as these forms are capable of expressing all essential differences in the mode of judging. There are, as was seen in our earlier chapters, three main stages in the organization of knowledge — the stages of perception of things, of appreciation of universal relations, and of conception of system. Of course, in the totality of the knowledge of each one of us individually, and of mankind as a whole, we can find examples of each stage. In some domains we are in the last stage, in some in the second, and in TYPES OF JUDGMENT 81 others only in the first. Corresponding to each stage is a typical form of judgment. There is first the Categorical Judgment, or judgment of fact, such as " This ink is black," or " All these boys have passed the Cambridge Local Examination." Secondly, there is the Hypothetical Judgment, the typical judgment of universal relation or law, such as "If water is cooled to a temperature of 32° F. under the pressure of one atmosphere, it freezes." Thirdly, there is the Disjunctive Judgment,o\' typical judgment of system, as " Triangles are either equilateral, isosceles, or scalene." Stated thus, these seem to be strictly marked off from each other by their form. They are, however, only typical forms, and as knowledge makes no sudden jump fi-om one stage to another, but developes gradu- ally, so the judgments in which knowledge is expressed merge gradually into each other. Especially is this the case with the categorical and hypothetical judg- ments, as might be expected from the fact that the same analysis of reality which gives us exact know- ledge of individual things makes plain the relations of those things to others. Further, we have the distinction between affirma- tion and denial, the force and extent of which we shall have to examine. § 2. — We have now to trace the development of Deveiop- these t}T)es of judgment from the simplest forms, jlfdgment- and to show their relation to each other. We will trace this development first in the affirmative forms, and then consider the meaning of the negative forms. The simplest cases of categorical judgment are those ImpersonalJudgmentfi which express the general character of a nearly entirely unanalysed mass of present experience. They arise out of a mass of vague feeling, and analysis has only proceeded so far as to determine its general character. Such judg- G Impersonal Judgment!!. THE LOGICAL BASES OF EDUCATION chap- Demonstra- tive Jiulg- mcnts. J udfjments of Particular Relations. merits are exemplified by the " It hurts " or " How nice ! " of the child. Here the logiccal subject is the undifferentiated mass of present experience, and the whole force of the judgment practically rests in the predicate. We make similar judgments throughout life, e.g., "It rains," " It is foggy,"where the "it" which indicates the subject has the vaguest kind of general reference to the weather experiences of the moment. Closely allied to these are judgments which may be called Demonstrative, as they indicate, though they do not necessarily name, the element of reality which they interpret. In these cases there is frequently no formulation in words at all ; a demonstrative judg- ment is implied in the very simplest act of i^ecognition. When such a judgment is explicitly stated in words, the logical subject is generally represented by some such demonstrative word as ' This,' ' That,' " Here, ' Now,' as when one might say " Here is London," "This is an orchid," " Now's the day and now's the hour." When the analysis has been carried a step further, the new movement of thought starts from the result of such a judgment as we have just considered. The whole result of this judgment will now form the subject, and the new judgment will take such a form as " This book is very interesting " — which obviously assumes the judgment " This is a book." A further step in complexity is taken in what may be called the Judgment of Particular Relation, as " Brighton is to the south of London ; " " This book is heavier than that ." In such cases the an- alysis of experience is deeper, and has given us two terms and the relation between them. So far the judgments we have considered deal primarily with facts in present perception, though in asserting the predicate of the subject they necessarily TYPES OF JUDGMENT 83 pass bej'^ond present perception and bring in an idea derived from previous experiences. In the last two examples, moreover, the subjects also have a reference beyond the present, as "this book," " London," and " Brighton," are thought as having a continued existence. More obvious still is this growing width of refer- ence when the judgment is of what we may call a historical character, as when we say, " Ciesar con- quered Gaul." Hei'e the proper name represents a person, who did many actions which are united into that whole which we call a life by the fact that they were the actions of one individual. The personality is, therefore, a universal, or factor common to all those actions, and they are the different expressions in which the character of that universal becomes manifest. Such a judgment has, then, both an individual and a universal character, and it forms a kind of transition between the purely categorical judgments of fact and the judgments of universal relation or law which mark the next stage of knowledge. But the aim of thought is to reach universal judgments, that is, judgments which hold true of all cases of a similar kind. The first step in this direction is taken when a presen experience is found to agree with a number of remembered past experiences. Hence arise all Judgments of Enumeration, such as " My ho]ida3's for the last five years have been spent in Devonshire." In such a judgment there has been a .synthesis of remembered experiences with j^resent experience. When the remembered experiences have been all alike, we can sum them up in the word " all," as when one might say " All my attempts to pa.ss examinations have been successful." But memory construction, even when we take it G 2 Historical Singular Judgments. Eiiumerative Judgments. 84 THE LOGICAL BASES OF EDUCATION chap. Search for in its widest sense as including the memories of the jitdgm'Z?'''' whole human race, can carry us no further ; it can never justify us in making assertions which pass beyond experience. How then are we to reach such a truly universal judgment as " All cows eat grass " 1 From our observation, even when supplemented by the testimony of others, we cannot be justified in as- serting more than " Some cows eat grass," for it is certain that cows not yet born have not been observed, to say nothing of innumerable cows in the past, and perhaps in the present, that have lived outside the observation of man. And it is equally certain that our judgment covers all those cows. No doubt uniformity of experience, especially when that experience is very extended, gives us a strong presumption in favour of universal agreement. But such presumption is not a logical justification ; it strengthens belief, but does not convert it into knowledge. Before the discovery of Australia, un- contradicted experience justified the judgment " All swans hitherto known are white,'" but had the really universal judgment " All swans are white " been made, the black swans of Australia would have proved it to be unjustified. Mere observation, then, however extended it may be, can never give logical justification for a really universal judgment. Such justification is always a matter of inference, and is the work, not of sense- experience, but of thought. Suppose a beginner in geometry has found that if he inscribes a triangle in a semi-circle, the angle which touches the circum- ference is a right angle. He has certainly no reason for thinking that any triangle whicli he might inscribe in any semi-circle would exhibit the same characteristic. The idea that this might be so would possibly suggest itself to him, and would VI TYPES OF JUDGMENT 85 be likely to do so if he inscribed sevei'al triano;les in semi-circles and found that each had a right angle touching the circumference. But the number of triangles that could be inscribed in any one semi- circle is infinite, and the number of possible semi- circles is also infinite, and no amount of experience in drawing diagrams and measuring angles could ever include them all, and so justif}' the judgment " Ever}' triangle inscribed in a semi-circle has a right- angle touching the circumference." It is only when by inference from the known nature of semi-circle and triangle he has proved that this judgment must be true that he is justified in asserting it. What is true in this case is true in every case. The Generic The universal judgment of the general form " Everj' "S is Q it is not P," unless we have evidence that P and Q cannot coexist in any one instance of S. § 3. — So far, we have limited the discussion to Negation. cases in which our universal assertions would stand the test of experience. We know, however, that this is not alwa}-^ the case. We meet with ex- ceptions to many statements which were at first thought to be general. Hence arise both negation and limitation of the scope of our judgments. We have all the force of negation whenever two judg- ments are made of the same subject which cannot 92 THE LOGICAL BASER OF EDUCATION chap. both be true, because theii' predicates are incompatible with each other, as when "on a particular occasion during a . . . visit of the Empress of Germany to London, ic became the duty of the reporters of the public journals to describe Her Imperial Majesty's dress. Subsequently the Globe collected the descrip- tions of the costume as they were given by different reporters, to this effect : Tlie Times stated that the Empress was in ' gold brocade,' while, according to the Daily Neivs, she wore a ' sumptuous white silk dress.' The Standard, however, took another view : ' The Empress wore something which we trust it is not vulgar to call light mauve.' On the other hand, the Daily Chronicle was hardly in accord with any of the others : ' To us it seemed almost a sea-green, and yet there was now a cream and now an ivory sheen to it.' No wonder that the Globe asks em- phatically, ' What did the Empress wear ?' " ^ Each of the judgments here quoted really negates all the others, because only one of them can possibly be true. No negation, however, appears on the face of any of these judgments. We get such explicit negation when the judgment takes the negative form, " S is not P." A consideration confined to this bare form would, however, lead us to a very wrong conception of the nature of negation and of its work in thought. For in form the negative judgment is bare denial, and the P is not limited to any system of predicates. The form would cover such a statement as " Virtue is not green," quite as well as " The dress of the Empress is not green." But it is obvious that of these two only the latter has any rational meaning. The former does not correspond to an act of thought at all ; in other words, it does not represent a real 1 Rooper, School and Home Life, pp. 83—84. VI TYPES OF JUDGMENT 93 judgment. As we have seen, every judgment is made under a certain limitation of reference which is made clear by the context in which it actually occurs. This is the same as saying that every judgment is made within a certain system. If the predicate is " green," the system is that of colour, and only things occupying space can be coloured, for they only are visible. Consequently we can only rationally deny any particular colour of things which occupy space. Further, it has been shown that in this limitation to system is found the justification for our judg- ments, and that no judgment can be made without a ground. Denial must, therefore, rest upon some ground. But bare denial only expresses ignorance, and knowledge cannot be constructed out of ignor- ance. Denial always rests, then, on a positive ground, and this ground is the presence of something in the reality with which the judgment deals which is incompatible with the proposed predicate. We can rationally assert that S is not P only when we know more or less definitely that S is Q, and that Q cannot co-exist with P in the same subject. Our apprehension of Q may, indeed, be by no means explicit ; we may only feel sure that if S were to receive P it would cease to be itself, but we cannot feel this unless we believe there is something in S which excludes P, and this something is the Q of our symbolic statement. It appears, then, that every negation rests upon an implicit disjunctive judgment, and as a consequence that denial and attirmation mutually imply each othei\ Every denial is based on an affirmation, and every affirmation negates all the other alternative and incompatible predicates in the system to which the judgment is limited. The use of the affirmative or the negative form shows which aspect is predominant 94 THE LOGICAL BASES OF EDUCATION chap. in thought, and this is determined in general by the purpose with which the judgment is made. § 4. — These considerations liave also made plain that the true function of negation in the work of constructing knowledge is to show the limitations within which our affirmations should be confined. Suppose that in opposition to the universal cate- gorical proposition " Every S is P," an exception is proved to exist. We have then to grant that " this S at any rate is not P." But the original judgment was based upon the generic judgment " S as such is P," which had been supposed to be true. We must now, therefore, grant that " S need not be P." But if the original judgment rested on any real evidence at all, it has not been entirely disproved, but only limited in its scope. We can still say " S may be P," or with more direct reference to pai-ticular facts, "Some S's are P." The distinguishing feature of such a judg- ment is the indefiniteness of the reference to S. Similar forms arise from unanalysed experience. We have seen that mere uniformity of occurrence will not justify us in making the universal judgment " Every S is P," but it will justify us in making the particular judgment " Some S's are P." And when we do so, we use the word ' some ' without prejudice to the possibility that ' every ' would be true in fact. ' Some ' means in such a case that our knowledge is professedly imperfect ; we know there are cases — one at least — in which S is P, but our knowledge of the nature of the reality thus expressed is insufficient to enable us \.o say whether every S is P. In other cases in which we use the word ' some,' we do intend to exclude 'all,' but this can only be assumed to be the case when the context makes it perfectly clear. For example, suppose on examining the tabulated results of an examination we found that certain candidates VI TYPES OF JUDGMENT 95 had failed in mathematics. We could immediately affirm that ' some ' candidates had so distinguished themselves. But it is conceivable that further examina- tion of the results might show that this ' some ' could with truth be expanded into ' all.' This discovery would not make the former judgment false, but only turn it from an indefinite into a definite assertion. So long, then, as we have nothing but the form to guide us, that is, whenever we have no context of knowledge to show that the ' some ' is meant to exclude * air, we must assume that ' some ' means " I am sure of at least one case, but I do not know how widely my judgment will apply." Even when the context shows that ' some ' is known not to be ' all ' as when we say " Some boys are idle and some are industrious," j'et the range of application of these particular judgments is always indefinite. They cannot, therefore, be a resting place for thought in its search after knowledge. By their \ery foi-m they challenge further enquir}^ But as the univei'sal judgment can only be reached by such an analysis of content as will lead to the generic or the hypothetical judgment, so the line our investigations must take to transmute the particular into the universal judgment is further and more accurate analysis of reality. This may result in the finding a condition M which necessitates P, and then we have the hj'pothetical " If S is M it is P," or the generic " S which is M is P," which are alter- native ways of expressing the same judgment. It is, indeed, in some such process of finding ex- ceptions to judgments supposed to be universal, and in the consequently more exact determination of those judgments througli further search into reality, tliat advance in knowledge generally consists. The foregoing discussion has brought out that the chief formal distinctions in categorical propositions 96 THE L0r4ICAL BASES OF EDUCATION CH. vi are those of Quality, between affirmative and negative, and of Quantity, between universal and particular. The latter distinction is determined by whether the proposition refers explicitly to all the individuals which bear the subject name, or whether its applica- tion is indefinite. § 5. — If we now ask whether the same distinctions can be applied to hypothetical and disjunctive judg- ments we find that this is only very partially the case. The negative form is perfectly appropriate to the hypothetical judgment, for a condition M may be found united with S, which is incompatible with P, and this is appropriately expressed by the form " If S is M it is not P." It is also possible to write par- ticular judgments in a hypothetical form, and say " If S is M it may be P," and " If S is M it need not be P." But this does not make the judgments really hypothetical, and is, therefore, misleading. Every particular judgment directly asserts fact, and for this the categorical is the appi'opriate form ; whilst the special function of the hypothetical is to express necessary connexion of a result with its conditions. As such a connexion must be universal, the hypothetical form should only be used for universal judgments. Similarly, as the function of the disjunctive form is to express known relations within a system, it is evi- dent that a statement of the form "S may be P or Q" has little of the essence of disjunction in it : it is mainly an expression of ignorance, and the under- lying judgment is categorical. Further, it is impossi- ble to have a negative disjunctive judgment. If we would deny the disjunctive " S is P or Q " we must say " S is neither P nor Q," but this is not disjunctive but categorical. In short, the denial of a system does not involve the affirmation of an opposed system. CHAPTER VII FORMAL RELATIONS OF PROPOSITIONS Dur- § 1. — We saw in the last chapter that the chief The Fou formal distinctions of judgments are those of Jf propos^* quality and quantit3^ It was by considering these, *'^°"^- and ignoring the content of judgments, that the four- fold scheme of categorical propositions, which has been traditional in logic since Aristotle, was produced. For it is evident that a proposition must by its very fomi either definitely refer to the whole range of reality indicated by the subject or leave the scope of its application doulitful. The former case is ex- pressed in the affirmative by " Every S is P " or " All S's are P," the latter by " Some S's are P ; " in the iiegative the former by " No S is P," and the latter by " Some S's are not P." It should bo noted that the form " Every S is not P" is not adapted to express the universal negative, because it is ambiguous. It may intend to deny P of every S which exists, when it is universal in its f(jrce ; or it may only intend to deny that we can affirm P of every S, and this would be true if P can be denied of a single S ; it is then particular. For instance if we afHrm that " All that glitters is not 11 98 THE LOGICAL BASES OF EDUCATION chap. gukl," we do not mean that no glittering things ai'e gold, but only that some glittering things are not gold. The pi'oposition is, therefore, particular. It is possible to express more or less adequately every categorical judgment in one or other of these four foi'ms, if we include the impersonal and demon- strative judgments under the particular ; and the judgments of particular relation and historical singu- lar judgments under the universal, on the ground that they definitely refer to the whole of their sub- jects. In doing so, however, we ignore the important distinction between such singular judgments and the true universals. Moreover, the form " Every S is P " is used indifferently for the mere results of counting, as "All the boys are tired," and the judgment of necessary connexion, such as " All equilateral triangles are equiangular." However, certain relations hold between these forms of proposition which we shall do well to examine briefly. The four forms of proposition are traditionally in- dicated by the letters A, I, E, O, which are the first two vowels in the Latin word affirmo, I affirm, and the vowels in nego, I deny. The symbols are thus distributed — A Universal Affirmative. . .Every S is P. I Particular „ ...Some S's are P. E Universal Negative No S is P. O Particular ,, Some S's are not P. Distribu- § 2. — We saw in chapter iii that every term has Terras. ^ meaning or content, and a denotation, or range of objects to which it is applicable. Both these aspects are always present in categorical judgments, but the denotation is the more prominent in the subject and the meaning or content in the predicate. As, how- ever, every term always has a reference to reality, it is VII FORMAL RELATIONS OF PROPOSITIONS 99 permissible to consider the denotation of the predi- cate as well as that of the subject. A term is technically said to be distributed when definite refer- ence is made to the whole of its denotation. Thus the subjects of the A and El forms of proposition are distributed. When the predicates are examined, it is seen that tliose of the affirmative propositions ai"e undistributed, for the assertion that P belongs to every S, or to some S's, evidently makes no definite refer- ence to the whole extent of the application of P ; other things besides the S's referred to in the proposition may be P. When we turn to the negative forms, however, we see that P is, in each case, distributed ; for whether it is every S or only some S's which are to be excluded from P, yet that exclusion is only made when they are shut out from every possible case of P, and P must therefore be explicitly referred to in its whole denotation. Summing up these results, we see that — E distributes both its terms. A ,, its subject only. ,, its predicate only. 1 „ neither term. § 3. — -Dependent on this is what is called Con- Conversiou. version, that is, the transposition of subject and pre- dicate in a proposition. In this process no undistri- buted term may be made distributed, for that would evidently be going beyond the assertion of the original proposition. It follows that E and I propositions can be con- verted simply ; that is, into propositions of the same form, as both the terms in each of these propositions arc tlie same in distriljution. Wliether we say " No S is P " or " No P is S " ; " Some S's are P " or " Some P's are S," in each of the two cases we are 100 THE LOGICAL BASES OF EDUCATION chap. expressing exactly the same idea, and the form in which we put it is a matter of no logical interest. It is also plain that an O proposition cannot be converted at all, for to pass from " Some S's are not P " to " Some P's are not S " would be to distribute S, and therefore to pass beyond the " Some S's " with which we start. If we now examine the A form of proposition, we see that it can only be converted to the I form, as the P is given us undistributed. This is appro- priately termed conversion by limitation. In this process, therefore, we pass from a more definite to a less definite assertion, for we lose sight of the distribution of S. From " All cats are animals " we reach by convei-sion " Some animals are cats ' ' which is only equivalent to "Some cats are animals." We have passed from expressing knowledge to expressing partial ignorance. As Dr. Bosanquet says, " We seem . . . only to have advanced to a doubt of what we knew."^ It is true that if we look at meaning- there is a difference of emphasis in passing from, say, " All sponges are animals " to " Some animals are sponges." But this is of psychological rather than of logical interest; the judgment underlying botli propositions is one single act of thought, and is the same in each case. To call these processes of conversion, inference, is only justifiable if every change of form is held to indicate a change of thought, and this is certainly not the case. " The transposition is . . . of rhetorical rather than logical value. ' Who deniges of it, Betsy 1 ' inquired Mrs. Gamp ; and then Mrs. Gamp, by reversing the order of the question, imparted a more awful solemnity to it, ' Betsy, who deniges of it ? ' This is the philosophy of all conversions and all ' Logic, vol. i, p. 327. vxi FORMAL RELATIONS OF PROPOSITIONS lOl substitutions of one verbal equivalent for another, in a nutshell." 1 § 4. — We have now to enquire how the truth or falsity of a proposition in any one of these four forms affects the truth or falsity of each of the other forms which deal with the same matter, that is, have the same subject and predicate. It has been traditional to call these relations of truth and falsity " the opposition of propositions," where the word " opposi- tion " merely means comparison of diffei'ences of form, whether those differences imply real opposition, i.e., incompatibility in meaning, or not. The re- lations have been for many centuries indicated in the following diagram, which is called " The Square of Opposition." Modes of Opposition. Examining the propositions in pairs as indicated Suiaitema- by the diagram we take first the Subaltern relation, a name derived from the diagram. I and O are ' Hobhouae, The Theory of Knowledye, pp. 259—260. 102 THE LOGICAL BASES OF EDUCATION chap. called " subalterns " to A and El respectively, because they are written under those letters in the diagram. We see at once that the assertion of a universal obviously includes the assertion of its subaltern, i.e., the particular of the same quality. Thus, to assert A is to assert I ; to assert E! is to assert O. But this will not hold in the case of denial. The fact that the hasty psalmist was unjustified in affirming that " All men are liars " by no means proves that the more modest assertion " Some men are liars " would not be true. On the other hand this latter proposition will not justify the former : we cannot affirm the universal on the basis of the particular. But if we deny the indefinite particular, our denial evidently applies yet more strongly to its corresponding universal. When we take propositions of opposite quality we see that A and O, E and I, respectively, are pairs of Contradictories. The essence of contradiction is that of two contradictory propositions one must always be true and the other false. Thus to assert A is implicitly to deny O, to deny A is implicitly to assert O ; whilst these relations also hold the other way, that is, to deny O is to assert A, and to assert O is to deny A, Similar relations hold between E and I. This all follows directly from the Principles of Contradiction and Excluded Middle, If the propositions considered are A and E then it is obvious that both cannot be true, but both may be false. That " No men are liars " would be as rash a statement as that " All men are liars." These propositions are called Contraries because the assertions made by them are the furthest removed from each other which it is possible to make about any one subject matter. Lastly, when we consider the two particular forms VII FORMAL RELATIONS OF PROPOSITIONS 103 of proposition, I and O, we see that they are Suh-con- formally indifferent to each other : both may be true '""^^' together, and this is always the case when the ' some ' is in fact limited to part of the denotation of S : that " Some men are liars " and that " Some men are not liars " are equally true. It is evident, however, that both these propositions cannot be false if there exist any S's at all ; this directly follows from the Principle of Excluded Middle. These propositions are technically called Sub-con- traries, simply because of their position in the diagram of the Square of Opposition. If we now collect our results we see that when summary of A is true, the truth of I and the falsity of both E and O are implied ; but when A is false the only implication is the truth of O. Corresponding results hold with E. Again, when O is false, the falsity of E and the truth of A and I are implied ; but when O is true, nothing is implied but the falsity of A. Similar implications are involved in the truth or falsity of I. To put it generally : the truth of a uniAersal, or the falsity of a particular carries with it implications as to the truth or falsity of each of the other members of the four-fold scheme ; but the falsity of a universal or the truth of a particular only implies the truth or falsity respectively of its contradictory. Opposition. CHAPTER VIII THE METHOD OF KNOWLEDGE Truth and Evidence. Natui'e ot Method. § 1. — In chapters v and vi we considered what is implied by the act of judgment at its various stages of development, and so found an answer to the fundamental question as to the meaning or content of judgment. There remain for examination the two much more difficult enquiries relating to truth and evidence, and these will occupy us through- out the remainder of the book. These two questions cannot well be separated. No one ever accepts as true a statement which does not rest on evidence which he deems sufficient. But evidence which appears conclusive to one mind is often rejected by another as insufficient or even as altogether worthless. Our task, then, is to consider what is the final test of truth, to examine the kind of evidence on which judgments which satisfy that test are grounded, and to ascertain how such evidence is procured. In brief, we have to seek an answer to the question : By what method does man attain knowledge 1 § 2. — Method implies orderly procedure, that is, procedure guided by some definite principle. It is only when a task is pursued methodically that it is CH. VIII THE METHOD OF KNOWLEDGE 105 well done, and the more difficult the task the greater is the need of method. To nothing does this apply so forcibly as to that most difficult of all tasks — the acquisition of knowledge. Without method a desultory collection of pieces of information may be picked up, but nothing that deserves the name of knowledge can be attained. The nearer the method in any science approaches perfection, the greater are the advances made in that branch of knowledge. This has always been recognized by thinkers, and it may be said that all systems of logic have been simply attempts to formulate the essential features of the methods by which knowledge has been sought at various times. Thus the logic current at* any time is relative to the test of truth or knowledge accepted at that time. Logic, as an organized body of doctrine, originated Doveiop- with the attempt of x\ristotle to systematize the Doctrine of methods by which men's thoughts and beliefs could Hyfjl^^^ be brought into harmony with each other, and so fulfil the test of truth accepted by Greek thinkers. In the Middle Ages this test of truth was ex- Maikevul changed for mere agreement with dogmas. Certain ^'^^"^' general propositions were accepted as self-evident, and the whole work of thought was to deduce the c(jnsequences of these principles. The mediajval logic was an attempt to set forth in detail all the conditions under which such deductions could be made. It wa.s extremely acute, but was naturally concerned with the bare form of thought, for truth was lield to consist merely in agreement with certain original propositions whose truth was unquestionably accepted. This logic was derived from that of Aristotle, but practically omitted all those parts of Aristotle's work which dealt with the establish- ment of true universal propositions. Another con- 106 THE LOGICAL BASES OF EDUCATION chap. sequence of the mediajval view of knowledge was a false conception of the function of logic. It was held that the province of logic was to legislate for thought ; to lay down the methods by which alone truth could be attained. With the development of natural and physical science which began in the sixteenth century the medijeval test of truth was gradually discarded, and the view aldose that the only test of truth is agree- ment with fact. Such agreement could be neither proved nor disproved by the mediaeval logic, and so the need for a new formulation of the method of knowledge was felt. This task was avowedly under- taken by Lord Bacon. Unfortunately, however, he retained the mediaeval view that the function of logic is to lay down with authority the methods which scientific investigation must follow. He himself had not studied the methods by which Copernicus, Galileo, and the other great pioneers of science, really worked. He believed that an enormous collection of facts, followed by careful comparison and classification, would make the hidden truths of nature immediately obvious. The method was fundamentally a mistaken one, and, as Jevons says, " it has not been followed by any of the great masters of science." ^ But it had the merit of drawing attention to the need of verifying theories by appeal to fact. " Against this . . . must be set the fact that by calling his method induction, and laying so much stress on the collection of facts, he fostered, and, indeed, fixed in the public mind the erroneous idea that the whole work of science consists in observa- tion." '^ This idea really makes method mechanical, in that it is regarded as an artificial arrangement in 1 Prinriples of Science, p. 507. " Minto, Logic, Inductive and Deductive, p. 253. v-iii THE METHOD OF KNOWLEDGE 107 a body of knowledge which is external to the mind and independent of its activity. This was indeed plainly claimed by Bacon himself : " Our method ... of discovering the sciences is one which leaves not much to acumen and strength of wit, but neai'ly levels all wits and intellects." ^ Bacon's idea of method, as we have said, had little Newton. influence on the actual work of scientific discoverers, and it is not to him but to Newton that modern science owes the first clear formulation of its general method. Logicians, however, long ignored the revolution mil. which was being effected in the method of know- ledge, and continued to expound the old mediasval logic, with all its claims to set forth the " art of thinking." This led naturally to logic itself falling into very general contempt ; its system was seen to be largely artificial, and out of relation to the modes of thought actually proved successful in every bi'anch of science. To Mill belongs the credit of rescuing logic from death by inani- tion. He grasped the truth that the function of logic is not to dictate method to science, but to accept the methods which science finds successful in the ascertainment of truth, and by analysis to make clear their essential general features. Then, he hoped, the same methods which had led to such advances in the natural and physical sciences, might be found ecjually fruitful in those sciences which deal with the mental and moral life of humanity, such as history, sociology, ethics, and psychology. This view of logic has Ijecome the accepted one ; logic no longer claims to be the lawgiver to the sciences, but owns itself dependent upon them in its formulation of method. ' Novum Onjauum, 1, 61. 108 THE LOGICAL BASES OF EDUCATION chap. Modern Since Mill's great work, the development of logic "^"'' has been chiefly in deepening and making more exact the conception of knowledge. It is seen that agree- ment with fact is not a sufficient test of truth, if ' fact ' is restricted to mean something observed by the senses. Science more and more finds truth in uni- versal relations and laws, of which particular facts are but manifestations and examples. Our test of truth is that ultimate consistency and relation of univei'sal judgments, verified by appeal to facts, which we mean by system. Thus the modern view is in one sense a return to that of Aristotle, but a return which lays emphasis also on that need of agreement with fact on which modern science rightly insists. Method and § 4. — This criterion of truth implies that method is essentially an order of thought, and not an order of things. It is that process of self-activity in which the mind of man satisfies its own rational nature by finding reason as the guiding principle of the uni- verse. It is not a process by which an order of external nature is stamped on a passively receptive mind. As Coleridge put it, " Method implies a pro- gressive transition, and it is the meaning of the word in the original language. . . . The term, method, cannot, therefore, otherwise than by abuse, be applied to a mere dead arrangement, containing in itself no principle of progression."^ It is the presence of such a principle of progression — of gradual development from incompleteness and imperfection towards com- pleteness and perfection of knowledge — which marks every true science. For a science is the result of mental activity bringing itself into harmony with world activity ; its success is marked by agreement with fact on the one hand, and by a growing appre- ^ The Friend, vol. iii, p. 116. Facts. VIII THE METHOD OF KNOWLEDGE 109 ciation of the ultimately rational chai*acter of the grounds of knowledge on the other. § 5. — Important, therefore, as it is to remember Method and that knowledge is mental construction, it is equall}'^ essential to bear in mind that it is construction based on experience, and subject throughout to the test of experience. A method of knowledge must, therefore, analyse the ways in which experience can be made clear and explicit ; in other words, enquire how an exact and definite knowledge of facts can be obtained. Now all human knowledge of material facts is derived in the last resort from direct observation. We shall have, then, to consider how we can guard against errors due to faulty or careless obser- vation, so that our fabric of knowledge may be based on a sure foundation. In a word we shall have to enquire how it is possible to obey the maxim " Make sure of your facts." But though in the last resort all knowledge of facts rests on direct observation, yet that last resort is unattainable for every one of us in an indefinitely large number of cases. Every searcher after know- ledge has to accept much on the testimony of others. "In the best scientific work, even as in the worst, much must be taken upon trust-; on the authority of the competent observer, skilled instrument maker, or original investigator." ^ A method of knowledge must, therefore, indicate what tests of truth can be applied to testimony, so that only the trustworthy may be accepted. No formulation of method can be satis- factory which drops out of sight '• the complex inter- change of opinion, observations, experimental results, criticisms — the division of labour — that constitutes the life of science." ^ * Ravenshear, Article, on Testimony and Authori/i/, Mind, N. S., vol. vii, p. (j3. - Iliid, p. G4. 110 THE LOGICAL BASES OF EDUCATION chap. inforeiitiai § G. — The ascertainment of facts is, however, only ooiethwi. the starting-point of knowledge. The very aim of every science is to extend knowledge beyond mere facts to those universal relations which can be found in those facts by the opei^ations of thought, and to reason from those laws to their consequences, thus reaching knowledge of other facts which have not been observed, and binding the whole into one comprehensive system of knowledge. All such operations of thought are included under the general name of Inference. The aim of inference and the final step of method is thus seen to be the construc- tion of system and the finding in system that explanation which is the ultimate goal of thought. Our examination of Method will, therefore, fall under three main heads : — Observation and Testimony ; Inference ; System and Explanation. But these must not be regarded as three stages of progress separated in time. They are inseparable in the actual development and construction of know- ledge, though for convenience and clearness we can consider them apart. We have seen that system is simply the completion of inference, and it is obvious that the testing of the trustworthiness of testimony must also be a process of inference. It is not so evident at first sight that observation also implies inference, but further con- sideration shows that it is so. This will be worked out in our discussion of observation.^ It is sufficient here to point out that wherever error is possible we shall do well to suspect the presence of inference. The impression on the senses is what it is, but even in the simplest cases it may appear to us to be some- thing else, and so the judgment which expresses what the sense-impression is to us — i.e., what observation 1 See Chapter xi. vm THE METHOD OF KNOWLEDGE 111 we have actually made — ma}'- be false.^ Now, the grounds of this falsity cannot be found in the mere sense impression, for that asserts nothing. It must, therefore, be sought in the act of mental construction by which we bring that impression under a certain idea. And such construction is of the nature of inference, for it asserts the character of an impression on the grounds of its resemblance to impressions not now experienced. For example, the rustic who takes a gravestone brightened by the moon for a ghost, in- fers the ghost from the similarity of the sense-im- pression he actually receives with the brightness and whiteness which form the essential features of his idea of the appearance of ghosts, his inference being supported by the midnight hour being the orthodox time for ghostly manifestations. It appears, then, that the method of knowledge is inference throughout, and it will be necessary to consider the nature of inference before entering on an examination of the precautions which should be taken to secure that observation is expressed in true judgments of fact. I 7. — Before taking up this enquiry, however, it character- will be well to consider more definitely what is Methodical implied in speaking of any process of thought as '^^'""^w. methodical. Such a process may combine an indefinite number Pm-poae. of inferences ; it may be of any length and of any degree of complexity. But whatever its length or complexity, it is methodical just in so far as it is dominated by a purpose. AH methodical thought, as we have seen, leads to system, and the idea of system is implicit in it from the first. Of course, in the beginning of an enquiry we have no system ready made. The actual concrete system which our 1 Cf. pp. 22, 92. 112 THE LOGICAL BASES OF EDUCATION chap. starting- point. enquiry aims at reaching is learned from the facts themselves. Observation of facts, then, suggests the kind of problems whose solution will constitute the system in which they have their place. So "in every science the next step after observing the facts is to formulate a series of questions according to some methodical system ; every science is composed of the answers to such a series of questions." ^ Often, indeed, an answer is suggested together with the question, and then this has to be tested. The process of finding or of testing the answers to the questions thus suggested will generally involve much more observation of facts, and this again will suggest other problems, and so one enquiry gi^ows out of another. But unless the original observations are accurately made, the whole enquiry is likely to prove futile. Or again, if in any enquiry we start from a general proposition whose truth we assume, and that proposition is in reality wholly or partially false, then our labour is vain. These considerations yield us two closely related and fundamental rules of method — 1. Have a definite jniijjose. 2. Makfl sure of your star'tmg-jjoint. § 8. — Neglect of one or both of these leads to Fallacy, that is, to invalid thought disguised as valid thought. This is most likely to occur in exposition or in argument. If the purpose is confused with the starting-point, we have the fallacy of Begging the Question, or, in its technical Latin name, Petitio Principii. This means the assumption, as the basis of proof, of the very proposition we set out to prove, or of a proposi- ^ Langlois and Seignobos, Introduction to the Study of History, Eng. trans, by Berry, p. 214. ^■I1I THE METHOD OF KNOWLEDGE 113 tioii implying it. The possibility of expressing the same judgment in various forms of words renders it easy for such fallacious arguments to pass current. The fallacy is committed, for instance, when, we are told that " opium produces sleep because it has a soporific quality," or that " the volume of a body diminishes when it is cooled, because the molecules then become closer." Perhaps the most common mode of committing this fallacy is the acceptance of sham axioms, generally received from tradition, and the use of them as bases for inference. Of these many thousands have been received amongst men, and many are still held with unquestioning faith. We will quote a few : That nature abhors a vacuum ; That other metals can be transmuted into gold ; That all men are equal ; That slavery is natural ; That all children are born wholly good ; That all children are born wholly inclined to evil ; That in all trading the gain of the one party is the loss of the other ; That dreams are prophetic ; That like cures like. An excellent example of this form of the fallacy is to be found in the First Chapter of IMr. Herbert Spencer's Education. After stating that " acquirement of every kind has two values — value as knowlechje and value as discipline,'''' the author discusses the value of most subjects from the point of view of knowledge. He then turns to disciplinary value and begins his remarks with the following petitiu : — " Having found what is best for the one end, we have by implication ff)und what is best for the other. AVe may be quite sure that the acquirement of those classes of facts which are most useful for regulating conduct, involves a mental exercise best fitted for strengthening the faculties. It would be utterly contrary to the beau- tiful economy of Nature, if one kind of culture were I lU THE LOGICAL BASES OF EDUCATION chap. needed for the gaining of information and another kind were needed as a mental gymnastic." ^ ifinoraiio A vague Conception of the purpose often leads to Eicnchi. y_^g fallacy of Arguimj besides the miark-^Ignoratio Elenchi as it is technically termed. To meet a man's arguments by a charge of inconsistency, or by personal abuse, is to furnish a case in point. " To knock a man down when he differs from you in opinion may prove your strength, but hardly your logic." ^ Another mode of committing the fallacy is to appeal to prejudice or to sentiment. The following " argu- ment " against the study of literature is a striking instance : " When a mother is mourning over a first-born that has sunk under the sequelae of scarlet- fever — when perhaps a candid medical man has confirmed her suspicion that her child would have recovered had not its system been enfeebled by over- study — when she is prostrate under the pangs of com- Inned grief and remorse ; it is but small consolation that she can read Dante in the original." ^ The fallacy may also be committed by ignoring the arguments by which your opponent supports his con- clusion, and setting up in their place a " man of straw " which you then triumphantly demolish. A good instance is furnished by the objection to a classical education that " throughout his after career, a boy, in nine cases out of ten, applies his Latin and Greek to no practical purposes." * Or again : " As the Orinoco Indian puts on paint before leaving his hut, not with a view to any direct benefit, but because he would be ashamed to be seen without it ; so, a boy's drilling in Latin and Greek is insisted on, not because of their intrinsic value, but that he may not be disgraced by being found ignorant of them — 1 Education, p. 4L " Stock, Deductive Logic, p. 313. •'' Spencer, Education, p 28. ■* Ibid, p. 2. VIII THE METHOD OF KNOWLEDGE 115 that lie may have ' the education of a gentleman ' — the badge marking a certain social position, and bringing a consequent respect." ^ Of course Mr. Spencer has no difficulty in showing that these are not valid grounds on which to select a curriculum. But such showing is the veriest beating of the air so far as the arguments based on the disciplinary value of classical studies ai'e concerned. And it is on these that the advocates of such studies mainly rely. In using illustrations, we need to be continually on our guard against this fallacy. An illustration is intended to make clear something which the learner finds obscure. But the teacher may mistake the difficulty, and so direct the illustration to the wrong point. The same error may be made by the learner. For, as De Morgan well says, " the greatest difficulty in the way of learners is not knowing exactly in what their difficulty consists ; and they are apt to think that when something is made clear, it must be the something." " Especially is this the case when an abstract relation is illustrated by concrete examples. There is always the danger that it is something in the particular examples really irrelevant to the point under consideration which has been understood, and generally " the minds which are best satisfied by material instances are also those which give themselves no further trouble." ^ Another form of this fallacy to which the use of illustrations is liable is that the learner may fail to see the analogy between the illustration and the difficulty it is meant to make clear. Such con- siderations show that great care is needed to make sure that an illustratioii really fulfils i(,s intended function. ' Spencer, Edncaiinv. p. 2. - Formal Logic, p. 260. 3 ll>i,], p. 267. I 2 116 THE LOGICAL BASES OF EDUCATION chap. Essence of § 9. — Methodical process must, theu, have a Process. definite starting-point and a definite purpose. But it is in the continuous transition from the former to the latter, that method is found. We cannot have orderly procedure unless we first know whence we are starting and whither we wish to go. But it is quite possible to know these and yet to wander by the way. How such wandering may be avoided in any particular case must be detei'mined by the special science concerned. Our task is only to find by the analysis of successful procedure, what are the general characteristics of such method. These character- istics may be summed up by saying that methodical 2)rocess omits nothing, takes up the points one hy one, arid takes them up in such an order-that it goes frorn the starting-jyoint to the fidjilment of the inirpose hy con- secutive steps, each of which is seen in its true relation to every other step arid to the enquiry as a tvhole. Xatme ot § 10. — It is evident that y in the process of Inference. ,]iscovery nothing more than an approximation to this ideal can be expected, just because the system is in the process of making. It is only when the process is complete and has become proof that all which really lies outside the direct path can be swept away, and the passage of thought from starting-point to goal be seen as a necessary and continuous transition. Such perfect examples are, for instance, found in many of Euclid's proofs of geometrical truths. A process of inference is, then, logically perfect when it has ceased to be discovery and has become proof. Whether the pi'ocess is familiar or neAv to any individual mind has nothing to do with its logical character. It is, therefore, a mistake to confine the term ' inference ' to cases in which an individual reaches a truth hitherto un- known to him. The essence of inference is that vin THE METHOD OF KNOWLEDGE 117 thought passes continuously from starting-point to conclusion in a path necessitated by the character of the system. The conclusion is ' new,' not in the sense of being unfamiliar to any particular person, but in the sense of not being apparent in the premises — or judgments from which the process starts — though it is a necessary consequence of their combination. The inference is the whole construction, not the mere passage of thought between beginning and end. The question of inference then is this : Given inference certain truths, how can we reach other truths which "'^^ ^^ ^"'" go beyond those which are given 1 The answer must be sought in the conception of system with which inference is indissolubly connected. When- ever we can put a given fact or a given judg- ment into a system, we are able to make it the starting-point of inference. For instance, suppose we have a small bud from a rose tree. What is apparent to observation is just a little green hard object about the size of a pea. If we pull it to pieces we can observe more, but we cannot observe in that rose-bud the full flower which would, under favourable conditions, have developed from it if it had been left on the tree. But when we see a rose-bud we are able, not simply to think about the rose-bud as it is now, but to carry our thoughts on to the full-blown rose. This is possible because wo have sufficient knowledge of the matter to know that bud and flower are parts of the one system of the life of the rose-tree, so related that flower is the natural outcome of bud. We are then able to construct that system in our minds, and from that construction to derive the judgment that the flower should follow the bud. Evidently the dcfiniteness of our conclusion is dependent 118 THE LOGICAL BASES OF EDUCATION chap. upon the extent of our knowledge of rose-tree life. One person ma}' be able to state only the general fact of sequence, aiiotlier will give more or less approximately the time the transition will occupy. The moi'e exact the mental construction, the more exact is the conclusion which that con- struction makes apparent. To borrow another example : " My train is half an hour late. I know T must miss my connexions at the station ahead ; for the train I am hoping to catch at that place is scheduled to leave five minutes after the time of arrival of the train I am now on. The time relations here necessitate my missing my connexions. This is rendered still more certain if they are rival roads ; on no account will one wait for the other. Moreover, the train I hope to make is made up and leaves the station in question, and so I cannot fall back upon the favouring chance that it also may be detained en route, and so enable me, after all, to reach it in time. Thus, with every additional knowledge of the system which forms the ground of my inference, and the various conditions which affect it, the validity of my inference is thereby increased." ^ Inference Inl'erence is, then, mental construction based on Pievioua knowledge of particular systems and of such a Knowledge, character that a result not explicitly given in the premises can be immediately apprehended by thought when the construction is made. It is obvious from this that our power of inference is in every case essentially relative to the amount of our knowledge of the appropriate system. For example, a little child or a savage sees a heap of gunpowder for the first time, so that to him it is merely a heap of some- thing like black sand. The civilized adult who ' Hibben, Inductive Logic, p. 10. VIII THE METHOD OF KNOWLEDGE 119 recognizes it as gunpowdex- puts it into h dififerent system, which embraces and goes beyond that of the child. From this system he can infer the effects of the appHcation of a hghted match — a result which the child or savage could only discover by an experiment which might be disastrous. But the gunpowder is the same, whether observed by child or gunner or chemist ; the difference is in the system of knowledge possessed by the observer. It is this which makes inference possible, though it is not inference itself. When we know a system we can pass from fact to inference fact within it. But the path from fact to fact is versais. always through a universal relation, tliat is, through some identical quality common to both the facts. All increase of knowledge is the finding such univer- sal. The more universal ideas we can think a thing under, the more we know about it, and every such idea is a relation. Inference cannot stir without universals, but it must be remembered that the uni versais are in the facts, only needing to be found there by thought, though they cannot be discerned by the senses. Inference, then, is the working out of system — the thinking facts under universal relations, and the finding universal relations exemplified in facts. A mere fact which cannot be brought into any system is meaningless to us ; and the greater the number of systems a fact can be placed in the more it means to us. Incidentally it may be pointed out here that the aim of teaching is not to impart facts but to dcvelope systems ; facts are only of value in so far as they are starting points for such development. S 11. — Inference, or the making explicit the con- Deductive " „ . 1 • 1 1 • /• ;i" Cf. pp. 116-117. K 130 THE LOGICAL BASES OF EDUCATION chap. Of these only the first is really an analysis of subsumptive inference, for it alone has a true major premise ; that is, a universal under which the minor is brought. In the other figures the premises ai-e the same in kind, and this involves that they cannot sive a certain universal affirmative conclusion. Their o most important function in the method of knowledge is that they are steps in induction. We shall, there- fore, postpone further consideration of them to a later stage.^ The mediaeval followers of Aristotle added a fourth figure showing the remaining possible arrange- ment of terms — Major Premise P — M Minor Premise M — S Conclusion '. S — P This is certainly a possible symbolic form, but it corresponds to nothing in the actual structure of thought, and should, therefore, be discarded. Hypo. § 4. — The universal judgment, as we have seen, Syllogisms, is often most exactly expressed in hypothetical form. We may, then, have syllogisms in which the minor premise brings a particular case under ja universal relation of the form "If S is M it is P." Now from this mere form we must not assume that M is the only possible condition under which S is P, for in most of the judgments of ordinary life neither M nor P are stated with sufficient accuracy.'^ We must, then, face the possibility that S may be P under other conditions, as X, Y, Z. For instance, "If a man (S) is shot through the heart (M) he dies (P)," but there are many other possible causes of death. It follows that we cannot infer "S is not P" from the conjunction of such a major premise with a minor of 1 See Chaps, xi. and xiv. - Cf. pp. 88, 90. rx DEDUCTIVE INFERENCE 131 the form " S is not M " ; for S may be X ur Y or Z, and in either of these cases it is P. Again, the assertion " S is P " united as minor with the major " If S is M it is P " will not justify us in asserting " S is M," for P may in this case be due to X or Y or Z. We have then only two forms of syllogism with a hypothetical major premise which yield a certain conclusion. They are — (1) If S is M it is P, But S is M ; Therefore, S is P. (2) If S is M it is P, But S is not P ; Therefore, S is not M. To put it generally : a certain and definite conclusion can be drawn from either affirming the antecedent or denying the consequent of the hypothetical major premise. But to deduce such a conclusion from denying the antecedent would be to commit a formal fallacy analogous to the illicit extension of the reference of the major term in categorical syllogism. This is evident when it is seen that every hypo- thetical syllogism can be expressed categorically by writing the major premise in the form •' Every S M is P." The minor " This S is not U " may be expressed : " This is not S M." If then these two propositions are combined Every S M-is P, This is not S M ; it becomes evident that wc arc not justified in con- cluding "This is not P." w o 132 THE LOGICAL BASES OF EDUCATION chap. Similarly, if we affirm the consequent, the syllogism may be categorically expressed Every S M is P, This is P ; and it is seen that the middle term P is not dis- tributed and consequently we are not justified in affirming " This is S M." Hence, it is a matter of indiflference, so far as the formal accuracy of our inference is concerned, whether we state it in a categorical or in a hypo- thetical syllogism. CONSTRUCTION Nature of § 5. — We must now consider tJie characteristics of tiou!*^'^^^'^ Construction. In such inferences as " A is north of B and B is north of C, therefore A is north of C," the conclusion follows obviously and immediately from the construction. But that construction is not syllogistic, for there is no middle term ; we have " B " in one premise and " north of B," in the other. No doubt we can put the whole into syllogistic form by using as a major " What is north of anything is north of that which the former is north of." But this is merely the construction itself generalized and put in a more abstract form ; it is not the ground on which the inference actually rests. In such inferences, as in all others, we must have a point of connexion between the premises. But the mere presence of the same term in each is not enough ; that term must stand in the same kind of relation in each. As Mr. Bradley says, " ' A runs faster than B and B keeps a dog (C),' ' A is heavier than B and B precedes C,' * A is worth more than B and B is on IX DEDUCTIVE INFERENCE 133 the table (C),' or ' A is like B and B is like C You may doubtless extract some kind of inference out of these premises, but you can hardly go from them to any definite and immediate relation between A and C." ^ Now, it is evident that the relations between things are indefinite in number, and consequently it is impossible to make a list of valid inferences. All that can be done is to consider the " tests of the general possibility of making a construction ; but of the actual construction there can be no canons." " S 6. — The general principle of such constructive Types of . Coiistruc- inferences is that the construction exhibits the whole tion— contents of the system. They are of two main classes (1) those in which the constructed whole is a mere sum of its elements, the typical examples being arithmetical constructions ; (2) those in which the elements united are relations, the most typical examples being geometrical constructions. In each case the process can be immediately generalized ; for as the whole of the system is explicit in the con struction, any precisely similar construction will yield a precisely similar result. If we consider the judgments of arithmetic we find Arithmetical they are based on the idea of a unit. Now in tmis. counting concrete objects " the mind always chooses its own unit ; it groups its objects as it pleases, and chooses as units the groups it has made : sometimes it counts by faggots, sometimes by single sticks." ^ The unit is, then, something determined not by the nature of things but only by the act of mind which discriminates things from each other. Objects alto- gether unlike in their qualities may be counted if we choose, just because they are alike in this one point, > The Prinripfex of Logir, p. 233. - Ihid., p. 246. ■* Bryant, Kdi(rri/io)inl'End.s, pp. 192—193. 134 THE LOGICAL BASES OF EDUCATION chap. that they can be discriminated from each other. Thus, a unit is a purely abstract individuality, and is at bottom nothing but an act of discrimina- tion. Counting may be aided by the presence of concrete objects, but it is independent of their nature ; its elements are the mental acts of discrimination. Hence, the constructed whole is purely abstract ; the elements and the whole are both made by the mind itself. Counting is the foundation of arithmetical judg- ments, and counting, beginning with one unit, is the gradual synthesis of units by adding one at a time, and sfiving; a distinctive name to each new whole. But, as we have seen, all synthesis involves analysis, and the whole constructed is, by that construction, seen as the sum of its units. It is, of course, also apprehended as a whole of a certain definite character which distinguishes it from other wholes. It is because of these various characteristics that an arithmetical operation is an inference. " In these cases we are given certain elements, and assert that these elements form a certain whole. Both the elements and the whole must be such as to be known othenvise than m relation to each other, or we get into tautology. Thus, if 8 only meant 5 + 3 the statement 5 + 3 = 8 would be an idle play on words. But 8 also means 4 + 4, 10-2, 4x2, and I will venture to say that it also and primarily means 8." ^ The primarily analytic operation with number is that of measuring, and this also rests on the conception of a unit. The object of measuring is to reduce what is given as a whole to a multiplicity of units, in order to compare it in respect of quantity with another whole similarly treated. Of course as a 1 Hobhouse, The Theory of Knowledge, p. 424. IX DEDUCTIVE INFERENCE 135 result the whole is apprehended as a synthesis of the units by which it is measured. It is unnecessary to pursue the subject further, our aim being only to make clear the character of the inference. Very few words need be added on constructions Geometrical of spatial relations. If we are given the definite ttons. spatial relations — that is, the distance and direction — of both A and C to B, our construction, whether it remains purely mental or is aided by drawing a diagram, makes evident the spatial relation of A and C. All inference from charts and maps and plans is of this character. It is on constructions of this kind that the validity of geometrical axioms rests. § 7. — As both arithmetical and geometrical con- inductive structions can be immediately generalized, they have construc- an inductive aspect. Indeed, there is reason to suppose that "mathematics in their primitive stages would have a quasi-inductive character. That is to .say, that (1) they would tend to deal with concrete objects, or classes of such objects ; that (2) their results would have the aspect of independent generalizations, rules of thumb, and so on ; and that (3) they would be encumbered with difficulties in rising from these first generalizations to higher, more comprehensive, and more abstract principles. All these points seem to be borne out by the little that is known, or probably inferred, as to the early liistory of arithmetic and geometr}'." ^ The bearing of this on the method of teaching these subjects to children is obvious. ^ Hobhouse, q?>. ri(., j). 4IiO. tiou. CHAPTER X OUTLINE OF INDUCTIVE METHOD Meaning of § 1. — INDUCTIVE inference starts with particular tion.'^° facts and proceeds by a process of analysis to find the universal relations they embody, and so to construct a system whose nature explains them. The word ' Induction,' however, has been used, and, indeed, still is used, in more than one sense. Aristotle confined ' induction ' to generalization from sense-perception : " Induction begins with facts of personal experience and reasons backward to the cause or principle." ^ But such reasoning does not give really scientific knowledge, the appropriate expression of which is the syllogism. This is admirably put : " Nor is it possible to obtain scientific knowledge by way of sense-perception. For even if sense-perception reveals a certain character in its object, yet we necessarily perceive this, here, and noiv. The universal, which is throughout all, it is impossible to perceive ; for it is not a this-now ; if it had been it would not have been universal, for what is always and everywhere we call universal. 8incp tlien demonstration (science) is 1 Anal. Pr., II, 68, b., 32. CH. X OUTLINE OF INDUCTIVE METHOD 137 universal, and such elements it is impossible to perceive by sense, it is plain that we cannot obtain scientific knowledge by way of sense." ^ It is just this establishment of universals which is the aim of modern science, and it is becoming more and more usual to apply the term ' induction ' to the whole process, instead of restricting it to that mere suggestion of a universal by sense-perception which corresponds to Aristotle's use of the term. ' Induction ' in this wide sense corresponds to the whole method of attaining knowledge, and includes deductive processes. § 2. — Using the word in this wide sense, the General question is. How can the universal be found in the induction. particular 1 Not by sense-perception or observation, as Aristotle has so clearly shown in the passage quoted above. The universal can only be found by thought, that is, by supposing the existence of a certain law and then testing this supposition. As De Morgan tersely puts it : " A few facts have suggested an hypothesis, which means a siippositioii proper to explain them. The necessary results of this supposition are worked out, and then and not till then, other facts are examined to see if these ulterior results are found in nature." ^ The main steps of inductive method, may, therefore, be thus stated — 1. A preliminary observation of facts. 2. The formation of a hypothesis suggested by this observation. 3. The testing of the hypothesis l)y comparison of its consequences with the results of a careful analysis of phenomena, with modification or even ' Aji. Ponf., 87, 1)., 28, (|iioteil l>y IJosaiKjuet, Eis. of Lofjic, p. \r)4. - BiidijiJ of I'arwloxcx, p. 5.j. 138 THE LOGICAL BASES OF EDUCATION chap. rejection if necessary. This process is Ccarried on till the hypothesis is proved, when it is more correctly called a Law or Theory, according to whether it states one Univel^sal relation or is a wider generalization covering many laws. It is in the third step that deduction is continually operative, for, as Dr. Bosanquet says, " nothing can be more deductive than the connexion of a hypothesis with the consequences by which it is verified." ^ § 3. — The testing, moulding, and verification take a moi'e direct, or a mainly indirect, form according to the nature of the case. When we are investigating a causal sequence in which the cause is simple and under control, we may try experiments with it, and our verification is a comparatively direct process. Even though the cause is not under our control, yet if the whole causal sequence can be observed under varying conditions, the process of testing and verification still remains partially direct. In this case, however, the more indirect method of de- ductively inferring the probable consequences of the cause and looking about to find if these consequences are really to be found in nature, will also be adopted. In all other cases this indirect method must be used nearly or altogether exclusively. " A cause . . . may be under control and yet be too dangerous to experiment with ; such as a proposed change of the constitution by legislation ; or even some minor Act of Parliament, for altering the Poor Law, or regu- lating the hours of labour. Here the first step must be deductive. We must ask what consequences are to be expected from the nature of the change (com- paring it with similar changes), and from the laws of the special circumstances in which it is to operate? And sometimes we may partially verify 1 Logic, vol. ii, p. 119. X OUTLINE OF INDUCTIVE METHOD 139 our deduction by trying experiments upon a small scale or in a mild form." ^ When the facts with which we start are effects, and the causal sequence cannot be observed but must be inferred from those effects, as, for example, is mainly the case in geology, then the indirect method of verification is the only one available. ^ Carvetb Read, Logic, Deductive and Inductive, j). 164. CHAPTER XI OBSERVATION § 1. — The scientific method of knowledge starts with facts and continually returns to facts to test and verify its hypotheses. If its supposed facts are fictions, the whole fabric falls to the ground. It is a funda- mental question, therefore, how an accurate know- ledge of facts is to be obtained, and to this there is but one answer — by exact observation. Every state- ment of fact rests directly or indirectly on observa- tion. In the former case, the only question is as to the correctness of the observation ; in the latter case we must add to this an enquiry into the competence and trustworthiness of the witness who records it. In the present chapter we are concerned only with direct observation. § 2. — At first sight it might seem that nothing need be said on this point. " Seeing is believing " is a proverb accepted by many as axiomatic. And, indeed, taken as expressing a common fact in the natui^al history of many minds, it is undeniably true. We are naturally apt to believe what we see, or rather, what we believe we see. But the mere fact of belief, as has been more than once insisted en. XI OBSERVATION 141 on, is no sufficient evidence of the truth of the judg- ment believed ; and what is commonly called '' the testimony of the senses " is by no means infallibly accurate. Every case of illusion is an instance of this. As Aristotle long ago pointed out, a pea appears double when it is placed between two crossed fingers of one hand and then rolled about. Again, the two flat pictures in a stereoscope combine into an appearance of solidity. An immense number of other instances could be given. Further, the testi- mony of the senses is apt to conti-adict itself. " The moon at its rising and setting appears much larger than when high up in the sky. This is, however, a mere erroneous judgment ; for when we come to measure its diameter, so far from finding our conclu- sion borne out by fact, we actually find it to measure materially less." ^ Nor is such false testimony of the senses confined to individual experiences. "A vague and loose mode of looking at facts very easily observ- able, left men for a long time under the belief that a body, ten times as heavy as anothei', falls ten times as fast ; that objects immersed in water are always magnified, without regard to the form of the surface ; that the magnet exerts an irresistible force ; that crystal is always found associated with ice ; and the like." - § 3. — The possibility of such wide-spread errors Dependence as those of which Whew ell here gives a few examples, tiou on proves that men are generally bad observers, and, as K^i'o'^'jcdgc. a consequence, that mere extended observation is no guarantee of truth. It is not how often an obser- vation lias been made, but liow accurately it has been made, that is the important point. And the accuracy which science demands is only possible ^ Hcrschel, Z)tscour«€ on Natural Philoaophy, § 12. 2 Whewell, Xoium Orfjanon Rtnovalnm, p. 61. 142 THE LOGICAL BASES OF EDUCATION chap. when the observer possesses special skill and know- ledge. " A person may well derive, perhaps in some unfamiliar department of knowledge, a degree of certainty from the affirmation of the qualified expert far surpassing anything he could reasonably derive from his own imperfect or untrained observation." ^ Observation, in other words, is not a mere matter of perfect sense-organs, even when these are united with a concentrated attention and an earnest pur- pose to observe well. Only he observes well who brings much pertinent previous knowledge to the observation. " To make a perfect observer," says Herschel, " an extensive acquaintance is requisite, not only with the particular science to which his observations relate, but with every branch of know- ledge which may enable him to appreciate and neu- tralize the effect of extraneous disturbing causes." ^ § 4. — This leads us to the very essence of the matter : observation always involves inference, and the correctness and value of every inference depends upon the truth and adequacy of its premises. For by ' observation ' we mean not the mere i^eception of sense-impressions, but the selection from amongst the whole mass of such impressions of those to which we will attend, and the interpretation of those attended to. And both selection and interpretation are matters of inference. When we select a phenomenon for observation we disregard a great deal more than we attend to, and we assume that this abstraction will not alter the character of what we are studying. But this assump- tion is a matter of inference and may be erroneous. In the seventeenth century Sir Kenelm Digby won much fame by the cures of wounds wrought by his ^ Ravenshear, Article on Testimony and Authority, Mind, N. S., vol. vii, p. 65. " O}) cit, § 127. XI OBSERVATION 143 sympathetic powder. Says De Morgan: "The sympa- thetic powder was that which cured by anointing the weapon with its salveinstead of thewound. I have long been convinced that it was efficacious. The directions were to keep the wound clean and cool, and to take care of diet, rubbing the salve on the knife or sword. If we remember the dreadful notions upon drugs which prevailed, both as to quantity and quality, we shall readily see that any way of not dressing the wound would have been useful."^ Similarly, "to-day, the Sufiolk farmer keeps the sickle with which he has cut himself free from rust, so that the wound may not fester." - The error, as these examples show, may be either in excluding elements which ought to be included, or in including as essential those which are immaterial. This matter of selection is, indeed, one of the most difficult in scientific discovery, and we shall have to consider it in more detail in a later chapter.^ All we wish to make clear at this point is that whether an element should be included as important, or excluded as irrelevant, to the matter in hand is an inference from the knowledge which the observer brings to the observation. All interpretation is also inferential, for it Rccogni- involves a reference to what is not now given in sense-perception. As an example let us consider the simplest possible case — that of recognition. We see a small yellow sphere of a certain size and we immediately recognize it as an orange. Doubtless, we are unconscious of any mental process, and so f i-om the psychological point of view we might refuse to call it inference at all. But it has Ijeon already pointed out tliat the question for logic is the kind of * Bndqet of Paradoxes, p. 66. 2 Clodrl, Tom Tit Tot, p. 64. 3 Cf. Ch. xiv. 144 THE LOGICAL BASES OF EDUCATION chap. evidence on which a judgment rests : if that is a mental construction from which a result necessarily follows we have inference. Now, the judgment " This is an orange " as an interpretation of the sight- perception we have spoken of, can only be justified by a construction such as the following — Oranges are spheres of a certain size and ap- pearance, This is a sphere of such size and appearance ; Therefore, this is an orange. Here the inferential character of the evidence on which our judgment rests appears plainly in the form of a syllogism in the second figure.^ But further, our conclusion carries much more with it than the visual qualities on which it is based. In calling the object perceived an ' orange ' we infer that it possesses many other qualities, as those of taste and smell and touch. And to this inference a very practical conclusion would be given by eating the orange. If we examine this second inference we shall find that it falls naturally into a syllogism in the first figuj-e — Oranges are sweet, juicy, &c.. This is an orange ; Therefore, this is sweet, juicy, &c. Now, if these two syllogisms are examined it will be seen that both are formally invalid, in that in neither is the middle term used universally. The conclusions drawn should then not be stated as certain but as only probable — " This is probably an orange"; "This may be {or is probably) sweet." But it will also be noticed that the conclusion in the 1 Cf. p. 129. XI OBSERVATION 145 former case is much more likely to be true than that in the latter, because the signs by which the object is classed as an orange are of a definite character and have been directly observed. It is possible that a waxen or stone image might be made to resemble an orange so closely in visual appearance that it might deceive all but the most careful and minute observers. But the test of the other senses is an easy one to apply and is decisive. Such verification involves an inference in the first figure such as we have quoted alcove, and the comparison of its con- clusion with a new sense-impression. If the inferred qualities are found to be absent, as in the case of the waxen or stone image, then the recognition from which they were inferred is rejected as unwarranted. This rejection, like the original recognition, can be analysed into a syllogism in the second figure — Oranges are sweet, juicy, ifcc, This is not sweet, juicy, &c. ; Therefore, this is not an orange. Here the conclusion is certain, as the middle term is used universally in the negative premise, and so there is no such formal invalidity as in the former case. The inference in the first step of recognition is altogether implicit. Ps3'chologically it is due to the habitual association of a certain group of attributes which we have learnt to sum up under the term ' orange,' an association so perfectly mechanical that the presence of one or two of those attributes immediately suggests the whole group. But this suggestion is vague ; no one attribute is singled out, and the only thing in full consciousness besides what is given in sense-perception is the name. If we now turn to the second step we see that the L 146 THE LOGICAL BASES OF EDUCATION chap. inference involved is somewhat nearer to being made explicit. From certain visual appearances we infer the presence of some definite non-visual quality or qualities, and we do so on the ground of their common inherence in the object we have recog- nized. There are, therefore, two chances that our conclusion is not true ; for the act of recognition may be unjustified, and, even if it is justified, our major premise may not be universal when we believe it to be so. The young child, for example, with ex- periences of only sweet oranges, would doubtless expect with the utmost confidence that any fresh example of orange would also be sweet ; the adult would know that this is open to considerable doubt, and would take for his major premise only the limited judg- ment " Some (or most) oranges are sweet." Now, when the child has his first experience of a sour orange, another conclusion is forced on him, and this also can find its justification in a syllogism, this time in the third figure — This is sour. But this is an orange ; Therefore ; oranges may be sour. Thus he proceeds to make his knowledge more exact and definite by forming sub-classes in his pre- viously wide and vague class ' oranges.' ^ The analysis which we have here applied to a very simple example holds true of every case of sense- perception. It shows that even in sense-perception we have all the essential features of the inductive method. The original recognition — liable to doubt, as we have seen it to be — is the hypothesis sug- ^ This connexion of sense-perception with syllogism was first worked out by Dr. W. T. Harris ; see his Psychologic Foundations of Education, pp. 62 — 89. OBSERVATION 14^ Vietweeu ' Observa- tion ' and ' Infer- ence' gested by a first observation of the facts ; then follows the inference of the results of that hypothe- sis, the testing of those results by further sense-ex- perience, and the consequent verification, modification, or rejection of the hj'pothesis. The most complex case of induction only contains the same steps, carried out, however, with infinitely greater difficulty and with infinitely greater liability to error, because the matter dealt with is infinitely more complex. Our anah'sis shows also that the possibilty of error Bistinction in observation is due to the inferential character of the process, whilst the fact that the inference is largely unconscious renders it easy in cases of any considerable complexity for error long to escape detection. But our analysis has also made it plain that inference enters into the process in vai'ving degrees ; there is less of it in the simple recognition than in the conclusion from that recognition that any particular quality, such as sweetness, will be found. Now it is evident that this second step may be developed to any extent, and may extend to conclu- sions which cannot be immediately tested by the senses. It is hei"e that ordinary convention draws the line between ' observation ' and ' inference.' So long as we remember that observation itself involves inference, this distinction is a useful one. Suppose that, having recognized the orange, I drew the conclusion that it had been grown in Tangiers, that would obviously be an inference. Now, nothing would seem simpler than to distinguish between observation and inference in this sense of the terms. Yet nothing is more common than to confuse them. " Not one eye-witness in a hundred can adequately distinguish what he saw or heard from what he inferred." ^ The reason .should now be evident. It ' Hobhouse, The Theory of Knowledge, p. 215. L 2 us THE LOGICAL BASES OF EDUCATION chap. is that psycliologically such an inference as that the orange came from Tangiers, and such a judgment as " the orange is probably sweet," rest on evidence of the same sort, that is, evidence drawn from the previous knowledge of the observer. Logically, there is the difference that the latter deals with something which is directly given and so can be immediately tested by sense-experience, whilst the former asserts what is not so given and cannot be so tested. An illustration of our point may be drawn from Dr. Conan Doyle's ideal embodiment of the powers of precise observation and accurate inference, Mr, Sherlock Holmes. In the introduction to The Sign of Four his ingenuous biographer, Dr. Watson, writes — " ' You spoke just now of observation and deduction. Surely the one to some extent implies the other.' 'Why, hardly,' he answered, leaning back luxur- iously in his arm-chair, and sending up thick blue wreaths from his pipe. ' For example, observation shows me that you have been to the Wigmore Street Post-office this morning, but deduction lets me know that when there you despatched a telegram.' ' Right ! ' said I, ' Eight on both points ! But I con- fess that I don't see how you arrived at it. It was a sudden impulse upon my part, and I have mentioned it to no one.' ' It is simplicity itself,' he remarked, chuckling at my surprise — ' so absurdly simple that an explan- ation is superfluous ; and yet it may serve to define the limits of observation and of deduction. Observa- tion tells me that you have a little reddish mould adhering to your instep. Just outside the AVigmore Street Office they have taken up the pavement and thrown up some earth, which lies in such a way that it is difficult to avoid treading in it in entering. The XI OBSERVATION 149 earth is of this peculiar reddish tint which is found, as far as I know, nowliere else in the neighbourhood. So much is observation. The rest is deduction.' ' How, then, did j'ou deduce the telegram 1 ' ' Why, of course I knew that you had not wi'itten a letter, since I sat opposite to you all the morning. I see also in your open desk there that you have a sheet of stamj^s and a thick bundle of post-cards. What could you go into the post-office for, then, but to send a wire 1 Eliminate all other factors, and the one which remains must be the truth ! ' " We are afraid that Mr. Sherlock Holmes fails here to justif}" the tone of somewhat supercilious superiority Avhich he adopts towards his friend. He begins by pooh-poohing a perfectly accurate remark of Dr. Watson, and he ends by a very unsafe inference, for he forgets to " eliminate " many factors, such as the purchase or the cashing of a postal order. But we have quoted the passage because he falls into the very confusion between observation and inference — or " deduction " as he calls it — which he has under- taken to show Dr. Watson how to avoid. In the ordinary sense of the words he observed the mud on his friend's boot ; he did not observe, but inferred, the visit to tlie post-office. And according to "his own principles that is where he should have drawn the line. § 5. — Our investigation has shown us clearly that observation ob.servation is always relative to the previous know- piejudice. ledge of the observer, and that it is accurate and fruitful exactly in proportion to the thoroughness and correctness of that previous knowledge. AV'hcn the previous knowledge is vague and indeterminate, the observation is wantingin definiteness and in depth, and is unfruitful in inferential results. When instead of knowledge, or mixed up with knowledge, there is 15U THK LOGICAL BASKS OF EDUCATION chap. a mass of unfounded belief, the observation is vitiated by bias and prejudice. The danger of not keeping out this element of error is one against which only the trained mind is on its guard. The savage interprets all his experiences in accordance with his superstitions, and so finds his false beliefs everywhere confirmed by his observations. His cattle sicken and die under the influence of the " evil eye '' unless he can get a stronger counteracting charm thrown over them. In these more civilized times men still believe in dreams and omens, and support their belief by instances they have observed, dwelling on a few cases of more or less close resemblance between a dream and some following event, and ignoring the enormous number of cases in which the dream does not " come true." Even the scientific enquirer finds it hard to observe quite fairly facts which make against his pet theories. § 6. — The dependence of observation on previous knowledge is brought out yet more clearly when observation is aided by .scientific instruments, which all embody whole sj^stems of knowledge. The accuracy of observations made with such instruments depends on the knowledge which produced the instrument as well as on that in tlie observer's mind. And that these are I'elated to each other is shown by the fact that only skilled observers can really make use of very delicate and complicated instru- ments. § 7. — Most strikingly of all is the dependence of observation on previous knowledge brought out when the observation takes the form of what is known as an experiment, that is, is made under con- ditions determined by the observer. The selection which, in ordinary observation, is merely mental is here made physical as well. The object of this selection is to omit all elements which have no XI OBSERVATION 151 influence on the phenomenon to be observed, and to retain, in known relations to each other, all those that have such influence. An error will vitiate the whole result, and the history of science is full of instances of erroneous conclusions due to the presence of unsuspected conditions which modified the phenomenon observed. It is evident, then, that no one can really experiment who has not extensive knowledge of the kind of phenomena he is dealing with. Whether he himself arranges the physical conditions is immaterial ; the essential thing is that he mentally determines those conditions. " Manipu- lation of the external world is not of the essence of experiment, which simply consists in selection and the purpose to observe, usually implying and result- ing in precise knowledge of the conditions." ^ The advantages of experiment over mere observa- tion are its greater definiteness and its subjection to control. When we can experiment we can observe when we will, without waiting for nature to present us with a specimen of the phenomenon we wish to study, and thus investigation can go on continuously and systematically. Again, when we have the condi- tions under our control we can vary them at pleasure, and systematically observe the results. In many cases, without experiment the knowledge we now possess would never have been attained. Many natural processes go on so slowly and gently that they escape observation. As Lavoisier remarked, the decom- position of water had been going on ever since the beginning of the world, but had never been observed before the experiments of Cavendish and himself brought it to light. But experiment is not always possible. When the process to be investigated goes ' ]'>08an(juet, Knowledije and litalily, \i. S.j. 152 THE LOGICAL BASES OF EDUCATION ch. xi on very slowly experiment is out of the question. The geologist, for instance, cannot experiment on the nature of the forces which have made the earth's crust what it is, nor the biologist on the evolution of species. CHAPTER XII TESTIMONY § 1. — If we examine the origin of our own know- Necessity of ledge, each one of us will find that by far the larger portion of it rests, not on his own personal experience, but on the testimony of others. In many cases such testimony can be directly tested, and its acceptance is then merely a matter of convenience ; as, for instance, when a person who has not quitted England accepts the testimony of others to the existence and characteristics of foreign countries. When the testimony is merely the expression of an opinion derived by inference from facts easily observable, such testing by others is always possible. But there are many cases in which facts cannot be observed again ; and then the acceptance of testi- mony is a matter of necessity, for without it all advance in knowledge would be impossible. "The uniformities shown in the return of certain of the comets are visible only to those who know how to rely upon records many hundred years old. The uniformities brought to light l)y statistics are nothing to him who cannot depend on an army of co- workers." ^ Testimony which can be tested by direct ' Ravenshear, Ttxtimony nnd Authority, Mind, N. >S., vol. vii, p. 6(5. 154 THE LOGICAL BASES OF EDUCATION chap. observation need not remain testimony, and so need not detain us. But we must enquire what tests of accuracy it is possible to apply to testimony which can never be thus superseded § 2. — The only testimony of this kind is to facts which cannot be again observed. But, as the testimony itself records an observation, it might be thought unnecessary to say anything further about it, and to regard it as simply observation at second- hand. This, however, would neglect the factor of reception of the testimony. When a piece of testi- mony is offered, we may either accept it, reject it, or remaui in doubt about it. In the two former cases we make a judgment as to its truth or falsity, and every such judgment rests on what seems to us sufficient evidence. In the last case we judge that the evidence available is not sufficient either to sustain or to destroy the testimony. In every case, then, we analyse and criticize testimony offered us, and such analysis and criticism is similar in character to the inference involved in the analysis and criticism of our observations, the difference being that it is exercised on judgments made by others instead of on facts forming the material of our own judgments. As with observation, so with the reception of testi- mony, absence from bias and adequate knowledge are essential if the testimony is to mean anything to us, and to be fruitful in our hands. Indeed, owing to the dependence of the meaning of words and sentences on their context, the danger of reading into testimony what is only in our own minds is even greater than that of falling into the correspond- ing error of confusing inference with observation. The more remote from our own experiences are the events with which the testimony deals, the more difficult is it to avoid misinterpretation. This is xii TESTIMONY 155 one reason why so much of the history of remote times is of a doubtful character. Another reason is the small number of contemporary documents. And these react on each other ; for, as the only safeguard against misinterpretation is adequate knowledge of the times, and as such knowledge itself rests on testimony, it is evident that such testimony must be supported by testimony, and, consequently, the smaller its amount the less is its combined force. § 3. — Having interpreted a piece of testimony as Tests of well as possible, the next question is whether it is to mony— be accepted or rejected. Here also we must be guided by previous knowledge. The savage and the child are extremely credulous of all that falls out- side the narrow range of personal experience. As they have no conception of a systematic universe permeated by law, they find in the abnormal and the supernatural no contradiction to the accepted order of things. And this credulity passes but slowly away. Englishmen of the time of James I. proliably found nothing incredible in Othello's " men whose heads do grow beneath their shouldei"s," and the superstitions still common even in the most civilized countries include many things equally unknown to science. It is, indeed, only the specialist in any subject who is a competent judge of the value of testimony dealing with that subject. Xow it is in science that we find the most perfect precision and accuracy to which human knowledge has yet attained. Science accepts nothing on bare authority, and in admitting testimony suljjects it to the most rigid tests. In addition to demanding that freedom from bias, good faith, and competence in the ol)server, with which we dealt in the last chapter, science retjuires that the observation bliall bo recorded immediately it is made, and that 156 THE LOGICAL BASES OF EDUCATION chap. tlie record shall be both full and precise. This is the ideal towards which in other departments of knowledge only an appi'oximation is possible. In history and in common life the only testimony available is generally that of the ordinary eye-witness, and i» more or less vitiated, not only by some or all of the faults of observation, but by confusions due to lapses of memory, which are supplied, often without the consciousness of the wit- ness, by inference or by the play of the imagination, and sometimes even by deliberate fabrication. " The evidence which has been adduced for clairvoyance. . . . would have hung a hundred men, but before the tri- bunal of science it is as nothing." ^ Even in the law- courts where the testimony of the ordinary e^^e-wit- ness is sifted in a way impossible in most other depart- ments of life, the standard of acceptance is much lower than in science. And this lower standard is necessary, for in ordinary life we have to act on reasonable presumptions ; were we to demand theoretical certainty in every case, life would stagnate. " You cannot leave practical matters open, to all eternity, as you can matters of specula- tive truth." ^ Good Faith. But though we cannot in most cases wait for absolute proof before accepting testimony, yet we must have some reasonable guarantee of its accuracy. Now, when a statement is false it may evidently be so either with or without the knowledge of him who makes it ; a man may intentionally say what is untrue or may simply be mistaken. The questions as to the trustworthiness of the testimony fall then under the two general heads of the good faith and the accuracy of the witness. The former of these is of 1 Bosanquet, Knowledge and Beality, p. 135. - Ibid., p. 136. XII TESTIMONY 157 logical interest only so far as it bears on the latter, that is, so far as our acceptance of the testimony rests on considerations as to the truthfulness of the witness. If we can test its accuracy independently, the question whether the assertor believes it or not is of little moment ; so long as a statement is false it is not of logical interest to distinguish whether it is a falsehood or a simple falsity.^ We are concerned, then, with sincerity only in so far as it is evidence of accuracy. And this is well, for nothing is so difficult to decide as good faith. " ' The accent of sincerity ' is the appearance of conviction ; an orator, an actor, an habitual liar, will put more of it into his lies than an undecided man into his statement of what he believes to be the truth. Energy of affirmation does not always mean strength of con- viction, but sometimes only cleverness or effrontery." ^ However, in unsupported testimony the question of sincerity is important. We must then consider whether any of the general conditions which cause men to lie are likely to be operative in this case. We must ask whether falsehood would appear to bring any personal advantage to the witness, whether he is likely to be swayed by fear, vanity, sympathy, antagonism, the desire to please, or the wish to astonish or amuse. We should be inclined to suspect all rhetorical flourishes, all dramatic detail, especially when any considerable time has elapsed between the occurrence of the event and the record of it. " Abundance and precision of detail, though they produce a vivid impression on inexperienced readers, do not guarantee the accuracy of the facts ; they give us no information about anything but the ' Cf. p. 71. - Langloia and Seignobos, Inlroduclion to Ihe S/udy of llixtory, p. 1G2. 158 TIIK LOGICAL BASES OF EDUCATION chap. imagination of the autliof when he is sincere, or his impudence wlien he is the reverse." ^ Accumcy. Granting the good faith of tlie witness, we must yet accept a narrative as true only when it endures certain critical tests. The main points to be considered are connected with the competence of the author as an observer and as a witness. The essentials of a good observer were dealt with in the last chapter. In enquiring whether our witness possesses the general prerequisite of freedom from bias, we must consider what sort of prejudices would be likely to influence him, such as those common to his condition in life, state of culture, country, and epoch. Especially is this important in estimating the value of testimony of old writers to the miraculous and extraordinary. Often an examination of a writer's works will show his dominant superstitions, bias, and prejudices, and any statement in which these play a part must be discounted accordingly. We must next consider the competence of the witness as an observer of the particular facts he records. And here, in addition to questions as to his general competence in observing facts of the kind in question, dependent on his special knowledge and his power of distinguishing between observation and infei'ence, we have to enquire whether he was in a favourable condition to observe these particular facts. The raodei^n newspaper reporter sometimes writes detailed accounts of meetings he has never attended, and ancient and modern historians have embellished their pages with scenes equally dramatic and equally imaginative. When the scenes recorded are com- plex, much of the detail must be matter of imagina- tion, of inference, or of the report of others. For 1 Langlois and Seignobos, Introduction to the Stud)/ of History, p. 162. XII TESTIMONY 159 example, when a general records his campaigns and his battles it is evident that but a small part of his testimony is really based on his own observations. Similarly, when a historian relates events which occu- pied long periods of time, or describes customs and movements which were common over a wide stretch of country, he derives much of what he states from others. In all such cases, therefore, a large part of the testimony which is ostensibly given us by one witness is really supplied by an unknown host of collaborators, whose good faith and competence Ave have no means of judging. But competence as an observer does not always imply competence as a witness. Some people seem to be constitutionally unable to make an accurate statement. " They are subject to ' chronic inac- curacy,' a disease of which the English historian Froude is a typical and celebrated case. Froude was a gifted writer, but destined never to advance any statement that was not disfigured by error ; it has been said of him that he was constitutionally inaccurate. For example, he had visited the city of Adelaide, in Australia : ' We saw,' says he, ' below us, in a basin with a river winding through it, a city of 150,000 inhabitants, none of whom has ever known, or will ever know, one moment's anxiety as to the recurring regularity of his three meals a day.' Thus Froude, now fur the facts : Adelaide is built on an eminence ; no river runs through it ; when Froude visited it the population did not exceed 75,000, and it was suffering from famine at the time." ^ Of course, such general inaccuracy in a modern writer is nearly certain to become known, but frequently there is no means of saying how far ancient writers suffered from the same disease. * Langlois and Seignobos, op. cit., p. 125. 160 THE LOGICAL BASES OF EDUCATION chap. Probably, however, the most frequent cause of in- accurate testimony on the part of competent obser- vers is lapse of memory. We all know that memory plays us strange tricks. Details drop out, and we fre- quently unconsciously fill the blanks Ijy constructive imagination and inference. Or we look at the past through spectacles coloured by our personal feelings of sympathy and antagonism. We are apt to attribute to ourselves the actual utterance of the repartee or witticism that has occurred to us later as appro- priate to the occasion, and we are constantly liable to misconstrue our own motives of action and to assume as facts the motives we have attributed to others, and from those assumed motives to infer the reality of certain conduct. Indeed, if it is difficult to distinguish inference of the absent from observa- tion of the present, still more hard is it to separate inference of the desirable from memory of the actual. It is for these reasons that memoirs are so frequently distrusted by historians, and that without any reflex- ion on the good faith of the writer. To guard against these dangers, science demands the immediate record of all observations which are to be offered as testi- mony to other workers. Anonymous § 4. — It follows from the above that a good deal Testimony. ^^^^^ j^g known about a witness before his testimony can be received as at all conclusive evidence to any fact. When a statement is made anonymously these tests cannot be applied. Hence, no rational mind attaches any weight to anonymous letters, for all that is known of the writer — that he has some reason for concealing his identity, and generally wishes to injure another person secretly — makes against his good faith, and leaves his competence a matter of speculation. This difficulty of anonymity is very great in his- XII TESTIMONY 161 tory. Unless it can be decided who made a certain statement, and when and where it was made, the testing of the competence of the witness becomes impossible. In modern books these points are usually decided by the title-page, or by other internal evidence, though even that cannot be held to be decisive as to authorship. Eikon Basilike claims throughout to be the work of Charles I, though it is quite certain that it is nothing of the kind. In the case of earlier writings, the question of authorship is often a very difficult one to decide. We all know that, in spite of the evidence of the original title-pages, valiant attempts have been made to prove that Lord Bacon wrote the plays attributed to Shakespeare. Without yielding to this wholesale scepticism as to our great dramatist, yet it is certain that some passages in his works are not by his hand, and only criticism can decide which these are. This criticism is based partly on the evidence of other writers, but mainly on peculiarities of style and of structure brought to light by internal examination of the text itself. By similar tests the approximate dates of the different plays are determined. With ancient documents such a criticism is even more necessary. Of old writings there are usually only copies extant, and these frequently the work of ignorant sci'ibes, full of errors, and often with forged passages interpolated in the text. Such errors and additions can only be eliminated by critical comparison of independent documents, that is, of dfxjuments which are not copies of the same copy. The great principle in deciding independence is that common errors may be assumed to have a common origin. " It is inconceivable that several copyists, independently reproducing an original free from errors, .should all introduce exactly the 162 THE LOGICAL BASES OF EDUCATION chap. same errors ; identity of errors attests community of origin." -"^ § 5. — All corroboration of testimony, indeed, to be of value must be independent. The law recognizes this, and refuses to accept mere hearsay, or inference, or evidence which is shown to be the result of collusion. Cross-examination is the most powerful weapon for detecting falsification, as well as for separating observation from inference and hearsay. When false testimony is manufactured it is apt to be too consistent with itself and more or less inconsistent with known facts. As to the first point, it is a commonplace of human nature that no two persons ever give from memory identical accounts of any event they have witnessed in ordinary life ; thus, too precise an agreement in details between witnesses suggests collusion rather than truth. That corroboration is the most above suspicion which agrees on the main points, but not on all the details of accompanying circumstances. Such concurrence of testimony receives additional strength when it is evident that the different witnesses have conflicting interests, or opposed sympathies, in the matter. "With regard to the second point, it is very unlikely that a manufactured story should take account of all the facts it may be brought into relation with, and it is in testing it by such facts that a cross- examiner shows his skill. Cross-examination is, then, a valuable process of sifting the true from the fake in oral testimony, though it has its own peculiar danger. A question nearly always suggests a certain kind of answer, either by its form, or by the context in which it occurs, or by the manner and tone of the questioner. This suggestion acts unconsciously on the mind of the person questioned and tends to ^ Langlois and Seignobos, oik cit., p. 81. xn TESTIMONY 163 modify the answer given. Some questions, of course, do this more markedly than others, and in the law courts these are ruled out by the judges as "leading questions." Cross-examination cannot, however, be applied to the dead authors of historical documents. We must, therefore, test their accuracy by certain more or less general considerations. Any of their state- ments may be accepted as probably true when the facts are such as to reduce liability to error or deception to a minimum. If the author had no con- ceivable motive to lie, or if the fact asserted was in itself so prominent as to make detection of falsehood certain, or was in opposition to the writer's known prejudices and wishes, then we may accept the record as being as near certain truth as the nature of the case will allow. Most historical testimony, however, itself rests on Tradition. testimony. Our aim is to get back to the record of the original observer ; but this is very often impos- sible. Now, if the testimony is simply passed on through a chain of witnesses, fresh chances of error are introduced at each link, and each successive witness is of less worth than his predecessor ; the longer the chain the weaker the evidence of the last link. This is the case with documents copied one from the other ; each reproduces the errors of its predecessors, and probably introduces some new ones of its own. But this liability of error is enormously increased when the testimony is oral. It is a well- known parlour game, but one which well illustrates our point, to relate secretly a written story to the first of a ring of people, who similarly passes it on to the second, and so on, till the last tells the story aloud, or better still, writes it and reads it aloud. The comparison of this last version with the first M 2 164 THE LOGICAL BASES OF EDUCATION chap. Indepen- dent Corrobora- tion. Inference from Ab- sence of Testimony. will be instructive to those who are disposed to accept all testimony given in good faith as certainly true. When oral tradition passes on from generation to generation the variations become more marked ; yet it is in this legendary form that the earliest history of all peoples comes down to us. Quite evident is it that we are unjustified in accepting any such legends as true ; they may contain some truth, but it is cer- tain they contain much error, and there are no means of sifting the true from the false. As Niebuhr says, a legend is " a mirage produced by an invisible object according to an unknown law of refraction." ^ Legends embody a people's ideas, but cannot be appealed to as records of facts. In other cases, however, the testimony of various witnesses support each other, either directly by recording the same fact independently, or by one set of witnesses testifying to the credibility of others. " In the acceptance of Livingstone's accounts of the countries through which he passed, are not the relevant grounds in part the esteem in which he was held by his contemporaries, coupled with their cre- dentials ; in part the credentials of the societies and other media of record and publication through which his work has in successive stages come to the individual reader ? If I submit myself to the knife of the surgeon, how have I assured myself that he will do the right thing, unless by relying upon a complex tissue of testimony as to the professional ability of a large number of persons ? " ^ § 6. — One last point must be noticed, and that is the danger of inferring from mere absence of testi- mony to non-existence in fact. Even in the present, absence of observation does not prove absence of 1 Quoted by Langlois and Seignobos, op. cit., p. 182. - Ravenshear, oj). cit., pp. 82 — 8.3. XII TESTIMONY 165 existence. Every scientific discovery is, indeed, testi- mony to the contrary. Within the last few years, for instance, several gases whose existence had pre- viously been unsuspected even by scientific experts, have been discovered in the atmosphere. A state- ment should be accepted on negative evidence only when the most careful precautions have been taken to secure the greatest possible completeness of that evidence. Darwin established on negative evidence that certain orchids secrete no nectar, but he only accepted the conclusion when he had observed the plants in question under every variety of cii'cumstance that could affect the result.^ Still more dangerous is it to infer that an event never occurred in the past because no record of it now remains. To render this probable we must have grounds for knowing that no such record ever did exist, and that the event would certainly have been recorded had it occurred. This much narrows tlie scope of the inference. When an author sets out to give a systematic account of a class of facts, we may assume that any fact of that kind which he does not mention did not exist, if that fact was such that it could not have escaped his notice had it existed, and must have been seen by him to be per- tinent to his record. In all otlier cases we can only suspend judgment and confess our ignorance. 1 Cf., Darwin, Fertilization of Orrhiih, pp. 38-39. CHAPTER XIII HYPOTHESES Nature of § 1 . — All reception of facts, whether by observa- Hypotheses. ^.^^ ^^ from testimony, challenges the mind to fit them into a system by relating them to each other and to the totality of knowledge already possessed. The answer to this challenge is a hypothesis, or supposed relation suggested by the facts themselves. The likelihood of such a supposal being true is, of course, largely dependent on the knowledge of the mind that makes it. The savage assumes magic and supernatural agency where the scientist looks for natural causation. All attempts at the organization of facts into knowledge proceeds, however, by way of hypothesis. Even simple recognition of an object is of the nature of hypothesis, though in most cases verification is immediate.^ In ordinary life we are always making hypotheses. I go to catch a train, and I act on the hypothesis that the railway service is uninterrupted ; I sit down to write this chapter guided by the supposition that my mind will follow a certain consecutive train of thought. These are hypotheses, for they are not 1 C/. pp. 146—147. CH. XIII HYPOTHESES 167 certainties. A fog or an accident may dislocate the railway service, and the state of one's health or some powerful disturbing cii'cumstance may render con- secutive thought impossible. Every supposition, then, as to the relations of facts is a hypothesis, whether it is made in ordinary life or in science. But as scientific thought differs from other thought only in its greater precision, the nature and uses of hypotheses will be best studied in connexion with scientific examples. It may be said, indeed, that the special work of science is the testing and verification of hypotheses, for, as Herschel says, " We must never forget it is prin- ciples, not phenomena — the interpretation, not the mere knowledge of facts, — which are the objects of enquiry to the natural philosopher." ^ li 2. — Hypotheses are suggested by facts, but Origin of they may be suggested in an indefinite number of ways. No rules can be given for forming them, and not every enquirer is equally prolific in hypotheses which turn out to be real " guesses at truth." Indeed, the great masters of science are marked above all else by an insight into the reasons of things at which the ordinary searcher after know- ledge can only wonder. In this sense, a great scientist, like a poet, is "born, not made." "The inventor of hypotheses, if pressed to explain his method, must answer as did Zerah Colburn when asked for his mode of instantaneous calculation. When the poor boy had been bothered for some time in this manner, he cried out in a huff, ' God put it into my head, and I can't put it into yours.' " "^ But knowledge also plays a part. A fact which means nothing to the unprepared mind may suggest ' Discourse on Natural Philofophy, § 10. - De Morgan, Budget of Paradoxes, p. 56. Hypotheses. 168 THE LOGICAL BASES OF EDUCATION chap. a far-reaching hypothesis to the mind which is stored with appropriate knowledge and governed by an appropriate interest. Thus the common experiences of falling bodies and of the motions of the moon suggested to Newton the great theory of gravitation. Some discoveries, it is said, are made by accident ; but such accidents only happen to those who are prepared to interpret them. Many crystals had been broken in the world before the accidental fracture of one suggested to the physicist Haiiy the laws of crystallization. As science advances, more and more discoveries are due to attempts to explain small deviations between observed facts and established laws. For example, the planet Uranus was observed to deviate from its calculated path, and to account for such deviations the hypothesis was formed that a hitherto unknown planet revolved round the sun at a still greater distance from it than Uranus. From the observed positions of Uranus the position of this supposed planet was calculated. Search with the telescope in that direction proved the accuracy of the hy- pothesis, and the new planet was named Neptune. In quite recent years an investigation suggested by a small unexplained difference between the weight of nitrogen olitained in the chemical laboratory and the gas which had hitherto been supposed to be pure nitrogen in the atmosphere, led to the dis- covery of argon. Many other instances could be given, but these are sufficient to show that in such cases not even the problem could suggest itself to a mind not conversant with the advances already made in the appropriate branch of knowledge. Hypotheses § 3. — Hypotheses, then, are suggested by facts to and Facts, ^y^^ mind prepared to interpret them. It does not follow, however, that the greater the number of xiii HYPOTHESES 169 facts, the more likely the hypothesis is to be right. The great difficulty always is to pick out the essential from the merely accidental in the whole mass of circumstances. Reality does not give us phenomena already sorted and selected, as the teacher of science presents them to his pupils in the class-i'oom, and the main difference between the successful discoverer and the unsuccessful worker lies just in the power to see what may safely be neglected. But too great a wealth of facts increases this difficulty, for each new fact brings in some fresh attendant circumstances. This is very well put by Dr. Conan Doyle in the Memoirs of Sherlock Holmes. After Mr. Holmes had solved the problem of the Naval Treaty he says : " The principal difficulty . . . lay in the fact of there being too much evidence. What was vital was overlaid and hidden by what was irrelevant. Of all the facts which were pre- sented to us, we had to pick out just those which we deemed to be essential, and then piece them together in their order, so as to reconstruct this very remarkable chain of events." When, indeed, we can get what is called a " pure case," that is, an instance in which only those con- ditions are present which we are investigating, then we can immediately assert the relation from one instance, and that, not as a more or less probable hypothesis, but as a certain truth. In mathematics we can do this, for we entirely determine the operative con- ditions ; our triangles, circles, (fee, are ideal and perfect, and we infer their consequences from single cases. If, for example, we prove that one right- angled triangle is inscribable in a semi-circle, this proof depends only on the ideal nature of our figures, and is consequently applicable to every possible example in so far as it fulfils these 170 THE LOGICAL BASES OF EDUCATION chap. conditions. Thus our generalization is the immediate result of our construction.^ But with concrete objects we cannot do this so thoroughly. In chemistry, it is to some extent possible. So long, for example, as the chemist means by ' water ' nothing but absolutely pure water, what he finds true of one drop he can affirm to be true of every other drop. But the actual water in natui'e contains all kinds of impurities in very various amounts, and it is very difficult to get a pure case even here. It is, then, because nature only presents us with relations in "a tangle of many threads which science has to unravel " " that we must resort to hypotheses. Danger of This resort, however, has its own dangers. Having Bias . c^ t^ guessed at an explanation, the mind naturally wishes to find it true, and thus there is the danger of bias in observing facts which bear on the hypothesis — the attitude of mind expressed by the saying, " if the facts do not agree with the theory, so much the worse for the facts." As Jevons truly says, " it is difficult to find persons who can with perfect fair- ness register facts for and against their own peculiar views. "* Nor is this the only danger. To infer the conse- quences of a hypothesis is generally a task of no great difficulty, whilst the careful testing and verifica- tion of a hypothesis by analysis of facts is laborious and often both difficult and tedious. There is, then, a temptation to be satisfied with the former process, and when this is yielded to, the result is the con- struction of elaborate systems of the universe out of all relation to fact. It is this tendency to substi- tute guess-work for real investigation, and imagination 1 Cf. p. 132. ^ Hobhouse, The Theory of Knoidedrje, p. 328. ^ The Principles of Science, p. 402. XIII HYPOTHESES 171 for observation, which has made the ordinary ' prac- tical man ' so suspicious of what he calls ' theory,' and so fond of contrasting it with ' practice,' and of telling us than " an ounce of fact is worth a ton of theory." No doubt this is so if the ' fact ' is true and the ' theory ' false, but between true theory and real fact there is no opposition at all. § 4. — The formation of a hypothesis, then, must Testing of not be taken as the establishment of a truth. All Hj-potheses. hypotheses must be held subject to revision, to modification, even to rejection, should further know- ledge of fact demand it. For though it is true that one single case is seldom sufficient to establish a hypothesis, it is equally true that one single fact which can be shown to be really in contradiction to a hypothesis overthrows it. Indeed, it is com- paratively seldom that the first hj'pothesis suggested to the mind is the true one. Kepler records that he tried and rejected nineteen hypotheses before he hit on the laws of the motions of the planets round the sun. Similarly, in the discovery of argon two hypotheses were tried and rejected before the third one — that a hitherto unknown element exists in the atmosphere — was found to be verified by the facts. False hypotheses, as well as true ones, are suggested by analogies between the new facts and facts whose relations are already known. It is the extreme complexity of nature which makes a plurality of hypotheses possible. Sometimes several possible hypotheses occur to the mind at once, at other times they occur successively, and, it may be, at long intervals of time. But whenever they occur, scientific hypo- theses are always grounded on some characteristic of the facts : they are never mere ran