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THE PKOVHTCE 
 
 OP 
 
 METHODS OF TEACHING. 
 
 A PROFESSIONAL STUDY. 
 
 BY 
 
 JAMES H. HOOSE, A.M., PH.D., 
 
 PRINCIPAL OF THE STATE NORMAL AND TRAINING 
 SCHOOL, COBTLAND, N. Y., 
 
 Author of "Studies in Articulation," "Notes on the Public School 
 
 System of England and Scotland," " Vindication of the free 
 
 School System," "Practical Suggestions to Americans 
 
 Visiting Europe," etc. t etc. 
 
 WITH AN INTRODUCTION 
 
 BY 
 
 CHARLES W. BENNETT, D.D., 
 
 PROFESSOR OF HISTORY AND LOGIC IN SYRACUSE UNIVERSITY. 
 
 SYRACUSE, N. Y. : 
 
 C. W. BARDEEN, PUBLISHER. 
 1886. 
 
 OF THE 
 
 TIB 17 E RSI IT 
 
COPYRIGHT, 
 
 BY 
 J. H. HOOSE. 
 
TO EDUCATORS 
 
 THIS STUDY IS RESPECTFULLY 
 
 AS A CONTRIBUTION 
 TO THE 
 
 PROFESSION OF TEACHING. 
 
PROFESSIONAL MAXIMS AND DEFINITIONS. 
 
 " In whatever line of study distinction is sought 
 the advantage of good teaching is great." I. TOD- 
 HUNTER. 
 
 " A point which I have incidentally brought for- 
 ward deserves some consideration ; I mean the grad- 
 ual decay in the educational value of a subject as it 
 falls into feebler hands to administer. ' ' IBID. 
 
 11 1 am afraid it must be allowed that no art of 
 equal importance to mankind, has been so little in- 
 vestigated scientifically as the art of teaching." 
 Sm HENRY SUMNER MAINE. 
 
 ' ' A good principle not rightly understood may 
 prove as hurtful as a bad. ' ' MILTON. 
 
 The Investigation of the Principles of Adjusting 
 Subject-matter to the Faculties and capabilities of the 
 learning Mind the Process of discovering Methods 
 of Teaching constitutes the conception of the Sci- 
 ence of Teaching. (See 214.) 
 
 The Investigation of Ways of applying Methods of 
 Teaching in practice The Invention of Modes of 
 Teaching is the conception of the Art of Teaching. 
 (See 215.) 
 
 The Investigation of the Science and the Art of 
 Teaching constitutes the Profession of Teaching. 
 (See 216.) 
 
TO THE PROFESSIONAL STUDENT. 
 
 " The Thoughtful^ person considers carefully, and 
 acts with reflection in regard to the circumstances of 
 a case." C. J. SMITH. 
 
 " When I have a case before me, I can't help think- 
 ing of it beforehand, and perhaps feeling grieved 
 too, afterward, if in any respect I might have con- 
 ducted it better. If I am at dinner, the merriment or 
 the philosophy of the table-talk suggests something, 
 which I put away into a pigeon-hole in my mind for 
 the case ; and when I read, be it poetry or prose, the 
 case hangs over the page like a magnet, and attracts 
 to itself whatever seems to be pertinent or applicable. 
 Success or failure leaves a bright or a dark hue on 
 my mind, often for days. " HORACE MANN, Life, 
 p. 74. 
 
 ' ' There is a certain reaction against the conserva- 
 tism of scientific men at the present time, and the 
 uneducated man believes that chance and genius out- 
 weigh years of the careful accumulation and sifting 
 of facts. . . It is, to say the least, improbable at 
 this stage of the world's progress that an ignorant or a 
 merely practical man should discover a new force in 
 Nature. That dame certainly does not put a pre- 
 mium on ignorance." The Nation, p. 396, No. 704, 
 Dec. 26, 1878. 
 
 ' ' Another error is the over-early and peremptory 
 reduction of knowledge into arts and methods ; from 
 which time commonly sciences receive small or no 
 augmentation. But as young men, when they knit 
 and shape perfectly, do seldom grow to a further 
 
TO THE PROFESSIONAL STUDENT. VII 
 
 stature ; so knowledge, while it is in aphorisms and 
 observations, it is in growth: but when it once is. 
 comprehended in exact methods, it may perchance 
 be further polished and illustrated and accommo- 
 dated for use and practice ; but it increaseth no- 
 more in bulk and substance. 
 
 ' ' Another error which doth succeed that which we 
 last mentioned, is, that after the distribution of par- 
 ticular arts and sciences, men have abandoned univer- 
 sality, or philosophia prima : which cannot but cease 
 and stop all progression. For no perfect discovery 
 can be made upon a flat or level : neither is it possi- 
 ble to discover the more remote and deeper parts of 
 any science, if you stand but upon the level of the 
 same science, and ascend not to a higher science." 
 BACON, Advancement of Learning, pp. 39, 40, Ed. 
 1866, Oxford. 
 
A LIST OF AUTHORS AND WORKS QUOTED IN 
 THIS VOLUME. 
 
 John W. Armstrong, D.D. "On Method" (An 
 Article). 
 
 Thomas Arnold, D.D. "Life and Correspondence," 
 by Arthur P. Stanley, M.A. 
 
 " The Art Journal." Monthly, New York. 
 
 Charles W. Bennett, D.D. " History of the Philos- 
 ophy of Pedagogics." 
 
 Alexander Bain, M.A. Article in " Mind." 
 
 " A Brief English Grammar on a Logical 
 
 Method." 
 
 ' Senses and Intellect." 
 
 Francis Bacon. <l Advancement of Learning." 
 Joseph Bosworth, D.D., F.R.S., F.S.A. "A Com- 
 pendious Anglo-Saxon and English Dictionary." 
 Wilhelm Adolf Becker." Charicles," translated by 
 
 Frederick Metcalfe, M.A. 
 Francis Bowen, LL.D. "A Treatise on Logic; or, 
 
 The Laws of Pure Thought." 
 M. Bautain, Professor at the Sorbonne. "The Art 
 
 of Extempore Speaking." 
 
 Joseph Butler, D.C.L. " The Analogy of Religion." 
 Henry Calderwood, LL. D. , F. R. S. E. < ' On Teaching : 
 Its Ends and Means." 
 
 " Hand-Book of Moral Philosophy." 
 
 Chambers' Encyclopaedia. 
 Henry Coppee, A.M. " Elements of Logic." 
 George Crabb, M.A. "English Synonyms." 
 B. F. Cocker, D.D., LL.D. " The Theistic Concep- 
 tion of the World." 
 
 Henry N. Day, LL.D." Elements of Logic." 
 "Outlines of Ontological Science." 
 
LIST OF AUTHORS AKD WORKS. IX 
 
 Dayies and Peck" Dictionary of Mathematics." 
 
 Epictetus "Discourses translated by George Long." 
 
 English Cyclopaedia Ed. 1867. 
 
 William Fleming, D.D. " The Vocabulary of Phi- 
 losophy. " 
 
 Leo H. Grindon ' ' Life. " 
 
 Thomas Henry Huxley, LL.D., F.R.S. " Lay Ser- 
 mons, Addresses, and Reviews." 
 
 Thomas Hill, LL.D." The True Order of Studies." 
 
 Levi Hedge, LL.D. " Elements of Logick." 
 
 Sir William Hamilton " Metaphysics." 
 
 W. Stanley Jevons, LL.D., M.A., F.R.S. Article in 
 "Mind." 
 
 " The Principles of Science." 
 
 "Elementary Lessons in Logic." 
 
 William James Article in " Mind." 
 
 Dionysius Longinus "On the Sublime," translated 
 by William Smith. 
 
 S. S. Laurie, A.M. " Inaugural Address Chair of 
 Education in University of Edinburgh." 
 
 "Synopsis of Lectures." 
 
 Horace Mann " Life," by his Wife. 
 
 " Mind " A Quarterly London. 
 
 J. D. M. Meiklejohn, M.A. "Inaugural Address, 
 Bell Chair of Education, University of St. 
 Andrews." 
 
 J. Clark Murray" Outlines of Sir William Hamil- 
 ton's Philosophy." 
 
 John Stuart Mill " A System of Logic, Ratiocinative 
 and Inductive ; being a Connected View of the 
 Principles of Evidence and the Method of Scien- 
 tific Investigation." 
 
 Michael Seigneur De Montaigne " Essays." 
 
 Sir Henry Sumner Maine, R.C.S.Q., LL.D., F.R.S. 
 "Village Communities and Miscellanies." 
 
 L. Mariotti "Conferences De Pedagogic." 
 
 Henry Longueville Mansel, B.D. " Metaphysics." 
 
 "Prolegomena Logica." 
 
 James McCosh, LL.D. "Intuitions of the Mind." 
 
X LIST OF AUTHOES AND WOKKS. 
 
 John Ferguson McLennan, M. A., LL.D." " Primi- 
 tive Marriage/' 
 
 J. H. Newman, M. A. "The Idea of A University." 
 
 " The Nation" A Weekly New York. 
 
 David P. Page, M.A." Theory and Practice of 
 Teaching." 
 
 Noah Porter, D.D. " The Human Intellect." 
 
 Jean Paul Frederick Richter "Levana." 
 
 Karl Rosenkranz " The Philosophy of Education, 
 or Pedagogics as a System," translated by Anna 
 C. Brackett. 
 
 Jean Jacques Rousseau " Emilius and Sophia," 4 
 vols. Ed. 1783. London. 
 
 James E. Thorold Rogers, M.A. " Education in 
 Oxford." 
 
 Laurence Sterne " Life and Opinions of Tris tram 
 Shandy." 
 
 Karl Schmidt Quoted by Dr. Bennett. 
 
 Henry Sidgwick, M.A. " The Methods of Ethics." 
 
 C. J. Smith "Synonyms Discriminated." 
 
 Herbert Spencer " Education." 
 
 J. A. Stewart Article in " Mind." 
 
 Sydney Smith "Essays." 
 
 Louis Sol dan " Method and Manner," in Transac- 
 tions of Nat. Ed. Association for 1874. 
 
 James Fitzjames Stephen, Q.C. "Liberty, Equality, 
 Fraternity." 
 
 I. Todhunter, M.A.,F.R.S." The Conflict of Studies, 
 and other Essays." 
 
 Edward B. Tylor, LL.D., F.R.S. " Primitive Cul- 
 ture," 2 volumes. 
 
 William Thompson, D.D. " An Outline of the 
 Necessary Laws of Thought." 
 
 Frederick Ueberweg " System of Logic, and History 
 of Logical Doctrines," translated by Thomas M. 
 Lindsay, M.A., F.R.S.E. 
 
 Varro Quoted by Rousseau. 
 
 William Whewell, D.D. " Novum Organon Reno- 
 vattim." 
 
 Richard Whately " Elements of Logic." 
 
PREFACE. 
 
 THE following STUDY has grown out of one branch 
 of the investigations which have occupied my time 
 more or less during an extended period of years of 
 public labors in teaching. This volume has gradually 
 assumed form for my own classes in professional re- 
 searches. I have been impressed long with the 
 thought that, as teachers and educators of the United 
 States, we are top impatient and superficial in our pro- 
 fessional inquiries. The consequences are, that our 
 theories of teaching rest too heavily upon notions of 
 present expediency and brief experience. As a body 
 we are in full sympathy with the general spirit of the 
 nation we are satisfied with only immediate results. 
 Parents urge us to hasten their children into the 
 mysteries of learning, for soon they must be placed 
 at work, or must enter the advanced schools. The 
 legitimate consequences are at pur doors : the cry 
 of the upper schools is, that candidates for admission 
 are too poorly prepared for the work in store for 
 them ; the experienced men of business complain 
 that the youth are not properly grounded in the prin- 
 ciples underlying their daily routine of labors ; the 
 educated unite in proclaiming the masses uneducated. 
 Thus have we been between these upper and nether 
 millstones, crushed and thrown out if immediate 
 scholarship was not forthcoming, while we are cen- 
 sured in after-years for not having secured more valu- 
 able products for the study expended by the children 
 in their early school-days. 
 
Xll PREFACE. 
 
 In this dilemma we have recollected the wisdom of 
 the Dutch proverb, ''Economy is a great revenue," 
 and the German, " Necessity teaches even the lame 
 to dance," and the Italian, " Even the dog gets bread 
 by wagging his tail," and have endeavored to insure 
 to the pupils a scholarship that is frequently too in- 
 sufficient to be valuable, but which has secured for 
 us an ephemeral reputation and a jeopardized sup- 
 port. Under all the circumstances, perhaps we have 
 done as Avell as we could in our schools. 
 
 Because we have yielded so far to the popular de- 
 mands, we are to-day without a sharply defined and 
 outlined philosophy in our theories of education and 
 of teaching. In our experimentation for sudden 
 fruitage we have apparently forgotten that the most 
 practical thing in existence is a thoroughly matured 
 philosophical theory. Experiments without this 
 theory are at random ; they may be successful 
 probably they will not be. Under a correct theory, 
 experiments can be tested philosophically, and fail- 
 ures reduced to a minimum in number and in degree 
 of disaster. In this respect we can learn much from 
 those nations that have passed their eager and experi- 
 mental age, and are now in their enlightened matur- 
 ity. In our ambition to " make scholars," irrespec- 
 tive of the elements of necessary time and applica- 
 tion, we have overlooked the fact that scholars can 
 never be "made;" they must grow: the faculties 
 become powers only as time and application enucleate 
 them. The active energies of the Profession have 
 been too much absorbed in inventing artificial aids, 
 helps, short-cuts, and "royal roads" to learning, to 
 enter into patient and continued study to discover 
 the philosophical nature of the Profession as an Art 
 and as a Science. It is time for us to turn our atten- 
 tion to find a firmer basis for our practice. This is 
 found only in Philosophy. 
 
 " The beginning of philosophy to him at least who 
 only enters on it in the right way and by the door, is 
 
PREFACE. X11I 
 
 a consciousness of his own weakness and inability 
 about necessary things. " EPICTETUS. 
 
 The work now submitted is an attempt to outline 
 one subject which is included within the conception 
 of a complete Philosophy of Education that of the 
 Province of Methods of Teaching. Although the sub- 
 ject is not first in the order of classification in the 
 general investigation of Education, yet because of its 
 practical nature it has been directly approached. 
 
 The treatment is somewhat out of the ordinary 
 mode of authorship. While I have steadily kept to the 
 line of the investigation, yet I have permitted a wide 
 range of related matter to incorporate itself into the 
 body of the text, even at the risk of seeming to be 
 pedantic. The disadvantages of this apparent hetero- 
 geneity are more than compensated by the greater 
 suggestiveness of the materials admitted. Besides, he 
 who would erect a " liberty- pole" that shall remain 
 permanently standing as a beacon must imbed it deep- 
 ly into the firmest of soil which the past and present 
 have deposited from the attrition of the Ages. 
 
 ' ' The reader will please to take it patiently if he find 
 what has been already printed again printed here. 
 What has been printed is necessary as the bond and 
 bast-matting of what has not been printed ; but the 
 bast-matting must not cover the whole garden, in- 
 stead of merely tying up the trees. But there are 
 two still better excuses. Known rules in education 
 gain new force if new experience verifies them. The 
 author has three times been in the position of trying 
 them upon different children of all ages and talents ; 
 and he now enjoys with his own the pedagogic jus 
 trium liberorum (law of three children) ; and every 
 other person's experience related in this book has been 
 made his own. Secondly, printing-ink now is like 
 sympathetic ink, it becomes as quickly invisible as 
 visible ; wherefore it is good to repeat old thoughts 
 in the newest books, because the old works in which 
 they stand are not read. New translations of many 
 truths, as of foreign standard works, must be given 
 
XIV PREFACE. 
 
 forth every half century. And, indeed, I wish that 
 even old German standard books were turned into 
 new German from time to time, and so could find 
 their way into the circulating libraries. 
 
 " Why are there flower and weed gleanings of 
 every thing, but no wine or corn gleanings of the in- 
 numerable works on education? Why should one 
 single good observation or rule be lost because it is 
 imprisoned in some monstrous folio, or blown away 
 in some single sheet ? For dwarfs and giants, even 
 in books, do not live long. Our age, this balloon, or 
 air- ship, which, by simultaneous lighting of new 
 lamps, and throwing out of old ballast, has constantly 
 mounted higher and higher, might now, I should 
 think, cease to throw out, and rather lovingly en- 
 deavor to collect than to disperse the old. 
 
 " However little so disjointed a collection of 
 thoughts could teach rules, it would yet arouse and 
 sharpen the educational sense, from which they orig- 
 inally sprung 
 
 1 ' Something very different from such a progressive 
 cabinet of noble thoughts, or even from my weak 
 Levana, with her fragments in her arms, is the usual 
 kind of complete system of education which one 
 person after another has written, and will write. 
 It is difficult, I mean the end, not the means. 
 For it is very easy to proceed with book-binder's and 
 bookmaker's paste, and fasten together a thousand 
 selected thoughts with five of your own, especially if 
 you conscientiously remark in the Preface that you 
 have availed yourself of the labors of your predeces- 
 sors, yet make no mention of one in the work itself, 
 but sell such a miniature library in one volume to 
 the reader as a mental fac-simile of yourself. How 
 much better in this case were a hole-maker than a 
 hole-hider ! How much better were it if associated 
 authors (I mean those friendly hundreds who move 
 along one path, uttering precisely the same sound) 
 entirely died out as Humboldt tells us that in the 
 tropical regions there are none of those sociable 
 
PREFACE. XT 
 
 plants which make our forests monotonous, but next 
 each tree a perfectly different one grows. A diary 
 about an ordinary child would be much better than 
 a book upon children by an ordinary writer. Yes, 
 every man's opinion about education would be valu- 
 able if he only wrote what he did not copy. The 
 author, unlike a partner, should always only say 
 'I,' and no other word." JEAN PAUL RICHTER. 
 Levana, Author's Preface, pp. xii-xv, ed. 1863. 
 
 Although Methods of Teaching occupied the atten- 
 tion of some of the Greek philosophers, and have con- 
 tinued before the minds of educators in portions of 
 Europe down to the present date, and have of late 
 engaged thought in the United States, yet they have 
 been confounded generally with Methods of Educa- 
 tion, Modes and Manners of Teaching, rather than 
 apprehended as constituting a province by them- 
 selves. The subject of the inquiry being intricate 
 in its character, it has been no easy task to elaborate 
 it. I have diligently sought nothing but Truth. 
 Should subsequent researches, observations, or ex- 
 perience, from whatever source, reveal aught of error 
 in the positions advanced, no one shall outdo the 
 author in haste to accept the facts as they shall ap- 
 pear. If this investigation, with all of its imperfec- 
 tions of style, matter, and treatment, shall prove as 
 interesting to the Fraternity as it has to the writer, 
 it will serve its purpose. " Indeed, its largeness, 
 its infinity, embarrass me. It is like an attempt to 
 lift the earth : the arms are too short to get hold of it. 
 However, I hope to get hold of a few handfuls." 
 HORACE MANN, Life, p. 87, Boston, 1865. 
 
 <4 1 have long known that no man can apply himself 
 to any worthy subject, either of thought or action, 
 but he will forthwith find it develop into dimensions 
 and qualities of which before he had no conception. 
 If this be true of all subjects worthy of rational at- 
 tention, how extensively true is it of the all-compre- 
 hending subject of education ! This expansion of 
 any object to which our attention is systematically 
 
XVI PREFACE. 
 
 directed may be compared to the opening of a con- 
 tinent upon the eye of an approaching mariner. At 
 first he descries some minute point, just emerging in 
 f he distance, the lofty summit of some mountain. 
 As he approaches, other elevated points seem to rise 
 out of nothing, and stand upon the horizon ; then 
 they are perceived to be connected together ; then 
 hills, cities, towns, plains, rivers, which the eye can- 
 not count for their numbers, nor embrace for their 
 distance, fill up the admiring vision. So it is in ap- 
 proaching any of the intellectual or moral systems 
 which Nature has established. "Ibid. , pp. 84, 85. 
 
 J. H. H. 
 
ANALYTICAL TABLE OF CONTENTS. 
 
 PAGE 
 
 DEDICATION iii 
 
 PROFESSIONAL MAXIMS v 
 
 To THE PROFESSIONAL STUDENT vi-vii 
 
 A LIST OF AUTHORS AND WORKS QUOTED viii-x 
 
 PREFACE xi-xvi 
 
 TABLE OF CONTENTS xvii-xxx 
 
 INTRODUCTION By Dr. Charles W. Bennett xxxi-xxxvii 
 
ANALYTICAL TABLE OF CONTENTS. 
 
 PAET FIRST. 
 
 INTRODUCTORY DISCUSSION On Pedagogics, Education, 
 Teaching, Authorities 
 
 I. ON PEDAGOGICS. 
 
 SECTION PAGE 
 
 1. Pedagogics definition of From Soldan 3 
 
 2. Pedagogics definition of From Rosenkranz 4 
 
 3. Pedagogics definition of From Schmidt, quoted by 
 
 Bennett 4 
 
 II. ON EDUCATION. 
 
 4. Education province of 5 
 
 5. Education province of From Rousseau 5 
 
 6. Education province of From Rosenkranz 6 
 
 7. Education province of From Rogers 9 
 
 8. Education province of From Bain 9 
 
 9. Education province of From Jevons 20 
 
 10. Education province of From Varro 22 
 
 11. Education and Training From Smith 2*2 
 
 12. Education province of From Hill 23 
 
 13. Education province of From Page 24 
 
 14. Education province of From Huxley 26 
 
 15. Education province of From Laurie 30 
 
 16. Education province of From Richter 34 
 
 17. Education vs. Instruction From Richter 42 
 
 18. Education vs. Teaching 43 
 
 19. Education vs. Teaching From Caldenvood 43 
 
ANALYTICAL TABLE OF CONTENTS. Xix 
 III. ON TEACHING. 
 
 SECTION PAGE 
 
 SO. Language represents 44 
 
 21. Teaching meaning of From the Greek 45 
 
 22. Teaching meaning of From the Latin 47 
 
 23. Teaching meaning of From the Anglo-Saxon 49 
 
 24. Methods of Teaching expression determined 50 
 
 25. Authority in Anglo-Saxon Conception of Teaching- 
 
 illustrated From Todhunter 51 
 
 26. Same idea illustrated From Jevors 51 
 
 27. Same idea illustrated From Caldenvood 52 
 
 28. Conception of Teacher limited to Persons 54 
 
 29. Teach, Instruct, Inform defined From Crabb 55 
 
 30. Teach, Instruct, Inform defined From Smith 57 
 
 IV. ON AUTHORITIES. 
 
 31. Authority denned From Crabb 60 
 
 32. Authority defined From Smith 60 
 
 33. Authority, Consent, Assent, Belief defined. 
 
 From Fleming 61 
 
 34. Authority general discussion From Bacon 69 
 
 35 V. RECAPITULATION 77 
 
 PART SECOND. 
 
 ON METHOD IN GENERAL. 
 
 36. Method defined 79 
 
 37. Method refers to subject-matter 80 
 
 38. Methods of Business customary use of Expression 80 
 
 39. Methods of Business illustrated. .From li The Nation " 81 
 
 40. Three distinct Elements in an Investigation (1) Object- 
 
 matter, the end ; (2) Way in which faculties pro- 
 ceed ; (3) State of Investigator 82 
 
 41. I. Object-matter of Study considered ends in System. 83 
 
 42. II. Ways of Procedure of Mind considered Are modes 
 
 of method 85 
 
 43. (a) Analysis defined 85 
 
XX ANALYTICAL TABLE OF CONTENTS. 
 
 SECTION PAGE 
 
 44. Analysis vs. Separation 86 
 
 45. (b) Synthesis defined 87 
 
 46. Synthesis and Definition 87 
 
 47. Abstraction defined 87 
 
 48. Analysis and Synthesis are parts of same Method. 
 
 From Hamilton 87 
 
 49. Synthesis vs. Reconstruction 88 
 
 50. (c) Generalization defined 89 
 
 51. (d) Classification defined 89 
 
 52. (e) Induction defined 90 
 
 53. Induction vs. Interpretation 90 
 
 54. Induction vs. Repetition 92 
 
 55. (/) Deduction defined 93 
 
 56. HI. State, or Ways of Investigator give rise to Manner. 93 
 
 57. Manner Systematized is Mode 94 
 
 PART THIRD. 
 
 I. ON THE THEORY OF METHODS OP TEACHING. 
 
 58. IntroductionNeed of Better Methods From Maine 96 
 
 59. Theory of Methods of Teaching hased upon Psychology 
 
 and nature of subject-matter 98 
 
 60. Nature of Faculty defined 98 
 
 61. Character of Faculty defined. 98 
 
 62. Psychology defined 98 
 
 63. Psychology province of From Stewart 98 
 
 64. Objects and Limitations of Present Investigation 101 
 
 65. Knowing forms of knowledge From Ueberweg 102 
 
 66. Form and Matter From Thompson 103 
 
 67. Form and Matter From Jevons 105 
 
 68. Form and Matter From McCosh 105 
 
 69. Form and Matter From Newman 107 
 
 70. Form of Matter (a) Illustrated. . .From "The Nation 11 
 
 (o) Illustrated From Rousseau 107 
 
 71. Knowledge, Learning, Erudition defined.. From Crabb 108 
 
ANALYTICAL TABLE OF CONTENTS. Xxi 
 
 SECTION PAGE 
 
 72. Knowledge defined From Day 110 
 
 73. Knowledge defined From Day 111 
 
 74. Knowledge aim of, is truth From Ueberweg 112 
 
 75. Knowledge stages of, in acquiring : (1) Source of re- 
 
 sides in mind ; (2) Rational way of procedure is 
 under Will ; (3) End of activity is Knowledge 113 
 
 76. Teaching defined 114 
 
 77. Self-Informed is Self-educated defined and amplified. . . 114 
 
 78. Teachers are a Necessity to Learners Teacher, what is 
 
 Adjust, defined From Smith 115 
 
 79. Teaching defined 116 
 
 80. Teacher duties of, to analyze and separate subject- 
 
 matter 117 
 
 81. Teacher duty to note both form and matter of knowl- 
 
 edge in mind of learner 117 
 
 82. How to Teach ? is great question 118 
 
 83. Teaching Conception of, requires examination of : (1) 
 
 Mind of learner learner ; (2) Mind of teacher- 
 teacher ; (3) Things to be learned subject-matter. . 118 
 
 84. Teaching Conception of, resolves itself into: (1) Teacher 
 
 must know subject-matter ; (2) Teacher must know 
 mind ; (3) Teacher must know Way in which mind 
 proceeds when learning Constitute Profession of 
 Teaching 119 
 
 85. Recapitulation of 82, 83 120 
 
 86. PROVINCE OF METHODS OF TEACHING that of Princi- 
 
 ples of Adaptation of Subject-matter to Faculties of 
 Mind 121 
 
 87. Principle defined From Fleming 122 
 
 88. Principle defined. . . From Smith 122 
 
 89. Methods of Teaching require system of subject-matter. 123 
 
 90. Systems and Methods compared 123 
 
 91. Province of Methods of Teaching, not that of Pedagogics 
 
 or Ethology 125 
 
 92. Ethics defined . . .-. From Sidgwick 125 
 
 93. Teaching is Handmaid of Education. 126 
 
 94. Methods of Pedagogics, Scope of equivalent to Meth- 
 
 ods of Education 127 
 
XX11 ANALYTICAL TABLE OF CONTENTS. 
 
 SECTION PAGE 
 
 95. Methodick of Education defined. (1) Educator must be 
 
 a Guide Processes : Analytic, Synthetic, Inductive. 
 (2) Educator must guide Morals Methodick of Edu- 
 cation is Methodology, Way, Procedure Method- 
 ick rests on the Will. Departments of particu- 
 lar methods From Laurie 129 
 
 96. Methods of Education regard Growth of Mind as an 
 
 End They consider : (1) What Subjects to be 
 Taught purpose of. (2) How to Instruct for Right 
 Judgments. Answers : To (1) Doctrine of the Real 
 To (2) Formal Discipline From Laurie 131 
 
 97. Growth and Development contrasted... From Spencer 132 
 Growth defined From Smith 132 
 
 98. Methods of Teaching regard Growth of Mind as a Means 135 
 
 99. Methods of Teaching Examined in their Relation to 
 
 " How to Study " 136 
 
 100. Methods of Teaching do not distinguish between Truth 
 
 and Error of Subject-matter taught 138 
 
 101. Methods of Teaching assume innate Activity of Mind- 
 
 Examined in relation to " Waking up Mind" Con- 
 ception of " Variety" examined 139 
 
 102. Attention defined and examined From Richter 139 
 
 103. Excite, Awaken, Rouse, Incite, Stimulate defined. 
 
 From Smith 141 
 
 104. Methods of Teaching not responsible for Form of 
 
 Knowledge in Mind of Learner 142 
 
 105. " Development of Ideas 11 analyzed 144 
 
 1l06. Thorough Teaching defined 144 
 
 107. Develop, Unfold, Unravel defined From Smith 145 
 
 108. Methods of Teaching must regard Procedure of Facul- 
 
 ties when learning. . 148 
 
 109. Methods of Discovery and of Instruction. From Jevons 149 
 
 110. Methods of Teaching must respect Inherited "Cast of 
 
 Mind" 160 
 
 111. Methods of Teaching difficult to suit, because of evan- 
 
 escence of psychological phenomena 162 
 
 112. Methods of Teaching in present state of Psychology, 
 
 not absolutely invariable 163 
 
ANALYTICAL TABLE OF CONTENTS, xxiii 
 
 SECTION PAGE 
 
 113. Methods of Teaching examined in relation to " Class- 
 
 Drill" 164 
 
 114. Methods of Teaching do not regard Individuality of 
 
 Teacher 16 5 
 
 115. Manner Examined and defined 165 
 
 116. Teacher can have "His Manner," not "His Method". 166 
 
 117. Methods of Teaching are not method in general . . 166 
 
 118. Method and Manner contrasted From Soldau 167 
 
 119. Mode of Teaching defined 168 
 
 120. Methods, Modes, Manners compared 168 
 
 121. In Perfect Knowledge, all Teachers would Teach alike 
 
 in their Modes 169 
 
 122. Methods of Teaching Misconception of occasions Mis- 
 
 use of the Expression 170 
 
 123. Mode, Manner defined From Smith 
 
 Mode, Manner used From " The Nation" 171 
 
 124. System, Method defined From Smith 
 
 System defined From Jevons 172 
 
 125. Method, Procedure defined From Mariotti 172 
 
 126. Method, Mode defined From Armstrong 173 
 
 127. Principle, Law, Rule defined From Armstrong 173 
 
 128. Method, Mode, Manner difference, (a) Illustrated by 
 
 Figure of a Bridge; (ft) Illustrated by Water as 
 buoying-up power ; (c) Illustrated by Gravity, Ani- 
 mal Power, Steam ; (tf) Illustrated by Horse Power, 
 Carriage, Landau v 174 
 
 129. Mode properly used From Page 175 
 
 130. Mode of Teaching illustrated From Page 175 
 
 131. Method improperly used From Rousseau 176 
 
 132. Method Socratic Mode illustrated. . .From Epictetus 178 
 
 133. Methods of Teaching for Modes and Manners Cri- 
 
 tique upon From Meiklcjohn 184 
 
 134. "Methods of Nature" Conception of, Examined 
 
 Illustration From Rousseau 
 
 Illustration From McLennan 188 
 
 135. Artificial Conception of, examined 190 
 
 136. Natural, in general, is not Natural in the Individual.. . . 192 
 
 137. Natural defined ... From Butler 193 
 
XXiv ANALYTICAL TABLE OF CONTENTS. 
 
 SECTION PAGE 
 
 138. Nature defined From Cocker 193 
 
 139. Nature Law of defined From Cocker 194 
 
 140. Nature Universality of Order of defined not Inva- 
 
 riable From Cocker 194 
 
 141. Nature defined From Fleming 196 
 
 142. Natural Instance of From Epictetus 200 
 
 143. Natural and Artificial Education discriminated. 
 
 From Huxley 202 
 
 II. ON THE PRACTICE or METHODS or TEACHING. 
 (A) On the Knowing Faculties of the Mind. 
 
 144. Purpose of this Division is to submit a Basis for Meth- 
 
 ods of Teaching 203 
 
 145. Psychological Phenomena classified. (1) Phenomena 
 
 of Cognitions ; (2) Phenomena of Feelings ; (3) Phe- 
 nomena of Conations From Hamilton 204 
 
 146. Consciousness defined. Involves : (1) A Knowing Sub- 
 
 ject, the Ego ; (2) A Recognized Modification of 
 Ego ; (3) A Recognition by the Subject of the Modi- 
 fication (a) From Hamilton 
 
 (b) From James 204 
 
 147. I. Presentative Faculties From Hamilton 205 
 
 148. II. Memory Faculty of From Hamilton 207 
 
 149. III. Reproductive Faculty From Hamilton 207 
 
 150. IV. Imagination From Hamilton 208 
 
 151 . -V. Elaborative Faculty From Hamilton 208 
 
 152. VI. Regulative Faculty. . .! From Hamilton 209 
 
 153. Recapitulation of Cognitive Faculties. .From Hamilton 210 
 
 154. Will, the Principal Faculty in acquiring Knowledge. 
 
 From Richter 211 
 
 155. Will same idea From Laurie 213 
 
 156. Will same idea From Cocker 213 
 
 157. Imagination (a) The Poetic From Porter 214 
 
 158. Imagination 0) The Philosophic From Porter 214 
 
 159. Imagination (c) The Ethical Uses of From Porter 216 
 
 160. Imagination (d} Relation to Religious Faith. 
 
 From Porter 217 
 
 161. Imagination is Over-developed in the Youth of India. 
 
 From Maine 218 
 
ANALYTICAL TABLE OF CONTENTS. XXV 
 
 SECTION PAGE 
 
 105. Memory Modification defined 219 
 
 163. Memory Active Childhood need not Understand all 
 
 it Learns From Arnold 219 
 
 164. Memory, Imagination, and Hope are the.same Faculty. 
 
 From Hansel 220 
 
 165. Memory Permanence of From Grindon 221 
 
 166. Memory Limited in its Growth From Richter 224 
 
 167. Memory Eetains best from Contrasts ... From Kichter 226 
 
 168. Memory a Goddess From Montaigne 227 
 
 169. Memory a Personal Reminiscence From Montaigne 227 
 
 170. Memory and " Cram" From Maine 235 
 
 171. Memory and " Cram" From Todhunter 240 
 
 172. Memory and "Cram," and Thinking Faculties A 
 
 Question-Begging Epithet; Analysis of "Cram;" 
 "Good Cram" and ; 'Bad Cram" defined ; Dulness 
 and 'Cram;" Book- work and "Cram;" Exami- 
 nations are Tests ; Repetition in Teaching Neces- 
 sary ; Purpose of "Good Cramming;" Intense 
 u Cramming" is Real Education; Remarks of 
 Home-Secretary Cross ; Mr. Cross Answered ; Slow 
 and Deliberate Teaching compared with Rapid; 
 Object of School ; Purpose of Liberal Education ; 
 Not Desirable to Remember things Taught in 
 School ; Source of Error not in Memory, but in 
 Distinguishing between Form and Matter; Reten- 
 tion ; Barristers must Forget ; Work of Teachers 
 not to make Philosophers, and Scholars, and Ge- 
 niusesthese are Born ; Business of Educator is 
 " to Cram" From Jevons 241 
 
 173. Knowing, Act of defined From Ueberweg 257 
 
 174. Knowledge defined From Ueberweg 258 
 
 175. Human Thought determined From Ueberweg 258 
 
 176. Knowledge Activity necessary to From Ueberweg 258 
 
 177. Knowledge defined From Calderwood 259 
 
 178. Thought Difference between, and other Phenomena 
 
 of Mind Intuition, Conception, Concept, Con- 
 sciousness, Representation, Perception, Imagina- 
 tion From Mansel 259 
 
XXVI ANALYTICAL TABLE OF CONTENTS. 
 
 SECTION PAGE 
 
 179. Thought defined From Mansel 265 
 
 180. Thought Faculty of defined Judgment ; Apprehen- 
 
 sion ; Conception is a Psychological Judgment ; 
 Conceiving ; Language is a sign of Intuitions ; Ab- 
 straction; Concept; Common Language and Com- 
 mon Thought ; Identity ; Reasoning defined ; Syl- 
 logism ; Recapitulation From Mansel 266 
 
 181. Powers Mental, employed in acquiring Knowledge- 
 
 Discrimination; Power of Detecting Identity; Power 
 of Retention From Jevons 274 
 
 182. Identity and Difference Laws of. (1) Law of Identity; 
 
 (2) Law of Contradiction ; (3) Law of Duality. 
 
 From Jevons 277 
 
 183. Thought First Gradation of, is the Formation of Judg- 
 
 mentProposition ; Sentence ; Concept ; Conceiv- 
 ing ; Reasoning ; Perception ; Regulative Faculty, 
 or Faculty of Intuition ; Being ; Existence ; Matter 
 of Thought ; Analysis ; Abstraction ; Attention ; 
 Comparison; Synthesis; Subject; Predicate; Terms 
 of a Proposition ; Copula From Day 279 
 
 184. Thought Second Gradation of, is the Formation of 
 
 Concept Judgments ; Forming Concepts ; Terms ; 
 Concept in Comprehension ; Conception; Faculty; 
 Act ; Product ; Law of Identity ; Base ; Relative 
 Cognition ; Concepts differ from Judgments ; Con- 
 cept not Expressed ; Concept implies Judgments ; 
 Base of Concept; Concepts are Products of Thought; 
 Thought aggregated by single Words From Day 288 
 
 185. Thought Third Gradation of, is Reasoning Reason- 
 
 ing derived from Judgment ; Reasoning not a Con- 
 clusion ; Reasoning defined ; Ratiocination ; Dis- 
 course ; Discursive ; Argumentation ; Inference 
 or Illation ; Conclusion ; Syllogism ; Parts of Rea- 
 soning ; Antecedent ; Consequent ; Immediate Rea- 
 soning ; Mediate Reasoning -. From Day 296 
 
 186. Reason has no Relation to Body From Grindon 301 
 
 187. Thinking is Conversation of Soul with itself. 
 
 From Mansel 301 
 
ANALYTICAL TABLE OF CONTENTS. XXV11 
 
 (B) On the Nature of Subject-Matter. 
 
 SECTION PAGE 
 
 188. Methods of Teaching Teacher to discover, must know 
 
 Mind and Nature of Subject-matter 302 
 
 189. Subject-matterdefined 302 
 
 190. Subject-matter Material Exists outside of Mind 302 
 
 191. Subject-matter Immaterial Created wholly by Mind. 302 
 
 192. Object Teaching Conception of, Analyzed 303 
 
 193. Object Teaching when Valuable . . 304 
 
 194. Object Teaching when Possible 304 
 
 195. Illustrative Teaching defined 304 
 
 196. Ideas Succeed each other according to Laws of Asso- 
 
 ciation 305 
 
 197. Illustrations defined, by Illustrations defin- 
 ed From Smith 
 
 Analogy defined From Smith 
 
 Analogy and Induction Difference From Fleming 305 
 
 198. Illustrations Example of From Sterne 306 
 
 199. Illustrative Teaching Analogous Extension of Mean- 
 
 ing of Words From Jevons 309 
 
 200. Illustration differs from Example 309 
 
 201. Illustrative Teaching is Objective Teaching 309 
 
 202. Illustrative Teaching Conception of, misunderstood 
 
 for Object Teaching, has occasioned abuse of the 
 Expression 310 
 
 203. Mathematics cannot be taught by Object Teaching 
 
 only Illustratively 310 
 
 204. Mathematics Nature of Arithmetical Numbers . 
 
 From Jevons 
 Number defined From Davies and Peck 312 
 
 205. Mathematical Judgments on Nature of . .From Mansel 314 
 
 206. Mathematical Judgments on Arithmetic, Geometry. 
 
 From Eng. Cycl. 324 
 
 207. Mathematical Judgments on Numeration . 
 
 From Whewell 326 
 
 208. Object Teaching Branches that can be Taught in this 
 
 way 327 
 
 209. Objects when their Value ceases in Teaching and 
 
 Learning 328 
 
 210. Object Teaching must be succeeded by Thought 329 
 
XXY111 ANALYTICAL TABLE OF CONTENTS. 
 (C) On Discovering Methods of Teaching Special Subjects. 
 
 SECTION PAGE 
 
 211. System of Subject-matter must be constructed by 
 
 Teacher Principle of Adaptation must be Discov- 
 ered for Method of Teaching 330 
 
 212. Addition on Discovering the Method of Teaching it. . . 331 
 
 (1) On the Nature of the Subject-matter 331 
 
 (2) On the Faculties primarily active in Learning Ad- 
 
 dition 332 
 
 (3) On Inventing the Mode of Teaching Addition 333 
 
 213. Mode and Manner of Teaching Addition Recapitu- 
 
 lated 333 
 
 214. SCIENCE OP TEACHING denned 334 
 
 215. ART OF TEACHING denned 334 
 
 216. PROFESSION OF TEACHING denned 334 
 
 HI. CONCLUDING REFLECTIONS. 
 
 217. To Teach Qualifications Requisite 335 
 
 218. Growth Evil effects of missing Opportunities for. 
 
 From Meikle John 335 
 
 219. Teacher Should be a Learner From Arnold 336 
 
 220. Teacher Value of Common-Sense From Sidgwick 338 
 
 221. Teacher Value of Common-Sense for.. From Whately 339 
 
 222. Teacher Best Talent for, is Judging Right upon Im- 
 
 perfect Materials From Stephen 344 
 
 223. Difference between Theory and Practice of Degree 
 
 only, not of Kind From Mansel 344 
 
 224. Science of Human Nature Possible From Mill 344 
 
APPENDIX OF QUOTATIONS. 
 
 SECTION PAGE 
 
 225. A. On METHOD. 
 
 1. From Hedge 346 
 
 2. From Coppee 347 
 
 3. From Day 348 
 
 4. From Fleming 350 
 
 5. From Bain 356 
 
 6. FromWhewell. 357 
 
 7. From Bowen 361 
 
 8. From Day 368 
 
 9. From Comte 373 
 
 226. B. On SYSTEM. 
 
 1. From Fleming 376 
 
 227. C. On ANALYSIS. 
 
 1. From Fleming 380 
 
 228. D. On SYNTHESIS. 
 
 1. From Fleming 383 
 
 229. E. On DEFINITION. 
 
 1. From Fleming 385 
 
 2. From Mill 389 
 
 230. F. On ABSTRACTION. 
 
 1. From Fleming 390 
 
 231. G. On GENERALIZATION. 
 
 1. From Fleming... 392 
 
 2. From Jevone 395 
 
 232. H. On CLASSIFICATION. 
 
 1 . From Fleming 398 
 
 2. From Jevons . . 401 
 
 233. I. On INDUCTION. 
 
 1. From Smith 413 
 
 2. From Day 415 
 
XXX APPENDIX OF QUOTATIONS. 
 
 SECTION TAGZ 
 
 3. From Fleming 416 
 
 4. From Whewell 422 
 
 5. From Eng. Cyclop 423 
 
 6. From Jevons 434 
 
 7. From Mill 451 
 
 234. J. On INTERPRETATION. 
 
 1. From Davies and Peck 473 
 
 2. From Smith 477 
 
 235. K. On DEDUCTION, 
 
 1. From Fleming 478 
 
 2. From Day 480 
 
 3. From Bowen 482 
 
 4. From Hedge , 484 
 
INTRODUCTION. 
 
 BY 
 
 CHARLES W. BENNETT, D.D. 
 
THE subject of education is each year assum- 
 ing growing prominence. It cannot be justly 
 charged that the Eastern, Middle, and Western 
 States of the American Union have been indiffer- 
 ent to the claims of their citizens to enjoy op- 
 portunities of instruction and enlightenment. 
 Nearly all of them have made generous provi- 
 sions for primary and intermediate instruction, 
 and in some have been elaborated complete sys- 
 tems of education from lowest to highest. 
 
 Nor has the question of Training Schools for 
 teachers been neglected. Good general educa- 
 tion presupposes good schools, and good schools 
 presupposes good teachers ; hence that State 
 which fails to provide for good teachers exhibits 
 a plain lack of practical wisdom. These Nor- 
 mal or Training Schools have been subjected to- 
 severe criticism, both as to the scope and charac- 
 ter of their work, as well as the products which 
 they have yielded to the State. Many able 
 thinkers have believed that the nature and prov- 
 ince of the instruction in these State schools 
 was not sufficiently definitive to warrant their 
 independent existence and exceptional support ; 
 
XXXIV INTRODUCTION. 
 
 that the Common Schools, Academies, and Sem- 
 inaries of the State were doing essentially all 
 which was accomplished by the expensive ma- 
 chinery of Normal Schools ; that the conception 
 of the use and design of Teachers 7 Training 
 Schools, as entertained by those who had inaug- 
 urated and managed them, was essentially erro- 
 neous ; that they had failed to elevate teaching 
 to the dignity, honor, and emoluments of a pro- 
 fession ; that a large fraction of those who had 
 been thus educated chiefly at the public expense 
 had not rendered to the State adequate remun- 
 eration in superior service and skilled labor. 
 Doubtless some of the writing and speaking on 
 this subject has been hypercritical ; since the 
 difficulties of the educational problem have not 
 been sufficiently appreciated, and the amount 
 and quality of the hard work done by those who 
 have had charge of these Training Schools have 
 not been properly recognized. Nevertheless, 
 that the expectations of the best friends of edu- 
 cation have not been fully satisfied must be 
 frankly acknowledged. Too much time and en- 
 ergy have been consumed in the mere prelimin- 
 aries to strictly Training Schools. The require- 
 ments for admission have been too low. The 
 three great departments of Psychology, History 
 of Pedagogics, and Methodology and Training, 
 which should occupy by far the largest portion 
 of the course of study, have been in too many 
 instances but meagrely examined, and in most 
 of these schools the historical examination has 
 scarcely been touched upon at all. 
 
ItfTKODUCTION. XXXV 
 
 We, therefore, welcome the present work of 
 Dr. Hoose as a promise that a better day for 
 Normal School Training is dawning. It shows 
 that at least one Chief in these Schools is fully 
 awake to the necessity of careful and exact 
 thinking on one of the few subjects of study 
 which legitimately belong to Training Schools. 
 The importance of the branch of education here 
 treated can hardly be over-emphasized. Lack 
 of clearness here brings obscurity and partial 
 failure into the whole career of the teacher. He 
 may, by long experimentation with mind, cor- 
 rect some mistakes ; but unless the principle 
 which underlies Method is fully understood in 
 the outset, it is difficult to compute the mischief 
 which may ensue. 
 
 The work which is here presented professes to 
 reveal and discuss this principle. As stated in 
 his preface, during the ten years of his supervi- 
 sion of one of the largest Training Schools of 
 New York, the author has been continually study- 
 ing, and yearly developing this subject before the 
 classes which have been under his tuition. Like 
 most valuable products it has, therefore, been a 
 growth from the experience and close observa- 
 tion of an eminently practical teacher. This 
 should greatly enhance its value. In the direct- 
 ness, brevity, and pertinence of statement and il- 
 lustration, the author seems to have the wants 
 of his classes ever distinctly before him. Evi- 
 dently he is no recluse thinker, but a busy man 
 among busy men and women who need his help, 
 and whom he wants to help. 
 
XXXY1 INTRODUCTION. 
 
 The extended quotations from so many emi- 
 nent thinkers and educators may, in the opinion 
 of some, smack a little of pedantry. But since 
 one great object of such a work is to stimulate 
 to further research, as well as to instruct the un- 
 initiated, these references to and quotations 
 from the works of philosophic thinkers must be 
 regarded not only pertinent, but invaluable. 
 Moreover, the assumption of originality may be 
 cheap with those of slender information, but the 
 real student becomes quite content at times to 
 sit at the feet of those giants who have wrestled 
 with the hard problems of education, and endeav- 
 or to reduce their thoughts to practical and effi- 
 cient uses. He usually does most for his pupils 
 and readers who opens up to them the literature 
 of his subject, and directs them to the sources of 
 his own inspiration and quickening. The teacher 
 in Training Schools especially must ever consider 
 that he is dealing with minds of greater or less 
 maturity, who are, with himself, desirous to go 
 to the fountain-heads of knowledge and truth, 
 and there drink for themselves. While this 
 course of procedure may prove terribly iconoclas- 
 tic to those who may be worshipping the false 
 idol of originality, it will always be most help- 
 ful to the real lover of truth, and become most 
 beneficent to our fellow-workers. 
 
 It is highly probable that some positions of the 
 author will not pass unchallenged. Some read- 
 ers may be inclined to believe that his boldness 
 sometimes verges on rashness, and that in some 
 points he has not fully established what he 
 
INTRODUCTION. XXXYli 
 
 claims : but in all the work there breathes the 
 spirit of honest conviction ; and honest thinking 
 cannot long remain wrong thinking after the 
 wrong has been pointed out. If by frank and 
 generous criticism it shall be shown that the au- 
 thor has inadvertently been led to make any mis- 
 statements of fact or principle, these corrections 
 will probably be thankfully received, and can be 
 easily incorporated into the text of some future 
 edition. 
 
 The subject here presented by Dr. Hoose is 
 specially worthy of investigation and attention 
 on the part of the directors of Training Schools ; 
 indeed, none are of greater value. Hence we 
 must believe that this work will be cordially wel- 
 comed by the teachers of Normal Schools, by 
 the graduating classes of these schools, and by 
 all thorough teachers, as supplying a long-felt 
 need. 
 
 CHAS. W. BENNETT. 
 SYRACUSE UNIVERSITY, January 1, 1879. 
 
PAET FIEST. 
 
 1-35. 
 
 INTRODUCTORY DISCUSSION. 
 
 I. ON PEDAGOGICS, . . " . . g 1-3. 
 
 II. ON EDUCATION, . . . 4-19. 
 
 III. ON TEACHING, . . . 20-30. 
 
 IV. ON AUTHORITIES, . . . 31-34. 
 
 V. RECAPITULATION, .... 35. 
 
U1TIVEESIT7 
 
 ON PEDAGOGICS. 
 
 1. "By Pedagogics we mean the science of 
 the realization of the human rational potentiality 
 into actuality. In the human mind lie certain 
 capabilities which do not manifest themselves 
 unless drawn out by external influence or an 
 inherent principle of development. Although 
 there be no development of these faculties, they 
 may still exist, but are not manifest. They re- 
 main in a dormant or latent state, they exist as 
 possibilities, or in potentia. By an educating 
 or developing influence these latent capabilities 
 become manifest, and from the state of potenti- 
 ality pass over to the state of actuality. To use 
 an illustration, we may say that the seed makes 
 the growth of the plant possible : it contains the 
 possibility of the plant. Hence, to express the 
 same thought in a different way : The seed is the 
 potentiality of the plant ; sun and soil will trans- 
 form this potentiality into actuality, the plant it- 
 self. All actual, finite existence must have passed 
 through the stage of potential existence. Peda- 
 gogics is the science of the transition of man 
 from his natural potentiality to actuality." 
 (Proceedings of the National Educational Asso- 
 
4 ON PEDAGOGICS. 
 
 elation, 1874, p. 246. Paper by Prof. Louis 
 Soldan.) 
 
 2. " Pedagogics as a science must (1) unfold 
 the general idea of Education ; (2) must exhibit 
 the particular phases into which the general work 
 of Education divides itself, and (3) must describe 
 the particular standpoint upon which the general 
 idea realizes itself, or should become real in its 
 special processes at any particular time. 
 
 It busies itself with developing a priori the idea 
 of Education in the universality and necessity of 
 that idea. . . . Pedagogics as an art is the 
 concrete individualizing of this abstract idea in 
 any given case. . . . The idea of Pedagog- 
 ics in general must distinguish, (1) The nature 
 of Education in general ; (2) Its form ; (3) Its 
 limits. ' ' (Rosenkranz, Pedagogics as a System, 
 pp. 7-9, ed. 1873. Translated by Anna C. 
 Brackett.) 
 
 3. " Pedagogics is the science and art of so 
 developing, by means of conscious influence on 
 the physical, intellectual, and moral powers of 
 man, the ideas of truth, freedom, and love, that 
 lie at the foundation of his God-derived nature, 
 that he can meet spontaneously, and indepen- 
 dently, his human responsibilities. ' ' (Schmidt, 
 Geschichte der Erziehung, p. 1, quoted by Dr. 
 C. W. Bennett in History of the Philosophy of 
 Pedagogies, p. 2, a paper published by E. Stei- 
 ger, New York, 1877.) 
 
II. 
 
 ON EDUCATION. 
 
 4. Man lives upon the earth as a member of a 
 family, as a member of society, as a member of 
 the state, and as an individual. These ethical re- 
 lations and the natural surroundings constitute 
 the environment which encircle and mould him. 
 Whatever influence this environment has upon 
 his native capacities and faculties to occasion 
 them to grow into powers, or habits, is called 
 Education. 
 
 5. " We are born weak, we have need of help ; 
 we are born destitute of every thing, we stand 
 in need of assistance ; we are born stupid, we 
 have need of understanding. All that we are not 
 possessed of at our birth, and which we require 
 when grown up, is bestowed on us by education. 
 This education we receive from nature, from 
 men, or from circumstances. The constitutional 
 exertion of our organs and faculties is the educa- 
 tion of nature ; the uses we are taught to make 
 of that exertion constitute the education given 
 us by men ; and in the acquisitions made by our 
 own experience, on the objects that surround us, 
 consists our education from circumstances. We 
 are formed, therefore, by three kinds of masters* 
 
6 02^ EDUCATION. 
 
 The pupil, in whom the effects of their different 
 lessons are contradictory, is badly educated, and 
 can never be consistent with himself. He, in 
 whom they are perfectly consonant, and always 
 tend to the same point, hath only attained the 
 end of a complete education. His life and ac- 
 tions demonstrate this, and that he alone is well 
 brought up. Of these three different kinds of 
 education, that of nature depends not on our- 
 selves ; and but in a certain degree that of cir- 
 cumstances : the third, which belongs to men, is 
 that only we have in our power : and even of 
 this we are masters only in imagination ; for who 
 can flatter himself he will be able entirely to gov- 
 ern the discourse and actions of those who are 
 about a child ?" (Rousseau, Emilius and So- 
 phia, vol. 1, pp. 4, 5. London, 4 vols., 1783.) 
 6. " Education is the influencing of man by 
 man, and it has for its end to lead him to actual- 
 ize himself through his own efforts. 
 It is the nature of education only to assist in the 
 producing of that which the subject would strive 
 most earnestly to develop for himself if he had a 
 clear idea of himself. . . . Man, therefore, 
 is the only fit subject for education. We often 
 speak, it is true, of the education of plants and 
 animals ; but even when we do so, we apply, 
 unconsciously perhaps, other expressions, as * rais- 
 ing ' and ' training, ' in order to distinguish these. 
 The general form of Education is determined by 
 the nature of the mind, that it really is nothing 
 but what it makes itself to be. The mind is (1) 
 immediate (or potential), but (2) it must 
 
OX EDUCATION. 7 
 
 estrange itself from itself as it were, so that it 
 may place itself over against itself as a special 
 object of attention ; (3) this estrangement is fin- 
 ally removed through a further acquaintance 
 with the object. . . . Education cannot 
 create : it can only help to develop to reality the 
 previously existent possibility ; it can only help 
 to bring forth to light the hidden life. 
 Education seeks to transform every particular 
 condition so that it shall no longer seem strange 
 to the mind or in any wise foreign to its own 
 nature. This identity of consciousness, and the 
 special character of any thing done or endured by 
 it, we call Habit (habitual conduct or behavior). 
 It conditions formally all progress ; for that 
 which is not yet become habit, but which we 
 perform with design and an exercise of our will, 
 is not yet a part of ourselves. . . . The 
 limits of Education are found in the idea of its 
 nature, which is to fashion the individual into 
 theoretical and practical rationality." (Rosen- 
 kranz, Pedagogics as a System, pp. 723, ed. 
 1872, St. Louis. Translated by Anna C. Brac- 
 kett.) 
 
 7. " Education differs from information or 
 knowledge. The latter is of a special character, 
 the purport of which is to fit a man for bringing 
 about certain definite results by the immediate 
 operation of that knowledge which he possesses. 
 We talk, indeed, of the education of a lawyer, 
 a doctor, and a clergyman of an engineer, a 
 soldier, or a sailor ; generally meaning by it the 
 information or knowledge which he has acquired 
 
ON EDUCATION. 
 
 for the immediate exercise of his vocation. But 
 law, medicine, divinity, mechanics, strategics, 
 and navigation, are not education. A man may 
 possess any one of them and be well-nigh illite- 
 rate, though of course some can more possibly 
 co-exist with want of education than others. 
 One can conceive that a man may have a pro- 
 found practical acquaintance with law, and be an 
 uneducated person. Again, to quote an in- 
 stance, the first Duke of Marlborough was one 
 of the most skilful generals ever known, but he 
 could not spell, and hardly write. Some men 
 who have had the most marvellous aptitude and 
 quickness in mechanical science, have been un- 
 able, from sheer ignorance, to sustain a common 
 conversation. Education, on the other hand, 
 deals with formalities. It does not so much 
 aim at setting the mind right on particular points, 
 as on getting the mind into the way of being 
 right. It does not deal with matter, but with 
 method. It purposes to train the thinking pow- 
 ers of man, not to fill the mind with facts. 
 Hence, were it perfect, it would cultivate the in- 
 telligence so largely as to render easy the acqui- 
 sition of any knowledge. It deals, in short, 
 cither directly or indirectly, with logical order 
 and the reasoning powers. That it falls short of 
 effecting what it purposes, is due to defects 
 in its system, to defects in man's mind, to de- 
 fects in this or that man's mind. As, however, 
 its operation is not immediate, but only indi- 
 rect, its best methods are frequently cavilled at 
 !as useless. It may teach logical method of 
 
ON EDUCATION. 9 
 
 thinking and reasoning. This, however, is gen- 
 erally too abstract for most minds, except they 
 be more or less matured, and more or less in- 
 formed on some one or two subjects. In place 
 of this, then, it teaches ordinarily something, 
 which is as exact an illustration of logical 
 method as can be, and which, being unfailing in 
 its inferences, trains the mind in method, and 
 often stores it with facts. In a greater or less 
 degree, but in some degree at least, this inculca- 
 tion of an abstract method is necessary for any 
 kind of education, and even, except it be a mere 
 knack, for information." (Rogers, Education 
 in Oxford , pp. 13. London, 1861.) 
 
 8. In the following quotation the extension 
 of the term education is limited substantially to 
 the work of the teacher. This limitation is un- 
 usual, and the advantages gained by it are hard- 
 ly evident : ' l First, let me quote the definition 
 (of Education) embodied in the ideal of the foun- 
 ders of the Prussian National System. It is 
 given shortly as * the harmonious and equable 
 evolution of the human powers ;' at more length, 
 in the words of Stein, ' by a method based on 
 the nature of the mind, every power of the soul 
 to be unfolded, every crude principle of life 
 stirred up and nourished, all one-sided culture 
 avoided, and the impulses on which the strength 
 and worth of men rest, carefully attended to. ' 
 (Donaldson's Lectures on Education, p. 38.) 
 This definition, which is pointed against narrow T - 
 ness generally, may have had special reference to 
 the many omissions in the schooling of the fore- 
 
10 ON EDUCATION. 
 
 gone times : the leaving out of such things as 
 bodily or muscular training ; training in the 
 senses or observation ; training in art or refine- 
 ment. It farther insinuates that hitherto the 
 professed teacher may not have done much even 
 for the intellect, for the higher moral training, 
 nor for the training with a view to happiness or 
 enjoyment. . . 
 
 " In the very remarkable article on education 
 contributed by James Mill to the Encyclopaedia 
 Britannica, the end of education is stated to be 
 * to render the individual, as much as possible, 
 an instrument of happiness, first to himself, and 
 next to other beings. ' This, however, should be 
 given as an amended answer to the first question 
 of the Westminster Catechism ' What is the 
 , chief end of man ? ' The utmost that we could 
 \expect of the educator, who is not everybody, 
 is to contribute his part to the promotion of hu- 
 man happiness in the order stated. No doubt 
 the definition goes more completely to the root 
 of the matter than the German formula. It does 
 not trouble itself with the harmony, the many- 
 sidedness, the wholeness, of the individual de- 
 velopment ; it would admit these just as might 
 be requisite for securing the final end. 
 
 " James Mill is not singular in his over -grasp- 
 ing view of the subject. The most usual sub- 
 division of Education is into Physical, Intellect- 
 ual, Moral, Religious, Technical. Now when we 
 inquire into the meaning of Physical Education, 
 we find it to mean the rearing of a healthy hu- 
 man being, by all the arts and devices of nursing 
 
ON EDUCATION. 11 
 
 feeding, clothing, and general regimen. Mill in- 
 cludes this subject in his article, and Mr. Her- 
 bert Spencer devotes a very interesting chapter to 
 it in his work on Education. It seems to me, 
 however, that this department may be kept quite 
 separate, important though it be. It does not 
 at all depend upon the principles and considera- 
 tions that the educator, properly so called, has in 
 view in the carrying on of his work. The dis- 
 cussion of the subject does not in any way help 
 us in educational matters, as most commonly un- 
 derstood ; nor does it derive any illumination 
 from being placed side by side with the arts of 
 the recognized teacher. The fact of bodily 
 health or vigor is a leading postulate in bodily 
 or mental training, but the trainer does not take 
 upon himself to lay down the rules of hygiene. 
 
 " The inadvertence, for so I regard it, of 
 coupling the Art of Health with Education is eas- 
 ily disposed of, and does not land us in any ard- 
 uous controversies. Very different is another 
 aspect of these definitions: that wherein the end 
 of Education is propounded as the promotion of 
 human happiness, human virtue, human perfec- 
 tion. Probably the qualification will at once be 
 conceded, that Education is but one of the means, 
 a single contributing agency to the all-including 
 end. Nevertheless, the openings for difference 
 of opinion as to what constitutes happiness, vir- 
 tue or perfection, are very wide. Moreover, the 
 discussion has its proper place in Ethics and in 
 Theology, and if brought into the field of Educa- 
 tion, should be received under protest. 
 
12 Otf EDUCATION. 
 
 " Before entering upon the consideration of 
 this difficulty, the greatest of all, I will advert to 
 some of the other views of education that seem 
 to err on the side of taking in too much. Here, 
 I may quote from the younger Mill, who, like 
 his father, and unlike the generality of theorists, 
 starts more scientifieo with a definition. Edu- 
 cation, according to him, ' includes whatever we 
 do for ourselves, and whatever is done for us by 
 others, for the express purpose of bringing us 
 nearer to the perfection of our nature ; in its 
 largest acceptation, it comprehends even the in- 
 direct effects produced on character and on the 
 human faculties by things of which the direct 
 purposes are different ; by laws, by forms of 
 government, by the industrial arts, by modes of 
 social life ; nay even by physical facts not depen- 
 dent on the human will ; by climate, soil, and 
 local position.' He admits, however, that this 
 is a very wide view of the subject, and for his 
 own immediate purpose advances a narrower 
 view, namely, ' the culture which each genera- 
 tion purposely gives to those who are to be its 
 successors, in order to qualify them for at least 
 keeping up, and if possible for raising, the im- 
 provement which has been attained. ' (Inaugu- 
 ral Address at St. Andrew's, p. 4.) 
 
 " Besides involving the dispute as to what 
 constitutes 4 perfection, ' the first and larger state- 
 ment is, I think, too wide for the most compre- 
 hensive Philosophy of Education. The influ- 
 ences exerted on the human character by climate 
 and geographical position, by arts, laws, govern- 
 
ON EDUCATION. 13 
 
 ment and modes of social life, constitute a very 
 interesting department of Sociology, and have 
 their place there and nowhere else. What we 
 do for ourselves, and what others do for us, to 
 bring us nearer to the perfection of our nature, 
 may be education in a precise sense of the word, 
 and it may not. I do not see the propriety of 
 including under the subject the direct operation 
 of rewards and punishments. No doubt we do 
 something to educate ourselves, and society does 
 something to educate us, in a sufficiently proper 
 acceptation of the word ; but the ordinary influ- 
 ence of society, in the dispensing of punishment 
 and reward, is not the essential fact of Educa- 
 tion, as I propose to regard it, although an ad- 
 junct to some of its legitimate functions. 
 
 " Mill's narrow expression of the scope of the 
 subject is not exactly erroneous ; the moulding 
 of each generation by the one preceding is not 
 improperly described as an Education. It is, 
 however, grandiose rather than scientific. Noth- 
 ing is to be got out of it. It does not give the 
 lead to the subsequent exposition. 
 
 " I find in the article ' Education,' in Cham- 
 bers' s Encyclopaedia, a definition to the following 
 effect : i In the widest sense of the word a man 
 is educated, either for good or for evil, by 
 every thing that he experiences from the cradle 
 to the grave [say, rather, " formed, " " made," 
 "influenced"]. But in the more limited and 
 usual sense, the term Education is confined to 
 the efforts made, of set purpose, to train men in 
 a particular way the efforts of the grown-up 
 
14 ON EDUCATION. 
 
 part of the community to inform the intellect 
 and mould the character of the young [rather too 
 much stress on the fact of influence from with- 
 out] ; and more especially to the labours of pro- 
 fessional educators or schoolmasters. ' The con- 
 cluding clause is the nearest to the point the 
 arts and methods employed by the schoolmas- 
 ters ; for, although he is not alone in the work 
 that he is expressly devoted to, yet he it is that 
 typifies the process in its greatest singleness and 
 purity. If by any investigations, inventions or 
 discussions, we can improve his art to the ideal 
 pitch, we shall have done nearly all that can be 
 required of a science and art of Education. " 
 (Bain, Education as a Science, Art. I., in Mind, 
 pp. 1-4, No. 5, January, 1877.) 
 
 9. " The true view of education is to regard 
 it as a course of training. The youth in a gymna- 
 sium practises upon the horizontal bar, in order 
 to develop his muscular powers generally ; he 
 does not intend to go on posturing upon hori- 
 zontal bars all through 'life. School is a place 
 where the mental fibres are to be exercised, 
 trained, expanded, developed, and strength- 
 ened. . . . It is the very purpose of a lib- 
 eral education, as it is correctly called, to de- 
 velop and train the plastic fibres of the youthful 
 brain, so as to prevent them taking too early a 
 definite i set/ which will afterwards narrow and 
 restrict the range of acquisition and judgment. 
 I will even go so far as to say that it is hardly 
 desirable for the actual things taught at school 
 to stay in the mind for life. The source of 
 
Otf EDUCATION. 15 
 
 error is the failure to distinguish between the 
 form and the matter of knowledge, between the 
 facts themselves and the manner in which the 
 mental powers deal with facts. . . . It is 
 the purpose of education so to exercise the fac- 
 ulties of mind that the infinitely various experi- 
 ence of after-life may be observed and reasoned 
 upon to the best effect/' (Jevons, in Mind, 
 pp. 197-207, No. VI., April, 1877.) (Rein- 
 serted under " Memory and Cram," 172.) 
 
 10. " Educit obstetrix, educat nutrix, insti- 
 tuit pedagogus, docet magister. " (Varro. 
 See also An. and St j d Lat. Lex., unabridged.) 
 
 11. " TRAINING (Fr. Cramer) is development 
 by instruction, exercise, and discipline, and is 
 applicable to the whole nature of a man, or, 
 specifically, to the faculties which he possesses. 
 It denotes no more than a process of purposed 
 habituation, and is equally applicable to the phy- 
 sical and mental powers, so that it may include 
 both at the same time." (Smith, Syn. Discri- 
 minated, Art. Education, ed. 1878.) This 
 sense of training is the ordinary meaning now 
 attached to education. 
 
 12. "A thorough and complete education 
 ought to preserve and increase the pupil's bodily 
 health and strength ; give him command of his 
 own muscular and mental powers ; increase his 
 quickness in perceiving through his five senses, 
 and quicken his mental perception ; form in him 
 the habit of prompt and accurate judgment ; 
 lead to delicacy and depth in every right feel- 
 ing ; and make him inflexible in his conscien- 
 
 OT THE 
 
 [UIUYIESITY] 
 
16 ON EDUCATION. 
 
 tious and steadfast devotion to all his duties. 
 In other words, an integral education must in- 
 clude at least these four branches : gymnastics, 
 or care of the body ; noetics, or training of the 
 mind ; aesthetics, or cultivation of the tastes ; 
 and ethics, which shall include religion as well 
 as duty. And in every part of each branch of 
 education, there will be a double end in view, 
 namely, the increase of knowledge, and the in- 
 crease of skill. Each study may be made the 
 object of thought, or the object of action ; in 
 the one case it is pursued as a science ; in the 
 other case as an art." (Thomas Hill, The True 
 Order of Studies, pp. 7, 8, ed. 1876.) 
 
 13. " The conclusions of the honest and in- 
 telligent inquirer after the truth in this matter, 
 will be something like the following : That edu- 
 cation (from e and duco, to lead forth) is devel- 
 opment ; that it is not instruction merely 
 knowledge, facts, rules communicated by the 
 teacher, but it is discipline, it is a waking up 
 of the mind, a growth of the mind, growth by 
 a healthy assimilation of wholesome aliment. It 
 is an inspiring of the mind with a thirst for 
 knowledge, growth, enlargement, and then a dis- 
 ciplining of its powers so far that it can go on to 
 educate itself. It is the arousing of the child's 
 mind to think, without thinking for it ; it is the 
 awakening of its powers to observe, to remem- 
 ber, to reflect, to combine. It is not a cultiva- 
 tion of the memory to the neglect of every thing 
 else ; but it is a calling forth of all the faculties 
 into harmonious action. If to possess facts sim- 
 
ON EDUCATION. 17 
 
 ply is education, then an encyclopaedia is better 
 educated than a man." (Page, Theory and 
 Practice of Teaching, p. 70, ed. 1853.) 
 
 14. " Suppose it were perfectly certain that 
 the life and fortune of every one of us would, 
 one day or other, depend upon his winning or 
 losing a game at chess. Don't you think that 
 we should all consider it to be a primary duty to 
 learn at least the names and the moves of the 
 pieces ; to have a notion of a gambit, and a keen 
 eye for all the means of giving and getting out 
 of check ? Do you not think that we should 
 look with disapprobation amounting to scorn, 
 upon the father who allowed his son, or the 
 state which allowed its members, to grow up 
 without knowing a pawn from a knight ? 
 
 ' * Yet it is a very plain and elementary truth, 
 that the life, the fortune, and the happiness of 
 eyery one of us, and, more or less, of those who 
 are connected with us, do depend upon our 
 knowing something of the rules of a game infin- 
 itely more difficult and complicated than chess. 
 It is a game which has been played for untold 
 ages, every man and woman of us being one of 
 the two players in a game of his or her own. 
 The chess-board is the world, the pieces are the 
 phenomena of the universe, the rules of the 
 game are what we call the laws of Nature. The 
 player on the other side is hidden from us. 
 We know that his play is always fair, just, and 
 patient. But also we know, to our cost, that 
 he never overlooks a mistake, or makes the small- 
 est aMowance for ignorance. To the man who 
 
18 ON EDUCATION. 
 
 plays well the highest stakes are paid, with that 
 sort of overflowing generosity with which the 
 strong shows delight in strength. And one who 
 plays ill is checkmated without haste, but with- 
 out remorse. 
 
 " My metaphor will remind some of you of 
 the famous picture in which Retzsch has de- 
 picted Satan playing at chess with man for his 
 soul. Substitute for the mocking fiend in that 
 picture, a calm, strong angel who is playing for 
 love, as we say, and would rather lose than win 
 and I should accept it as an image of human 
 life. 
 
 " Well, what I mean by Education is learning 
 the rules of this mighty game. In other words, 
 education is the instruction of the intellect in the 
 laws of Nature, under which name I include not 
 merely things and their forces, but men and 
 their ways ; and the fashioning of the affections 
 and of the will into an earnest and loving desire 
 to move in harmony with those laws. For me, 
 education means neither more nor less than this. 
 Any thing which professes to call itself education 
 must be tried by this standard, and if it fails to 
 stand the test, I will not call it education, what- 
 ever may be the force of authority, or of num- 
 bers, upon the other side. 
 
 " It is important to remember that, in strict- 
 ness, there is no such thing as an uneducated 
 man. Take an extreme case. Suppose that an 
 adult man, in the full vigour of his faculties, 
 could be suddenly placed in the world, as Adam 
 is said to have been, and then left to do as he 
 
ON EDUCATION. 19 
 
 best might. How long would he be left unedu- 
 cated ? Not five minutes. Nature would begin 
 to teach him, through the eye r the ear, the 
 touch, the properties of objects. Pain and 
 pleasure would be at his elbow telling him to do 
 this and avoid that ; and by slow degrees the 
 man would receive an education, which, if nar- 
 row, would be thorough, real, and adequate to 
 his circumstances, though there would be no ex- 
 tras and very few accomplishments. 
 The great mass of mankind are the * Poll, ' who 
 pick up just enough to get through without much 
 discredit. Those who won't learn at all are 
 plucked ; and then you can't come up again. 
 Nature's pluck means extermination. 
 Nature's discipline is not even a word and a 
 blow, and the blow first ; but the blow without 
 the word. It is left to you to find out why your 
 ears are boxed. ' ' (Huxley, Lay Sermons, pp. 
 31-34, ed. 1870. London.) 
 
 15. " As theory, Education allies itself to 
 Psychology, Physiology, and Sociology. The 
 materials of its teaching it draws from these phi- 
 losophies, from the practice of the schoolroom, 
 and from the rich domain of History. . . . 
 I have some sympathy with the cynical Love 
 Peacock, who, in describing certain social bores 
 in the shape of men of one idea who hold forth 
 in season and out of season, says : i The worst 
 of all bores was the third. His subject had no 
 beginning, middle, nor end. It was Education. 
 Never was such a journey through the desert 
 of mind, the great Sahara of intellect. The 
 
20 ON EDUCATION. 
 
 very recollection makes me thirsty/ Such men 
 are not educationists in any sense in which that 
 term is applicable within these walls. They are 
 men of leisure who have restless minds, and if 
 they have not one fixed idea or crotchet, will 
 find another. An educationist has no crotchets. 
 That man has crotchets who, having seized on 
 that particular corner of a large and many-sided 
 subject which has some secret affinity with his 
 own mind, or affords the quickest passage to no- 
 toriety, pursues it to the death. Now, an edu- 
 cationist is, by virtue of his very name and vo- 
 cation, inaccessible to all petty fanaticisms. He 
 has to deal with a subject of infinite variety, and 
 so variously related to life, that he is more apt 
 to be lost in hesitations and scepticisms than to 
 be the victim of a fixed idea. If you wish to 
 meet with educational crotchets, you must go to 
 the specialist in this or that department of 
 knowledge, who is unfortunate enough to take 
 up the question of Education, as you see he 
 often in moments of aberration takes up other 
 subjects which are outside his own range of in- 
 tellectual experience. It is only in such cases 
 that you will find the confidence and self-assur- 
 ance which is born of limited knowledge, and 
 the pertinacious insistence which flows from 
 these habits of mind. To him whose subject is 
 Education crotchets are prohibited, because his 
 opinions on this or that point are related on the 
 one side to rational and comprehensive theory, 
 and on the other to the daily practice of the 
 schoolroom and the needs of life. . . . 
 
ON EDUCATION. 21 
 
 The more abstract treatment of the theory of Ed- 
 ucation is doubtless, if true in its philosophy, of 
 universal application. It sweeps the whole field. 
 But this will engage our attention only within 
 carefully prescribed limits, and when we leave 
 this portion of our subject, we have to restrict 
 ourselves on all sides. The education of every 
 human being is determined by potent influences- 
 which do not properly fall within the range of 
 our consideration here. The breed of men to 
 which the child belongs, the character of his pa- 
 rents, the human society into which he is born, 
 the physical circumstances by which he is sur- 
 rounded, are silently but irresistibly forming 
 him. The traditions of his country, its popular 
 literature, its very idioms of speech, its laws and 
 customs, its religious life, its family life, consti- 
 tute an aggregate of influence which chiefly 
 make him what he is. ... By their con- 
 stant presence they mould the future man, him- 
 self unconscious. They are the atmosphere of 
 the humanity of his particular time and place, 
 and in breathing it he is essentially a passive 
 agent. . . . The passive activity of our na- 
 ture is not to be ignored in our educational 
 methods ; it is to be turned to use as one of our 
 most potent instruments, but it is mainly the 
 self-conscious forces that we have to educe and 
 direct. Even in doing this we are bound by ex- 
 ternal conditions, and must take note not only of 
 the almost irresistible forces around us, but of 
 minor conditions of time, place, and circum- 
 stance. Each successive century, and the tra- 
 
~2 ON EDUCATION. 
 
 ditions and circumstances of each country, nay, 
 the genius of each people, present to us the ed- 
 ucational problem in ever-changing aspects. 
 Educational systems cannot be manufactured in 
 the study. Our theory of the end of all educa- 
 tion and the means by which that end has to be 
 attained may be, or rather ought to be, always 
 the same ; but the application of that theory 
 must vary with varying external conditions. 
 What present defects have we here and now, 
 and to what dangers are we exposed ? is the 
 form which the practical question must take with 
 us. ' ' (Laurie, Inaugural Address, Chair of Ed- 
 ucation, pp. 21-24. Edinburgh, 1876.) 
 
 16. " To write upon education, means to 
 write upon almost every thing at once ; for it has 
 to care for, and watch over, the development 
 of an entire, though miniature, world in little, 
 a microcosm of the microcosm. All the ener- 
 gies with which nations have labored and signal- 
 ized themselves once existed as germs in the 
 hand of the educator. *If we carried the sub- 
 ject still further, every century, every nation, 
 and even every boy and every girl, would require 
 a distinct system of education, a different primer, 
 and domestic French governess, &c. . . . But 
 although the spirit of education, always watch- 
 ing over the whole, is nothing more than an en- 
 deavor to liberate, by means of a freeman, the 
 ideal human being which lies concealed in every 
 child ; and though, in the application of the di- 
 vine to the child's nature, it must scorn some 
 useful things, some seasonable, individual, or im- 
 
ON EDUCATION. 23 
 
 mediate ends ; yet it must incorporate itself in 
 the most definite applications, in order to be 
 clearly manifested. 
 
 " But who then educates in nations and 
 ages ? Both ! The living time, which for 
 twenty or thirty years struggles unceasingly with 
 men through actions and opinions, tossing them 
 to and fro as with a sea of waves, must soon 
 wash away or cover the precipitate of the short 
 school years, in which only one man, and only 
 words taught. The century is the spiritual cli- 
 mate of man, mere education the hot-house and 
 forcing-pit, out of which he is taken and planted 
 forever in the other. By century is here meant 
 the real century, which may as often truly con- 
 sist of ten years, as of ten thousand, and which 
 is dated, like religious eras, only from great men. 
 What can insulated words do against living pres- 
 ent action ? The present has for new deeds- 
 also new words ; the teacher has only dead lan- 
 guages for the, to all appearance, dead bodies of 
 his examples. The educator has himself been 
 educated, and is already possessed, even without 
 his knowledge, by the spirit of the age, which he 
 assiduously labors to banish out of the youth (as 
 a whole city criticises the spirit of the whole 
 city). Only, alas ! every one believes himself to 
 stand so precisely and accurately in the zenith of 
 the universe, that, according to his calculation, 
 all suns and nations must culminate over his 
 head ; and he himself, like the countries at the 
 equator, cast no shadow save into himself 
 alone. . . . The spirit of the nation and of 
 
24 ON EDUCATION. 
 
 the age decides, and is at once the schoolmaster 
 and the school ; for it seizes on the pupil to 
 form him with two vigorous hands and powers ; 
 with the living lesson of action, and with its 
 unalterable unity. If to begin with unity ed- 
 ucation must be, like the Testament, a continu- 
 ous endeavor to withdraw the force of interrupt- 
 ing mixtures, then nothing builds up so strong as 
 the present, which ceases not for a moment, and 
 eternally repeats itself ; and which, with joy and 
 sorrow, with towns and books, with friends and 
 enemies, in short, with thousand-handed life, 
 presses and seizes on us. No teacher of the peo- 
 ple continues so uniformly one with himself as 
 the teaching people. Minds molten into masses 
 lose something of their free movements : which 
 bodies, for instance, that of the world, perhaps 
 that of the universe, seem to gain by their very 
 inassiveness, and, like a heavy colossus, to move 
 all the more easily along the old, iron-covered 
 track. For however much marriages, old age, 
 deaths and enmities, are in the individual case 
 subject to the law of freedom, yet in a whole na- 
 tion, lists of births and deaths can be made, by 
 which it may be shown that in the canton of 
 Berne (according to Mad. de Stael) the number 
 of divorces, as in Italy that of murders, is the 
 same from year to year. Must not, now, the 
 little human being placed on such an eternally 
 and ever similarly acting world, be borne as 
 upon a flying earth, where the only directions 
 that a teacher can give avail nothing, because he 
 
ON EDUCATION. 26 
 
 has first unconsciously received his line of move- 
 ment upon it ? 
 
 " Thence, in spite of all reformers and inform- 
 ers, nations, like meadows, reach ever a similar 
 verdure ; thence, even in capital cities, where all 
 school-books and schoolmasters, and even par- 
 ents of every kind, educate, the spirit main- 
 tains itself unalterably the same. Repetition is 
 the mother not only of study, but also of educa- 
 tion. . . . Certainly one might say that also 
 in families there educates, besides the popular 
 masses, a pedagogic crowd of people ; at least, 
 for instance, aunt, grandfathers, grandmothers, 
 father, mother, god-parents, friends of the fam- 
 ily, the yearly domestics, and at the end of all 
 the instructor beckons with his forefinger, so that 
 could this force continue as long as it would 
 gladly be maintained a child, under these many 
 masters, would resemble, much more than one 
 thinks, an Indian slave, who wanders about with 
 the inburnt stamps of his various masters. But 
 how does the multitude disappear compared 
 with the higher one, by which it was colored ; 
 just as all the burnt marks of the slave yet can- 
 not overcome the hot black coloring of the sun, 
 but receive it as a coat of arms in a sable field ? 
 . . . The end desired must be known before 
 the way. All means or arts of education will 
 be, in the first instance, determined by the ideal 
 or archetype we entertain of it. But there floats 
 before common parents, instead of one arche- 
 type, a whole picture cabinet of ideals, which 
 they impart bit by bit, and tattoo into their 
 
26 OK EDUCATION. 
 
 children. If the secret variances of a large class 
 of ordinary fathers were brought to light, and 
 laid down as a plan of studies, and reading cata- 
 logue for a moral education, they would run 
 somewhat after this fashion : In the first hour 
 pure morality must be read to the child, either 
 by myself, or the tutor ; in the second, mixed 
 morality, or that which may be applied to one's 
 own advantage ; in the third, * Do you not see 
 that your father does so and so ? ' in the fourth, 
 ' You are little, and this is only fit for grown- 
 up people ;' in the fifth, i The chief matter is 
 that you should succeed in the world, and be- 
 come something in the state ;' in the sixth, 
 * Not the temporary, but the eternal, determines 
 the worth of a man ;' in the seventh, i Therefore 
 rather suffer injustice, and be kind ;' in the 
 eighth, ' but defend yourself bravely if any one 
 attack you ;' in the ninth, i Do not make such a 
 noise, dear child ;' in the tenth, l A boy must 
 not sit so quiet ; 7 in the eleventh, ' You must 
 obey your parents better ;' in the twelfth, ' and 
 educate yourself. 1 So by the hourly change of 
 his principles the father conceals their untena- 
 bleness and one-sidedness. As for his wife, she 
 is neither like him, nor yet like that harlequin 
 who came on to the stage with a bundle of pa- 
 pers under each arm, and answered to the in- 
 quiry what he had under his right arm, ' orders, ' 
 and to what he had under his left, ' counter- 
 orders ;' but the mother might be much better 
 compared to a giant Briareus, who had a hun- 
 dred arms, and a bundle of papers under each. 
 
ON EDUCATION. 27 
 
 The majority of educated men are, 
 therefore, at present an illumination which burns 
 off by fits and starts in the rain, shining with in- 
 terrupted forms, and depicting broken charac- 
 ters. But the bad and impure spirits of educa- 
 tional systems are yet to be reduced into other 
 divisions. Many parents educate their children 
 only for themselves, that is, to be pretty 
 blocks, or soul-alarums, which are not set to 
 move or sound when stillness is required. The 
 child has merely to be that on which the teacher 
 can sleep most softly or drum most loudly ; who, 
 having something else to do and to enjoy, wishes 
 to be spared the trouble of education, duly but 
 most unreasonably expecting its fruits. 
 Related to those teachers who wished to be ma- 
 chine-makers are the educators for appearances 
 and political usefulness. Their maxims, thor- 
 oughly carried out, would only produce pupils, 
 or rather sucklings, passively obedient, boneless, 
 well -trained, patient of all things, the thick, 
 hard, human kernel would give place to the 
 soft, sweet fruit-pulp, and the child's clod of 
 earth, into which growing life should breathe a 
 divine spirit, would be kept down and manured 
 as though it were but a corn-field, the edifice 
 of the state would be inhabited by mere spin- 
 ning-machines, calculating-machines, printing 
 and pumping apparatus, oil-mills, and models, 
 for mills, pumps, and spinning-machines, &c. 
 Education can neither entirely consist 
 of mere unfolding in general, or, as it is now 
 better called, excitement, for every continued 
 
28 ON EDUCATION. 
 
 existence unfolds, and every bad education ex- 
 cites, just as oxygen positively irritates, nor in 
 the unfolding of all the powers, because we can 
 never act upon the whole amount of them at 
 once ; as little as in the body susceptibility and 
 spontaneity, or the muscular and nervous system, 
 can be strengthened at the same time." (Rich- 
 ter, Levana, Preface, ix, and pp. 7-33. Boston. 
 1863.) 
 
 17. " A treatise on education does not in- 
 clude the theory of instruction, whose wide realm 
 embraces the mistakes of all sciences and arts ; 
 nor the theory of remedies, which would require 
 libraries instead of volumes for the complication 
 of mistakes, years, positions, and relations. At 
 the same time no science is entirely disconnected 
 from the rest ; the feet cannot move without the 
 hands." (Ibid., p. 390.) 
 
 18. The education that any one receives de- 
 pends upon the ethical relations by which he is 
 surrounded. But education must regard the 
 nature and powers of the mind of him who is to 
 be educated. Hence education, as a product, is 
 founded upon ethical relations upon the one 
 hand, and the nature of mind, or Psychology, 
 upon the other. Education, in part, is depend- 
 ent upon teaching or instruction as a means for 
 securing its ends. Teaching, then, directly 
 busies itself with the subject-matter that is to be 
 learned, and with the mind which is to learn it. 
 
 19. " The educator of youth does not merely 
 communicate so much instruction from year to 
 year ; he develops the receptive and acquisitive 
 
ON EDUCATION. 
 
 29 
 
 tendencies of mind, which are afterwards to 
 play their part in the intellectual activity of the 
 nation. He trains the intelligence of those who 
 are afterwards to be the teachers of others, as 
 well as of those who are only to be interested in- 
 quirers after truth. " (Calderwood, On Teach- 
 ing, p. 49, ed. 1875, New York.) 
 
in. 
 
 ON TEACHING. 
 
 20. Having briefly considered the notion of 
 the terms Pedagogics and Education, the reader 
 is directed to the conception of the term Teach- 
 ing. 
 
 Thought is the modification of the activity 
 called Intelligence, and Language is its Form. 
 Language is the mirror which reflects the ideas 
 that are in the mind of him who utters it. Lan- 
 guage is a record of thought. Language, in its 
 widest signification, is the instrument for per- 
 petuating the life of a nation, or rather it is the 
 life of a people perpetuated. Language is the 
 form of the matter which once existed in the 
 consciousness of the person who uttered it ; it is 
 a product of thought ; perhaps more exactly it 
 is thought itself. "It is only as there is a 
 XoyoS in the outer world, answering to the 
 XoyoS or internal reason of the parties, that men 
 can come into a mutual understanding in regard 
 to any thought-state whatever." (Grindon, 
 Life, p. 349.) 
 
 " By Language we do not mean the mere art 
 of speaking and writing according to some 
 specific, arbitrary mode, which though intelli- 
 
ON TEACHING. 31 
 
 gible in one country, is unintelligible in another. 
 We mean that beautiful and inevitable flowering 
 forth in speech of the inner, living intellect of 
 man, which, older and more excellent than all 
 prosody and spelling, is an integral work of na- 
 ture ; and which, wen., ^ possible for the acci- 
 dental forms which it may hold at any given 
 epoch, as English and French, Latin and Greek, 
 to be suddenly and totally abolished, would in 
 itself be unaffected, and speedily incarnate 
 afresh, unchanged save in the extrinsic circum- 
 stances of costume." (Ibid, pp. 153, 154, third 
 ed., London.) Nations differ in their language 
 these differences measure those differences 
 that exist among the ideas or notions which are 
 substantially common to many peoples. The 
 content and extent of words having the same 
 general meaning, when expressed in different 
 languages, are hardly equivalent nor precisely 
 identical. No two nations live and act exactly 
 alike, and as language follows life, it is but in 
 the harmony of things that this should occasion 
 different notions of life and -actions in the minds 
 of the various peoples, and hence in language. 
 Two or three examples will illustrate the case : 
 
 21. To indicate a certain notion, the Greeks 
 used deiknumi, the English equivalents of which 
 are : " To bring to light, to display, to portray, 
 to represent to the life as in statuary, to shew, 
 to point out, to make known by words, to tell, 
 to explain, to teach, to prove, to offer, to prof- 
 fer." Buttmann traces the prefix deik to a root 
 dek, which contains the common notion of 
 
32 ON TEACHING. 
 
 stretching out the right hand either to point, 
 or to welcome, (Liddell and Scott, Greek- 
 English Lexicon , Oxford, 1871.) The essential 
 idea seems to rest upon the action of pointing 
 to, or towards, a thing. The Greeks cultivated 
 the graces of action as well as the harmony of 
 sounds, and it is not difficult to conceive the 
 elders among the people pointing out, showing, 
 portraying as artists, the things before them to 
 the youth, much as a traveller would do at the 
 present time to a youthful companion. The fact 
 that Socrates was at so great pains to develop in 
 his pupils the power to reason would argue that, 
 in his opinion, before his time the powers of per- 
 ception and memory of the youth had been rec- 
 ognized as of greater value in acquiring an edu- 
 cation than the reflective powers. The word 
 teaching also appears to exhibit some one as in 
 the action of directing the attention of another 
 to something through, or by means of, the ges- 
 tures of his right hand it does not so much 
 seem to exhibit one as showing a thing, object, 
 immediately and directly, as it shows indirectly 
 through words and general gestures, and by illus- 
 trative sketches it implies an exhortation to at- 
 tend to this thing which is in mind as a philo- 
 sophical truth. It would seem to indicate an ex- 
 planation of memorized words. " When the 
 children could read, and understand what they 
 read, the works of the poets were put in requi- 
 sition, to exercise their minds, and awaken their 
 hearts to great and noble deeds. Plato, Leg. 
 vii. p. 810, approves of this, and also recom- 
 
OK TEACHING. 33 
 
 mends committing whole poems, or select pas- 
 sages, to memory ; and this method of instruc- 
 tion appears to have been universal. Above all, 
 the poems of Homer were thought to contain, 
 by precept and example, every thing calculated 
 to awaken national spirit, and to instruct a man 
 how to be beautiful and good." (Becker, 
 Charicles, trans, by Frederick Metcalfe, ed. 
 1866, p. 233.) 
 
 22. The Latins conveyed a certain notion by 
 doceo, which is rendered in English by : " To 
 teach, to inform, to instruct, to show, to point 
 out, to represent, to exhibit. " It is compared 
 with edocere, which means " to make one learn, 
 to make acquainted with, more energetic than 
 docere." Perdocere means " to teach per- 
 fectly, to instruct thoroughly." Erudire im- 
 plies * ' to initiate in learning. ' ' Instruct, in and 
 struo, means : To join together, to pile tip, 
 heap up, to erect, to build, to set in array, to 
 join together, to construct. (Bullion, Lat.-Eng. 
 Diet., ed. 1869.) The essential .idea with the 
 Latins seems to be that of laying before one 
 some matters as objects to be seen, handled, 
 piled up in layers one upon another (instruct), 
 to show as in an exhibition. The word pictures 
 one as standing at work upon some visible ob- 
 jects, and calling the attention of another to these 
 objects as he piles them up, one 1 upon another. 
 This sense is virtually different from the thought 
 with the Greeks, who rather withdrew them- 
 selves from the presence of the things about 
 which they discoursed, and crowded the thought 
 
34 OK TEACHING. 
 
 home to the conviction of the hearer by words 
 and exhortatory gestures of the right hand. 
 This notion of doceo corresponds with the gene- 
 ral characteristics of the Latins, who were a peo- 
 ple pre-eminently skilful in the affairs of practi- 
 cal business. They regarded the objects of bus- 
 iness directly, rather than through philosophy. 
 Hence, the one would instruct a youth in law by 
 exhibiting to him law practice in the courts, 
 while the other would lecture the youth about 
 the principles of law in the abstract, while seated 
 in his stone chair, or while walking about the 
 groves. 
 
 23. The Anglo-Saxons expressed a certain 
 notion by the word t&can, which is rendered in 
 English : " To teach, to instruct, to show, to di- 
 rect, to command, to see to, to provide, to or- 
 der, to convince, to prove." (Bosworth, An- 
 glo-Saxon and Eng. Diet., London, 1860.) In 
 this case the notion has an element of poiver and 
 authority in it ; it shows, with power to com- 
 mand attention ; it directs, but it is imperative 
 about something towards somebody ; it does not 
 simply exhort the attention of somebody towards 
 an idea by the right hand in persuasion or wel- 
 come, as does the Greek deiknumi nor does 
 it call the attention of somebody to what the ex- 
 hibitor has before him, piling it up in order, as 
 do the Latin doceo and instruo ; but it shows 
 something to somebody, meaning that this some- 
 body shall attend to this something. This word 
 tgecan discloses the characteristic trait of the 
 Anglo-Saxon life, the disposition to do something 
 
ON TEACHING. 35 
 
 for another, and then to command him to respect 
 what has been placed before him. The word re- 
 gards with emphasis both what is provided, and 
 him for whom it is provided. 
 
 24. These three instances illustrate the differ- . 
 ences which exist among peoples when they ex- 
 press a notion that is ordinarily regarded as the 
 same by them all. Each people has its own set- 
 ting of thoughts which control the form, and as- 
 sist in conserving the meaning of subsequent no- 
 tions. These thoughts, notions, conserved in 
 form, are language. The words " instruct " and 
 " teach' 7 are both in common use at this time, 
 practically as synonyms 7 . Following the lines of 
 their ancestry, and considering the tendency of 
 the present age, it is determined to use the word 
 teaching rather than instruction in the expres- 
 sion Methods of Teaching. As illustrating the 
 deep-seated element of authority which exists in 
 the Anglo-Saxon notion of teaching, the follow- 
 ing quotations are subjoined : 
 
 26. "I hope I may be excused for one re- 
 mark on a tendency in education at present, 
 more especially with regard to the modern sub- 
 jects, to render the process interesting, as it is 
 usually called, but amusing would probably be 
 the more correct word. It would be absurd to 
 recommend that any subject should be proposed 
 in a purposely repulsive form to students, espec- 
 ially to youth ; but, on the other hand, it seems 
 to me a most enervating practice to shrink from 
 demanding even irksome attention whenever it is 
 necessary. The lesson that success in any pur- 
 
36 ON TEACHING. 
 
 suit demands serious toil must be learned eventu- 
 ally, and like most lessons is learned with least 
 pain in early years. " (Todhunter, Conflict of 
 Studies and other Essays, p7 21. London, 
 1873.) 
 
 26. " Parents and the public have little idea 
 how close a resemblance there is between teach- 
 ing and writing on the sands of the sea, unless 
 either there is a distinct capacity for learning on 
 the part of the pupil, or some system of ex- 
 amination and reward to force the pupil to ap- 
 ply. " (Jevons, paper in Mind, p. 195, No. VI., 
 April, 1877.) (Reinserted under Memory and 
 "Cram," 172.) 
 
 27. u Whatever the age and attainment of 
 the pupils under charge, the first requisite for 
 communicating instruction is to gain and keep 
 their attention. Teaching, to be successful, 
 must therefore be adapted to win attention. At 
 the earlier stages of school life this is the one 
 pressing require-ment. Somehow, attention must 
 be made possible even to the most restless little 
 ones, to whom the first restraints of school life 
 are irksome. Accustomed to have every new 
 object attract their interest just as long as they 
 recognized any thing attractive in it permitted 
 to change from one engagement to another as 
 caprice dictated they must be made familiar 
 with restriction. They must begin to be regu- 
 lated by the will of another. Taking this as 
 self-evident, we are prone to say that they must 
 do so, whether they will or not. This is one of 
 our superficial current phrases which cover over 
 
ON TEACHING. 37 
 
 many points needing careful consideration. At- 
 tention is not to be secured by mere exercise of 
 authority. Authority has a great deal to do 
 through the whole course of school life, but we 
 cannot ' command ' attention, as we say, by 
 merely demanding that it be given. A radical 
 mistake is made if a teacher lean on his authority 
 in the school as the guarantee for attention by the 
 scholars. He must consider the requirements 
 of the undisciplined mind, and adapt himself to 
 them. Children attend to what interests them. 
 This must determine the kind of assistance to- 
 be given them in acquiring habits of attention. 
 To help them in this is an obvious part of a 
 teacher's work. . . . The master of a school 
 in this respect shares a task which is common to 
 all who essay to teach others. In this appears 
 the true place and power of the profession.'* 
 (Calderwood, On Teaching, pp. 47-49, ed. 1875.) 
 28. The conception of Teaching which pre- 
 vails in these inquiries is limited to that assistance 
 which one person (teacher) consciously gives to 
 another person or thing (learner), when this lat- 
 ter is learning something. Teachers are not 
 necessarily educators. Any thing educates the 
 child that helps to mould its character, or that 
 stimulates its self-control. Fire educates in an 
 imperative manner, but it does not teach. The 
 authority of the parent educates his child, while 
 the child may be taught nothing in regard to the 
 nature or source of authority. A teacher's per- 
 sonal influence may educate a school in ways of 
 virtue, while he has taught them nothing about the 
 
38 OK TEACHING. 
 
 nature of virtue. Teaching regards the purely 
 intellectual capacities of Man. Education refers 
 to all the capabilities of Mind. The intellect is 
 taught by a person, and educated by persons and 
 things. The will is educated by any power. 
 Teaching sets the subject-matter, trusting the 
 mind to accept the truth ; educating may exert 
 a power without giving any reason or instruc- 
 tion. Teachers should be educators. Parents 
 are educators they may also be teachers. Good 
 teaching and good educating put the mind of 
 him who is taught or educated, into a frame 
 which acknowledges and accepts testimony and 
 authority from whatever source they spring. 
 That teaching or educating is pernicious which 
 leaves the mind of the learner in a state of un- 
 due skepticism towards testimony and authority. 
 (See 31-34.) 
 
 29. " The communication of knowledge in 
 general is the common idea by which these 
 words inform^ instruct, teach &IQ connect- 
 ed with each other. Inform is the general term ; 
 the other two are specifick. To inform is the 
 act of persons in all conditions ; to instruct and 
 teach are the acts of superiours, either on one 
 ground or another : one informs by virtue of an 
 accidental superiority or priority of knowledge ; 
 one instructs by virtue of superior knowledge, 
 or superior station : one teaches by virtue of 
 superiour knowledge, rather than station : diplo- 
 matick ao-ents inform their governments of the po- 
 litical transactions in which they are concerned ; 
 government instructs its different functionaries 
 
ON TEACHING. 39 
 
 and officers in regard to their mode of proceed- 
 ing ; professors and preceptors teach those who 
 attend a publick school to learn. 
 
 ' i To inform is applicable to matters of general 
 interest ; we may inform ourselves or others on 
 every thing which is a subject of inquiry or curios- 
 ity ; and the information serves either to amuse 
 or to improve the mind ; to instruct is applica- 
 ble to matters of serious concern, or that which 
 is practically useful ; it serves to set us right in 
 the path of life. A parent instructs his child in 
 the course of conduct he should pursue ; a good 
 child profits by the instruction of a good parent 
 to make him wiser and better for the time to 
 come ; to teach respects matters of art and 
 science ; the learner depends upon the teacher 
 for the formation of his mind, and the establish- 
 ment of his principles. Every one ought to be 
 properly informed before he pretends to give an 
 opinion ; the young and inexperienced must be 
 instructed before they can act ; the ignorant 
 must be taught, in order to guard them against 
 errour. Truth and sincerity are all that is neces- 
 sary for an informant ; general experience and 
 a perfect knowledge of the subject in question 
 are requisite for the instructor; fundamental 
 knowledge is requisite for the teacher. Those 
 who give information upon the authority of 
 others are liable to mislead ; those who instruct 
 others in doing that which is bad, scandalously 
 abuse the authority that is reposed in them ; 
 those who pretend to teach what they themselves 
 
40 ON TEACHING. 
 
 do not understand, mostly betray their ignorance 
 sooner or later. 
 
 " To inform and to teach are employed for 
 things as well as persons ; to instruct only for 
 persons : books and reading inform the mind ; 
 history or experience teaches mankind. ' ' (Crabb, 
 Synonyms, ed. 1859.) 
 
 30. "Inform (Lat. in and forma, shape or 
 form) relates only to matters of fact made known 
 to one who could not have known them before. 
 Instruction (Lat. instruere, instructus) relates 
 to principles drawn from known facts. Teach- 
 ing (A. S. t#can, to teach), as distinct from 
 instruction, is applied to practice (it may be the 
 practice of an art or branch of knowledge). A 
 child is instructed in grammar, and taught to 
 speak a language. Teach has a purely mechani- 
 cal application, which does not belong to instruct. 
 A dog may be taught a trick ; but he could not 
 be instructed in any thing. The two processes 
 of teaching and instruction may thus go on 
 simultaneously. In mathematics there is no in- 
 formation, because the propositions are not state- 
 ments of fact, but are based upon principles 
 assumed. . Information is of new facts ; instruc- 
 tion is of undeveloped truths. Information 
 extends knowledge ; instruction gives additional 
 understanding ; teaching, additional power of 
 doing. Acquaint (Fr. accointer, Lat. accognit- 
 are, from cognosce, cognitus, to know), Apprise 
 (Fr. appris, from apprendre, the Lat. appre- 
 hendere ), and Advise ( Fr. aviser, Lat. ad and 
 videre, visus, to see) closely resemble inform, 
 
ON TEACHING. 41 
 
 inasmuch as they relate to the communication of 
 matters of fact. I inform a man when I simply 
 tell him a fact which he did not know before. 
 I acquaint him with that of which I furnish 
 him with all the details. So I inform him of the 
 fact, and acquaint him with the particulars of it. 
 I apprise him of what particularly concerns him 
 to know, whether it be a good or an evil, or a 
 danger, or a probability of any sort. I advise 
 him of that which I impart to him formally, 
 officially, or as in duty bound, of what occurs in 
 due course. " (Smith, Syn. Discr.) 
 
IV. 
 
 ON AUTHORITIES. 
 
 31. il So in literature, men of established re- 
 putation, of classical merit, and known veracity, 
 are quoted as authorities in support of any 
 position/ 7 (Crabb, Synonyms.} 
 
 32. " Authority may come from superior 
 knowledge or information, or from natural as 
 well as social or professional relationship/* 
 (Smith, Synonyms Discriminated.) 
 
 33. " The Principle of Authority. 4 The 
 principle of adopting the belief of others, on a 
 matter of opinion, without reference to the par- 
 ticular grounds on which the belief may rest/ 
 
 " The Argument from Authority. It is an 
 argument for the truth of an opinion that it has 
 been embraced by all men, In all ages, and in all 
 nations. Quod semper, ubique, et ab omni- 
 bus, are the morks of universality, according to 
 Vincentius Lirinensis. l This word is sometimes 
 employed in its primary sense, when we refer to 
 any one's example, testimony, or judgment ; as 
 when, e.g., we speak of correcting a reading in 
 some book on the authority of an ancient MS., 
 or giving a statement of some fact on the author- 
 ity of such and such historians, etc. In this 
 
ON AUTHORITIES. 43 
 
 sense the word answers pretty nearly to the Lat- 
 in auetoritas. It is a claim to deference. Some- 
 times, again, it is employed as equivalent to 
 potestas, power, as when we speak of the 
 authority of a magistrate. This is a claim to 
 obedience. ' 
 
 " Consent. ' Believing in the prophets and 
 evangelists with a calm and settled faith, with 
 that consent of the will, and heart, and under- 
 standing, which constitutes religious belief, I 
 find in them the clear annunciation of the king- 
 dom of God upon earth. ' 
 
 " Assent is the consequence of a conviction 
 of the understanding. Consent arises from the 
 state of the disposition and the will. The one 
 accepts what is true; the other embraces it as 
 true and good and worthy of all acceptation. ... 
 
 i i i These things are to be regarded as first 
 truths, the credit of which is not derived from 
 other truths, but is inherent in themselves. As 
 for probable truths, they are such as are admitted 
 by all men, or by the generality of men, or by 
 wise men ; and among these last, either by all 
 the wise, or by the generality of the wise, or by 
 such of the wise as are of the highest authority.' 
 
 " Assent is that act of the mind by which we 
 accept as true a proposition, a perception, or an 
 idea. It is a necessary part of judgment ; for if 
 you take away from judgment affirmation or de- 
 nial, nothing remains but a simple conception 
 without logical value, or a proposition which 
 must be examined before it can be admitted. It 
 is also implied in perception, which would 
 
44 ON AUTHORITIES. 
 
 otherwise be a mere phenomenon which the mind 
 had not accepted as true. 
 
 * l Assent is free when it is not the unavoidable 
 result of evidence, necessary when I cannot 
 withhold it without contradicting myself. The 
 Stoics, while they admitted that most of our 
 ideas came from without, thought that images 
 purely sensible could not^be converted into real 
 cognitions without a spontaneous act of the 
 mind, which is just assent or belief. 
 ' Assent of the mind to truth is, in all cases, the 
 work not of the understanding , but of the 
 reason. Men are not convinced by syllogisms ; 
 but when they believe a principle, or wish to be- 
 lieve, then syllogisms are brought in to prove it.' 
 
 " Belief. ' Belief , assent, conviction, are 
 words which I do not think admit of logical defi- 
 nition, because the operation of mind signified by 
 them is perfectly simple, and of its own kind. 
 Belief must have an object. For he who believes 
 must believe something, and that which he be- 
 lieves is the object of his belief. Belief is always 
 expressed in language by a proposition wherein 
 something is affirmed or denied. Belief admits 
 of all degrees, from the slightest suspicion to the 
 fullest assurance. There are many operations of 
 mind of which it is an essential ingredient, as 
 consciousness, perception, remembrance. We 
 give the name of evidence to whatever is a 
 ground of belief. What this evidence is, is more 
 easily felt than described. The common occa- 
 sions of life lead us to distinguish evidence into 
 different kinds ; such as the evidence of sense, 
 
0]$" AUTHORITIES. 45 
 
 of memory, of consciousness, of testimony, of 
 axioms, and of reasoning. I am not able to find 
 any common nature to which they may all be 
 reduced. They seem to me to agree only in this, 
 that they are all fitted by nature to produce 
 belief in the human mind, some of them in the 
 highest degree, which we call certainty, others in 
 various degrees according to circumstances. ' 
 
 ' ' St. Austin accurately says, * We know what 
 rests upon reason ; we believe what rests upon 
 authority. ' The original data of reason do not 
 rest upon reason, but are necessarily accepted 
 by reason on the authority of what is beyond 
 itself. These data are, therefore, in rigid pro- 
 priety, beliefs or trusts. Thus it is, that in the 
 last resort, we must, perforce, philosophically 
 admit, that belief is the primary condition of rea- 
 son, and not reason the ultimate ground of belief. 
 We are compelled to surrender the proud Intel- 
 lige ut credas of Abelard, to content ourselves 
 with the humble Crede ut intelligas of Anselm. 
 
 " To believe is to admit a thing as true, on 
 grounds sufficient, subjectively; insufficient, 
 objectively. The word believing has been 
 variously and loosely employed. It is frequently 
 used to denote states of consciousness which 
 have already their separate and appropriate ap- 
 pellations. Thus it is sometimes said, I believe 
 in my own existence and the existence of an ex- 
 ternal world, I believe in the facts of nature, 
 the axioms of geometry, the affections of my 
 own mind, as well as, I believe in the testimony 
 
46 ON AUTHOKITIES. 
 
 of witnesses, or in the evidence of historical 
 documents. 
 
 " Setting aside this loose application of the 
 term, I propose to confine it, first, to the effect 
 on the mind of the premises in what is termed 
 probable reasoning, or what I have named con- 
 tingent reasoning in a word, the premises of all 
 reasoning, but that which is demonstrative ; and, 
 secondly, to the state of holding true when that 
 state, far from being the effect of any premises 
 discerned by the mind, is dissociated from all 
 evidence. I propose to restrict the term belief 
 to the assent to propositions, and demarcate it 
 from those inferences which are made in the 
 presence of objects and have reference to them. 
 I would say, we believe in the proposition ' Fire 
 burns, ' but know the fact that the paper about 
 to be thrust into the flame will ignite." (Flem- 
 ing, Vocab. of Phil.) 
 
 34. " Another error is a conceit that of for- 
 mer opinions or sects after variety and examina- 
 tion the best hath still prevailed and suppressed 
 the rest ; so as if a man should begin the labour 
 of a new search, he were but like to light upon 
 somewhat formerly rejected, and by rejection 
 brought into oblivion : as if the multitude, or 
 the wisest for the multitude's sake, were not 
 ready to give passage rather to that which is 
 popular and superficial, than to that which is 
 substantial and profound ; for the truth is, that 
 time seemeth to be of the nature of a river or 
 stream, which carrieth down to us that which is 
 
ON AUTHOKITIES. 47 
 
 light and blown up, and sinketh and drowneth 
 that which is weighty and solid 
 
 " Another error hath proceeded from too 
 great a reverence, and a kind of adoration of the 
 mind and understanding of man ; by means 
 whereof, men have withdrawn themselves too 
 much from the contemplation of nature, and the 
 observations of experience, and have tumbled 
 up and down in their own reason and conceits. 
 Upon these intellect ualists, which are notwith- 
 standing commonly taken f >r the most sublime 
 and divine philosophers, Heraclitus gave a just 
 censure, saying, Men sought truth in their own 
 little worlds, and not in the great and com- 
 mon world; for they disdain to spell, and so 
 by degrees to read in the volume of God's 
 works : and contrariwise by continual meditation 
 and agitation of wit do urge and as it were in- 
 vocate their own spirits to divine and give oracles 
 unto them, whereby they are deservedly deluded. 
 
 " Another error that hath some connexion with 
 this latter is, that men have used to infect their 
 meditations, opinions, and doctrines, with some 
 conceits which they have most admired, or some 
 sciences which they have most applied; and given 
 all things else a tincture according to them, utter- 
 ly untrue and improper. So hath Plato inter- 
 mingled his philosophy with theology, and 
 Aristotle with logic ; and the second school of 
 Plato, Proclus and the rest, with the mathematics. 
 For these were the arts which had a kind of 
 primogeniture with them severally. So have the 
 alchy mists made a philosophy put of a few ex- 
 
48 OX AUTHORITIES. 
 
 periments of the furnace ; and Gilbertus our 
 countryman hath made a philosophy out of the 
 observations of a loadstone. So Cicero, when, 
 reciting the several opinions of the nature of the 
 soul, he found a musician that held the soul was 
 but a harmony, saith pleasantly, Hie ab arte sua 
 non recessit, etc. But of these conceits Aristotle 
 speaketh seriously and wisely when he saith, ftui 
 respiciunt ad pauca de facili pronunciant. 
 
 " Another error is an impatience of doubt, 
 and haste to assertion without due and mature 
 suspension of judgment. For the two ways of 
 contemplation are not unlike the two ways of 
 action commonly spoken of by the ancients : the 
 one plain and smooth in the beginning, and in 
 the end impassable ; the other rough and trouble- 
 some in the entrance, but after a while fair and 
 even : so it is in contemplation ; if a man will 
 begin with certainties, he shall end in doubts ; 
 but if he will be content to begin with doubts, 
 he shall end in certainties. 
 
 1 ' Another error is in the manner of the tra- 
 dition and delivery of knowledge, which is for 
 the most part magistral and peremptory, and not 
 ingenuous and faithful ; in a sort as may be soon- 
 est believed, and not easiliest examined. It is 
 true that in compendious treatises for practice 
 that form is not to be disallowed : but in the 
 true handling of knowledge, men ought not to 
 fall either on the one side into the vein of 
 Velleius the Epicurean, Nil tarn metuens, quam 
 ne dubitare aliqua de re videretur ; nor on the 
 other side into Socrates his ironical doubting of 
 
OK AUTHORITIES. 4!) 
 
 all things ; but to propound things sincerely 
 with more or less asseveration, as they stand in a 
 man's own judgment proved more or less. 
 
 " Other errors there are in the scope that men 
 propound to themselves, whereunto they bend 
 their endeavours ; for whereas the more constant 
 and devote kind of professors of any science 
 ought to propound to themselves to make some 
 additions to their science, they convert their 
 labors to aspire to certain second prizes : as to 
 be a profound interpreter or commenter, to be a 
 sharp champion or defender, to be a methodical 
 compounder or abridger, and so the patrimony 
 of knowledge cometh to be sometimes improved, 
 but seldom augmented. 
 
 " But the greatest error of all the rest is the 
 mistaking or misplacing of the last or furthest 
 end of knowledge. For men have entered into 
 a desire of learning and knowledge, sometimes 
 upon a natural curiosity and inquisitive appetite ; 
 sometimes to entertain their minds with variety 
 and delight ; sometimes for ornament and repu- 
 tation ; and sometimes to enable them to victory 
 of wit and contradiction ; and most times for 
 lucre and profession ; and seldom sincerely to 
 give a true account of their gift of reason, to 
 the benefit and use of men : as if there were 
 sought in knowledge a couch whereupon to rest 
 a searching and restless spirit ; or a terrace for 
 a wandering and variable mind to walk up and 
 down with a fair prospect ; or a tower of state, 
 for a proud mind to raise itself upon ; or a fort 
 or commanding ground, for strife and conten- 
 
50 ON AUTHORITIES. 
 
 tion ; or a shop, for profit or sale ; and not a 
 rich storehouse for the glory of the Creator and 
 the relief of man's estate. But this is that which 
 will indeed dignify and exalt knowledge, if con- 
 templation and action may be more nearly and 
 straitly conjoined and united together than they 
 have been ; a conjunction like unto that of the 
 two highest planets, Saturn, the planet of rest 
 and contemplation, and Jupiter, the planet of 
 civil society and action. Howbeit, I do not mean, 
 when I speak of use and action, that end before- 
 mentioned of the applying of knowledge to lucre 
 and profession; for I am not ignorant how much 
 that diverteth and interrupteth the prosecution 
 and advancement of knowledge, like unto the 
 golden ball thrown before Atalanta, which while 
 she goeth aside and stoopeth to take up, the 
 
 race is hindered. 
 
 " Neither is my meaning, as was spoken of 
 Socrates, to call philosophy down from heaven 
 to converse upon the earth ; that is, to leave 
 natural philosophy aside, and to apply knowl- 
 edge only to manners and policy. But as both 
 heaven and earth do conspire and contribute to 
 the use and benefit of man ; so the end ought to 
 be, from both philosophies to separate and reject 
 vain speculations, and whatsoever is empty and 
 void, and to preserve and augment whatsoever is 
 solid and fruitful." (Bacon, Advancement of 
 Learning, pp. 39-43, ed. 1868.) 
 
V. 
 
 KECAPITULATIOK 
 
 35. This brief Introductory Discussion, re- 
 capitulated, exhibits the following synopsis : 
 
 I. PEDAGOGICS INCLUDES 
 
 1. Education, 
 
 2. Ethics, 
 
 3. Psychology. 
 
 II. EDUCATION KESTS UPON MATERIALS CON- 
 TAINED WITHIN 
 
 1. Ethics, 
 
 2. Psychology. 
 
 III. EDUCATION, IN PART, DEPENDS UPON 
 
 1. Teaching. 
 
 IV. TEACHING ASSUMES A KNOWLEDGE OF THE 
 
 TWO ELEMENTS 
 
 1. The mind that is to be taught- 
 
 Psychology, 
 
 2. The subject-matter that is to be 
 
 learned, drawn from 
 
 (a) Ethics, 
 
 (b) Psychology. 
 V. ON AUTHORITIES. 
 
PART SECOND. 
 
 ^. 
 
 36-57. 
 
 ON METHOD IN GENERAL. 
 
 METHOD, . . . . . . 36-9. 
 
 SYSTEM, 41. 
 
 ANALYSIS, . . i . . . . 43. 
 
 SEPARATION, 44. 
 
 SYNTHESIS, 45. 
 
 DEFINITION, .... 46 
 
 ABSTRACTION, 47. 
 
 RECONSTRUCTION, 49. 
 
 GENERALIZATION, . . . . . . 50. 
 
 CLASSIFICATION, 51. 
 
 INDUCTION, . . 52. 
 
 INTERPRETATION, 53. 
 
 REPETITION, 54. 
 
 DEDUCTION, 55. 
 
 MANNER, 56. 
 
 MODE, 57. 
 
ON METHOD IN GENERAL. 
 
 36. Method signifies literally the way to 
 seek after a thing. The Greek philosophers used 
 the word in this general sense, which has been 
 retained to the present. Although writers agree 
 substantially in assigning to the term the notion 
 of way, a principle which determines direction, 
 or orderly arrangement, yet the precise limita- 
 tions of the way are not attributed with equal 
 clearness and uniformity. By some, the term 
 implies the only way in which a thing can be 
 done. By others, Method is the only philosophi- 
 cal way of proceeding in an investigation, in- 
 volving actually two operations, analysis and 
 synthesis. Still others see in the word only a 
 particular way of doing a given thing, which way 
 may or may not depend upon the individuality 
 of those who achieve the task. (See Appendix 
 A, 225.) 
 
 37. Method in general never has respect to 
 the mind of the learner, but always has reference 
 to the subject studied. It assumes intellectual 
 activities and products. It is simply the way in 
 which the mental products are utilized and 
 unified into science. This field is that of logic. 
 " I adopt the opinion of Mr. Herbert Spencer, 
 that logic is really an objective science, like 
 
56 O!N" METHOD IK GENERAL. 
 
 mathematics or mechanics. " (Jevons, Pri. 
 Sci., p. 4, ed. 1877.) 
 
 38. The conception of Method resting upon 
 substantial data at either end of the process, it 
 is within the province of the term to speak of 
 methods of business, when referring to this or 
 that general way by which business transactions 
 are accomplished. (See Appendix A, 225.) 
 
 39. " The result has been half a century of 
 steady and unprecedented material growth, ac- 
 companied with corresponding improvement in 
 the structure of Government, which is probably 
 unequalled to-day in the success with which 
 scientific methods are made to work through 
 popular forms." (The Nation, No. 700, p. 328, 
 November 28, 1878.) " In a commercial country, 
 which depends so much on the maintenance of 
 credit, nothing is so important as that the credit 
 should rest on solid foundations not merely that 
 the bases of the several transactions should be 
 secure, but that the methods of business should 
 be regular, legitimate, and trustworthy. The 
 credit of an individual and of a bank depends 
 much more on the known fact that the business 
 done is done in a regular way, and with the 
 habitual observance of certain rules of safe con- 
 duct, than upon a knowledge of the particular 
 securities which accompany it. The one fact 
 should be certified to the public in all possible 
 ways, the other is in its nature private. (Ibid., 
 p. 330.) 
 
 40. In any investigation three distinct elements 
 are presented to the inquirer : (1) The object- 
 
ON METHOD IN GENERAL. 57 
 
 matter, which is the end of the inquiry ; (3) 
 The way in which the activities of the examiner 
 move forth and continue, while arriving at the 
 end ; (3) The state or condition of the one who 
 is putting forth the exertion to secure the end. 
 A direct discussion suggests these questions : 
 (1) Does Method regard immediately and solely 
 the object-matter of the investigation, how it is 
 finally left, or to be left, by the student, whether or 
 not it shall be in an orderly arrangement, as 
 of Classification? (2) Or does it regard only 
 the way in which the inquiry proceeds, as by An- 
 alysis, Synthesis, Induction, Deduction, Classifi- 
 cation, or Generalization ? (3) Or does it con- 
 sider especially the way in which the scholar, as 
 as a particular individual, carries on his work, 
 whether in this or that state of mind or body, 
 or by means of these or those carefully chosen 
 and utilized expedients and appliances which are 
 peculiar to himself alone ? 
 
 That is, in recapitulation : (1) Does Method 
 point sharply and first to the object investigated, 
 in what shape, form, or condition it shall be 
 left ? (2) Or does it indicate the direction, or 
 way in, or over, which the energy of the mind 
 moves in its activity ? (3) Or does it judge the 
 characteristics which are the difference between 
 the mind of the examiner and that of other men ? 
 In order to answer these questions, it becomes 
 necessary to attend to each in turn. 
 
 41. I. Consider the object-matter of study, 
 whatever it may be, as arithmetic, botany, or 
 grammar. The purposes of examining any ob- 
 
58 ON METHOD IN GENERAL. 
 
 ject are to know it ; to apprehend its parts, as 
 single things ; to discover the relations which 
 exist among those parts ; to rearrange its parts 
 and relations, if thereby the mind can better 
 seize, comprehend, or remember them, singly 
 and collectively ; to classify these parts into 
 some new whole, which is the product solely of 
 intellectual activity called thought, reflection, or 
 simply reason. The student finds the object- 
 matter of his attention in an apparently hetero- 
 geneous mass of disorder and confusion he 
 leaves it reduced into a congruous condition he 
 has been entirely unconscious of his own eccen- 
 tricities, or individuality, or expedients, or ways 
 in which his activities and energies have pro- 
 ceeded, whether by this or by that process or 
 route he has steadfastly and daily kept his at- 
 tention upon the object-matter, as to what it is, 
 and how he shall finally leave it adjusted, part 
 to part, part to the whole, and the whole to 
 other parts and wholes himself and the ways 
 by which his thought-powers went along in their 
 work have dropped entirely out of consideration. 
 In this case the idea of searching out is not 
 found, because the attention rests exclusively 
 upon the object-matter which incited and de- 
 termined the action called seeking after that 
 is, the student considers the purposes attained, 
 and not the routes or ways through or by which 
 his powers brought forth those classified and 
 organized ends. It follows, hence, that this is 
 not a case of Method. The result or end spoken 
 
ON METHOD IN GENERAL. 59 
 
 of is properly a system, economy, or constitu- 
 tion. (See 124, and Appendix B, 226.) 
 
 42. II. Consider exclusively tlie ways over 
 which the activities of the intellect proceed when 
 they are engaged in an investigation. These may 
 be called Modes of Method in General. 
 
 43. () The faculties of observation are on 
 the alert to discriminate the parts of the wholes 
 of the object -matter of investigation, and the at- 
 tributes or characteristics of those parts or wholes 
 these parts and attributes are likewise observed 
 under the light of thought or reflection, called 
 comparison, by which the analogous elements of 
 similars are discovered. This way, by which the 
 powers of the mind must pass in order to discover 
 the individual Facts, known as elements, for the 
 relations called similars and dissimilars, is prop- 
 erly denominated Analysis. (See Appendix C, 
 227.) 
 
 44. A rigid distinction should be observed 
 between analysis and separation, or division. 
 Separation sets apart one thing from another the 
 thing set aside may be a part of that from which 
 it is now placed, or it may be some other whole 
 thing placed apart from the former. Division 
 implies a taking asunder, and ordinarily refers 
 to some whole which is cut into parts. In separa- 
 tion or division the process ends with the action, 
 while in analysis these parts are not only made or 
 found, but they are examined for the purpose of 
 discovering similarities. Separation and division, 
 having set apart the portions, give them no farther 
 examination nor attention. An artisan takes a 
 
60 ON METHOD IN GENERAL. 
 
 watch into its parts for the purpose of cleaning 
 and repairing the time-piece. His examination of 
 each part is to the sole end of discovering whatever 
 particles of dust may be adhering to it. There is 
 no examination in the interests of science or 
 higher truth, either theoretical or practical. This 
 is a case of separation, rather than of analysis. 
 
 46. (&) Assuming the foregoing analysis com- 
 plete, the powers of thought apprehend the 
 elements, which are to constitute the similars, 
 and from them create a new intellectual product. 
 In this process the unassirnilative elements are 
 rejected by the mind, and form no portion of the 
 new products. The way or route by which the 
 mind proceeds in creating these intellectual pro- 
 ducts is called Synthesis. (See Appendix D, 
 228.) 
 
 46. Sometimes the elements of a synthesis 
 are the products of Definition. (See Appendix 
 E, 229.) 
 
 47. The process of assorting and rejecting 
 the analytical elements is known as Abstraction. 
 (See Appendix F, 230.) 
 
 48. " Analysis and synthesis, though com- 
 monly treated as two different methods, are, if 
 properly understood, only the two necessary 
 parts of the same method. Each is the relative 
 and the correlative of the other. Analysis, with- 
 out a subsequent synthesis, is incomplete ; it is 
 a mean cut off from its end. Synthesis, without 
 a previous analysis, is baseless ; for synthesis 
 receives from analysis the elements which it re- 
 
ON METHOD IK GENERAL. 61 
 
 composes." (Sir W. Hamilton, Metaphysics, 
 p. 69, ed. 1871, Boston.) 
 
 49. Synthesis should be discriminated from 
 Reconstruction it is Construction, Recon- 
 struction is the opposite of separation or division ; 
 it simply re-makes the whole by re-adjusting those 
 elements or parts which were set aside from each 
 other it fashions no new whole. Synthesis is 
 Construction ; it fabricates an original product 
 which essentially and materially differs in its 
 nature from any and all of the wholes that were 
 separated by analysis. In the supposition of the 
 watch ( 44), if the parts be restored to their 
 former position, and the watch ' ' put together ' ' 
 again, it is a case of reconstruction, rather than 
 of synthesis. There is no new product created 
 by the procedure. 
 
 50. (c) Analogous elements being assumed 
 in the possession of the student, he proceeds by 
 synthesis to " comprehend, under a common 
 name, several objects agreeing in some point 
 which he abstracts from each of them, and which 
 that common name serves to indicate. " This 
 way of proceeding is usually known under the 
 name of Generalization. (See Appendix G, 
 
 231-) 
 
 51. (d) Generalization, in its ways of pro- 
 ceeding, is but another name for classification, 
 although in the extent to which they are carried 
 in science classification is the more comprehen- 
 sive term. By some writers, generalization is 
 used in reference to the object-matter of cause 
 and effect, while investigation proceeding on the 
 
62 ON METHOD IN GENERAL. 
 
 idea of observed resemblances, is the province of 
 Classification. (See Appendix H, 232.) 
 
 52. (e) When generalization or classification 
 is complete in extension at any point in the 
 ascending degrees, and the scholar, by his powers 
 of thought, extends the generalization by infer- 
 ence so as to include objects which the preced- 
 ing generalization does not cover in his experience 
 or observation thus making a new creation, 
 known as a universal, sometimes as a general 
 the product is called an Induction, (See Ap- 
 pendix /, 233.) 
 
 53. Induction should not be confounded with 
 pure explanation, or what is known as Mathe- 
 matical Interpretation. Induction creates a 
 new inferential product, the elements of which are 
 discovered only by the examination of many ob- 
 jects, and the inference extends over unexamined 
 and unexplored territory. Interpretation places 
 itself at the point of completion of a single 
 observation, operation, or process, and retraces 
 the steps over the way followed, and explains 
 fully the meaning, extensive and intensive, of 
 what is observed, predicting simply that all similar 
 examples will be traced along the same way, and 
 the same ends reached. Sciences founded upon 
 general definitions instead of observation and ex- 
 periment, are not inductive. The Pure Mathe- 
 matical sciences are not properly inductive, and 
 from their nature cannot be. What is usually 
 called Mathematical Induction is Interpretation. 
 The so-called Perfect Induction is hardly Induc- 
 tion in its nature, because no product is created 
 
ON METHOD IN GENERAL. 63 
 
 beyond a generalization, or classification, and 
 nothing is gained by using two terms for the 
 same thing, when there are two notions to be 
 distinguished from each other. (See Appendix 
 /, 233, Nos. 4, 5, and 7. Also Appendix J y 
 
 234 -) 
 
 54. Another point should be clearly outlined : 
 The mere Repetition of examples, substantially 
 identical, does not increase the force and certi- 
 tude, nor extend the range, of an inference. One 
 example covers the whole territory, and it, to- 
 gether with all others of the kind, does no more 
 than illustrate the original principle established 
 directly or indirectly by definition. In arith- 
 metic, for example, repetition of examples adds 
 nothing to the elements of which the " rule" 
 is made it simply serves to impress the way, 
 the procedure, upon the mind of a learner, simi- 
 larly to the repetition in the finger exercises 
 upon the piano. (See 204-7.) 
 
 It should be observed that there is a great 
 variety of opinions among authors concerning the 
 nature of Induction. The citations in the Ap- 
 pendix exhibit some of the views. 
 
 55. (/) If a scholar assume the possession of 
 generals or uni\ r ersals, furnished either by In- 
 duction, by Definition, or by Intuition, and then 
 use them with which to compare individual facts 
 or truths, and by this means establish individual 
 truths of like kind as an end of the process, the 
 way of proceeding is known as Deduction. (See 
 Appendix K, 235.) 
 
 56. III. Consider the way in which the 
 
64 ON METHOD IK GENERAL. 
 
 individual student addresses himself to his tasks. 
 He may be proceeding by any of the above- 
 named modes, or ways, usually called Methods, 
 and his own characteristics of disposition, habits, 
 eccentricities, may be prominent. These may or 
 may not be aids in securing valuable results of 
 his labors. In any case, these are simply and 
 solely individualities they belong exclusively to 
 the investigator they are no necessary part of 
 the mode or Method he is following they are 
 his Manner. 
 
 Critical discrimination should be made be- 
 tween what is necessary to a way, and what is 
 purely incidental to the individual who is pro- 
 ceeding over that way. Indifference to this 
 discrimination is followed by the pedantic asser- 
 tion that each man can have a method of his 
 own. Methods are ways which are independent 
 of this or that man, and which are determined 
 by the nature of the mind of man, or by the 
 nature of the object-matter to be investigated. 
 But Manner is his individuality when proceeding 
 in a Method. (See 123.) 
 
 57. When one's Manner is well ordered in its 
 System, it is designated by the term Mode. (See 
 123.) 
 
PART THIRD. 
 
 58-216. 
 
 ON METHODS OP TEACHING. 
 
 I. ON THE THEORY OF METHODS 
 OF TEACHING, . 
 
 II. ON THE PRACTICE OF METHODS 
 OF TEACHING, .... 
 
 (A) On the Knowing Faculties 
 of the Mind, .... 
 
 (B) On the Nature of Subject- 
 Matter, 
 
 (C) On Discovering Methods of 
 Teaching Special Subjects, 
 
 III. CONCLUDING REFLECTIONS, 
 
 58-143 
 144-216 
 144-187 
 188-210 
 
 211-216 
 S 217-224 
 
I. 
 
 ON THE THEORY OF METHODS OF 
 TEACHING. 
 
 58. " I am afraid it must be allowed, that no 
 art, of equal importance to mankind, has been 
 so little investigated scientifically as the art of 
 teaching. No art is in the hands of practition- 
 ers who are so apt to follow so blindly in the old 
 paths. I say this with the full recollection that 
 there has been great improvement in England 
 lately, and that the books of teaching, most in 
 use, have been purged of many gross errors both 
 of statement and of method. But one line of 
 enquiry there is which has never been sufficiently 
 followed, though one would have thought it ante- 
 cedently the most promising of all, the study of 
 the human mind through actual observation, and 
 the study of the expedients by which its capacity 
 for receiving and retaining knowledge may be en- 
 larged. The field of investigation has been al- 
 most wholly neglected, and therefore it may just 
 be that we are on the eve of great discoveries in 
 education, and that the processes of these teach- 
 ers are only a rough anticipation of the future. 
 The fact that the methods of teaching follow- 
 ed in England are almost wholly empirical, that 
 
68 ON THE THEORY OF 
 
 for the most part they entirely neglect individual 
 differences of character and temperament, that 
 they certainly work counter to the known laws 
 according to which some of the mental faculties 
 operate, for example ; the memory all these 
 facts seem to my mina to point at possibilities 
 and chances of improvement, which a few 
 persons, by expedients which, I frankly allow, 
 seem even to me somewhat ignoble, have perhaps 
 had the good fortune to realize beforehand." 
 (Maine, Village Communities and Miscellanies, 
 ed. 1876, pp. 285, 286.) 
 
 59. A complete discussion of the Theory of 
 Methods of Teaching would include a full inves- 
 tigation of Psychology and of the nature of sub- 
 ject-matter to be taught it would be an exhaus- 
 tive examination of the relations which exist be- 
 tween the various faculties of the mind and the 
 many kinds of objects to be learned. It would 
 inquire, first, how mind acts as an original cause 
 of activity, then what are the nature and char- 
 acter of its capacities, and lastly what are the 
 products of its activity. This investigation is 
 purely psychological, and lies anterior to the 
 province of logic it is supra-logical, and regards 
 the function, nature, and character of the activi- 
 ties and faculties of the mind that learns, and 
 that grows by introsusception. 
 
 60. By the nature of a faculty is meant not 
 only its function, but that native endowment of 
 its Potentiality out of which grow all those suc- 
 cessive degrees of power that manifest themselves 
 in a reality. 
 
METHODS OF TEACHING. 69 
 
 61. By the character of a faculty is designat- 
 ed the state in which it exists at any specified 
 stage in its growth. 
 
 62. By Psychology is meant the introspective 
 study of the experience of the mind itself. 
 
 63. " No student of Locke and Hume can 
 read the psychological works of the present day 
 without feeling anxiety for the future of the study 
 of Mind or Experience. The modern psycholo- 
 gist is profoundly dissatisfied with his subject ; 
 the exact and the classificatory sciences, by the 
 brilliance of their methods and results, fill him 
 with envy ; he is painfully conscious that mental 
 phenomena are not definite enough to be the ob- 
 jects of a science ; he must therefore connect 
 them with other phenomena which are. Hence 
 the i Physiological Psychology ' of our day. But 
 surely this is not psychology, or the study of ex- 
 perience, but physiology. Let us keep clearly 
 before our minds that psychology is the study 
 
 of experience Psychology then, if we 
 
 retain the word, is a critique, a Method, a 
 certain thoughtful attitude in science, morals, and 
 literature. It is the critical examination of my 
 own adult opinions, desires and tastes in rela- 
 tion to present objects No amount 
 
 of information respecting the evolution of belief 
 or sentiment, and no amount of mental physiol- 
 ogy can ever take the place of acquaintance with 
 my own real opinions and desires. Modern works- 
 on mental science, with very few exceptions, 
 forget this. The conditions of ideation, the 
 origin of moral and aesthetic feelings, and such 
 
70 ON THE THEORY OF 
 
 like, are fully discussed ; but we look in vain 
 for a home-question like this i After all, do t 
 really desire nothing for myself but Happiness. ' 
 Individualism thoughtful reference to one's 
 own experience is indeed a rare quality now. " 
 (Stewart, Psychology, in Mind, pp. 445-451, 
 No. IV, October, 1876.) 
 
 64. Methods of Teaching, having an ac- 
 quaintance with Mind, consider the nature of 
 intellectual products, show in what order they 
 follow each other, reveal the way in which the 
 activities of Mind proceed with these products, 
 classify them, and build up Science out of them. 
 This is the arena of Logic, and has reference to 
 System, or subject-matter as such it is infra r 
 psychological. Succeeding this comes a thorough 
 discussion of subject-matter that is to be learned 
 by the mind of the student. A treatment so 
 elaborate could not be concluded in one brief 
 Study, were it desirable to attempt it. Another 
 occasion must serve portions of this work, as it 
 may occur. No more will be essayed at this 
 time than to survey the line of the investigation 
 as well as may be, by " blazing" the way, some- 
 times l ' doubling upon the track, ' ' so that others 
 may follow and clear up the obscurities and re- 
 move the errors, that lie upon this intricate 
 way, and enlarge the practical value which must 
 result from a scientific research. 
 
 65. " Since the human mind must conscious- 
 ly reproduce what actually exists, the act of 
 knowing is conditioned in two ways : a. Sub- 
 jectively, by the essence and natural laws of the 
 
METHODS OF TEACHING. 71 
 
 human mind, especially by those of the human 
 powers of knowledge ; b. Objectively, by the 
 nature of what is to be known. The constitu- 
 tions and relations of what is to be known, so far 
 as these require different ways of representation 
 in the act of knowing, we call forms of existence 
 (e.g., subsistence and inherence). The notions 
 of these forms of existence are the metaphysical 
 categories. The different ways, corresponding 
 to these forms of existence, in which what actual- 
 ly exists is taken hold of and copied in the act 
 of knowledge, are the forms of knowledge (e.g., 
 the categorical judgment). The actual copy, the 
 result of the activity of knowledge, is the con- 
 tent of knowledge. . . . The laws of 
 knowing, as such, determine only the ways of 
 representation (copying), or the forms of knowl- 
 edge, not its contents. . . . These forms 
 of knowledge correspond to the forms of exist- 
 ence, and they are conditioned by the objective 
 reality." (Ueberweg, Log. Doct., pp. 3, 4, ed. 
 1871.) 
 
 66. " The sense attached at the present day 
 to the words form and matter, is somewhat dif- 
 ferent from, though closely related to, these 
 (form and law). The form is what the mind 
 impresses upon its perceptions of objects, which 
 are the matter ; form therefore means mode of 
 viewing objects that are presented to the mind. 
 When the attention is directed to any object, 
 we do not see the object itself, but contemplate 
 it in the light of our own prior conceptions. A 
 rich man, for example, is regarded by the poor 
 
72 ON THE THEORY OF 
 
 and ignorant under the form of a very fortunate 
 person, able to purchase luxuries which are 
 above their own reach ; by the religious mind 
 under the form of a person with more than or- 
 dinary temptations to contend with ; by the 
 political economist, under that of an example of 
 the unequal distribution of wealth ; by the trades- 
 man, under that of one whose patronage is 
 valuable. Now, the object is really the same to 
 -all these observers ; the same rich man has been 
 represented under all the different forms. And 
 the reason that the observers are able to find 
 many in one, is that they connect him severally 
 with their own prior conceptions. The form, 
 then, in this view, is mode of knowing ; and 
 the matter is the perception, or object, we have 
 to know." (Thompson, Outline of Laws of 
 Thought, p. 34, 2d ed.) 
 
 67. " Form is something which may remain 
 uniform and unaltered, while the matter thrown 
 into that form may be varied. Medals struck 
 from the same dies have exactly the same form, 
 but they may be of various matter, as bronze, 
 copper, gold, or silver. A building of exactly 
 the same form might be constructed either of 
 stone or bricks ; furniture of exactly similar 
 shape may be made of oak, mahogany, walnut 
 wood, etc." (Jevons, El. Les. Logic, ed. 1878, 
 pp. 4-5.) 
 
 68. "Distinction between Form and Mat- 
 ter. This phraseology was introduced by Aris- 
 totle, who represented every thing as having in 
 itself both matter and form. It had a new 
 
METHODS OF TEACHING. 73 
 
 signification given to it by Kant, who supposes 
 that the mind supplies from its own furniture a 
 form to impose on the matter presented from with- 
 out. The form corresponds to the a priori ele- 
 ment, and the matter to the a posteriori. But 
 the view thus given of the relation in which the 
 knowing mind stands to the known object is 
 altogether a mistaken one. It supposes that the 
 mind in cognition adds an element from its own 
 resources, whereas it is simply so constituted as 
 to know what is in the object. This doctrine 
 needs only to be carried out consequentially to sap 
 the foundations of all knowledge, for if the 
 mind may contribute from its own stores one 
 element, why not another ? Why not all the 
 elements ? In fact, Kant did, by this distinction, 
 open the way to all those later speculations 
 which represent the whole universe of being as 
 an ideal construction. There can, I think, be 
 no impropriety in speaking of the original prin- 
 ciples of the mind as forms or rules, but they 
 are forms merely, as are the rules of grammar, 
 which do not add any thing to correct speaking 
 and writing, but are merely the expression of the 
 laws which they follow. As to the word i mat- 
 ter, ' it has either no meaning in such an appli- 
 cation, or a meaning of a misleading character. ' ' 
 (McCosh, Int. of Mind, p. 312, ed. 1870.) 
 
 69. " The drift and meaning of a branch of 
 knowledge varies with the company in which it 
 is introduced to the student. If his reading is 
 confined simply to one subject, however such 
 division of labor may favor the advancement of a 
 
74 OK THE THEORY OF 
 
 particular pursuit, a point into which I do not here 
 enter, certainly it has a tendency to contract his 
 mind. If it is incorporated with others, it de- 
 pends on these others as to the kind of influnce 
 which it exerts upon him. Thus the Classics, 
 which in England are the means of refining the 
 taste, have in France subserved the spread of re- 
 volutionary and deistical doctrines. In Meta- 
 physics, again, Butler's Analogy of Religion, 
 which has had so much to do with the conversion 
 to the Catholic faith of members of the Univer- 
 sity of Oxford, appeared to Pitt and others, who 
 had received a different training, to operate only 
 in the direction of infidelity. . . It is not so 
 much this study or that, as it is the setting into 
 other studies that moulds the impression. In 
 this is the notion of being liberally educated 
 that any subject is received without prejudice. ' ' 
 (Newman, Idea of A University, p. 100, ed. 
 1873.) 
 
 70. " The policy of the present Minister of 
 Public Instruction (Russia) has been to discoun- 
 tenance the study of natural science, as the source 
 of mutiny and insubordination, and encourage 
 that of the classics, as favorable to discipline 
 and authority and to the state of religion." 
 (The Nation*^. 704, Dec. 26, 1878, p. 393.) 
 
 " The generality of travellers enveloped for- 
 ever in customs, habits, prejudices, and wants 
 peculiar to themselves, move, as it were, in an 
 atmosphere of their own, which divides them 
 from the places through which they pass, as from 
 so many different worlds. A Frenchman would 
 
METHODS OF TEACHING. 75 
 
 fain carry all France along with him ; as soon as 
 he misses the smallest of his accustomed con- 
 veniences, he overlooks its equivalent, and be- 
 lieves himself lost. Comparing continually 
 what he sees with what he has quitted, he thinks 
 it worse only because it is not the same, and 
 cannot sleep in the Indies if his bed is not made 
 as it was at Paris. ' ' (Rousseau, Emilius, vol. iv. , 
 pp. 226-7.) 
 
 71. ff Knoivledge is a general term which im- 
 plies the thing known: science, learning, and 
 erudition, are modes of knowledge qualified by 
 some collateral idea : science is a systematick 
 species of knowledge which consists of rule and 
 
 . order ; learning is that species of knowledge 
 which one derives from schools, or through the 
 medium of personal instruction ; erudition is 
 scholastick knowledge obtained by profound re- 
 search ; knowledge admits of every possible de- 
 gree, and is expressly opposed to ignorance ; sci- 
 ence, learning, and erudition, are positively high 
 
 degrees of knowledge Learnin g is 
 
 less dependent on the genius, than on the will of 
 the individual ; men of moderate talents have 
 overcome the deficiencies of nature, by labour and 
 perseverance, and have acquired such stores of 
 learning as have raised them to a respectable 
 station in the republick of letters. Profound eru- 
 dition is obtained but by few ; a retentive mem- 
 ory, patient industry, and deep penetration, are 
 requisites for one who aspires to the title of an 
 erudite man. " (Crabb, Synonyms.} 
 
 72. All knowledge that we possess must be 
 
76 ON THE THEORY OF 
 
 in some form it would be well to say shape, if 
 intellectual products or impressions could have 
 shape. The term knowledge is sometimes used 
 in two meanings : as completed thought, which 
 is a product ; and as the action of the mind, the 
 completion of which is a product. There is 
 greater philosophical precision if the term be 
 assigned only one signification that of the 
 noun, act or product. " Knowledge in its ex- 
 actest definition is, in its positive form, A Con- 
 scious identification of Attribute with its sub- 
 ject, as in the affirmative proposition, the sun is 
 bright. In its negative form, it is A Conscious 
 differencing of an Attribute from its subject, 
 as in the negative proposition, the sun is not 
 dark." (Day, Outl. Ontolog. Science, p. 32, ed. 
 1878.) 
 
 73. " Knowledge is the act or product of a 
 rational nature. As such it ever tends to a sys- 
 tem which is characterized by singleness of 
 source and aim ; and this tendency is along the 
 line which reason prescribes to a movement 
 from a recognized source to the proposed end. 
 There are different specific sources, as there are 
 manifold specific aims in knowledge, indeed ; but 
 reason is one and its field is one and its aim 
 one, comprehensive of all special objects and all 
 special aims. There is such a thing, therefore, 
 as a method in all true rational knowledge. 7 ' 
 (Ibid., p. 31.) 
 
 74. In these three distinct things the source, 
 the end, and the ivay of knowledge the last is 
 the method of knowledge. " The aim of knowl- 
 
METHODS OF TEACHING. 77 
 
 edge is Truth. Knowledge arrived at the cer- 
 tainty of truth i& Science. Material (or real) 
 truth must be distinguished from (formal) cor- 
 rectness. Material truth in the absolute sense, 
 or simply truth, is the agreement of the content 
 (attributes) of knowledge with what actually 
 exists. Material truth in the relative sense, or 
 phenomenal truth, is the agreement of the me- 
 diately acquired content of thought with the im- 
 mediate outer or inner perceptions which exist 
 when the soundness of the mind and of the 
 bodily organs is undisturbed, or would exist 
 under the corresponding outer conditions." 
 {Ueberweg, Logical Doct., pp. 5, 6, ed. 1871.) 
 
 75. All these illustrations of the province of 
 knowledge compel attention to the stages of the 
 process of acquiring knowledge by the mind of 
 the learner. (1) There is the source of the 
 activity residing in the innate power of the 
 mind to act responsively and intuitively at the 
 presence of objects to be known. This in- 
 nate power of the mind is called the ultimate 
 ause of Knowledge, or simply the Cause. (2) 
 There is the rational way in which this activity 
 proceeds, usually at the dictation of the power 
 of the Will. This way is known as the Method 
 of Thought. (3) There is, lastly, the end of the 
 activity. This consummation of the process into 
 completeness is known as the act, or product of 
 knowledge, or simply Knowledge. 
 
 76. The preceding discussion relates, in the 
 most general sense, to the consideration of 
 knowledge as acquired by the learner. In or- 
 
78 OST THE THEORY OF 
 
 dinary acceptance the notion of learning is as- 
 sociated with two persons the one an instruc- 
 tor or teacher of the other, who is called the 
 learner, student, scholar, child, or pupil. When 
 the pupil learns through the instrumentality of a 
 living teacher he is said to be taught. 
 
 77. When he learns without this instrumen- 
 tality, he is said to be self -informed, or self- 
 educated. The self-informed student applies 
 himself to understand whatever engages his atten- 
 tion, whether books, or objects of nature, or works 
 of art ; he applies his powers of observation and 
 of reason to the things that he finds scattered 
 about him as a heterogeneous mass ; he constructs 
 his own questions for himself, invents his own 
 illustrations, creates his own hypotheses, and ad- 
 judges the validity of his own arguments and 
 conclusions that is, he alone pronounces upon 
 the form and matter of his knowledge, - and 
 way of approaching it. In very many impor- 
 tant matters he must leave it for time and experi- 
 ence to inform him whether his knowledge is 
 correct in fact. The element of time spent in 
 arriving at truth by the self-educated student is 
 often great for the amount and quality of knowl- 
 edge gained. The difficulties that present them- 
 selves to this learner are frequently sufficient to 
 deter any but the most persevering and venture- 
 some from attempting to surmount them. The 
 fields of learning are so many and so extensive, 
 and human life so short, that the imperative 
 demands of our brief years give a practical 
 value to some kinds of knowledge over others. 
 
METHODS OF TEACHING. 79 
 
 The exclusively self-informed student is not as- 
 sured that his learning is best calculated to pro- 
 mote the welfare of himself and his fellow-man. 
 A well-authenticated instance, related to the 
 writer by Dr. J. Dorman Steele, will illustrate 
 this statement : A young man of excellent 
 parts entered college. He had adopted the 
 theory that self -education is the only way to 
 learning, and refused to consult or study books 
 to prepare his lessons. He attended the recita- 
 tions, observed closely what was said there, and 
 depended upon his genius, or " inner conscious- 
 ness, " to evolve from himself the knowledge 
 he possessed. In process of time he was grad- 
 uated, and dropped into obscurity. After five 
 or six years he suddenly appeared at the office 
 of the president of the college. He desired to 
 submit to the president a law in physics which 
 he had discovered by his own unaided obser- 
 vations during the past six years. If approved 
 by the president, he would publish his discov- 
 ery. He had discovered " that heat expands 
 metals, and cold contracts them." The presi- 
 dent called his little daughter, and asked her, 
 what is the " first law in Natural Philosophy "? 
 She said, " That heat expands metals, and cold 
 contracts them." Said the president, " You 
 see how many valuable years you have lost by 
 neglecting to study books as well as objects, 
 depending entirely upon your own inner con- 
 sciousness for your knowledge." 
 
 78. These considerations of reason and ex- 
 perience bring forward the idea of aiding the 
 
80 ON THE THEORY OF 
 
 youth of the State by means of appropriating 
 to their benefit the learning and experience of 
 some of the older members of the State. Those 
 who consciously and methodically aid the young 
 in acquiring learning and experience are known 
 as Teachers. The efforts, which they put forth 
 to advance their pupils in knowledge, constitute 
 the idea that is designated Teaching. 
 
 79. Teaching is consciously adjusting ob- 
 jects and acts to the proper faculties and ca- 
 pacities of the learner. "Adjust is to set right 
 (Fr. juste, straight, right). Hence the word 
 implies some relative order, shape, or standard, 
 to which matters have to be brought, or some 
 antecedent condition of inherent fitness to 
 which they have to be reduced. " (Smith, Syn. 
 Discr.) The order in which objects are to be 
 presented to the pupil is determined by the 
 teacher. Nature, as the child finds her, pre- 
 sents objects to it in an unclassified, promis- 
 cuous mass. The pupil may see a cat, then an 
 elephant, then a thunder-storm, all in one hour. 
 The teacher would present objects in a sequence 
 determined by previous study and classification. 
 This order is artificial to the child, compared 
 to the heterogeneous order in which Nature ex- 
 hibits objects to it. From this view, it may be 
 said that teaching is the conscious and philo- 
 sophic adjustment of object-matter to the abili- 
 ties of the pupil. 
 
 80. The teacher has other duties towards his 
 pupil. He presents before the mind of the 
 learner some entire object Nature also usually 
 
METHODS OF TEACHING. 81 
 
 does this, but she leaves the mind to struggle 
 with the whole at once the teacher, finding the 
 whole too vast for the pupil, separates it, prac- 
 tically and virtually, into parts. This process 
 of dissection may be accomplished by using the 
 scalpel, the hammer, or by questions ; for ques- 
 tions are but knives that dissect out parts to 
 display to the pupil, or they are colter-shares 
 that cut out furrows in the turf, narrower or 
 wider, for the pupil to turn over, according to 
 his strength. 
 
 81. The teacher has still other duties in the 
 case. He is to note both- the form and the 
 matter of the knoivledge which the learner 
 acquires, whether it stand in his mind correct in 
 its impression and true in its essence. To se- 
 cure these ends requires consummate skill of the 
 teacher : his reason must be well trained and 
 certain in its logical processes, his wit must be 
 ready at analogies, his imagination must be fer- 
 tile in illustration, his hands must be cunning in 
 constructing, his understanding must be pro- 
 found, and his knowledge must be overflowing 
 in its quantity. Here lie the purely professional 
 regions of teaching here also are the processes 
 called Methods of Teaching. 
 
 82. T ne teacher has now reached the great 
 question of the Profession : How to teach. ? 
 For it is in teaching and with teachers, as it is 
 in Logic, " Where two conditions are found or 
 assumed : Firstly, that there exist certain men- 
 tal laws to which every sound thinker is bound 
 to conform. Secondly, that it is possible to 
 
82 ON THE THEOKY OF 
 
 transgress those laws, or to think unsoundly/' 
 (Mansel, Prolegomena Logica, p. 16, ed. 1860.) 
 
 83. In order to answer this question, How 
 to teach ? even approximately, it is necessary 
 to enter into a more critical examination of the 
 conception of the word Teaching. To teach 
 requires, obviously : (1) The mind of the 
 learner, or the learner ; (2) The mind of the 
 instructor, or the teacher ; (3) The objects, ac- 
 tions, or things to be learned by the student, 
 which are commonly designated, collectively, 
 as subjects, subject-matter, objects, or object- 
 matter. The intellectual activities of the teacher 
 proceed under certain fixed laws of mind. His 
 intellectual faculties conform to spheres of ac- 
 tivity into which they are necessitated or deter- 
 mined by their very nature. He cannot remem- 
 ber with his faculty of imagination, nor reason 
 with memory. He must perceive with his senses, 
 reason with his reflective powers, and retain by 
 his memory. As with the teacher so with the 
 learner, whose mental faculties and capabilities 
 may differ from those of the teacher in original 
 quantum of functional endowment, and in de- 
 grees of power, but not in kind or function. 
 
 84. This being true, the case resolves itself 
 into this : (1) If the teacher knew subject-mat- 
 ter thoroughly he could arrange its parts into 
 any order of dependence, or steps, or points, or 
 classifications, that circumstances or exigencies 
 might necessitate, or expediency demand. This 
 would enable him to arrange and present his 
 system of subject-matter. (2) If, in addition 
 
METHODS OF TEACHING. 83 
 
 to tliis, he knew mind thoroughly, in its facul- 
 ties, powers, capabilities, laws of growth in 
 short, in its nature and character, he would know 
 exactly how to adjust the subject-matter to be 
 learned to the mind that is to learn it. 
 Varying circumstances of state or condition, would 
 not prevent this certainty of adj ustment it would 
 be like the scientist adjusting the object that 
 he is examining to the focus of his microscope 
 so that his eye can see it in defined outline. 
 (3) If, succeeding these two suppositions, the 
 teacher now turns his attention for the time ex- 
 clusively to consider the ways in which his sys- 
 tem of subject-matter shall be set before, or in 
 the presence of, those faculties which are the 
 native ones to acquire learning from this sys- 
 tem, if he does this, he will be carrying on in- 
 vestigations in a province which is original and 
 peculiar to the Profession of Teaching. 
 
 86. A recapitulation of these points presents : 
 1) The first field opened for the teacher-candi- 
 " is that of subject-matter to be taught by 
 him, and that is to be learned by the student. 
 This is the region of System, of scholarship in 
 the ordinary branches of learning as they are 
 found in our schools, or as he may analyze and 
 classify for presenting to his pupils. (2) The 
 second field for the teacher-in-expectancy is also 
 that of subject-matter, and is included within the 
 range of our schools. It is special, however, to 
 the Profession of Teaching, and is known by 
 the name of Psychology, Mental Philosophy, or 
 Intellectual Philosophy. (3) The third field is 
 
84 ON THE THEORY OF 
 
 that of the science and art of adapting object- 
 matter to the capabilities of the mind to be 
 taught, that of adjusting objects to the focus 
 of the intellectual vision of the pupil. 
 
 86. This is properly the Province of Meth- 
 ods of Teaching. This province is that of 
 Principles it is that of those Principles which 
 exist in the constitution of things, and according 
 to which certain subject-matter must be ac- 
 quired by the mind in a certain fixed way, pro- 
 vided it ever becomes an actual knowledge 
 within that mind. Some subject-matter is 
 learned by one faculty, some by another. In- 
 termediate between every kind of subject-matter 
 and knowledge of it, there is the faculty which 
 is native to the acquiring of that knowledge. 
 If the proper faculty be not approached, true 
 knowledge cannot be the product from this 
 conclusion there is no escape. 
 
 87. "A principle is that which being derived 
 from nothing, can hold to nothing. 
 
 What is common to all first principles is that 
 they are the primary source from which any 
 thing is, becomes, or is known." (Fleming, 
 Vocab. of Phil.) 
 
 88. "A Principle is a central or representa- 
 tive truth in philosophy, science, art, religion, 
 or morals, which is fundamental and general, 
 and out of which other matters of a speculative 
 or practical character flow, and become its prac- 
 tical illustration. ' He who fixes upon false 
 principles treads upon infirm ground, and so 
 sinks ; and he who fails in his deductions from 
 
METHODS OF TEACHING. 85 
 
 right principles stumbles upon firm ground , 
 and so falls. South." (Smith, Syn. Discr., 
 Doctrine. ) 
 
 ' t Principle carries knowledge with it, and is- 
 applicable to action as a guide or basis of pro- 
 ceeding. A principle is a fundamental truth, 
 or comprehensive law, from which others are 
 derived, or on which they are founded. It may 
 be observed, generally, that principles are last in 
 the order of investigations, and first in the order 
 of practice. They are arrived at by analysis, 
 and when found become bases or starting-points- 
 for action or scientific inquiry. " (Ibid., Prov- 
 erb.) 
 
 89. Methods of Teaching are principle* 
 of adapting subject-matter to the capaci- 
 ties and powers of the pupil. When the 
 teacher says that this subject-matter should be 
 presented for cognizance by this or that faculty 
 of the mind, and in such and such quantities, 
 according to the strength of those faculties, he is. 
 acting within the province of Methods of Teach- 
 ing. But when the teacher says that this point 
 or step of this subject-matter should succeed that 
 or that step or point, he is acting within the 
 scope of a System of subject-matter. 
 
 90. These two distinct operations are often 
 confounded, or used indiscriminately, causing 
 great confusion in the proper use of terms. In 
 the following the word System is properly used : 
 " The Gospel of St. John, adapted to the Ham- 
 iltonian System, by an Analytical and Interline- 
 ary Translation from the Italian, with full In- 
 
86 ON THE THEORY OF 
 
 structions for its use, even by those who are 
 wholly ignorant of the language. For the Use 
 of Schools. By James Hamilton, Author of the 
 Hamiltonian System, London, 1825." (Sydney 
 Smith, Essays, p. 74, late ed.) In the expres- 
 sion, il Grube's Method of Teaching Number," 
 the word Method is improperly used. It should 
 be " Grube's System," because the author ar- 
 ranges the subject-matter in such a way that the 
 processes of addition, subtraction, multiplica- 
 tion, and division, must be taught in such and such 
 a sequence of order, and in such and such an 
 order of steps. The teacher in this case is not 
 investigating what faculties are to be incited to 
 learn these steps, nor in what quantities the sub- 
 ject-matter shall be set to those faculties, as 
 Methods require. The same remarks apply to 
 the so-called " A, B, C Method" of teaching 
 children to read, the " Word Method," and all 
 similar expressions, where Method is used im- 
 properly for System. 
 
 91. The questions relating to what branches 
 shall be taught or studied, do not belong, in 
 strict analysis, to the Province of Methods of 
 Teaching. They are questions of Ethics and 
 of Psychology, of the relations of the individual 
 to the Family, the Society, and the State, of 
 which he is a member and a part, according to 
 the estimate of these relations by each people 
 or nation for itself. They also are within the 
 field of the development of man as man, in his 
 subjective condition that is, in his psychological 
 estate. They belong to the wider field of Peda- 
 
METHODS OF TEACHING. 87 
 
 gogics, or Education, or to what Mr. J. fci. Mill 
 calls '* Ethology, the science of which education 
 is the art." (Chamb. Encycl., article Educa- 
 tion.) 
 
 92. " Ethics may be defined as the Science 
 of Practice or Conduct : the latter term is pref- 
 erable, as Practical Science is more conveni- 
 ently used to include along with Ethics the cog- 
 nate studies of Jurisprudence and Politics. 
 
 ' ' All three alike are distinguished from specu- 
 lative sciences by the characteristic that they 
 attempt to determine not the actual but the 
 ideal : what ought to exist, not what does ex- 
 ist. An objection is sometimes taken to the ap- 
 plication -of the term ' Science ' to such studies 
 as these. It is said that a Science must neces- 
 sarily have some department of actual existence 
 for its subject-matter : and there is no doubt that 
 the term ' Moral Sciences ' is frequently per- 
 haps more frequently used to denote studies that 
 deal with the actually existent : viz. Psychology, 
 or a portion of it ; what Mr. Mill calls Ethology, 
 or the inquiry into the laws of the formation of 
 character ; and Sociology, or (as it has also been 
 termed) the Physiology of Society. " (Sidg- 
 wick, The Methods of Ethics, p. 1, ed. 1874, 
 London.) 
 
 93. Voluntary and conscious instruction and 
 teaching are the handmaids of education, and 
 are ways of approaching mind, setting before 
 that mind those branches of study which Ethics 
 and Psychology determine are best. 
 
 94. Those principles of Ethics and Psychology 
 
88 ON" THE THEORY OF 
 
 According to which peoples, families, or individ- 
 uals, determine what branches of study shall be 
 pursued in schools and elsewhere, are properly 
 denominated Methods of Pedagogics. The 
 term Education being used by English and Amer- 
 ican authors as nearly or quite the equivalent of 
 the German Pedagogics, Methods of Educa- 
 tion will be used instead of Methods of Peda- 
 gogics. Methods of Education regard the future 
 man as a member of a given society ; they 
 consider what the child is to become ; they 
 are subjects of choice by nations, communities, 
 families, or individuals, because they determine 
 the uses to be made of the learning and disci- 
 pline which nations or families require of the 
 young. In Germany, Methods of Education are 
 determined by the condition of the body-politic, 
 and are well established. In France, the Meth- 
 ods of Education differ from those of Germany, 
 in so far as the purposes of the government differ 
 from those in Germany. In England, Methods 
 of Education still vary, as also they do in the 
 United States. Whatever purposes Methods of 
 Education propose for the young, they always 
 point distinctly to the end that these young- 
 persons, when grown up, shall be good and loyal 
 citizens of that Community or State. Methods 
 of education in France are not calculated to pro- 
 duce good citizens for Germany, but for France. 
 It is the same with every nation. Families 
 adopt Methods of Education which aim at giv- 
 ing specific direction to the energies of the 
 children in those families, referring immediately 
 
METHODS OF TEACHING. 89 
 
 to the positions which these children shall come 
 to occupy, as professional, diplomatic, or gov- 
 ernmental. These Methods inquire what is to 
 be studied by the learner, in order that he may 
 attain a certain end desired. Methods of Teach- 
 ing are concerned in Methods of Education only 
 so far as to ask in what way shall the branches 
 determined by the family or the nation be pre- 
 sented to the mind. Methods of Teaching know 
 no nationality nor family ; Methods of Education 
 preserve nationality and family attainments. To 
 elaborate the subject of Methods of Education 
 would require an extended treatise, and must be 
 set aside until a more convenient time shall pre- 
 sent itself for the work. 
 
 95. In the following quotation the province 
 of Methods of Teaching is not discriminated from 
 that of Methods of Education, although the no- 
 tion of Method in general is very clearly out- 
 lined : 
 
 " The Methodick : (1) The Educator must 
 guide the pupil to knowledge of the outer 
 world by aiding him to acquire it for himself in 
 accordance with the natural operation, succes- 
 sive movements or procedure of Intelligence ; 
 that is to say, according to the way or method 
 whereby Intelligence proceeds and must proceed. 
 These processes, as we have seen, are, in the first 
 instance, Analytic, but have Synthesis and In- 
 duction for their end. When ascertained, they 
 yield the doctrine of Method in Education The 
 Methodick of Education. 
 
 " (2) The Educator must perform the same 
 
90 OK THE THEORY OF 
 
 task with reference to the higher feelings and 
 emotions, with a view to constitute them habit- 
 ual motives. In things of sense or of thought 
 the learner learns by truly knowing : in things 
 of action the learner learns through the action 
 of others, and by his own action. The doc- 
 trine of The Methodick of Education is to be 
 called Methodology, and embraces the applica- 
 tion of Method to every subject of intellectual 
 study and to every stage of ethical training 
 alike (page 16). . 
 
 " The way of carrying out the Educative 
 process to a successful issue, both intellectual 
 and ethical, is, as we have seen, The Method- 
 ick of Education (p. 18.) . . . How must 
 I convey instruction so as to insure assimilation 
 by the pupil ? . . . The answer to this ques- 
 tion contains the Doctrine of Method, and rests 
 on the process of the Will in its movements 
 towards knowledge. Dependent on this are 
 Particular Methods." (Laurie, Synopsis of 
 Lect., p. 20, 1877.) 
 
 96. Methods of Education have regard for the 
 growth of mind as an end or habit unto itself, 
 an object to be attained for itself, and also for 
 knowledge or matter, as an end. (1) " What 
 subjects of instruction must I teach in order to 
 give to the future man the materials of right 
 judgment ? (The Real.) This leads us into a 
 discussion of subjects of Instruction generally 
 and their relative values. (2) How must I in- 
 struct so as most effectually to exercise the in- 
 telligence of the pupil in making those distinc- 
 
METHODS OF TEACHING. 91 
 
 tions on which the Tightness of judgment de- 
 pends ? (The Senses. The Formal as Will-power 
 in reference to Intelligence.) The answer to the 
 first of these questions contains the Doctrine of 
 the Real with reference to the outer world the 
 substance of Knowledge. The answer to the 
 second questions contains the Doctrine of Formal 
 discipline in its intellectual relations." (Laurie, 
 Synopsis of Led., p. 20, 1877.) 
 
 97. " It is a physiological law, first pointed 
 out by M. Isidore St. Hilaire, and to which 
 attention has been drawn by Mr. Lewes in his 
 essay on Dwarfs and Giants, that there is an 
 antagonism between growth and development. 
 By growth, as used in this antithetical sense, is 
 to be understood increase of size ; by develop- 
 ment, increase of structure. And the law is, 
 that great activity in ' either of these processes 
 involves retardation or arrest of the other. A 
 familiar illustration is furnished by the cases of 
 the caterpillar and the chrysalis. In the cater- 
 pillar there is extremely rapid augmentation of 
 bulk ; but the structure is scarcely at all more 
 complex when the caterpillar is full-grown than 
 when it is small. In the chrysalis the bulk doe& 
 not increase ; on the contrary, weight is lost 
 during this stage of the creature's life ; but the 
 elaboration of a more complex structure goes on 
 with great activity. The antagonism, here so 
 clear, is less traceable in higher creatures, be- 
 cause the two processes are carried on together. 
 But we see it pretty well illustrated among our- 
 selves by contrasting the sexes. A girl develops 
 
92 OX THE THEORY OF 
 
 in body and mind rapidly, and ceases to grow 
 comparatively early. A boy's bodily and men- 
 tal development is slower, and his growth 
 greater. At the age when the one is ma- 
 ture, finished, and having all faculties in full 
 play, the other, whose vital energies have been 
 more directed towards increase of size, is rela- 
 tively incomplete in structure ; and shows it in a 
 comparative awkwardness, bodily and mental. 
 Now this law is true not only of the organism as 
 a whole, but of each separate part. The abnor- 
 mally rapid advance of any part in respect of 
 structure involves premature arrest of its growth ; 
 and this happens with the organ of the mind as 
 certainly as with any other organ. The brain, 
 which during early years is relatively large in 
 mass but imperfect in structure will, if required 
 to perform its functions with undue activity, 
 undergo a structural advance greater than is ap- 
 propriate to the age ; but the ultimate effect 
 will be a falling short of the size and power that 
 would else have been attained. And this is a 
 part cause probably the chief cause w r hy preco- 
 cious children, and youths who up to a certain 
 time were carrying all before them, so often 
 stop short and disappoint the high hopes of their 
 parents." (Herbert Spencer, Education, pp. 
 271, 272, ed. 1870.) 
 
 " To grow is the process of which to in- 
 crease is the result or manifestation. Trade has 
 been growing for years past, and is now consid- 
 erably increased. To increase, however, does 
 not necessarily imply to grow ; rapid expansion 
 
METHODS OF TEACHING. 93 
 
 or dilatation of parts will produce increase in 
 bulk ; but the process of growth implies either 
 an accretion of parts by external apposition, or 
 an assimilative power from within, as in the vi- 
 tal force. The snowball grows by accretion, 
 and so increases as it rolls. The tree grows by 
 its own vitality, and increases also in size." 
 (Smith, Syn. Discr.] 
 
 98. Methods of Teaching consider the growth 
 of the faculties of the mind, and the quantity of 
 knowledge, not as ends, but as necessary knowl- 
 edge from which to project anew procedures in 
 teaching while the mind of the learner is grow- 
 ing. This is essential in order that the teacher 
 may set to this learner, at any stage of his 
 growth, the maximum quantity of subject-mat- 
 ter which the present attainments and powers 
 of the learner can master ; to set less than 
 this amount to a pupil is puerile, and to set 
 more is to prevent his powers from compre- 
 hending it. Yet the faculties of mind grow into 
 powers far more rapidly by attempting to com- 
 prehend the unknown, the mysterious, by trying 
 to enlarge the maximum degrees of efforts, than 
 by resting contentedly with efforts near the 
 minimum of degrees. " Mental dyspepsia' 7 
 comes from starvation, as well as from plethora 
 of subject-matter. " A well-regulated course of 
 study will no more weaken the mind than hard 
 exercise will weaken the body ; nor will a strong 
 understanding be weighed down by its knowl- 
 edge, any more than an oak is by its leaves, or 
 than Samson was by his locks. He whose sinews 
 
94 . OST THE THEORY OF 
 
 are drained by his hair, must already be a weak- 
 ling." (Grindon, Life, p. 197.) " If the child 
 of eight years old finds his improved language 
 understood by a child of three, why should you 
 contract yours to his vocabulary ? Always em- 
 ploy a language some years in advance of the 
 child (men of genius in their books speak to us 
 from the vantage-ground of centuries) : speak to 
 the one-year-old child as though he were two, 
 and to him as though he were six ; for the 
 difference of progress diminishes in the inverse 
 proportion of years. Let the teacher, especially 
 he who is too much in the habit of attributing all 
 learning to teaching, consider that the child al- 
 ready carries half his world, that of mind, the 
 objects, for instance, of moral and metaphysical 
 contemplation, ready formed within him ; and 
 hence that language, being provided only with 
 physical images, cannot give, but merely illum- 
 ine, his mental conceptions." (Richter, Le- 
 vana, pp. 347-8.) 
 
 99. In this immediate connection it will be 
 profitable to give a brief attention to the pop 
 ular expression, " Teachers should teach pupils 
 how to learn, how to use their faculties in order 
 that they shall be able to continue their mental 
 activities by themselves, in subsequent years. ' ' 
 It is a plain fact in psychological phenomena, 
 that nearly all the faculties of mind grow, ' ' in- 
 crease in size, ' ' by exercise. This is emphatically 
 true of the faculties of Thought and Attention, 
 which are energies of the Will. Education is a 
 habit. Hence no one can be said to know how 
 
METHODS OF TEACHING. 95 
 
 to command his faculties, who has not the habit 
 of it, called education. This state is attained 
 by those, and those only, who actually exert 
 their faculties to the maximum degrees, so that 
 this state becomes habitual. Methods of Teach- 
 ing regard these degrees as their bases in Mind. 
 Mere Theory will never produce these habits. All 
 teaching of pupils " how to study/ 'which does 
 not demand of them their maximum efforts in 
 practice, is a delusion, and a fatal deception to 
 the learners. The arm of the smith does not 
 grow strong by his standing at the forge and 
 looking at the sledge-hammer, but by wielding 
 it. Intellectual growth comes not by thinking 
 how to study, but by mental application in 
 studying up to the measure of the highest de- 
 grees. 
 
 100. So far as Methods of Teaching are con- 
 cerned, the matter taught may be in itself, 
 either error or truth. Methods take whatever 
 subjects, in whatever form of text-books or ob- 
 jects, that are set to them, and convey them into 
 the presence of the corresponding faculties that 
 are to learn these subjects this conveying, if ac- 
 cording to a philosophical principle, is teaching ; 
 for no power external to the mind of the learner 
 can learn for that mind, nor compel it to learn. 
 The learning is a matter within the exclusive 
 province of the mind that is to learn, or to be 
 taught. 
 
 101. Methods of Teaching are not concerned 
 with what is popularly called ' ' waking up 
 mind, " for if Methods assume any thing pre- 
 
 OF 
 
96 ON THE THEORY OF 
 
 eminently, it is that subject-matter, when set 
 before mind according to the principles of adap- 
 tation, will incite the mind to activity, intui- 
 tively and spontaneously. " To wake up mind, " 
 implies, in practice, the false notion that the chil- 
 dren are to be excited or astonished at the man- 
 ner of the teacher, and at the irrelevancy of the 
 points he presents, rather than at the value of 
 the subject-matter set before them to be learn- 
 ed. This is mere charlatanism. Emotional ex- 
 citement, with dissipation of thought, can never 
 take the place of calm, deliberate, intense atten- 
 tion and continued thinking, when sound learn- 
 ing is sought. Nothing is more pernicious to 
 good habits of thought than the introduction 
 into class-rooms of what is called " variety," as 
 the term is practically exemplified. The only 
 " variety" permissible, is that which follows upon 
 progress, pointedly, into additional subject-mat- 
 ter of the lesson, not into this or that subject 
 which has no direct and close relationship to the 
 recitation, and which permits attention and power 
 to be dissipated, not concentrated. The mind 
 of childhood is always awake it may need to 
 be centred on this subject. 
 
 102. " Bonnet calls attention the mother of 
 genius, but she is in fact her daughter ; for 
 whence does she derive her origin, save from 
 the marriage contracted in heaven between the 
 object and the desire for it ? Hence attention 
 can really be as little preached or flogged into 
 a person as ability. ... A very important 
 distinction must be drawn between the power of 
 
METHODS OF TEACHING. 97 
 
 attention diffused among the generality of men, 
 and that appertaining solely to men of genius. 
 The latter can only be recognized, protected, and 
 cherished, but not created. ... On the 
 other hand, common every-day attention needs 
 not so much to be aroused, as to be distributed 
 and condensed ; even careless, inattentive chil- 
 dren possess the faculty, but it is dissipated upon 
 all passing objects. ... In what manner 
 can you arouse the innate desire of mental prog- 
 ress ? The impulses of the senses excite and 
 then stupefy, but help not to produce it. To 
 overwhelm the mind with lessons, that is, with 
 mere summaries of accounts, resembles the Si- 
 berian custom of giving the sacrament of the 
 Lord's Supper to infants. . . . Philosophy 
 begins with what is highest and most difficult ; 
 mathematics, with what is nearest and easiest. 
 . What, then remains ? The metaphys- 
 ics of the eye ; the knowledge forming the 
 boundary between experience and abstraction. " 
 (Richter, Levana, pp. 353-9.) 
 
 103. " To Excite (Latin, excitare) is to call 
 out into greater activity what before existed 
 in a calm or calmer state, or to rouse to an 
 active state faculties or powers which before 
 were dormant. The term is also used of purely 
 physical action. We excite heat by friction. 
 Awaken (A. S., awaccian, awecian) is to 
 rouse from a state of sleep, or, analogously, to 
 rouse any thing that has lain quiet, and, as it 
 were, dormant, as to awaken suspicion, and is 
 applicable only to intelligent subjects. Bouse 
 
98 ON THE THEOKY OF 
 
 (A. S., rasian) is to awaken in a sudden or start- 
 ling manner, so as to bring into an energetic 
 state by a strong impulse. To incite (Latin, 
 incitare) is to excite to a specific act or end 
 which the inciter has in view. To stimulate is 
 to quicken into activity (stimulus, a spur) 
 and to a certain end. Men are incited when 
 their passions are roused ; they are stimulated 
 when they are induced to make greater exer- 
 tions, as by a hope of reward or any other exter- 
 nal impulse. They are awakened out of indiffer- 
 ence, roused out of lethargy and torpor, incited 
 by the designing influences of others, stimulated 
 by new motives of action. Men are incited to 
 what otherwise they would not have given their 
 efforts. They are commonly stimulated to 
 something which they are pursuing, or intend- 
 ing to pursue, but with want of energy. " 
 (Smith, Syn. JDiscr.) 
 
 104. As to the Form in which knowledge 
 is left in the mind, when all the circumstances 
 attending the presentation have been rigidly 
 based upon the nature of the case, Methods of 
 Teaching have no responsibility that ends when 
 the presentation is completed. The mind, as a 
 cause unto itself, and its prior state of knowl- 
 edge, are responsible for the form or impression, 
 in which the matter, under these conditions, ex- 
 ists within itself. If this form lacks certitude, 
 or " material truth in the absolute sense," it 
 can only be corrected by presenting to the learn- 
 ing mind other subject-matter. But what this 
 subject-matter shall be is no concern of Methods 
 
METHODS OF TEACHING. 99 
 
 of Teaching, as has been shown in a previous 
 section of this investigation. If the subject-mat- 
 ter be not properly separated into parts, and 
 those parts sharply freed from adventitious mat- 
 ter, so that it may be brought boldly and une- 
 quivocally into the conscious presence of the cor- 
 responding faculties if there be a want here, 
 it is the fault of the System of the teacher. 
 Methods of Teaching demand only that the prin- 
 ciples of adaptation be not violated. The 
 Methods assume the subjects placed in the hands 
 of the teacher. The teacher has two important 
 things to do : (1) To consider if his System of 
 subject-matter is so constructed that it is capa- 
 ble of being presented to this individual learner ; 
 (2) To reflect upon the principles which under- 
 lie the actual procedure of teaching. He must 
 attend to System and then to Method. 
 
 106. In connection with Methods of Teaching 
 \ one often hears the expressions, " Develop the 
 idea in the mind of the learner, " " Lead the 
 mind gradually up to the idea. ' ' To simple per- 
 ception there can be no development work, for 
 perception is intuitive, and is ultimate in its au- 
 thority, upon the presence in consciousness of 
 the object. Development exists within the Prov- 
 ince of Thought. 
 
 Notions, or conceptions, or ideas, are aggre- 
 gations of simpler elements, which constitute the 
 group or Unit of notions. When the faculties of 
 the mind are too feeble to comprehend the unit 
 group, the elements of the unit are separated 
 and set before the mind of the learner in sue- 
 
100 OK THE THEORY OF 
 
 cession until all are seen as one. The process 
 (Mode), called " development," is that by which 
 the teacher analyzes and presents the notion that 
 is to be taught, and the synthetical process by 
 which the learner apprehends, and combines or 
 reconstructs, the elements into a notion that is 
 similar to that possessed by the teacher. 
 
 106. The process by which a student is in- 
 ducted into a prehension and a comprehension 
 of an aggregation of ideas, which bear an inti- 
 mate and necessary relation to each other, is 
 called Thoroughness. A student who is thor- 
 oughly taught surveys from the centre, a group 
 of ideas which constitute a structure created by 
 Thought. 
 
 107. " To Develop is to open out what was 
 contained in another thing, or the thing itself 
 (Fr. developper). In develop these two ideas 
 
 , are inherent, the gradual opening of the whole 
 containing, and the gradual exhibition of the 
 particular contained. So we might say, i Time 
 developed his character,' or ' circumstances de- 
 veloped the cruelty which was latent in his char- 
 acter. ' Unlike Unfold, develop is not used of 
 purely physical processes. We speak of the de- 
 velopment of plans, plots, ideas, the mind ; and 
 also of the development of the body in growth ; 
 but these are scientific terms involving other* 
 ideas, as of the vital functions in growth. We 
 should never speak of the development of a flag 
 or a tablecloth. In other words, it is not used 
 of manual or mechanical unfolding. On the 
 other hand, in the sense of the mechanical pro- 
 
METHODS OF TEACHING. 101 
 
 cess of gradually opening, unfold is used as well 
 as in the other ; but in this latter develop ex- 
 presses far more than unfold, and relates to the 
 laws of expansion by which a thing unfolds in 
 definite sequence of expansion, and in conform- 
 ity with principles which conserve the type de- 
 veloped. Hence we speak. of a true and a vic- 
 ious development. To Unravel (old German, 
 reffen, to pluck) is purely a mechanical effort of 
 separating what is complicated, whether naturally 
 or accidentally, and expresses simple disentangle- 
 ment, not growth or expansion. As the former 
 indicate ordinary processes of nature or art, so 
 the latter indicates extraordinary and counterac- 
 tive processes, and commonly implies the abnor- 
 mal state of that which needs to be unravelled. 
 
 " ' Then take him to develop if you can, 
 
 And hew the block off and get out the man. ' 
 
 Pope. 
 
 u ' Several pieces of cloth, the largest we had 
 seen being fifty yards long, which they un- 
 folded and displayed so as to make the greatest 
 show possible.' Cook's Voyages. 
 
 4 ' ' What ridge's this ? Unfold yourself, dear 
 Robin. ' Ben Jonson. 
 
 * ' ' That great chain of causes which, linking 
 one to another, even to the throne of God Him- 
 self, can never be unravelled by any industry of 
 ours.' Burke." (Smith, Syn. Discr., ed. 
 1878, Develop.} 
 
 108. Methods of Teaching must have refer- 
 ence to the ways according to which the learner's 
 
102 ON THE THEORY OF 
 
 faculties proceed when he is applying him- 
 self to study. Unless this be understood, the 
 faculties of the pupil will be embarrassed in their 
 normal activities. This will cause discourage- 
 ment to both teacher and pupil. 
 
 109. " There exist nevertheless certain gen- 
 eral modes of treating any subject which can be 
 clearly distinguished by the student. Logic 
 oannot teach him exactly how and when to use 
 each kind of method, but it can teach him the 
 natures and powers of the methods, so that he 
 will be more likely to use them rightly. We must 
 distinguish : 
 
 " 1. The method of discovery, 
 
 " 2. The method of instruction. 
 
 " The method of discovery is employed in 
 the acquisition of knowledge, and really consists 
 in those processes of inference and induction, by 
 which general truths are ascertained from the 
 collection and examination of particular facts. 
 The second method only applies when knowl- 
 edge has already been acquired and expressed in 
 the form of general laws, rules, principles or 
 truths, so that we have only to make ourselves 
 acquainted with these and observe the due mode 
 of applying them to particular cases, in order to 
 possess a complete acquaintance with the subject. 
 
 " A student, for example, in learning Latin, 
 dreek, French, German, or any well-known lan- 
 guage, receives a complete Grammar and Syntax 
 setting forth the whole of the principles, rules 
 and nature of the language. He receives these 
 instructions, and takes them to be true on the 
 
METHODS OF TEACHING. 103 
 
 authority of the teacher, or the writer of the 
 book ; and after rendering them familiar to his 
 mind he has nothing to do but to combine and 
 apply the rules in reading or composing the lan- 
 guage. He follows, in short, the method of In- 
 struction. But this is an entirely different and 
 opposite process to that which the scholar must 
 pursue who has received some writings in an un- 
 known language, and is endeavoring to make out 
 the alphabet, words, grammar, and syntax of the 
 language. He possesses not the laws of gram- 
 mar, but words and sentences obeying those 
 laws ; and he has to detect the laws if possible 
 by observing their effects on the written lan- 
 guage. He pursues, in short, the method of dis- 
 covery consisting in a tedious comparison of let- 
 ters, words, and phrases, such as shall disclose 
 the more frequent combinations and forms in 
 which they occur. The process would be a 
 strictly inductive one, such as I shall partially 
 exemplify in the Lessons on Induction ; but it is> 
 far more difficult than the method of Instruction, 
 and depends to a great extent on the happy use 
 of conjecture and hypothesis, which demands a 
 certain skill and inventive ability. 
 
 " Exactly the same may be said of the inves- 
 tigation of natural things and events. The prin- 
 ciples of mechanics, of the lever, inclined plane, 
 and other Mechanical Powers, or the Laws of 
 Motion, seem comparatively simple and obvious 
 as explained to us in books of instruction. But 
 the early philosophers did not possess such 
 books ; they had only the Book of Nature, in 
 
104 O!S" THE THEORY OF 
 
 which is set forth not the laws, but the results of 
 the laws, and it was only after the most patient 
 and skilful investigation, and after hundreds of 
 mistakes, that those laws were ascertained. It 
 is very easy now to understand the Copernican 
 system of Astronomy, which represents the plan- 
 ets as revolving round the sun in orbits of vari- 
 ous magnitude. Once knowing the theory we 
 oan readily see why the planets have such var- 
 ious movements and positions, and why they 
 sometimes stand still ; it is easy to see, too, 
 why in addition to their own proper rrotions 
 they all go round the earth apparently every day 
 in consequence of the earth's diurnal rotation. 
 But all these changes were exceedingly puz- 
 zling to the ancients, who regarded the earth as 
 standing still. 
 
 " The method of discovery thus begins with 
 facts apparent to the senses, and has the difficult 
 task of detecting those universal laws or general 
 principles which can only be comprehended by 
 intellect. It has been aptly said that the method 
 of discovery thus proceeds from things better 
 known to us, or our senses (nobis notiora), to 
 those whicli are more simple or better known in 
 nature (notiora naturae). The method of In- 
 struction proceeds in the opposite direction, be- 
 ginning with the things notiora naturae, and 
 proceeding to show or explain the things nobis 
 notiora. The difference is almost like that be- 
 tween hiding and seeking. He who has hidden 
 a thing knows where to find it ; but this is not 
 the position of a discoverer, who has no clue ex- 
 
METHODS OF TEACHING. 105 
 
 cept sucli as he may meet in his own diligent 
 and sagacious search. 
 
 ' ' Closely corresponding to the distinction be- 
 tween the methods of Discovery and Instruction 
 is that between the methods of Analysis and 
 Synthesis. It is very important indeed that the 
 reader should clearly apprehend the meanings of 
 these terms in their several applications. Analy- 
 sis is the process of separating a whole into its 
 parts, and synthesis the combination of parts 
 into a whole. The analytical chemist, who 
 receives a piece of mineral for examination, 
 may be able to separate completely the several 
 chemical elements of which it is composed and 
 ascertain their nature and comparative quantities ; 
 this is chemical analysis. In other cases the 
 chemist mixes together carefully weighed quan- 
 tities of certain simple substances and combines 
 them into a new compound substance ; this is 
 chemical synthesis. Logical analysis and syn- 
 thesis must not be confused with the physical 
 actions, but they are nevertheless actions of 
 mind of an analogous character. 
 
 " In logical synthesis we begin with the 
 simplest possible notions or ideas, and combine 
 them together. We have the best possible ex- 
 ample "in the elements of Geometry. In Euclid 
 we begin with certain simple notions of points, 
 straight lines, angles, right angles, circles, &c. 
 Putting together three straight lines we make a 
 triangle ; joining to this the notion of a right 
 angle, we form the notion of a right-angled tri- 
 angle. Joining four other equal lines at right 
 
106 OST THE THEORY OF 
 
 angles to each other we gain the idea of a 
 square, and if we then conceive such a square 
 to be formed upon each of the sides of a right- 
 angled triangle, and reason from the necessary 
 qualities of these figures, we discover that the 
 two squares upon the sides containing the right 
 angle must together be exactly equal to the 
 square upon the third side, as shewn in the 
 47th Proposition of Euclid's first book. This is 
 a perfect instance of combining simple ideas into 
 more complex ones. 
 
 11 We have often, however, in Geometry to 
 pursue the opposite course of Analysis. A 
 complicated geometrical figure may be given to 
 us, and we may have, in order to prove the prop- 
 erties which it possesses, to resolve it into its 
 separate parts, and to consider the properties of 
 those parts each distinct from the others. 
 
 ' i A similar distinction between the analytical 
 and synthetic methods can be traced throughout 
 the natural sciences. By keeping exact registers 
 of the appearance and changes of the weather 
 we may readily acquire an immense collection of 
 facts, each such recorded fact implying a multi- 
 tude of different circumstances occurring to- 
 gether. Thus in any storm or shower of rain 
 we have to consider the direction and force of 
 the wind ; the temperature and moistness of the 
 air ; the height and forms of the clouds ; the 
 quantity of rain which falls, or the lightning 
 and thunder which occur with it. If we pro- 
 ceed by analysis only to explain the changes of 
 the weather we should have to try resolving 
 
METHODS OF TEACHING. 107 
 
 each storm or change of weather into its separate 
 circumstances, and comparing each with every 
 other to discover what circumstances usually go 
 together. We might thus ascertain no doubt 
 with considerable certainty what kinds of clouds, 
 and what changes of the wind, temperature, 
 moisture, <fec., usually precede any kind of 
 storm, and we might even in time give some im- 
 perfect explanation of what takes place in the 
 atmosphere. 
 
 " But we might also apply with advantage 
 the synthetical method. By previous chemical 
 investigations we know that the atmosphere 
 consists mainly of the two fixed gases, oxygen 
 and nitrogen, with the vapour of water, the latter 
 being very variable in quantity. We can try 
 experimentally what takes place when portions 
 of such air of various degrees of moistness are 
 compressed or allowed to expand, or are mixed 
 together, as often happens in the atmosphere. 
 It is thus discovered that whenever moist air is 
 allowed to expand cloud is produced, and it may 
 be drops of rain. Dr. Hutton, too, found that 
 whenever cold moist air is mixed with warm 
 moist air cloud is again produced. We can 
 safely argue from such small experiments to 
 what takes place in the atmosphere. Putting 
 together synthetically, from the sciences of 
 chemistry, mechanics, and electricity, all that 
 we know of air, wind, cloud and lightning, we 
 are able to explain what takes place in a thunder- 
 storm far more completely than we could do by 
 merely observing directly what happens in the 
 
108 ON THE THEORY OF 
 
 storm. We are here however anticipating the 
 methods of inductive investigation, which we 
 must consider in the following lessons. It wiM 
 appear that Induction is equivalent to analysis, 
 and that the deductive kinds of reasoning which 
 we have treated in prior lessons are of a synthetic 
 character. 
 
 11 It has been said that the synthetic method 
 usually corresponds to the method of instruction 
 and the analytic method to that of discovery. 
 But it may be possible to discover new truths by 
 synthesis and to teach old ones by analysis. Sir 
 John Herschel in his well-known Outlines of 
 Astronomy partially adopts the analytic method ; 
 he supposes a spectator in the first place to survey 
 the appearances of the heavenly bodies and the 
 surface of the earth, and to seek an explanation ; 
 he then leads him through a course of arguments 
 to show that these appearances really indicate 
 the rotundity of the earth, its revolution about 
 its own axis and round the sun, and its subor- 
 dinate position as one of the smaller planets of 
 the solar system. Mr. Norman Lockyer's Ele- 
 mentary Lessons in Astronomy is a clear example 
 of the synthetic method of instruction ; for he 
 commences by describing the sun, the centre of 
 the system, and successively adds the planets 
 and other members of the system, until at last 
 we have the complete picture ; and the reader 
 who has temporarily received everything on the 
 writer's authority, sees that the description cor- 
 responds with the truth. Each method, it must 
 
METHODS OF TEACHING. 109 
 
 be allowed, has its own advantages. (Jevons, 
 Lessons in Logic, ed. 1878, pp. 202-208.) 
 
 110. Methods of Teaching must respect that 
 inherited and national l ' cast of mind ' ' which 
 exhibits itself so prominently that it forms an 
 important element in teaching. Those national 
 bents of mind, traits of disposition, and survival 
 of tendencies, constitute a " prior knowledge," 
 or setting, which gives form to the knowledge 
 presented by the teacher. The Italian mind in- 
 herits peculiar adaptations for music. The Ger- 
 man mind, as revealed in the language, is dis- 
 posed to aggregate and accumulate conceptions. 
 The native tendency with the French mind, in 
 language, is towards separation and analysis. 
 The English mind, in language, evidently has 
 its form in directness, neither cumulative nor 
 over analytical. With some nations, gesticulation 
 forms a prominent inheritance of the people. 
 The United States, being peopled from all na- 
 tions, present a multitude of national peculiari- 
 ties to the teacher, who, herein, has a more deli- 
 cate work before him than teachers who labor 
 with a single nationality. This element, although 
 subtle, is powerful in any place where the schools 
 are composed of children of many nationalities. 
 While the psychological faculties are the same 
 in kind and function among all peoples, yet the 
 native quality of these faculties, or the bent 
 for giving form to knowledge, varies with the 
 peoples. These native qualities or bents are not 
 the differences in degrees of the same capacities 
 of people of the same nationality. They are 
 
110 ON THE THEORY OF 
 
 powers or forces wliich necessarily modify the 
 form of the same matter which is set before all 
 alike. This is done unconsciously to the chil- 
 dren who are taught. 
 
 111. Methods of Teaching are difficult to 
 suit, " as an object to a quality," in their daily 
 application, by reason of the intricacy and eva- 
 nescence of psychological phenomena. But the 
 province is established. The very delicacy and 
 mutability of the modifications of Mind lend a 
 zest to Methods, and consequently to teaching, 
 that must emphatically and forever banish all 
 tendencies to mere routine and formalism, when 
 teachers fully grasp the Spirit of Methods. Gen- 
 uine Methods of Teaching, from their nature, 
 must be universally successful for accomplishing 
 their objects. A principle can never become 
 spiritless the application of it may, if it be an 
 unintelligent one, but the principle must be as 
 constant and as enduring as the subjects to which 
 it relates, or out of which it springs. 
 
 112. Methods of Teaching are not, in the 
 present state of psychological science, absolutely 
 invariable. The one element in the foundations, 
 that of subject-matter, is firm, as science is firm. 
 The other element in the foundations, that of 
 psychology, is less firm, perhaps, because the Sci- 
 ence of Mind is not so well established in its full- 
 ness as are most other sciences which are pursued 
 in schools. No science or art is more stable or 
 lasting than its foundations. However, the main 
 principles of the science of psychology are very 
 thoroughly established, as they appear to-day 
 
METHODS OF TEACHING. Ill 
 
 rising up out of hundreds of years of diligent 
 study by the philosophers of the past and the 
 present. " In mental philosophy the general 
 statements have commonly a genuine fact, hut 
 mixed with this there is often an alloy. The 
 error may not influence the spontaneous action 
 of the primitive principle, but it may tell disas- 
 trously or ludicrously in the reflex application. ' ' 
 (McCosh, Int. of Mind, p. 60, ed. 1870.) 
 
 113. What are ordinarily denominated ' ' class- 
 drill " and " examinations, " are no legitimate 
 elements in the conception of Methods of Teach- 
 ing. They are no new things they are mere 
 repetitions. The value of repetition is purely a 
 psychological problem, not belonging to subject- 
 matter and mind, as do the problems of Methods. 
 " Repetition, else the mainspring of instruction, 
 is the chief destroyer of attention ; because, in 
 order to give attention to what is repeated, you 
 must first have found it worthy of a still greater 
 exertion of that faculty." (Richter, Levana, p. 
 356.) 
 
 1 14. Methods of Teaching, from their nature, 
 forbid the so-called Individuality of any teacher 
 to enter into them, as a constituent part of their 
 essence. The foundations of the Methods being, 
 the principles of adaptation between subject- 
 matter and mind, the eccentricities, idiosyncra- 
 sies, or peculiarities of any one mind form no fac- 
 tor in the Science and Art of Methods of Teach- 
 ing. " Every mind is more or less like every 
 other mind ; there is always a basis of similarity, 
 but there is a superstructure of feelings, im- 
 
112 ON THE THEORY OF 
 
 pulses, and motives which is distinctive for each 
 person. 77 (Jevons, Princ. of Science, p. 733, 
 ed. 1877.) 
 
 1 15. Teachers have their individuality, which 
 shows itself in greater or less degrees in their 
 school-room practice, while applying philosophi- 
 cal Methods of Teaching. This individuality is 
 exhibited in the way that one teacher illustrates a 
 point differently from another in the way he 
 speaks in the way he looks in the way he 
 thinks, it may be in the way in which his 
 questions are conceived in the impromptu ex- 
 pedients which he devises in what, in general, 
 is called " his way of doing things." This in- 
 dividuality of the teacher is known as Manner. 
 Misapprehension of the true province of scientific 
 Methods of Teaching has led many to apply the 
 term to any peculiar experiment or expedient 
 which may be selected, which things are in fact 
 but examples of Manner. The familiar expres- 
 sions so often heard ' l my method is thus and 
 so, " " my method is not that, but this, ' ' " I 
 illustrate by this method, using a bundle of 
 sticks instead of kernels of corn' 7 are simply ex- 
 amples of Manner. 
 
 - 116. A teacher has his own Manner of 
 Teaching he can not have his Method, be- 
 cause Methods are general or universal principles, 
 which are beyond the exclusiveness of the indi- 
 vidual. Mannerisms can be affected or imitated, 
 or devised, or invented ; but Methods of Teach- 
 ing, existing originally in the native constitution 
 of things, can not be invented they must be 
 
METHODS OF TEACHING. 113 
 
 discovered. Being discovered, they are no 
 more his who discovers them, than the principle 
 of gravity is the property of Newton because he 
 discovered its nature and laws. 
 
 117. This conception of Methods of Teaching 
 should not be confused with that of Methods in 
 general, which are ways of procedure in the in- 
 vestigations of subject-matter only they do not 
 aim at mind. Such expressions as " Homer's 
 Method of Approximation, " and the like, cor- 
 rectly use the word Method. 
 
 118. In the subjoined quotation the terms 
 Manner and Method are not sufficiently discrimi- 
 nated in demarcation each includes portions of 
 the conception of Mode. 
 
 ' * Perhaps this difference between method and 
 manner will appear better if we use an illustration 
 which is supported by the etymology of the 
 word method : Suppose it is proposed to estab- 
 lish a connection between two cities, for this 
 purpose a road is made ; this road will be used 
 by all that go from one city to the other, and by 
 all kinds of individuals ; it is the same road 
 for all and not liable to be changed by individual 
 whims or notions. But the manner in which 
 the road is used varies very much ; some will 
 walk, others will run, and others still will ride. 
 The road in our illustration represents the 
 method in pedagogics ; it may be used by the 
 most widely different individualities ; the way 
 in which people make use of it is the manner. 
 Manner cannot be thoroughly specified or de- 
 fined. Here the utmost freedom must be allowed 
 
114 OX THE THEORY OF 
 
 to teachers and pupils to develop their own in- 
 dividualities. " (Soldan, art. Method and Man- 
 ner, Nat. Ed. Ass. Proceedings, 1874, p. 249.) 
 
 119. When the Manner of a teacher has 
 " method in it," when it is more or less deter- 
 mined into a System when it has become a 
 somewhat systematized exposition or application 
 of the principle of adaptation, i.e., of Methods 
 of Teaching, when Manner has assumed this 
 state, it is called Mode. 
 
 120. Methods of Teaching are fundamental 
 and general principles " out of which other 
 matters of a speculative or practical character 
 flow, and become its practical illustrations" 
 they must be discovered, if known. They can 
 be investigated in their nature they can not be 
 copied, imitated, or assumed they can only be 
 stated as principles, which can be illustrated or 
 exemplified in practice in certain ways called 
 Modes, and sometimes Manners. Manner is the 
 term which contains prominently the individual- 
 ity of the teacher. Mode refers to the systematic 
 application or illustration of Methods it has lit- 
 tle of the notion of individuality in it. Manner- 
 can be imitated, but hardly taught. Mode 
 can be imitated and taught. If a teacher writes 
 out a lesson in a methodical order, point by point, 
 and question by question, such lesson is his Mode 
 and it may partake of his Manner. The more 
 nearly teachers comprehend the nature of sub- 
 ject-matter as related to knowing mind, and the 
 mind itself, the more nearly will their Modes be 
 identical when teaching the same subject-matter 
 
METHODS OF TEACHING. 115 
 
 to classes of similar attainments and the less of 
 mannerisms will be exhibited by the teachers. 
 
 121. If perfection of knowledge and of 
 adaptation were possible, it is extremely prob- 
 able that all perfect teaching would set the 
 same subjects to the same pupils in exactly the 
 same Mode, which would then reach a perfect 
 illustration of Method of Teaching. 
 
 122. The failure to discriminate the prov- 
 inces of Methods of Teaching, Modes, and 
 Manners, has led to considerable abuse of the 
 former expression. Mode and Manner can be 
 imitated by those even who do not comprehend . 
 the principle which is illustrated ; supposing a 
 principle involved in the case, which principle is 
 sometimes wholly imaginary in actual practice. 
 This being the state of affairs, teachers who rest 
 satisfied with copying another's Mode or Manner 
 must fail, because they do not apprehend the 
 animating principle, the Method of Teaching, 
 which underlies the Mode imitated. Those 
 teachers are dealing with the mere dress, lifeless 
 forms, of Methods. Methods are life, enduring 
 as mind. Modes have a portion of the life of 
 Methods, and a portion from that of the teacher. 
 Manner has only the life of the teacher whose 
 it is. 
 
 123. " While Mode (Lat. modus) is also ap- 
 plicable to way of being, Manner (Fr. maniere) 
 denotes way of action. Manner, too, is casual ; 
 mode, systematic. Mode might be defined reg- 
 ular manner. Hence manner of action im- 
 plies voluntariness on the part of the agent ; 
 
116 OK THE THEOKY OF 
 
 mode of action, uniformity in the thing acting. 
 Modes of existence. Manners of conduct or oper- 
 ation." (Smith, Syn. Discr., Mode.) " In 
 consequence of the authorship there being a 
 large number of different writers there is great 
 variety in the modes of treatment." (The 
 Nation, No. 700, p. 340, Nov. 28, 1878.) 
 " We all remember how rapidly the theory 
 grew up that in the greenbacks we had stumbled, 
 by a happy accident, on a new mode of acquir- 
 ing wealth and avoiding financial convulsions, 
 and how rapidly, too, in many minds, they began 
 to wear the air of weapons of war, like a grand- 
 father's sword or musket, hallowed by associa- 
 tions, and unfit subjects for scientific examination 
 or treatment." (Ibid., No. 704, p. 394, Dec. 
 26, 1878.) " Washburn's Outlines of Criminal 
 Law, A Manual of Criminal Law, including the 
 Mode of Procedure by which it is enforced. ' ' 
 (Ibid., No. 704, Dec. 26, 1878.) 
 
 124. " System (Gr. avarrj^a, from awi- 
 Gravai, to place together) regards fixed sub- 
 jects which have rational dependence or con- 
 nection. Method (Gr. JUST a, after, and odos, 
 a way) regards fixed processes. System is logi- 
 cal or scientific collocation. Method is logical 
 or scientific procedure. But, inasmuch as a 
 mode of procedure may be itself harmonized, 
 system is frequently used in place of method. 
 "We sometimes say, ' to go systematically to 
 work,' meaning methodically. Method lays 
 down rules for scientific inquiry, and is the way 
 which leads to system. ' All method,' says Sir 
 
METHODS OF TEACHING. 117 
 
 W. Hamilton, ' is a rational progress a prog- 
 ress toward an end.' When Watts says, ' The 
 best way to learn any science is to begin with a 
 regular system, or a short and plain scheme of that 
 science well drawn up into a narrow compass, * 
 he is recommending a method." (Smith, Syn. 
 Discr., art. System.} " System is a connected 
 body of knowledge. ' ' (Jevons, El. Les. Logic y 
 p. 346.) 
 
 125. In the following quotation, the defini- 
 tions are not strictly accurate, although they ex- 
 press the outlines : ' i In pedagogy, method is 
 the way chosen, the order followed by the teacher 
 to put his own thought, his intelligence, in re- 
 lation with the intelligence of his pupils ; mode 
 is the way of organizing the school according as 
 it is desired to convey lessons directly or indi- 
 rectly to the pupils ; and procedures are the 
 secondary means, ordinarily mechanical, which 
 are used to assure the success of the method. 
 They depend generally on the mode adopted. ' ' 
 (L. Mariotti, Conferences de Pedagogie, p. 146, 
 ed. 1873, Paris.) 
 
 126. In the following quotation (), or 
 " Applied/' under both the general and the 
 special, contains the conception of Mode. 
 
 "Definition of Method. 
 
 "General: (a) Theoretical: The laws ac- 
 cording to which the ten- 
 dency to acquire knowledge, 
 exerts itself, arranged so as- 
 
118 ON THE THEORY OF 
 
 to show their natural order 
 and relations. 
 
 (b) Applied: The same laws 
 translated into rules, and ar- 
 ranged in the same order. 
 '" Special: (a) Theoretical: The laws ac- 
 cording to which the ten- 
 dency to acquire a knowl- 
 edge of Physics, Logic, &c., 
 exerts itself, arranged so as 
 to show uieir natural order 
 and relations. 
 
 (6) Applied: -The same laws 
 translated into rules, and ar- 
 ranged in the same order. ' ' 
 (The late J. W. Arm- 
 strong, D.D. A Paper on 
 Method.) 
 
 127. " The tendency of any power or force 
 to act in any particular way is called a Principle, 
 The particular way in which a tendency operates 
 is called a Law. The statement of a law in such 
 form as will adapt it to the solution of problems 
 is called a Rule." (Ibid.) 
 
 128. (a) Method, Mode, and Manner of 
 Teaching, may be illustrated and contrasted, per- 
 haps not inaptly, by the following supposition : 
 Suppose an engineer desires to span a stream by 
 a bridge (1) he rears his abutments on either 
 side (2) he places the main timbers or " string- 
 ers' ' from abutment to abutment across the chasm 
 (3) he lays a roadway of planks upon the 
 stringers (4) he travels across the gulf upon 
 
METHODS OF TEACHING. 
 
 the bridge. In the analogy, (1) rearing the abut- 
 ments corresponds to the acquisition of a knowl- 
 edge of subject-matter (say arithmetic), and of 
 mind of the learner (Psychology), by the teacher 
 (2) throwing the stringers across the stream 
 illustrates the process of discovering the principles 
 of adjusting subject-matter to the mind of the 
 learner, which is the Method of Teaching (3) 
 covering these stringers (which represent the 
 principles of connection) with a flooring of what- 
 ever nature, suggests the invention of a Mode of 
 Teaching (4) the general or the particular 
 "air," or "style/' or " bearing,' 7 of the 
 teacher while teaching (crossing the bridge) indi- 
 cates his Manner of Teaching. Manner also in- 
 cludes a little of the notion of the flooring, as 
 that a part of it is laid of wood, a part of iron, 
 according to the fancy of the engineer. 
 
 (b) Another illustration : " Another thing 
 at Hillard on the Pacific railway on the use of 
 which Eastern people venture queer conjectures, 
 is a high, narrow tressel-work bridge supporting 
 a V-shaped trough an object familiar enough to 
 residents of the Pacific Coast. This is a l flume, ' 
 and the wood used in the kilns is floated through 
 it for a distance of twenty -four miles from the 
 mountains. Over 2,000,000 feet of lumber 
 were necessary in its construction, and from 
 its mouth it falls 2,000 feet, the stream rush- 
 ing through it and sweeping the logs on its 
 bosom with a rapidity and ease that makes us 
 wonder why people ever haul wood in cumber- 
 some waggons." (D. Appleton & Co., The Art 
 Journal, New Series, No. 27, p. 71.) 
 
120 ON THE THEORY OF 
 
 In this illustration, the principle of conveyance 
 is known in popular language as the " buoying 
 up power of water, ' ' the relative specific gravity. 
 This is the Method, by floating on water. The 
 contrivance, a V-shaped trough, instead of the 
 surface of a river, exhibits the Mode of applying 
 the principle or Method. Whatever is peculiar, 
 or individual about the trough, or the prepara- 
 tion of the wood, or the letting of the water into 
 the flume, indicates the Manner involved in the 
 case. 
 
 (c) Another illustration : " A railroad has 
 been constructed to the mines of Summit Hill, 
 about nine miles W. of the town (Mauch Chunk 
 Mawk Chunk' in Pennsylvania). The cars, 
 loaded with coal, descend by their own gravity 
 to the landing, and after being emptied have 
 been heretofore drawn up the plane by mules. 
 But now the labors of the mules are superseded. 
 A ' back track ' has been constructed, which is 
 regarded as a master piece of bold and success- 
 ful engineering. From the chutes where the 
 coal cars are unloaded at the town of Mauch 
 Chunk, they return by their own weight to the 
 foot of Mount Pisgah. They are then drawn 
 to the top of that mountain on an inclined plane 
 by means of a stationary engine. From the 
 liead of this plane they pass by their own gravity 
 along a railway of 6 miles, to the foot of 
 another inclined plane. To the top of this they 
 are again raised by steam, and thence descend to 
 the different mines, where they are filled with 
 coal, and again descend by their own weight to 
 
METHODS OF TEACHING. 121 
 
 the chutes." (J. Thomas, Lippincottfs Pro- 
 nouncing Gazetteer , ed. 1868, Mauch Chunk.) 
 
 In this illustration, three principles of motive 
 power are introduced gravity, animal-power, 
 and steam. They are the Methods of transpor- 
 tation. The principle of gravity is utilized by 
 carriages on wheels, instead of carriages on run- 
 ners ; the principle of animal -power was utilized 
 by using mules, instead of horses ; the principle 
 of steam-power is utilized by means of a sta- 
 tionary, instead of a movable, engine. The car- 
 riages on wheels, the mules, and the stationary 
 engine, arc objects which are used to apply the 
 Methods, and are Modes of transportation. 
 Whatever is individual, or peculiar, in any of 
 these not necessary, used instead of something 
 else in form, rate of motion, or way of applica- 
 tion, or in construction, exhibits Manner. 
 
 (d) Another illustration : A gentleman em- 
 ploys a span of horses to draw his carriage. 
 Horse-power is the principle involved in convey- 
 ing it is the Method of transporting the car- 
 riage. A carriage on wheels is used, instead of 
 a sleigh, or ' ' carriage on runners, ' ' as the way 
 of showing the application of the principle of 
 horse-power this represents the Mode of con- 
 veyance used by the gentleman. His particular 
 kind of carriage is a landau, instead of a wag- 
 onette this notion, together with whatever of 
 ' ' style, ' ' or " air, ' ' he may choose to introduce, 
 exhibits his Manner of riding in his landau. 
 (See, also, Mill's use of these terms in 224.) 
 
 129. Mr. Page uses Mode correctly in this : 
 
122 ON THE THEORY OF 
 
 " Right Modes of Teaching^ -Pouring-in Pro- 
 cess, or lecturing ; Drawing- out Process, or 
 questioning." (Theory and Practice of Teach- 
 ing, p. 5, Contents, ed. 1853.) 
 
 130. The subjoined illustrates Mode, Man- 
 ner, and the idea of * ' leading' ' the pupil : 
 
 i 'The class were puzzled to understand the 
 resistance of the various media. ' I do not 
 know as I understand what media means/ said 
 one of the boys. ' A medium is that in which 
 a body moves, ' read the teacher from a book. 
 4 A medium ? ' ' Yes ; we say medium when 
 we mean but one, and media when we mean 
 more than one.' After a time, the pupil still 
 gaining no light, the regular teacher approached : 
 ' John, ' taking his watch in his hand 
 ' would this watch continue to go, if I should 
 drop it into a pail of water ? ' i I should think 
 it would not long. ' ' Why not ? ' ' Because 
 the water would get round the wheels and 
 stop it, I should think. ' l How would it be if I 
 should drop it into a quart of molasses ? ' The 
 boys smiled. i Or into a barrel of tar ? ' * Sup- 
 pose I should force it, while open, into a quantity 
 of lard. ' John said, ' The watch would not go 
 in any of the articles.' ' Articles, why not 
 say Media?' * Oh, I understand it now.' " 
 (Ibid., pp. 319-321.) 
 
 131. In the annexed extract, the author uses 
 " Manner" properly, but substitutes Method for 
 Mode : " The agreeable talents are too much 
 confined to method. They are rendered too ab- 
 stracted by being reduced to maxims and pre- 
 
METHODS OF TEACHING. 123 
 
 cepts ; and hence those things which should 
 constitute the amusement of young people, are 
 made disgusting to them, as the study of an art. 
 I cannot conceive any thing more ridiculous, than 
 to see an old singing or dancing-master, approach 
 a young, lively, giggling girl, with a frigid and 
 formal air ; and assume, in teaching his frivolous 
 science, a more pedantick and magisterial tone, 
 than if he were teaching her the catechism. Is 
 it that the art of singing, for instance, depends 
 on the knowledge of written musick ? Is it not 
 possible to acquire a just command of voice, to 
 learn to sing with taste, and even to accompany 
 an instrument, without knowing a single note ? 
 Is the same manner of singing adapted to all 
 voices ? Doth the same method of teaching 
 suit equally every genius ? It is impossible to 
 make me believe, that the same attitudes, the 
 same steps, the same motions and gestures, or 
 even the same dances, are equally proper for a 
 little, lively, sharp-eyed brunette, and a tall 
 beauty with languishing eyes and flaxen hair. 
 When I see a dancing-master give the same les- 
 son, therefore, indiscriminately to both, I say 
 to myself, this man follows the customs of hi& 
 profession, but he understands nothing of his 
 art." (Kousseau, JZmilius, vol. 3, p. 205, ed* 
 1783, London.) 
 
 132. In the extract following, the Socratic 
 Mode, often improperly called Method, is illus- 
 trated : " Now a guide, when he has found a 
 man out of the road leads him into the right 
 way : he does not ridicule or abuse him and 
 
124 ON THE THEORY OF 
 
 then leave him. Do you also show the illiterate 
 man the truth, and you will see that he follows. 
 But so long as you do not show him the truth, 
 do not ridicule him, but rather feel your own 
 incapacity. How then did Socrates act ? He 
 used to compel his adversary in disputation to 
 bear testimony to him, and he wanted no other 
 witness. Therefore he could say, * I care not 
 for other witnesses, but I am always satisfied 
 with the evidence (testimony) of my adversary, 
 and I do not ask the opinion of others, but only 
 the opinion of him who is disputing with me.' 
 For he used to make the conclusions drawn 
 from natural notions so plain that every man saw 
 the contradiction (if it existed) and withdrew 
 from it (thus): Does the envious man rejoice ? 
 By no means, but he is rather pained. Well, do 
 you think that envy is pain over evils ? and 
 what envy is there of evils ? Therefore he made 
 his adversary say that envy is pain over good 
 things. Well then, would any man envy those 
 who are nothing to him ? By no means. Thus 
 having completed the notion and distinctly 
 fixed it he would go away without saying to his 
 adversary, Define to me envy ; and if the ad- 
 versary had defined envy, he did not say, You 
 have defined it badly, for the terms of the defi- 
 nition do not correspond to the thing defined 
 These are technical terms, and for this reason 
 disagreeable and hardly intelligible to illiterate 
 men, which terms we (philosophers) cannot lay 
 aside. But that the illiterate man himself, who 
 follows the appearances presented to him, should 
 
METHODS OF TEACHING. 125 
 
 be able to concede any thing or reject it, we can 
 never by the use of these terms move him to 
 do. Accordingly being conscious of our own 
 inability, we do not attempt the thing ; at least 
 such of us as have any caution do not. But the 
 greater part and the rash, when they enter into 
 such disputation, confuse themselves and con- 
 fuse others ; and finally abusing their adver- 
 saries and abused by them, they walk away. 
 
 " Now this was the first and chief peculiarity 
 of Socrates, never to be irritated in argument, 
 never to utter any thing abusive, any thing insult- 
 ing, but to bear with abusive persons and to put 
 an end to the quarrel. If you would know what 
 great power he had in this way, read the Sym- 
 posium of Xenophon, and you will see how many 
 quarrels he put an end to. Hence with good 
 reason in the poets also this power is most highly 
 praised, 
 
 * Quickly with skill he settles great disputes. ' 
 HESIOD, TJieogony, v. 87. 
 
 Well then ; the matter is not now very safe, 
 and particularly at Rome ; for he who attempts 
 to do it, must not do it in a corner, you 'may be 
 sure, but must go to a man of consular rank, if 
 it so happen, or to a rich man, and ask him, 
 Can you tell me, Sir, to whose care you have 
 entrusted your horses ? By all means. Well 
 then ; can you tell me to whom you entrust 
 your gold or silver things or your vest- 
 ments f I don't entrust even these to any one 
 indifferently. Well ; your own body, have you 
 
126 OST THE THEORY OF 
 
 already considered about entrusting the care 
 of it to any person ? Certainly. To a man 
 of experience, I suppose, and one acquainted with 
 the aliptic, or with the healing art ? With- 
 out doubt. Are these the best things that you 
 have, or do you also possess something else 
 which is better than all these ? What kind of 
 a thing do you mean ? That I mean which 
 makes use of these things, and tests each of 
 them, and deliberates. Is it the soul that you 
 mean ? You think right, for it is the soul 
 that I mean. In truth I do think that the 
 soul is a much better thing than all the others 
 which I possess. Can you then show us in 
 what way you have taken care of the soul ? for 
 it is not likely that you, who are so wise a man 
 and have a reputation in the city, inconsiderately 
 and carelessly allow the most valuable thing that 
 you possess to be neglected and to perish. 
 Certainly not. But have you taken care of 
 the soul yourself ; and have you learned from 
 another to do this, or have you discovered the 
 means yourself ? Next, if you persist in troub- 
 ling him, there is danger that he may raise his 
 hands and give you blows. I was once myself 
 also an admirer of this mode of instruction until 
 I fell into these dangers. " (Epictetus, Dis- 
 courses, chap, xii.) 
 
 133. In the following extract the conceptions 
 of Mode and Manner of Teaching are not dis- 
 tinguished from that of Methods of Teaching. 
 "Another * peccant humour ' which at present 
 infects the body of education is the employment 
 
METHODS OF TEACHING. 127 
 
 of Mechanical Methods. These methods were 
 perhaps not at first mechanical ; they have be- 
 come so by degeneration in the hands of merely 
 imitative persons. If a method is not thoroughly 
 assimilated by the teacher so as to become a liv- 
 ing part of his own mind, if it does not marry 
 itself willingly to his own thought and his own 
 habits, if it is adopted as a mere plan for saving 
 himself trouble and for escaping from his usual 
 amount of work, it has a tendency to degenerate 
 into a kind of machine, into something that 
 cannot call forth thought and mental activity from 
 his pupils. The essential requisite of a method 
 is that it shall be living and possess the adapta- 
 bility of life, and that it shall not interfere with 
 but promote the spontaneous interest which the 
 pupil may be inclined to feel in his subject. But 
 our ancient and standing enemy routine is at 
 hand here also, and is always ready to turn the 
 best method into a monotonous device, or a crank- 
 like exercise of activities. Man is by nature a 
 hunting animal, and the heuristic method in 
 teaching is ore of the most potent for developing 
 the mental powers. But in the degeneration 
 which is natural to all human things, unless the 
 breath that created them at first breathes through 
 them again, among the destructive powers which 
 produce this degeneration, there is none -more 
 potent than the habit of imitation. Question 
 and answer from the pupil as well as from the 
 teacher is one of the best ways of searching out 
 truth that are given to human faculties. But no 
 sooner is this perceived than some one writes a 
 
128 O^T THE THEORY OF 
 
 book on what he calls this method, and the life 
 is killed out of the method by the very process 
 which seemed to preserve it it is strangled in 
 the grasp of stereotype. And there are now 
 hundreds of books, used mostly in ladies' schools, 
 in which this base-born plan is still followed, to 
 the irretrievable loss of those who are subjected 
 to the process. An eminent Cambridge mathe- 
 matician at present trains -all his pupils on this 
 heuristic method and without book ; and his 
 success at the university as well as in school is 
 marked and solid. But if he were to give a 
 sketch of his method in writing, it would be ig- 
 nobly stuck to and slavishly followed to the 
 death of the very method he had been endeavour- 
 ing to set forth and recommend. If we could 
 only train all our teachers to the use and constant 
 practice of the heuristic method, we should make 
 them themselves more strong in thought and 
 purpose, more firm and real in their intellectual 
 life, and more capable of firing their pupils with 
 a single and undivided zeal for truth. . . . 
 We are in fact overdone with machinery ; our 
 education is choked by the means we use to 
 promote it ; and the informing spirit is too often 
 absent. . . . 
 
 44 ... Our mechanical methods blind us to 
 the necessity of seeking to analyse our subjects in 
 the fullest manner, and so to arrange the steps 
 that the children may go up with ease and plea- 
 sure. We are constantly giving knowledge 
 prematurely ; we are every day anticipating re- 
 sults which the child will reach for himself ; and 
 
METHODS OF TEACHING. 129 
 
 all over our pupils suffer in their brains from the 
 malady of the day imperfect digestion. ' ' (Mei- 
 klejohnj Inaug. Address, Bell Chair, of Education, 
 pp. 33-36, 1876.) 
 
 134. The expressions " Methods of Nature," 
 "Nature's Methods," " Consult Nature for 
 Methods of Education and Teaching, ' ' are heard 
 from time to time. It may be profitable to ex- 
 amine this conception a little. What is Nature ? 
 How does she work ? Where shall we find her ? 
 We find her about us everywhere, as a wild, in- 
 congruous, heterogeneous, restless mass of objects 
 and activities. The most natural things in the 
 world, probably, are a swamp and barbarism, for 
 they are "fresh from the hand of Nature." 
 The most natural road across the swamp is a 
 corduroy road. The most natural action of a 
 boy is to kick another boy when he dislikes 
 him. The most natural way to occupy land is 
 to tent upon it, and by force keep others away 
 from it, as the nomadic peoples do. The most 
 natural of plows is the Asiatic the fork of a 
 tree. The most natural apple is that which 
 grows from the natural seed, not the welcome 
 fruit of the graft. We also say that these works 
 of art, all high art, are natural. What, then, is 
 Nature ? Nature is not simply the fact that is 
 presented to man she is not alone an object 
 formed without the help of man she is not a 
 single objective thing by itself. Nature is a 
 term for Capacities and Possibilities, whether 
 of matter or of mind. We speak of capacities 
 of the human mind, all of which are natural ; 
 
130 OK THE THEORY OF 
 
 and the developments of them are all natural. 
 Nothing can be produced which is outside of 
 the range of possibilities, and, hence, that is 
 outside of Nature. But by way of distinc- 
 tion, those things which man himself has been 
 instrumental in directing and controlling are 
 called Artificial. If the swamp and the barba- 
 rian are very natural, drained meadows and civ- 
 ilization are very artificial. Yet in all these 
 cases man never can go beyond what his own 
 natural powers can naturally do. No man ever 
 constructs a bridge or paints a madonna that his 
 natural powers do not naturally accomplish. 
 It is all of Nature, and all natural just as natural 
 as it was for Demosthenes to stammer or, subse- 
 quently, to move all Greece by his eloquence. 
 One man uses his right hand familiarly, another 
 his left, and still another both with equal facility 
 which is the natural one ? An Icelander natu- 
 rally resists cold an African naturally resists 
 heat an American resists both heat and cold. 
 Which is the natural case ? A honey bee gath- 
 ers honey in temperate zones, but, moved south- 
 ward, ceases what is the naturalness in the 
 case ? In these cases one is just as natural as 
 another they all are so because of native en- 
 dowments, capacities, or possibilities. What is 
 the most natural language to speak, for a child, 
 English, French, or Italian ? ' ' Man, by nature, 
 is formed to suffer with patience, and die in 
 peace. It is the physicians with their prescrip- 
 tions, the philosophers with their precepts, and 
 the clergy with their prayers and exhortations, 
 
METHODS OF TEACHING. 131 
 
 that have debased the heart of man, and made 
 him ignorant how to die/' (Rousseau, Emilius, 
 vol. 1. p. 47.) In the following, which is the 
 natural stage of relationship, compared to that 
 now established by law and custom in the United 
 States at the present time ? " We shall endeavour 
 to establish the following propositions : 1 . That 
 the most ancient system in which the idea of 
 blood-relationship was embodied, was the system 
 of kinship through females only. 2. That the 
 primitive groups were, or were assumed to be, 
 homogeneous. 3. That the system of kinship 
 through females only tended to render the exo- 
 gamous groups heterogeneous, and thus to super- 
 sede the system of capturing wives. 4. That 
 in the advance from savagery the system of 
 kinship through females only was succeeded by 
 a system which acknowledged kinship through 
 males also ; and which, in most cases, passed 
 into a system which acknowledged kinship 
 through males only. 5. That the system of kin- 
 ship through males tended to rear up homoge- 
 neous groups, and thus to restore the original 
 condition of affairs where the exogamous preju- 
 dice survived as regards both the practice of 
 capturing wives and the evolution of the form 
 of capture. 6. That a local tribe, under the 
 combined influence of exogamy and the system 
 of female kinship, might attain a balance of per- 
 sons of different sexes regarded as being of 
 different descent, and that thus its members might 
 be able to intermarry with one another, and 
 wholly within the tribe, consistently with the 
 
132 ON THE THEORY OF 
 
 principle of exogamy. 7. That a local tribe, 
 having reached this stage and grown proud 
 through success in war, might decline intermar- 
 riage with other local tribes and become a caste. 
 8. That on kinship becoming agnatic, the mem- 
 bers of such a tribe might yield to the universal 
 tendency of rude races to eponomy, and feign 
 themselves to be all derived from a common an- 
 cestor, and so become endogamous. And 9. 
 That there is reason to think that some endo- 
 gamous tribes became endogamous in this same 
 manner. . . . The earliest human groups can have 
 had no idea of kinship. . . . The idea must be re- 
 garded as a growth. , . . Individuals had been 
 affiliated not to persons, but to some group. . . . 
 As distinguished from men of other groups, 
 they would be the group-stock, and named after 
 the group.' 7 (McLennan, Primitive Marriage, 
 pp. 118-123, ed. 1876, London.) 
 
 135. The question is really, not what is nat- 
 ural ? but what is artificial ? If the word has 
 any proper signification and scope, they must be 
 something like this : Artificial things include 
 all those products and results which have been 
 developed from the capacities and possibilities of 
 Nature by the direct agency of man. Under 
 this definition come all that man has ever done 
 in civilization and in history Le., in civilization. 
 " Culture or Civilization, taken in its wide eth- 
 nographic sense, is that complex whole which in- 
 cludes knowledge, belief" (religious and other- 
 wise), u art, morals, law, custom, and any other 
 capabilities and habits acquired by man as a mem- 
 
METHODS OF TEACHING. 133 
 
 berof society." (Tylor, Primitive Culture, vol. 
 i., p. 1, ed. 1874, New York.) In so far as the 
 faculties of the mind are native to. the mind, they 
 are natural but in so far as they are developed 
 into power by this or that kind of life, or by 
 this or that branch of knowledge, and for this or 
 that purpose, the developed powers and the re- 
 sulting products of effort, although quite natural, 
 are known as artificial. Methods of Educa- 
 tion are artificial. Modes of Teaching are arti- 
 ficial, yet, if based upon principles, they are na- 
 turally founded upon the native powers of the 
 learning mind and the subject-matter to be learned. 
 This subject-matter is both natural and artificial, 
 although all produced by the capacities of Na- 
 ture. Methods of Teaching, being founded upon 
 the innate nature of things, are natural. 
 
 136. It is also true that the term " natural, " 
 as commonly understood when applied to the 
 human conditions, means the general idea or no- 
 tion that people acquire as an induction from 
 experience. An action is pronounced natural in 
 proportion as it approaches spontaneous favor 
 from the greatest number of observers. In pro- 
 portion as it diverges from this it is called 
 " affected, " " false," " sham," " unnatural/' 
 ' i monstrous. ' ' Still all these phases of experi- 
 ence and observation are within the capacities of 
 Nature, and hence natural. A broad discrimi- 
 nation should be made between the term natural 
 as applied to one individual, and as applied in 
 the sense of the inductive general idea. The 
 author who can gather up the sense of the 
 
134 ON THE THEORY OF 
 
 .greatest number of people into one picture or 
 character, or trait of experience, is called the 
 most life-like and natural in his writings. But 
 he is no more natural than the man who stam- 
 mers, or squints, or says, as the child, " I be 
 going." 
 
 137. " But the only distinct meaning of that 
 word (natural) is, stated, fixed, or settled; since 
 what is natural as much requires and presup- 
 poses an intelligent agent to render it so, i.e. to 
 effect it continually, or at stated times, as what 
 is supernatural or miraculous does to effect it 
 once." (Butler, Analogy, Malcom's ed., 1860, 
 p. 94.) 
 
 138. " According to its derivation, nature 
 (natura nascitur) means that which is born or 
 produced the becoming ; that which has a be- 
 ginning and an end ; that which has not the 
 cause of its existence in itself, and the cause of 
 which must be sought in something antecedent 
 to and beyond itself that is, nature is the phe- 
 nomenal, This the word expresses in the strong- 
 est manner. That which begins to be, as the nec- 
 essary consequence of antecedent conditions, is 
 natural. The co-existence, resemblance, and 
 succession of phenomena constitute the order of 
 nature ; and the uniformity of these relations 
 among phenomena are the laws of nature. . . . 
 The word ' nature ' is also employed to denote 
 the essential properties of matter, and the vari- 
 ous forms of energy, potential and kinetic." 
 (Cocker, Theistic Conception of the World, pp. 
 193-4, ed. 1875.) 
 
METHODS OF TEACHING. 135 
 
 139. li Nature is the aggregate or totality of 
 all material or physical phenomena. A Law of 
 Nature is the statement of a certain uniformity 
 observed in the relations among phenomena. The 
 laws of nature are ' simply expressions of phe- 
 nomenal uniformities, having no coercive power 
 whatever.' (Carpenter.) 
 
 140. " The Uniformity of the Order of Na- 
 ture may mean either ' uniformity of co-exist- 
 ence ' or ' uniformity of succession. ' l Uniformity 
 of co-existence ' means that the same substances 
 must always ha ye the same essential properties 
 and the same permanent relations to other sub- 
 stances. . . . The constancy of the course 
 of nature or the uniformity of causation is not a 
 self-evident and necessary truth. In so far as it 
 is a scientific truth it is purely an induction from 
 experience, an experience which is necessarily 
 limited, and therefore does not warrant a uni- 
 versal conclusion. . . . It is an immediate 
 fact of consciousness that the will is a cause 
 which is adequate to the production of a diver- 
 sity of effects. . . . Physical science itself 
 does not teach that the course of nature is abso- 
 lutely uniform. . . . i Nature,' says Dr. 
 Cohn, of Breslau, ' is an equation with very 
 many unknown quantities. It is the work of 
 natural science to determine the value of these 
 quantities.' " (Ibid., pp. 325-33.) 
 
 141. " According to its derivation, nature 
 should mean that which is produced or born ; 
 but it also means that which produces or causes 
 to be born. . . . The term nature is used 
 
136 OX THE THEORY OF 
 
 sometimes in a wider, sometimes in a narrower 
 extension. When employed in its most exten- 
 sive meaning, it embraces the two worlds of 
 mind and matter. When employed in its more 
 restricted signification, it is a synomym for the 
 latter only, and is then used in contradistinction 
 to the former. In the Greek philosophy, . . . 
 the word was general in its meaning ; and in- 
 cluded not only the sciences of matter, but also 
 those of mind. With us, the term nature is 
 more vaguely extensive than the terms physics, 
 physical, physiology, or even than the adjective 
 natural ; whereas, in the philosophy of Germany, 
 natur and its correlatives, . . . are, in gen- 
 eral, expressive of the world of matter in contrast 
 to the world of intelligence. 
 
 "Nature as opposed to art, all physical 
 causes, all the forces which belong to physical 
 beings, organic or inorganic. The nature or es- 
 sence of any particular being or class of beings, 
 that which makes it what it is. 
 
 " l The word nature has been used in two 
 senses, viz., actively and passively ; energetic 
 ( forma formans), and material (= forma 
 formata). Tn the first it signifies the inward 
 principle of whatever is requisite for the reality 
 of a thing as existent ; while the essence, or es- 
 sential property, signifies the inner principle of 
 all that appertains to the possibility of a thing. 
 Hence, in accurate language, we say the essence 
 of a mathematical circle or geometrical figure, 
 not the nature, because in the conception of 
 forms, purely geometrical, there is no expression 
 
METHODS OF TEACHING. 137 
 
 or implication of their real existence. In the 
 second or material sense of the word nature, we 
 mean by it the sum total of all things, as far as 
 they are objects of our senses, and consequently 
 of possible experience the aggregate of phe- 
 nomena, whether existing for our outer senses, or 
 for our inner sense. The doctrine concerning 
 nature, would therefore . . be more properly 
 entitled phenomenology, distinguished into its 
 two grand divisions, somatology (= doctrine of 
 the general properties of bodies or material sub- 
 stances), and psychology.' (Coleridge.} 
 
 " ' There is no such thing as what men com- 
 monly call the course of nature, or the power of 
 nature. The course of nature, truly and prop- 
 erly speaking, is nothing else but the will of 
 God producing certain effects in a continued, 
 regular, constant, and uniform manner ; which 
 course or manner of acting, being in every move- 
 ment perfectly arbitrary, is as easy to be altered 
 at any time as to be preserved.' (Clarice.) 
 
 " t All things are artificial,' said Sir Thomas 
 Browne, ' for nature is the art of God. ' The 
 antithesis of nature and art is a celebrated doc- 
 trine in the peripatetic philosophy. Natural 
 things are distinguished from artificial, inasmuch 
 as they have, what the latter are without, an in- 
 trinsic principle of formation. (Arist.) 
 
 " Dr. Reid said that nature is the name we 
 give to the efficient cause of innumerable effects 
 which fall daily under observation. But if it be 
 asked what nature is ? whether the first universal 
 cause or a subordinate one ? whether one or 
 
138 ON THE THEORY OF 
 
 many ? whether intelligent or unintelligent ? 
 upon these points we find various conjectures 
 and theories, but no solid ground upon which 
 we can rest. And I apprehend the wisest men 
 are they who are sensible that they know noth- 
 ing of the matter. ' ' (Fleming, Vocab. of Phil. ) 
 142. " When he was visited by one of the 
 magistrates, Epictetus inquired of him about 
 several particulars, and asked if he had children 
 and a wife. The man replied that he had ; and 
 Epictetus inquired further, how he felt under 
 the circumstances. Miserable, the man said. 
 Then Epictetus asked, In what respect, for men 
 do not marry in order to be wretched, but rather 
 to be happy. But I, the man replied, am so 
 wretched about my children that lately, when 
 my little daughter was sick and was supposed 
 to be in danger, I could not endure to stay with 
 her, but I left home till a person sent me news 
 that she had recovered. Well then, said Epic- 
 tetus, do you think that you acted right ? I 
 acted naturally, the man replied. But convince 
 me of this that you acted naturally, and I will 
 convince you that everything which takes place 
 according to nature takes place rightly. This is 
 the case, said the man, with all or at least most 
 fathers. I do not deny that.: but the matter 
 about which we are inquiring is whether such be- 
 haviour is right ; for in respect to this matter we 
 must say that tumours also come for the good 
 of the body, because they do come ; and gene- 
 rally we must say that to do wrong is natural, 
 because nearly all or at least most of us do wrong. 
 
METHODS OF TEACHING. 139 
 
 Do you show me then how your behaviour is nat- 
 ural. I cannot, he said ; but do you show me 
 how it is not done according to nature, and is 
 not rightly done." (Epictetus, Discourses, Book 
 I., Chap. XL, Long' trans.) 
 
 143. " The object of what we commonly 
 call education that education in which man in- 
 tervenes and which I shall distinguish as artificial 
 education is to make good these defects in 
 Nature's methods ; to prepare the child to re- 
 ceive Nature's education, neither incapably nor 
 ignorantly, nor with wilful disobedience ; and to 
 understand the preliminary symptoms of her dis- 
 pleasure, without waiting for the box on the ear. 
 In short, all artificial education ought to be an 
 anticipation of natural education. And a liberal 
 education is an artificial education, which has 
 not only prepared a man to escape the great evils 
 of disobedience to natural laws, but has trained 
 him to appreciate and to seize upon the rewards, 
 which Nature scatters with as free a hand as her 
 penalties. . . . Ignorance is visited as 
 sharply as wilful disobedience incapacity meets 
 with the same punishment as crime. " (Huxley, 
 Lay Sermons, p. 34, ed. 1870.) 
 
II. 
 
 ON THE PRACTICE OF METHODS OF 
 TEACHING. 
 
 (A) ON THE KNOWING FACULTIES OF THE MIND. 
 
 144. In discussing these Elements of Meth- 
 ods of Teaching, no attempt is made to present 
 a systematic view of Psychology. To do this 
 would require a volume by itself, and must be 
 reserved for another occasion as opportunities 
 shall permit. Sufficient data are introduced to 
 serve as bases for Methods of Teaching. With- 
 out endeavoring to classify the matter inserted, 
 it is used as it best serves the scope of the inves- 
 tigation. This matter is also very valuable to 
 the student for its suggestiveness, even when it 
 does not bear directly upon the line of the in- 
 quiry. Those professional students, who are al- 
 ready familiar with some system of Psychology, 
 will need to be delayed only a short time on this 
 division of the volume. 
 
 145. Adapting from Sir William Hamilton's 
 Metaphysics, Murray's text, edition of 1874, pp. 
 3966, psychological phenomena of conscious- 
 ness are classified under three great divisions : 
 (1) Cognitions, or the faculties which have the 
 
OF THE MIND. 141 
 
 power to know ; (2) Feelings, or sensibilities, 
 those which are susceptible of giving pain or 
 pleasure ; (3) Conations, which are " tendencies 
 to action, and are divisible into classes, as such 
 tendencies are either blind and fatal, or deliberate 
 and free. The former are desires, the latter, 
 volitions, (p. 226). For present purposes it is 
 necessary to elaborate only the first division, 
 cognitions, including consciousness. 
 
 146. (a) " Consciousness is the recognition 
 by the thinking subject of its own acts or affec- 
 tions. It is an actual and not a potential knowl- 
 edge. It is an immediate, not a mediate knowl- 
 edge. It supposes a contrast, a discrimination 
 as the ego and non-ego, the discrimination of 
 states or modifications of the internal subject or 
 self from each other, and the distinction be- 
 tween the parts and qualities of the outer world. 
 It involves judgment, or the mental act by 
 which one thing is affirmed or denied of an- 
 other. It is conditioned upon memory, for 
 without this our mental states could not be held 
 fast, compared, distinguished from each other, 
 and referred to self. Consciousness in its sim- 
 plicity necessarily involves three things, (1.) a 
 recognizing or knowing subject, ego ; (2.) a 
 recognized or known modification ; and (3.) a 
 recognition or knowledge by the subject of the 
 modification (pp. 39-42). 
 
 (b) " Comparison requires a tertium quid, a 
 locus call it what you will in which the two 
 QiaiwaJExL existences may meet on equal terms. 
 r Hubifaam is what is known as a consciousness. 
 
142 ON THE KNOWING FACULTIES 
 
 Even sensations cannot be supposed, simply as 
 such, to be aware of their relations to each other. 
 A succession of feelings is not (as James Mill 
 reiterates) one and the same thing with a feeling 
 of succession, but a wholly different thing. The 
 latter feeling requires a self -transcendency of 
 each item, so that each not only is in relation, 
 but knows its relation, to the other. This self- 
 transcendency of data constitutes the conscious 
 form. Where we suppose it to exist we have 
 mind ; where mind exists we have it. ... 
 Thus, then, tbe words Use, Advantage, Interest, 
 Good, find no application in a world in which no 
 consciousness exists. Things there are neither 
 good nor bad ; they simply are or are not. Ideal 
 truth to exist at all requires that a mind also ex- 
 ist which shall deal with it as a judge deals with 
 the law, really creating that which it professes 
 only to declare. . . . This category (of 
 consciousness, or personality) might be defined 
 as the mode in which data are brought together 
 for comparison with a view to choice. Both 
 these points, comparison and choice, will be 
 found alike omnipresent in the different stages 
 of its activity. The former has always been rec- 
 ognized ; the latter less than it deserves. Many 
 have been the definitions given by psychologists 
 of the essence of consciousness. One of the most 
 acute and emphatic of all is that of Ulrici, who 
 in his Leib und Seele and elsewhere exactly re- 
 verses the formula of the reigning British school, 
 by calling consciousness a discriminating activity. 
 But even Ulrici does not pretend that conscious- 
 
OF THE MLN T D. 143 
 
 ness creates the differences it becomes aware of 
 in its objects. They pre-exist and consciousness 
 only discerns them ; so that after all Ulriei's defi- 
 nition amounts to little more than saying that 
 consciousness is a faculty of cognition a rather 
 barren result. I think we nia^ go farther and 
 add that the powers of cognition, discrimination 
 and comparison which it possesses, exist only for 
 the sake of something beyond themselves, name- 
 ly, Selection. Whoever studies consciousness, 
 from any point of view whatever, is ultimately 
 brought up against the mystery of interest and 
 selective attention. There are a great many 
 things which consciousness is in a passive and 
 receptive way by its cognitive and registrative 
 powers. But there is one thing which it does, 
 suft sponte, and which seems an original peculi- 
 arity of its own ; and that is, always to choose 
 out of the manifold experiences present to it at 
 a given time some one for particular accentua- 
 tion, and to ignore the rest. And . . from its 
 simplest to its most complicated forms, it exerts 
 this function with unremitting industry. ' ' (James, 
 Article in Mind, No. XIII. , January, 1879, pp. 
 6-9.) 
 
 147. "I. In the first place, as we are en- 
 dowed with a faculty of Cognition, or Conscious- 
 ness in general, and since it cannot be maintained 
 that we have always possessed the knowledge 
 which we now possess, it will be admitted that 
 we must have a faculty of acquiring knowledge. 
 But this acquisition of knowledge can only be 
 accomplished by the immediate presentation of a 
 
144 OK THE KNOWING FACULTIES 
 
 new object to consciousness ; in other words, by 
 the reception of a new object within the sphere 
 of our cognition. We have thus a faculty which 
 may be called the Acquisitive, or the Presenta- 
 tive, or the Receptive. Now, new or adventi- 
 tious knowledge may be either of things external 
 or of things internal. If the object of knowledge 
 be external, the faculty receptive or presentative 
 of the qualities of such object will be a conscious- 
 ness of the non-ego. This has obtained the 
 name of External Perception, or of Perception 
 simply. If, on the other hand, the object be 
 internal, the faculty receptive or presentative of 
 the qualities of such subject-object, will be a 
 consciousness of the ego. This faculty obtains 
 the name of Internal or Reflex Perception, or 
 of Self-consciousness. By the foreign psychol- 
 ogists this faculty is termed also the Internal 
 Sense." (Hamilton.) 
 
 " The two classes of sense-perceptions thus 
 characterized are the original and the acquired. 
 They are thus defined : an original perception is 
 one that is performed by a single sense, when 
 exercised alone. Whatever the mind knows in 
 this way, either of an object or of its relations, 
 is known directly and by an original endowment 
 of man. It is a pure work or operation of na- 
 ture, and cannot be traced to art. An acquired 
 perception is one which we gain by experience or 
 exercise. We use the knowledge given directly 
 by one sense, as the sign or evidence of the 
 knowledge which we might, but do not, in this 
 particular case, gain by another. " (Porter, 
 
OF THE MLtfD. 145 
 
 The Human Intellect, p. 159, ed. 1869.) Con- 
 tinuing from Hamilton : 
 
 148. " II. In the second place, inasmuch, 
 as we are capable of knowledge, we must be en- 
 dowed not only with a faculty of acquiring, but 
 with a faculty of retaining or conserving it when 
 acquired. We have thus, as a second necessary 
 faculty, one that may be called the Conserva- 
 tive or Retentive. This is Memory, strictly so 
 denominated. 
 
 149. " III. But, in the third place, if we 
 are capable of knowledge, it is not enough that 
 we possess a faculty of acquiring, and a faculty 
 of retaining it in the mind, but out of conscious- 
 ness. We have a reproductive power. This Re- 
 productive faculty is governed by the laws which 
 regulate the succession of our thoughts, the 
 laws, as they are called, of Mental Association. 
 If these laws are allowed to operate without the 
 intervention of the will, this faculty may be 
 called Suggestion, or Spontaneous Suggestion ; 
 whereas, if applied under the influence of the 
 will, it will properly obtain the name of Remin- 
 iscence, or Recollection. By reproduction, it 
 should be observed, that I strictly mean the pro- 
 cess of recovering the absent thought from un- 
 consciousness, and not its representation in con- 
 sciousness. 
 
 150. " IV. In the fourth place, as capable 
 of knowledge, we must not only be endowed with 
 a presentative, a conservative, and a reproductive 
 faculty ; there is required for their consummation 
 a faculty of representing in consciousness, and 
 
146 OK THE KKOWIJSTG FACULTIES 
 
 of keeping before the mind the knowledge pre- 
 sented, retained, and reproduced. We have thus 
 a Representative faculty ; and this obtains the 
 name of Imagination or Phantasy. 
 
 151. "V. In the fifth place, all the faculties 
 we have considered are only subsidiary. They 
 acquire, preserve, call out, and hold up, the ma- 
 terials, for the use of a higher faculty which ope- 
 rates upon these materials, and which we may 
 call the Elaborative or Discursive faculty. 
 This faculty has only one operation, it only 
 compares. It may startle you to hear that the 
 highest function of mind is nothing higher than 
 comparison ; but, in the end, I am confident of 
 convincing you of the paradox. From this mere 
 act of Comparison, there are created the intellec- 
 tual products known as Collective Notions, Ab- 
 stractions, Generalizations, Judgments, and 
 Reasoning. 
 
 152. " VI. But, in the sixth and last place, 
 the mind is not altogether indebted to experience 
 for the whole apparatus of its knowledge. What 
 we know by experience, without experience we 
 should not have known ; and as all our experi- 
 ence is contingent, all the knowledge derived 
 from experience is contingent also. But there 
 are cognitions in the mind which are not contin- 
 gent, which are necessary, which we cannot 
 but think, which thought supposes as its funda- 
 mental condition. These cognitions, therefore, 
 are not mere generalizations from experience. 
 But if not derived from experience, they must be 
 native to the mind. These native cognitions are 
 
OF THE MIND. 147 
 
 the laws by which the mind is governed in its 
 operations, and which afford the conditions of its 
 capacity of knowledge. These necessary laws, 
 or primary conditions of intelligence, are phe- 
 nomena of a similar character ; and we must, 
 therefore, generalize or collect them into a class ; 
 and on the power possessed by the mind of mani- 
 festing these phenomena we may bestow the name 
 of the Regulative faculty. (Lect. on Metaph., 
 XX.) 
 
 153. " The following is a tabular view of 
 the distribution of the Special Faculties of 
 Knowledge. 
 
 COGNITIVE FACULTIES. 
 
 T Prpqpntfltivp jl- External Perception. 
 
 ltlve la. Internal Self -consciousness. 
 II. ConservativeMemory. 
 
 III. Reproductive 
 
 IV. Representative Imagination or Phantasy. 
 V. Elaborative Comparison, or the Faculty of 
 
 Relations. 
 VI. Regulative Reason or Common Sense. ' ' 
 
 154. " Some writers on education call the 
 desire of intellectual progression the faculty of 
 obtaining knowledge, that is to say, they call 
 painting seeing, or the intellectual powers, and 
 think of the senses and the memory as also exert- 
 ing an educational influence ; or they speak of 
 the development of spontaneous activity, as if the 
 will itself were not such a developing power. 
 . . The will reproduces itself only, and 
 acts only within, not without, itself ; for external 
 
148 ON THE KNOWING FACULTIES 
 
 action is as little the new act of the particular vo- 
 lition, as are the words signifying it of the par- 
 ticular thought. The desire of mental progress, 
 on the contrary, enlarges its world for the recep- 
 tion of new creatures, and is as dependent on ob- 
 jects as the pure will is independent of them. 
 The will could reach its ideal, but finds a strange 
 opposition to it, whereas no power stands op- 
 posed to thought, but only the difference be- 
 tween its steps, and the impossibility of seeing 
 whither they reach. . . . The mental desire 
 of advancement which, in a higher sense than 
 the physical, works by means of, and in ac- 
 cordance with, the will, that is to say, creates 
 new ideas out of old ideas, is the distinguish- 
 ing characteristic of man. No will restrains 
 the order of a beast's actions. In our wak- 
 ing moments we are actually conscious that 
 we think ; in our dreams we receive, if I may 
 so express it, that consciousness. In the man 
 of genius the formation of ideas appears actually 
 creative ; in ordinary men, merely recoil ective 
 and necessary. " (Richter, Levana, pp. 342-4.) 
 
 155. " The Intelligence reaches its end ac- 
 cording to a certain way, process, or method. 
 . . . The Formal movements of intelligence 
 accordingly fall under two heads, thus : (a) 
 Will-power, (b) Process or Method of reaching 
 Knowledge. " (Laurie, Syn. of Lectures, p. 10, 
 ed. 1877.) 
 
 156. "No act of intelligence can be per- 
 formed without some determination of the Ego, 
 no act of determination without some cognition, 
 
OF THE MIKD. 
 
 and no act of the one or the other without some 
 amount of feeling being mingled in the process. 
 Thus, while each mental state may have its dis- 
 tinctive characteristics, there is unity at the root 
 the identical Ego, spirit, Will (p. 36). . . . 
 When, therefore, it is asked, What causes the 
 will to effect one volition rather than another ? 
 our answer is, Nothing whatever ! Of its own 
 effect, Will 9 in its proper conditions, is not a 
 partial, but a full and adequate cause. ' ' (Cocker, 
 Theistic Conception of the World, p. 391.) 
 
 167. In continuation of what has been said 
 there is added the following, adapted from Por- 
 ter on the Imagination : " The imagination has 
 various applications, (a) The poetic imagina- 
 tion is that creative power which is employed for 
 the gratification of the emotional nature in the 
 production of pictures more or less elevating in 
 their associations, which are fixed and expressed 
 by means of rhythmical language. 
 
 158. (b) " The philosophic imagination is- 
 that without which philosophic invention and 
 discovery are impossible. To invent or discover, 
 is always to recombine. It is to adjust in new 
 positions, objects or parts of objects which have 
 never been so connected before. The discoverer 
 of a new solution for a problem, or a new dem- 
 onstration for a theorem in mathematics, the 
 inventor of a new application of a power of na- 
 ture already known, or the discoverer of a power 
 not previously dreamed of, the discoverer of a 
 new argument to prove or deduce a truth or a 
 
150 ON" THE KNOWING FACULTIES 
 
 new induction from facts already accepted, the 
 man who evolves a new principle or a new defi- 
 nition in moral or political science must all ana- 
 lyze and recombine in the mind things, acts, or 
 events, with their relations, in positions in which 
 they have never been previously observed or 
 thought of. This recombination is purely men- 
 tal. If there be a discovery or invention, there 
 has never before been such a juxtaposition of the 
 materials nor of their parts in the world of fact 
 or in the thoughts of men. These objects and 
 parts are now for the first time brought together 
 in the mind i.e., the imagination of the dis- 
 coverer. Every discovery is, in fact, a work of 
 the creative imagination. ... In the com- 
 munication of scientific truth there can be no ques- 
 tion that a large measure of imagination is of 
 essential service. He that would amply illus- 
 trate, powerfully defend, or effectively enforce 
 the principles and truths of science, is greatly 
 aided by a brilliant imagination. This, of all 
 other gifts, delivers him from that tendency to the 
 dry and abstract, to the general and the remote, 
 to which the expounder of science is continually 
 exposed from his familiarity with principles 
 which are strange to his pupils and readers, and 
 which need to be continually explained and illus- 
 trated by fresh and various examples. The 
 philosophic writer or teacher who is gifted with 
 imagination is more likely to be clear in state- 
 ment, ample in illustration, pertinent in his ap- 
 plication and exciting in his enforcement of the 
 
OF THE MIND. 151 
 
 truths with which his science is conversant, what- 
 ever may be the subject-matter with which the 
 science is concerned. 
 
 159. " (c) The practical or ethical uses of 
 the imagination are numerous and elevated. 
 These are sufficiently obvious from the single 
 consideration, that the law of duty is and must 
 be an ideal law : for whether it is or is not ful- 
 filled, it must precede the act which reaches or 
 falls short of itself. Every ethical rule must be 
 a mental creation, an ideal formed by the crea- 
 tive power, and held before the soul as a guide 
 and law. 
 
 160. " (d) The relation of the imagination to 
 religious faith is interesting and important. 
 The objects of our faith, by their very definition, 
 have never been subjected to direct or intuitive 
 knowledge. Neither sense-perception nor self- 
 consciousness, have confronted them directly or 
 brought report of them. And yet the imagina- 
 tion pictures these objects as real and most im- 
 portant." (Human Intellect, pp. 366-73, ed. 
 1869.) 
 
 161. " The fact is, that the educated Native 
 mind requires hardening. That culture of the 
 imagination, that tenderness for it, which may 
 be necessary in the West, is out of place here ; 
 for this is a society in which, for centuries upon 
 centuries, the imagination has run riot, and 
 much of the intellectual weakness and moral 
 evil which afflict it to this moment, may be 
 traced to imagination having so long usurped the 
 place of reason. What the Native mind re- 
 
152 ON THE KNOWING FACULTIES 
 
 quires, is stricter criteria of truth ; and I look 
 for the happiest moral and intellectual results 
 from an increased devotion to those sciences by 
 which no tests of truth are accepted, except the 
 most rigid." (Maine, Village Communities, pp. 
 275-6, ed. 1876, Address to University of Cal- 
 cutta, March, 1866.) 
 
 162. Concerning the subject of memory 
 more should be said, because it is a faculty 
 which performs so lasting and important a part 
 in the existence of man. Various views of 
 memory are expressed by writers who study 
 Psychology ; the prevailing notion appears to be 
 that it is a faculty which retains and reproduces 
 in Consciousness the mental products that former- 
 ly were there. Another view of memory is 
 this : Memory is that endowment of the Mind by 
 which it is able to reproduce its previous modi- 
 fications. "Modification is properly the bring- 
 ing a thing into a certain mode of existence." 
 {Hamilton, Metaphysics, Murray, p. 33.) 
 
 163. Regarding the nature of memory as a 
 factor in the conception of teaching, the follow- 
 ing opinions are appended : " With regard to 
 younger boys, he said, * It is a great mistake to- 
 think that they should understand all they learn; 
 for God has ordered that in youth the memory 
 should act vigorously, independent of the under- 
 standing whereas a man cannot usually recollect 
 a thing unless he understands it. ' " (Life of Dr. 
 Tho. Arnold, pp. 133-4, ed. 1870, Boston.) ' 
 
 164. " Imagination, Memory, and Hope, 
 are psychologically one and the same faculty. In 
 
OF THE MLNT). 153 
 
 Imagination, the presence of the image is neces- 
 sarily accompanied by a conviction of the possi- 
 ble existence of the corresponding object in an 
 intuition. Memory is the presence of the same 
 image, accompanied by a conviction of the fact, 
 that the object represented has actually existed 
 in a past intuition. Hope, in like manner, is 
 the presence of the same image, together with 
 an anticipation, more or less vivid, of the actual 
 existence of the object in a future intuition. 
 Imagination, memory, and hope, are thus 
 (whether formed by a reflective process or not) in 
 their actual results partly presentative, partly rep- 
 resentative. They are presentative of the im- 
 age, which has its own distinct existence in con- 
 sciousness, irrespectively of its relation to the ob- 
 ject which it is supposed to represent. They 
 are representative of the object, which that im- 
 age resembles, and which, either in its present 
 form or in its several elements, must have been 
 presented in a past act of intuition. Thus there 
 is combined an immediate consciousness of the 
 present with a mediate consciousness of the past. 
 An immediate or presentative consciousness of 
 the past or the future, as such, is impossible. 
 Imagination, being representative of an intuition, 
 is, like intuition, only possible on the condition 
 that its immediate object should be an indi- 
 vidual. ... On the other hand, my no- 
 tion of a man in general can attain to univer- 
 sality only by surrendering resemblance ; it be- 
 comes the indifferent representative of all man- 
 kind, only because it has no special likeness to 
 
154 ON THE KNOWING FACULTIES 
 
 any one in particular. This distinction must be 
 carefully borne in mind in comparing imagina- 
 tion with the cognate process of conception. 
 Memory is sometimes considered as the 
 result of a process of thought." (Mansel, Meta- 
 physics, pp. 128-9, ed. 1871.) 
 
 165. " ' The resuscitation of thoughts which 
 in some shape or other have previously occupied 
 the mind,' is nothing more or less than a prel- 
 ude to what will unquestionably form a chief 
 part of our intellectual experience of futurity ; 
 namely, the inalienable and irrepressible recolleV 
 tion of the deeds and feelings played forth while 
 in the flesh, providing a beatitude or a misery 
 forever. Ordinarily, this resuscitation is of such 
 a medley and jumbled character, that not only is 
 the general product unintelligible, but the par- 
 ticular incidents are themselves too fragmentary 
 and dislocated to be recognised. But it is not 
 always so. There must be few who have not 
 experienced in their sleep, with what peculiar 
 vividness, unknown to their waking hours, and 
 with what minute exactitude of portraiture, 
 events long past and long lost sight of, will not 
 infrequently come back, shewing that there is 
 something within which never forgets, and which 
 only waits the negation of the external world, to 
 leap up and certify its powers. . . . That 
 which so vividly remembers is the Soul ; and if 
 in the sleep which refreshes our organic nature, 
 it utters its recollections brokenly and indistinct- 
 ly, it will abundantly compensate itself when the 
 material vesture which clogs it shall be cast 
 
OF THE MIND. 155 
 
 away. Much of the indistinctness of dreams 
 probably arises from physical unhealthiness. If 
 a sound body be one of the first requirements to 
 a sound mind, in relation to its waking employ- 
 ments, no less must it be needful to the sanity 
 and precision of its sleeping ones. Brilliant as 
 are the powers and functions of the spiritual 
 body, the performance of them, whether sleep- 
 ing or waking, so long as it is investured with 
 flesh and blood, is immensely, perhaps wholly, 
 contingent on the health of the material body. ' ' 
 (Grindon, Life, pp. 290-291, 3d ed., London.) 
 
 166. " Memory, a receptive, not a creative 
 faculty, is subjected to physical conditions more 
 than all other mental powers ; for every kind of 
 weakness (direct and indirect, as well bleeding as 
 intoxication) impairs it, and dreams interrupt it ; 
 it is not subject to the will, is possessed by us 
 in common with the beasts ; and can be most 
 effectually strengthened by the physician: a bit- 
 ter stomachic will increase it more than a whole 
 dictionary learnt by heart. For if it gained 
 strength by what it receives, it would grow with 
 increasing years, that is, in proportion to its , 
 wealth in hoarded names ; but it can carry the 
 heaviest burdens most easily in un practiced youth, 
 and it holds those so firmly that they appear 
 above the gray hairs of age as the evergreens of 
 childhood. " (Richter, Levana, pp. 370-1 *) . . . 
 
 " No one has a memory for everything, be- 
 cause no one feels an interest in everything. 
 And the physical powers set bounds even to the 
 strengthening influence of desire on the memory > 
 
156 ON THE KNOWING FACULTIES 
 
 think of that when with children, for in- 
 stance, if a Hebrew bill of exchange for a thou- 
 sand pounds were promised, on condition of de- 
 manding its payment in the very words of the 
 document, as once read aloud, everybody would 
 try to remember them, but, unless he were a 
 Jew, the words and the form would fail him. 
 . . . I myself, however, would not choose v 
 any of these proposed methods of catching and 
 yoking attention (artificial arts of memory), but 
 would adopt that of steady industry. I do be- 
 lieve that a rod would help a creeping child to 
 walk better than crutches under his arms, which 
 at first carry, but afterwards are carried by him. 
 Yea yea, nay nay, are the best double watch- 
 words for children. . . . Fear cripples the 
 memory, both by producing physical weakness 
 and mental irritation ; the frost of cold fear 
 chains every living power which it approaches. " 
 (Richter, Levana, pp. 374-6.) 
 
 167. "It is incomprehensible to me, how 
 people fancy they can teach children to read or 
 write the letters easily by pointing out their re- 
 semblances, and laying before them at once i y, c 
 C, or, in writing, i r, h k, &c. The very oppo- 
 site plan ought to be pursued ; i should be 
 placed next g, v next z, o next r ; the contrast, 
 like light and shadow, make both prominent ; 
 until reflected lights and half shades can separate 
 them anew from each other. The fast-rooted 
 dissimilarities serve at last to hold fast the re- 
 semblance that exists among them. So the old 
 plan of teaching spelling by lists of words alpha- 
 
OF THE MIND. 157 
 
 betically arranged is bad, on account of the diffi- 
 culty of distinguishing similar sounds ; whereas 
 that of classing together derivations from the 
 same Latin or Greek word assists the remem- 
 brance, because the radical word does not alter. ' ' 
 (Richter, Levana, pp. 375-6.) 
 
 168. " There is not a man living, whom it 
 would so little become to speak of memory as 
 myself, for I have none at all ; and do not think 
 that the world has again another so treacherous 
 as mine. My other faculties are all very ordi- 
 nary and mean ; but in this I think myself very 
 singular, and to such a degree of excellence, that 
 (besides the inconvenience I suffer by it, which 
 merits something) I deserve methinks, to be 
 famous for it. and to have more than a common 
 reputation : though, in truth the necessary use 
 of memory considered, Plato had reason when he 
 calPd it a great and powerful Goddess. In my 
 country, when they would decypher a man that 
 has no sense, they say, such a one has no mem- 
 ory." (Montaigne, Essays, p. 33, third ed., 
 London.) 
 
 169. " I am oblig'd to fortune for having so 
 oft assaulted me with the same sort of weapons ; 
 she forms and fashions me by usance, hardens 
 and habituates me so, that I can know within a 
 little for how much I shall be quit. For want 
 of natural memory, I make one of paper ; and as 
 any new symptom happens in my disease, I set 
 it down ; from whence it falls out, that being 
 now almost past all sorts of examples, if any as- 
 tonishment threaten me, tumbling over these lit- 
 
158 OK THE KKOWIXG FACULTIES 
 
 tie loose notes, as the Sibyls leaves, I never fail 
 of finding matter of consolation from some fa- 
 vourable prognostick in my past experience. " 
 (Ibid., p. 652.) 
 
 ' 1 Memory is a faculty of wonderful use, and 
 without which the judgment can very hardly per- 
 form its office : for my part I have none at all : 
 what any one will propose to me, he must do it 
 by parcels, for to answer a speech consisting of 
 several heads, I am not able. I could not re- 
 ceive a commission by word of mouth, without 
 a note-book : and when I have a speech of con- 
 sequence to make, if it be long, I am reduc'd 
 to the miserable necessity of getting it word for 
 word what I am to say by heart ; I should other- 
 wise have neither fashion nor assurance, being 
 in fear that my memory would play me a slippery 
 trick. But this way is no less difficult to me 
 than the other. I must have three hours to 
 learn three verses. And besides, in a work of a 
 man's own, the liberty and authority of altering 
 the order, of changing a word, incessantly vary- 
 ing the matter, makes it harder to stick in the 
 memory of the author. The more I mistrust it, 
 the worse it is, it serves me best by chance, I 
 must negligently sollicit it, for I press it, 'tis as- 
 tonish' d, and after it once begins to stagger, the 
 more I sound it, the more it is perplex 'd ; it 
 serves me at its own hour, not at mine. And 
 the same defect I find in my memory, I find also 
 in several other parts. I fly command, obliga- 
 tion and constraint. That which I can other- 
 wise naturally and easily do : if I impose it upon 
 
OF THE MIND. 159 
 
 myself by an express and strict injunction, I can- 
 not do it. Being once in a place where it is 
 looked upon as the greatest discourtesie imagina- 
 ble not to pledge those who drink to you, 
 though I had there all liberty allowed me, I 
 try'd to play the good fellow, out of respect to 
 the ladies that were there, according to the cus- 
 tom of the country ; but there was sport 
 enough, for this threatning and preparation, that 
 I was to force myself contrary to my custom 
 and inclination, did so stop my throat, that I 
 could not swallow one drop ; and was depriv'd 
 of drinking so much as to my meat. I found 
 myself gorg'd, and my thirst quench' d by so 
 much drink as my imagination had swallow 'd. 
 This effect is most manifest in such as have the 
 most vehement and powerful imagination : but 
 it is natural notwithstanding, and there is no one 
 that does not in some measure find it. They 
 offer'd an excellent archer, condemn 'd to dye, 
 to save his life, if he would shew some notable 
 proof of his art, but he refused to try, fearing 
 least the too great contention of his will would 
 make him shoot wide, and that instead of saving 
 his life, he should also lose the reputation he had 
 got of being a good marks-man. A man that 
 thinks of something else, will not fail to take over 
 and over again the same number and measure of 
 steps, even to an inch, in the place where he 
 walks : but if he makes it his business to mea- 
 sure and count thorn, he will find that what he 
 did by nature and accident, he cannot so exactly 
 do by design. My library, which is of the best 
 
160 ON THE KNOWING FACULTIES 
 
 sort of country libraries, is situated in a corner 
 of my house ; if anything comes into my head 
 that I have a mind to look on or to write ; lest I 
 should forget it in but going cross the court, I 
 am fain to commit it to the memory of some 
 other. If I venture in speaking to digress never 
 so little from my subject, I am infallibly lost, 
 which is the reason that I keep myself in dis- 
 course strictly close. I am forced to call the 
 men that serve me either by the names of their 
 offices, or their country ; for names are very hard 
 for me to remember. I can tell indeed that 
 there are three syllables, that it has a harsh 
 sound, and that it begins or ends with such a let- 
 ter, but that's all : and if I should live long, I 
 do not think but I should forget my own name, as 
 some others have done. Messela Corvinus, was 
 two years without, any trace of memory, which 
 is also said of Georgius Trapezuntius. For 
 my own interest, I often meditate what a kind 
 of life theirs was, and if, without this faculty, I 
 should have enough left to support me with any 
 manner of ease, and prying narrowly into it, I 
 fear that this privation, if absolute, destroys all 
 the other functions of the soul. 
 
 Plenus rimarum sum, hac atque iliac perfluo. 
 Ter. Eun. act. 1. fc. 2. 
 " I'm full of chinks, and leak out every way." 
 
 It has befall'n me more than once to forget the 
 word I had three hours before given or receiv'd, 
 and to forget where I had hid my purse, what- 
 ever Cicero is pleas' d to say : I help myself to 
 
OF THE MIND. 161 
 
 lose what I have a particular care to lock safe up, 
 ' Memoria certe non modo philosophiam, sed om- 
 nis vita3 usum, omnesque artes, una maxime con- 
 tinet.' Cicero. * The memory is the recepta- 
 cle and sheath of all science ;' and therefore 
 mine being so treacherous, if I know little, I can- 
 not much complain ; I know in general the names 
 of the arts, and of what they treat, but nothing 
 more. I turn over books, I do not study them ; 
 what I retain I do not know to be anothers, and 
 is only what my judgment has made its advan- 
 tage of ; discourses and imaginations in which it 
 has been instructed. The author, place, words, 
 and other circumstances, I immediately forget, 
 and am so excellent at forgetting, that I no less 
 forget my own writings and compositions than 
 the rest. I am very often quoted to myself, and 
 am not aware of it ; and whoever should enquire 
 of me where I had the verses and examples that 
 I have here huddled together, would puzzle me 
 to tell him, and yet I have not borrow' d them 
 but from famous and known authors, not satisfy- 
 ing myself that they were rich ; if I moreover 
 had them not from rich and honourable hands, 
 where there is a concurrence of authority as well 
 as reason. It is no great wonder if my book 
 run the same fortune that other books do, and if 
 my memory lose what I have writ as well as what 
 I have read, and what 1 give, as well as what I 
 receive. Beside the defect of memory, I have 
 others which very much contribute to my igno- 
 rance ; I have a slow and heavy wit, the least 
 cloud stops its progress, so that, for example, I 
 
162 o:sr THE KNOWING FACULTIES 
 
 never proposed to it any never so easie a riddle 
 that it could find out. There is not the least 
 idle subtility, that will not gravel me. In games, 
 where wit is required, as chess, draughts, and the 
 like, I understand no more but the motions of 
 the men, without being capable of anything of 
 design. I have a slow and perplex' d apprehen- 
 sion, but what it once apprehends, it apprehends 
 well, for the time it retains it." (Ibid., pp. 404- 
 406.) 
 
 170. " But the objection which is common- 
 est, and which most intimately concerns us here, 
 is, that the knowledge communicated by the sub- 
 ordinate Colleges and verified by this University 
 is worthless, shallow, and superficial. The 
 course of the University of Calcutta is sometimes 
 said to be in fault, and it is alleged, to use a 
 term at once expressive and fashionable, that it 
 encourages * cramming.' Now there are some 
 things in our Calcutta course, of which I do not 
 altogether approve. But it was settled after 
 long discussion, shortly after I became Vice- 
 Chancellor, and it would be absurd to be per- 
 petually changing that which of all things ought 
 to be fixed and permanent, on account of small 
 defects which are, after all, disputable. I wish, 
 however, to say something of the whole class of 
 objections implied in that one word * cram- 
 ming. ' If there is anything in them, you know, 
 I suppose, that they have a far wider application 
 than their application to this University. They 
 are constantly urged against the numerous com- 
 petitive systems which are growing up in Eng- 
 
OF THE MLSTD. 163 
 
 land, and in particular against the system under 
 which the Civil Service of India, probably the 
 most powerful official body in the world, is re- 
 cruited, and will be recruited. 
 
 " The discredit which has been successfully 
 attached to certain systems by this word is a 
 good illustration of the power of what a famous 
 writer called dyslogistic expression, or, to put it 
 more simply, of giving a thing a bad name. And 
 here I must say, that the habit Englishmen have 
 of importing into India these common-place cen- 
 sorious opinions about systems and institutions, 
 is a great misfortune for the Natives. Even in 
 the mouths of Englishmen who invented them, 
 they generally have very little meaning, for they 
 are based on a mere fragment of truth ; when 
 passed about among the multitude, they have 
 still less ; and, at last, when exported hither, 
 and repeated by the Natives in a foreign tongue, 
 they have simply no meaning at all. 
 
 " As far as I understand the word, it means 
 nothing more than the rapid communication of 
 knowledge, communication, that is to say, at 
 a rate unknown till recently. Some people, I 
 know, would add something to the definition, 
 and would say that cramming is the rapid com- 
 munication of superficial knowledge ; but the 
 two statements will generally be found identical, 
 and that they mean by superficial knowledge, 
 knowledge which has been rapidly acquired. 
 The true point, the point which really has to be 
 proved is, whether knowledge rapidly acquired 
 is more easily forgotten than knowledge 
 
164 ON THE KNOWING FACULTIES 
 
 has been slowly gained. The point is one upon 
 which, to some extent, everybody can judge for 
 himself or herself. I do not assert the negative, 
 but I am rather surprised at the readiness with 
 which the affirmative has been usually taken for 
 granted ; no doubt, if it be true, it is a curious 
 psychological fact, but surely there are some rea- 
 sons for questioning the reality. It might plausi- 
 bly be argued that knowledge slowly acquired, 
 has been acquired at the cost of frequent inter- 
 vals of inattention and forgetfulness. Now 
 everybody knows that inattention and forgetful- 
 ness tend to become habits of the mind, and it 
 might be maintained that these habits would be 
 likely to recur, in association with a subject of 
 thought, even when that subject has for once 
 been successfully mastered. On the other hand, 
 it might be contended that knowledge rapidly 
 acquired has been necessarily acquired under a 
 certain strain and tension of the mental faculties, 
 and that the effects of this tension are not likely 
 to be so readily lost and dissipated. 
 
 " The simple truth is, that under the strong 
 stimulus applied by that system of examinations 
 by which the entrance to almost every English 
 profession is now barred, there has sprung up an 
 active demand for knowledge of a more varied 
 description than was once coveted, and above 
 all, for knowledge rapidly imbibed and mastered. 
 To meet this demand, a class of teachers has 
 sprung up who certainly produce remarkable 
 results with remarkable rapidity. I hear it said, 
 that they are men of a lower order of mind and 
 
OF THE MIKD. 165 
 
 accomplishment than the teachers who follow 
 the old methods. It may be so ; but that only 
 renders the probability greater, that some new 
 power has been brought into play." (Maine, 
 Village Communities and Miscellanies, pp. 
 282-5, ed. 1876, Address to Univ. of Calcutta, 
 March, 1866.) 
 
 171. "I have had some opportunity myself 
 of making a comparison, and my judgment is. 
 decidedly in favour of the present system (of com- 
 petitive examinations). I am aware that many 
 persons think the matter is settled by asserting 
 that all we do by our examination system, is to 
 encourage cram ; but unfortunately no definition 
 is given of what is reprobated by this much 
 employed word. It seems to me that at least 
 one very prominent tendency of the competitive 
 system is extremely valuable ; namely, that of 
 securing from the teacher attention to the prog- 
 ress of his pupils individually." (Todhunter, 
 Conflict of Studies, ed. 1873, pp. 63-4.) 
 
 172. u Fortunately, too, for the opponents 
 of examination, an admirable ' cry ' has been 
 found. Examination, they say, leads to * cram, ' 
 and ' cram ' is the destruction of true study. 
 People who know nothing else about examination 
 know well enough that it is * cram. ' The word 
 has all the attributes of a perfect question-beg- 
 ging epithet. It is short, emphatic, and happily 
 derived from a disagreeable physical metaphor. 
 Accordingly, there is not a respectable gentleman 
 distributing prizes to a body of scholars at the 
 end of the session, and at a loss for something to 
 
166 OK THE KKOWLtfG FACULTIES 
 
 say, who does not think of this word ' cram, ' and 
 proceed to expatiate on the evils of the examina- 
 tion-system. 
 
 " I intend in this article to take up the less 
 popular view of the subject and say what I can 
 in favour of examinations. I wish to analyse the 
 meaning of the word ' cram,' and decide, if 
 possible, whether it is the baneful thing that so 
 many people say. There is no difficulty in see- 
 ing at once that ' cram ' means two different 
 things, which I call ' good cram ' and ' bad 
 cram. ' A candidate, preparing for an important 
 competitive examination, may put himself under 
 a tutor well-skilled in preparing for that examina- 
 tion. This tutor looks for success by carefully 
 directing the candidate's studies into the most 
 4 paying ' lines, and restricting them rigorously 
 to those lines. The training given may be of an 
 arduous, thorough character, so that the faculties 
 of the pupil are stretched and exercised to their 
 utmost in those lines. This would be called 
 4 cram ' because it involves exclusive devotion 
 to the answering of certain examination-papers. 
 I call it ' good cram. ' 
 
 " ' B#d cram,' on the other hand, consists in 
 temporarily impressing upon the candidate's mind 
 a collection of facts, dates, or formulae, held in a 
 wholly undigested state and ready to be dis- 
 gorged in the examination-room by an act of 
 mere memory. A candidate, unable to appre- 
 hend the bearing of Euclid's reasoning in the 
 first book of his Elements, may learn the propo- 
 sitions off by heart, diagrams, letters and all, like 
 
OF THE MISTD. 167 
 
 a Sunday scholar learning the collects and gos- 
 pels. Dates, rules of grammar, and the like, 
 may be i crammed ' by mnemonic lines, or by 
 one of those wretched systems of artificial mem- 
 ory, teachers of which are always going about. 
 In such ways it is, I believe, possible to give an- 
 swers which simulate knowledge, and no more 
 prove true knowledge, than the chattering of a 
 parrot proves intellect. 
 
 " 1 am far from denying the existence of 
 4 bad cram ' of this character, but I hold that it 
 can never be advantageously resorted to by those 
 who are capable of ' good cram.' To learn a 
 proposition of Euclid by heart is far more labo- 
 rious than for a student of moderate capacity to 
 master the nature of the reasoning. It is ob- 
 vious that all advantages, even in an examina- 
 tional point of view, are on the side of real 
 knowledge. The slightest lapse of memory in 
 the bad ' crammer, ' for instance the putting of 
 wrong letters in the diagram, will disclose the 
 simulated character of his work, and the least 
 change in the conditions of the proposition set 
 will frustrate his mnemonic devices altogether. 
 If papers be set which really can be answered by 
 mere memory, the badness is in the examiners. 
 
 * ' Thorough blockheads may be driven to the 
 worst kind of ' cram, ' simply because they can 
 do nothing better. Nor do the blockheads suffer" 
 harm ; to exercise the memory is better than to 
 leave the brain wholly at rest. Some qualities 
 of endurance and resolution must be called into 
 existence, before a youth can go through the 
 
168 ON THE KNOWING FACULTIES 
 
 dreary work of learning off by heart things of 
 which he has no comprehension. Nor with ex- 
 aminers of the least intelligence is there any rea- 
 son to fear that the best directed ' bad cram ' 
 will enable a really stupid candidate to carry off 
 honours and appointments due to others. No 
 examination-papers even for junior candidates 
 should consist entirely of t book-work,' such as 
 to be answered by the simple reproduction of the 
 words in a text-book. In every properly con- 
 ducted examination, questions are, as a matter of 
 course, set to test the candidate's power of ap- 
 plying his knowledge to cases more or less differ- 
 ent from those described in the books. More- 
 over good examiners always judge answers by 
 their general style as well as by their contents. 
 It is really impossible that a stupid slovenly can- 
 didate can by any art of i cramming ' be enabled 
 to produce the neat, brief, pertinent essay, a 
 page or two long, which wins marks from the 
 admiring examiners. 
 
 " If we may judge from experience, too, ' bad 
 cram ' does not pay from the tutor's point of 
 view. That this is so we may learn from the 
 fact that slow ignorant pupils are ruthlessly re- 
 jected by the great ' coaches.' Those who have 
 their reputation and their living to make by the 
 -success of their candidates cannot afford to waste 
 their labor upon bad material. Thus it is not 
 the stupid who go to the i cramming ' tutors to 
 be forced over the heads of the clever, but it is 
 the clever ones who go to secure the highest 
 places. Long before the critical days of the 
 
OF THE MIKD. 169 
 
 official examination, the experienced ' coach ' se- 
 lected his men almost as carefully as if he were 
 making up the University boat. There is hardly 
 a University or a College in the kingdom which 
 imposes any selective process of the sort.~ An 
 entrance or matriculation examination, if it ex- 
 ists at all, is little better than a sham. All com- 
 ers are gladly received to give more fees and the 
 appearance of prosperity. Thus it too often 
 happens that the bulk of a college class consists 
 of untutored youths through whose ears the 
 learned instructions of the professor pass, harm- 
 lessly it may be, but uselessly. Parents and the 
 public have little idea how close a resemblance 
 there is between teaching and writing on the 
 sands of the sea, unless either there is a distinct 
 capacity for learning on the part of the pupil, or 
 some system of examination and reward to force 
 the pupil to apply. 
 
 * 4 For these and other reasons which might be 
 urged, I do not consider it worth while to con- 
 sider ' bad cram ' any further. I pass on to in- 
 quire whether l good cram J is an objectionable 
 form of education. The good * cramming ' tutor 
 or lecturer is one whose object is to enable his 
 pupils to take a high place in the list. With 
 this object he carefully ascertains the scope of 
 the examination, scrutinises past papers, and esti- 
 mates in every possible way the probable charac- 
 ter of future papers. He then trains his pupils 
 in each branch of study with an intensity pro- 
 portioned to the probability that questions will 
 be asked in that branch. It is too much to as- 
 
170 OK THE KNOWING FACULTIES 
 
 sume that this training will be superficial. On 
 the contrary, though narrow it will probably be 
 intense and deep. It will usually consist to a 
 considerable extent in preliminary examinations 
 intended both to test and train the pupil in the 
 art of writing answers. The great i coaches ' at 
 Cambridge in former days might be said \o pro- 
 ceed by a constant system of examination, oral 
 instruction or simple reading being subordinate to 
 the solving of innumerable problems. The main 
 question which I have to discuss, then, resolves 
 itself into this : whether intense training direct- 
 ed to the passing of certain defined examinations 
 constitutes real education. The popular op- 
 ponents of l cram ' imply that it does not ; I 
 maintain that it does. 
 
 ' i It happened that, just as I was about to write 
 this article, the Home Secretary presided at the 
 annual prize-distribution in the Liverpool College, 
 on the 22d December, 1876, and took occasion 
 to make the usual remarks about ' cram. ' He ex- 
 pressed with admirable clearness the prevailing 
 complaints against examinations, and I shall there- 
 fore take the liberty of making his speech in 
 some degree my text. l Examination is not edu- 
 cation, ' he said. ' You require a great deal more 
 than that. As well as being examined, you must 
 be taught. ... In the great scramble for 
 life, there is a notion at the present moment of 
 getting hold of as much general superficial knowl- 
 edge as you can. That to my mind is a fatal 
 mistake. On the other hand, there is a great 
 notion that if you can get through your examina- 
 
OF THE MISTD. 171 
 
 tion and i cram up ' a subject very well, you are 
 being educated. That, too, is a most fatal mis- 
 take. There is nothing which would delight me 
 so much, if I were an examiner, as to baffle all 
 the i cramming ' teachers whose pupils came be- 
 fore me ' (laughter). 
 
 11 Let us consider what Mr. Cross really means. 
 Examination, he says, is not education ; we re- 
 quire a great deal more ; we must be taught as 
 well as be examined. With equal meaning I 
 might say, i Beef is not dinner ; we want a great 
 deal more ; we must have potatoes, bread, pud- 
 ding, and the like. ' Nevertheless beef is a prin- 
 cipal part of dinner. Nobody, I should think, 
 ever asserted or imagined that examination alone 
 was education, but I nevertheless hold that it is 
 one of the chief elements of an effective educa- 
 tion. As Mr. Cross himself said in an earlier 
 part of his speech, ' the examination is a touch- 
 stone and test which shows the broad distinction 
 between good and bad. . . . You may 
 manage to scramble through your lessons in the 
 ' half, ' but I will defy you to get through your 
 examinations if you do not know the subjects. ' 
 
 " Another remark of Mr. Cross leads me to 
 the main point of the subject. He said ' It is 
 quite necessary in the matter of teaching that 
 whatever is taught must be taught well, and noth- 
 ing that is taught well can be taught in a hurry. 
 It must be taught not simply for the examination, 
 but it must sink into your minds, and stay there 
 for life.' Both in this and his other remarks 
 Mr. Cross commits himself to the popular but 
 
172 ON THE KNOWING FACULTIES 
 
 wholly erroneous notion that what boys learn at 
 school and college should be useful knowledge 
 indelibly impressed upon the mind, so as to 
 stay there all their lives, and be ready at their 
 fingers' ends. The real point of the objections 
 to examination commonly is, that the candidate 
 learns things for the examination only, which, 
 when it is safely passed, he forgets again as 
 speedily as possible. Mr. Cross would teach so 
 deliberately and thoroughly that the very facts 
 taught could not be forgotten, but must ever af- 
 ter crop up in the mind whatever we are doing. 
 I hold that remarks such as these proceed from a 
 wholly false view of the nature and purposes of 
 education. It is implied that the mind in early 
 life is to be stored with the identical facts, and 
 bits of knowledge which are to be used in after 
 life. It is, in fact, Mr. Cross and those who 
 think with him, who advocate a kind of ' cram/ 
 enduring it is true, but still ' bad cram. ' The 
 true view of education, on the contrary, is to 
 regard it as a course of training. The youth in 
 a gymnasium practises upon the horizontal bar, 
 in order to develop his muscular powers general- 
 ly ; he does not intend to go on posturing upon 
 Horizontal bars all through life. School is a place 
 where the mental fibres are to be exercised, 
 trained, expanded, developed, and strengthened, 
 not * crammed ' or loaded with 4 useful knowl- 
 edge. ' 
 
 " The whole of a youth's subsequent career is 
 one long course of technical * cramming ' in which 
 any quantity of useful facts are supplied to him 
 
OF THE MIND. 173 
 
 nolens volens. The merchant gets his technical 
 knowledge at the clerk's desk, the barrister in 
 the conveyancer's offices or the law courts, the 
 engineer in the workshop and the field. It is 
 the very purpose of a liberal education, as it is 
 correctly called, to develop and train the plastic 
 fibres of the youthful brain, so as to prevent them 
 taking too early a definite * set, ' which will after- 
 wards narrow and restrict the range of acquisition 
 and judgment. I will even go so far as to say 
 that it is hardly desirable for the actual things 
 taught at school to stay in the mind for life. 
 The source of error is the failure to distinguish 
 between the form and the matter of knowledge, 
 between the facts themselves and the manner in 
 which the mental powers deal with facts. 
 
 " It is wonderful that Mr. Cross and those who 
 moralise in his strain do not perceive that the ac- 
 tual facts which a man deals with in life are infi- 
 nite in number, and cannot be remembered in a 
 finite brain. The psychologists, too, seem to me 
 to be at fault in this matter, for they have not 
 sufficiently drawn attention to the varying degrees 
 of duration required in a well organised memory. 
 We commonly use the word Memory so as to 
 cover the faculties of Retention, Reproduction 
 and Representation, as described by Hamilton, 
 and very little consideration will show that in 
 different cases we need the powers of retention, 
 of suggestion and of imagination in very differ- 
 'ent degrees. In some cases we require to re- 
 member a thing only a few moments, or a few 
 minutes ; in other cases a few hours or days ; in 
 
174 OK THE KNOWING FACULTIES 
 
 yet other cases a few weeks or months : it is an 
 infinitesimally small part of all our mental impres- 
 sions which can be profitably remembered for 
 years. Memory may be too retentive, and facil- 
 ity of forgetting and of driving out one train of 
 ideas by a new train is almost as essential to a 
 well-trained intellect as facility of retention. 
 
 4 1 Take the case of a barrister in full practice, 
 who deals with several cases in a day. His busi- 
 ness is to acquire as rapidly as possible the facts 
 of the case immediately before him. With the 
 powers of representation of a well-trained mind, 
 he holds these facts steadily before him, compar- 
 ing them with each other, discovering their re- 
 lations, applying to them the principles and rules 
 of law more deeply graven on his memory, or 
 bringing them into connection with a few of the 
 more prominent facts of previous cases which he 
 happens to remember. For the details of laws 
 and precedents he trusts to his text writers, the 
 statute book, and his law library. Even before 
 the case is finished his mind has probably sifted 
 out the facts and rejected the unimportant ones 
 by the law of obliviscence. One case done with, 
 he takes up a wholly new series of facts, and so 
 from day to day, and from month to month, 
 the matter before him is constantly changing. 
 The same remarks are even more true of a busy 
 and able administrator like Mr. Cross. The 
 points which come before him are infinite in va- 
 riety. The facts of each case are rapidly brought 
 to his notice by subordinates, by correspondence, 
 by debates in the House, by deputations and in- 
 
OF THE MIXD. 175 
 
 terviews, or by newspaper reports. Applying 
 well-trained powers of judgment to the matter in 
 hand, he makes a rapid decision and passes to the 
 next piece of business. It would be fatal to Mr. 
 Cross if he were to allow things to sink deep into 
 his mind and stay there. There would be no 
 difficulty in showing that in like manner, but in 
 varying degrees, the engineer, the physician, the 
 merchant, even the tradesman or the intelligent 
 artisan, deal every day with various combina- 
 tions of facts which cannot all be stored up in 
 the cerebral framework, and certainly need not 
 be so. 
 
 " The bearing of these considerations upon 
 the subject of examinations ought to be very 
 evident. For what is ' cram ' but the rapid ac- 
 quisition of a series of facts, the vigorous getting 
 up of a case, in order to exhibit well-trained 
 powers of comprehension, of judgment, before an 
 examiner ? The practised barrister ' crams ' up 
 his i brief ' (so called because, as some suppose, 
 made brief for the purpose) and stands an ex- 
 amination in it before a judge and jury. The 
 candidate is not so hurried ; he spends months 
 or it may be two or three years in getting up 
 his differential calculus or his inorganic chemis- 
 try. It is quite likely that when the ordeal is 
 passed, and the favourable verdict delivered, he 
 will dismiss the equations and the salts and com- 
 pounds from his mind as rapidly as possible ; but 
 it does not follow that the useful effect of his 
 training vanishes at the same time. If so, it fol- 
 lows that almost all the most able and successful 
 
176 OK THE KNOWING FACULTIES 
 
 men of the present day threw away their pains at 
 school and college. I suppose that no one ever 
 heard of a differential equation solving a nice point 
 of law, nor is it common to hear Sophocles and 
 Tacitus quoted by a leading counsel. Yet it can 
 hardly be denied that our greatest barristers and 
 judges were trained in the mathematical sciences, 
 or if not, that their teachers thought the classics 
 a better training ground. If things taught at 
 school and college are to stay in the mind to 
 serve us in the business of life, then almost all 
 the higher education yet given in this kingdom 
 has missed its mark. I come to the conclusion, 
 then, that well-ordered education is a severe 
 system of well-sustained ' cram.' . . . We 
 cannot consider it the work of teachers to make 
 philosophers and scholars and geniuses of various- 
 sorts : these, like poets, are born not made. 
 Nor, as I have shown, is it the business of the 
 educator to impress indelibly upon the mind the 
 useful knowledge which is to guide the pupil 
 through life. This would be ' cram ' indeed. It 
 is the purpose of education so to exercise the 
 faculties of mind that the infinitely various expe- 
 rience of after-life may be observed and reasoned 
 upon to the best effect. What is popularly con- 
 demned as t cram ' is often the best devised and 
 best conducted system of training towards this 
 all-important end." (Jevons, l Cram,' art. in 
 Mind, pp. 193-207, No. VI., April, 1877.) 
 
 173. " The act of knowing is that activity of 
 the mind by means of which it consciously repro- 
 duces in itself what actually exists. The act of 
 
OF THE MIKD. 177 
 
 knowing is partly immediate or outer and inner 
 . perception, partly mediate or thinking. The 
 regulative laws (injunctions, prescriptions) are 
 those universal conditions to which the activity 
 of knowledge must conform in order to attain to 
 the end and aim of knowledge/' (Ueberweg, 
 Hist. Log. Doct., p. 1, ed. 1871.) 
 
 174. "Knowledge, in the wider sense in 
 which we here use the word, comprehends both 
 cognition, which rests on perception (and on the 
 evidence transmitting perceptions of which we 
 are ignorant), and also knowledge in the stricter 
 sense, which is attained by thinking. 
 
 175. " The act of knowing, in so far as it is 
 the copying in the human consciousness of the 
 essence of the thing, is an after-thinking of the 
 thoughts which the divine creative thinking has 
 built into things. In action the preceding 
 thought determines what actually exists, but in 
 knowing the actual existence, in itself conform- 
 able to reason, determines the human thought. 7 ' 
 (Ibid., p. 2.) 
 
 176. " 1. The objective existence to be 
 known consists not merely of natural objects, 
 but also (as in history, etc.) of mental contents. 
 2. The mirroring in consciousness, although re- 
 production, cannot be accomplished without a 
 peculiar activity of the mind. 3. The whole ac- 
 tivity of the mind is not exhausted in knowledge. 
 There is besides the creative power of the phan- 
 tasy, reforming and refining what is given in the 
 conception, and ethical action." (Ibid., pp. 
 2-3.) 
 
178 OK THE KNOWING FACULTIES 
 
 177. "Knowledge of fact is knowledge by 
 onlook ; knowledge inferred is knowledge of one 
 thing through means of another ; knowledge of 
 first principles is knowledge by insight into truth 
 higher than fact. ' ' (Calderwood, Hand Book, 
 Moral Phil., p. 39, ed. 1879.) 
 
 178. In giving the difference between 
 Thought, properly so called, and other phenom- 
 ena of the mind, I cannot do better than to quote 
 the following : " Every state of consciousness 
 necessarily implies two elements at least : a con- 
 scious subject, and an object of which he is con- 
 scious. In every exercise, for example, of the 
 senses, we may distinguish the object seen, heard, 
 smelt, touched, tasted, from the subject seeing, 
 hearing, smelling, touching, tasting. In every 
 emotion of pleasure or of pain, there is a certain 
 affection, agreeable or disagreeable, existing 
 within me, and of this affection I am conscious. 
 In every act of volition, there takes place a certain 
 exercise of my will, and I am conscious that it 
 takes place. . . . But to constitute an act 
 of Thought, more is required than the immedi- 
 ate relation of subject to object in consciousness. 
 Every one of the above states might exist in a 
 mind totally incapable of thought. Let us sup- 
 pose, for example, a being, in whose mind every 
 successive state of consciousness was forgotten 
 as soon as it had taken place. Every individual 
 object might be presented to him precisely as it 
 is to us. Animals, men, trees, and stones, might 
 be successively placed before his eyes ; pleasure, 
 and pain, and anger, and fear, might alternate 
 
OF THE MIKD. 179 
 
 within him ; but, as each departed, he would re- 
 tain no knowledge that it had ever existed, and 
 consequently no power of comparison with simi- 
 lar or dissimilar objects of an earlier or later con- 
 sciousness. He would have no knowledge of 
 such objects as referred to separate notions ; 
 he could not say, this which I see is a man, or a 
 horse ; this which I feel is fear, or anger. He 
 would be deficient in the distinctive feature of 
 Thought, the concept or general notion resulting 
 from the comparison of objects. Hence arises 
 the important distinction between Intuitions, in 
 which the object is immediately related to the 
 conscious mind, and Thoughts, in which the ob- 
 ject is mediately related through a concept 
 gained by comparison. . . . By Intuition 
 is meant to include all the products of the per- 
 ceptive (external and internal) and imaginative 
 faculties ; every act of consciousness, in short, 
 of which the immediate object is an individual, 
 thing, act, or state of mind, presented under the 
 condition of distinct existence in space or time. 
 It is necessary to distinguish between the act of 
 thought and its product the former is desig- 
 nated by the term conception, the product by 
 concept, . . . Intuition contains two ele- 
 ments only, the subject and the object standing 
 in present relation to each other. Thought con- 
 tains three elements, the. thinking subject, the 
 object about which he thinks, and the concept 
 mediating between the two. Thus even the ex- 
 ercise of the senses upon present objects, in the 
 manner in which it is ordinarily performed by a 
 
180 ON THE KNOWING FACULTIES 
 
 man of mature faculties, does not consist of mere 
 intuition, but is accompanied by an act of 
 thought. In mere intuition, all that is simulta- 
 neously presented to the sense appears as one 
 whole ; but mere intuition does not distinguish 
 its several parts from each other under this or 
 that notion. I may see at once, in a single pano- 
 rama, a ship upon the sea, an island lying be- 
 hind it, and the sky above it. To mere intui- 
 tion this is presented only in confusion, as a sin- 
 gle object. To distinguish its constituent por- 
 tions, as sea and land, ship and sky, requires a 
 comparison and classification of them relatively 
 to so many separate concepts existing in the 
 mind ; and such classification is an act of 
 Thought. 
 
 In every act of Consciousness the ultimate ob- 
 ject is an individual. But in intuition this ob- 
 ject is presented to the mind directly, and does 
 not imply the existence, past or present, of any- 
 thing but itself and the mind to which it is pre- 
 sented. In thought, on the other hand, the in- 
 dividual is represented by means of a concept, 
 which contains certain attributes applicable to 
 other individuals of the same kind. This im- 
 plies that there have been presented to the mind 
 prior objects of intuition, originating the con- 
 cept or general notion to which subsequent objects 
 are referred. Hence arises another important 
 distinction. All intuition is direct and presen- 
 tative ; all thought is indirect and representative. 
 By representation are here included the 
 concept, which is representative of many indi- 
 
OF THE MIND. 181 
 
 viduals, and the image, which is representative 
 of one. . . . Perception is employed to de- 
 note all those states of Consciousness which are 
 presentative only, not representative. It will 
 thus include all intuitions except those of Imagi- 
 nation. . . . The office of the faculty of 
 Imagination, whose office is the production of 
 images representative of the several phenomena 
 of Perception, internal as well as external. . . . 
 Imagination, regarded as a product, may be de- 
 fined, the consciousness of an image in the mind 
 resembling and representing an object of intui- 
 tion. It is thus at the same time presentative 
 and representative. It is presentative of the 
 image which has its own distinct existence in 
 consciousness, irrespective of its relation to the 
 object which it is supposed to represent. It is 
 representative of the object which that image re- 
 sembles ; and such resemblance is only possible 
 on the condition that the image be, like the ob- 
 ject, individual. . . . The distinguishing 
 feature of a concept is, that it cannot in itself 
 be depicted to sense or imagination. It is 
 not the sensible image of one object, but an in- 
 telligible relation between many. A second im- 
 portant characteristic of all concepts is, that they 
 require to be fixed in a representative sign, 
 which is language." (Mansel, Prolegomena 
 Logics pp. L>()-6, ed. 1860.) 
 
 179. " In a psychological point of view, to 
 enumerate separate mental faculties and opera- 
 tions, as 'giving rise to the various products of 
 thought, is, to say the least, to encumber the 
 
182 OK THE KNOWING FACULTIES 
 
 science with unnecessary and perplexing distinc- 
 tions. It will be sufficient to refer them to the 
 single faculty of thought or reflection, the oper- 
 ation of which is, in all cases, comparison, The 
 unit of thought is always a judgment, based on a 
 comparison of objects ; and the several operations 
 of thought are, in ultimate analysis, nothing 
 more than judgments derived from different 
 data. In order to exhibit this in special in- 
 stances, it will be convenient to adopt provision- 
 ally the logical classification, and to examine the 
 phenomena of thought under the several heads 
 of Conception, Judgment, and Reasoning. " 
 (Mansel, Metaphysics, pp. 176-7, ed. 1871, New 
 York.) 
 
 180. " In a psychological point of view, to 
 enumerate separate mental faculties, as giving 
 rise to the various products of thought, is, to 
 say the least, to encumber the science with un- 
 necessary and perplexing distinctions. It will 
 be sufficient to refer them to the single faculty 
 of Thought, the operation of which is in all 
 cases Comparison (see Hamilton, Lect. on Meta- 
 physics, Lect. xxxiv.). But the faculty of 
 Thought, though uniform in its own nature and 
 in the manner of its operation, may yet give 
 rise to different products, according to the di- 
 versity of the materials upon which it operates ; 
 and this difference forms the basis of the classi- 
 fication usually adopted in Logic. Extending 
 the terms Apprehension and Judgment beyond 
 the region of Thought proper (into Psychology), 
 it may be laid down, as a general canon of Psy- 
 
OF THE MIND. 183 
 
 ehology, that the unit of consciousness is a 
 judgment; in other words, that every act of 
 consciousness, intuitive or discursive, is com- 
 prised in a conviction of the presence of its ob- 
 ject, either internally in the mind or externally 
 in space. The result of every such act must 
 thus be generally stated in the proposition, 
 " This is here." Consequently, at least with 
 reference to the primary and spontaneous, as 
 distinguished from the secondary and reflex acts 
 of consciousness, it is more correct to describe 
 Apprehension as the analysis of Judgments, than 
 Judgment as the synthesis of Apprehensions. In 
 a psychological point of view, therefore, it is in- 
 correct to describe Simple Apprehension as the 
 first operation of the mind. In one sense, in- 
 deed, the relation of prior and posterior is al- 
 together out of place : Chronologically, inas- 
 much as every Apprehension is simultaneous 
 with a Judgment, and every Judgment with 
 an Apprehension ; and logically, inasmuch as 
 Judgment cannot exist without Apprehension, 
 nor Apprehension without Judgment. In an- 
 other sense, however, we may properly say that 
 Judgment is prior to Apprehension ; meaning 
 that the subject and the object are first given 
 in their mutual relation to each other, before 
 either of them can itself become a separate 
 object of attention. But when a correspond- 
 ing division is adopted of the operation of 
 Thought, properly so called, the same order of 
 priority cannot be observed. Every operation 
 of thought is a judgment, in the psychological 
 
184 ON THE KNOWING FACULTIES 
 
 sense of the term ; but the psychological judg- 
 ment must not be confounded with the logical. 
 The former is the judgment of a relation between 
 the conscious subject and the immediate object 
 of consciousness ; the latter is the judgment of 
 a relation which two objects of thought bear to 
 each other. The former cannot be distinguished 
 as true or false, inasmuch as the object is there- 
 by only judged to be present at the moment 
 when we are conscious of it as affecting us in a 
 certain manner ; and this consciousness is nec- 
 essarily true. The latter is true or false accord- 
 ing as the relations thought as existing between 
 certain concepts are actually found in the ob- 
 jects represented by those concepts or not. 
 The logical judgment necessarily contains two 
 concepts (products of thought), and hence must 
 be regarded as logically and chronologically pos- 
 terior to the conception (act of thought), which 
 requires one only. The psychological judgment 
 is coeval with the first act of consciousness, and 
 is implied in every mental process, whether of 
 intuition or of thought. It cannot, therefore, be 
 called prior or posterior to any other mental op- 
 eration, for there is no mental operation in 
 which it does not take place ; but the judgments 
 of intuition are logically and chronologically 
 prior to the judgments of thought. Conception 
 is a psychological judgment, but not a logical 
 one, and is properly ranked as the first operation 
 of Thought, inasmuch as it is the simplest. . . . 
 Conceiving has been already explained as 
 the individualizing of certain attributes compre- 
 
OF THE MIND. 185 
 
 bended in a general notion and expressed in a gen- 
 eral term ; the representation, namely, of such 
 attributes as coexisting in a possible object of 
 intuition. Language is, ... in its earliest 
 operations, a sign, not of concepts, but of intu- 
 itions. Its earliest terms are employed tis the 
 proper names of individual objects. Conception 
 does not take place till after we have learned to give 
 the same name to various individuals presented 
 to us with certain differences of attributes, and 
 hence we associate it with a portion only, not 
 with the whole, of what is presented in each. 
 This may be distinguished as Abstraction, a 
 spontaneous, though not always a voluntary act, 
 the concentration of the mind on certain portions 
 only of a given object in relation to its name. 
 This must not be treated . . as a conscious process 
 of thought, being only a preliminary condition 
 to thinking, taking place in the majority of 
 cases unconsciously, during the gradual acquisi- 
 tion of speech. Our names thus gradually ac- 
 quire a signification, being transformed from 
 proper names to appellatives. Finally, the act 
 of conception consists in contemplating the at- 
 tributes thus combined in the signification of a 
 name as coexisting, along with individual fea- 
 tures, in a possible object of intuition, and hence, 
 apart from the individual features, as indiffer- 
 ently representing all such objects. This repre- 
 sentative collection of attributes, combined by 
 means of a sign, is a Concept. . . . As in 
 Conception a single general notion is considered 
 in its relation to a possible object of intuition, 
 
186 ON THE KNOWING FACULTIES 
 
 so in Judgment two such notions are considered 
 as related to a common object. When I assert 
 that A is B, I do not mean that the attributes 
 constituting the concept A are identical with 
 those constituting the concept B, for this is 
 only true in identical judgments, but that the 
 object in which the one set of attributes is found 
 is the same as that in which the other set is found. 
 The common language and common 
 thought of mankind assume, whether they ex- 
 plain it or not, that a certain smell and color 
 and form, which are distinct attributes, are in 
 some way related, as parts or qualities, to some 
 one thing which we call a rose ; and that, when 
 I assert that the rose is fragrant, I imply that 
 the thing which affects in a certain way my 
 power of sight is in some manner identical (Iden- 
 tity) with that which affects in a certain way my 
 power of smell. . . . Reasoning is the most 
 complex of the three operations, as in it two 
 concepts are determined to be in a certain man- 
 ner related to each other, through the medium 
 of their mutual relations to a third concept. 
 This operation is therefore treated last in order. 
 The several relations asserted in the premises 
 and deduced in the conclusion, are of the same 
 nature as those implied in Judgment. 
 It will be sufficient to attempt . . a definition of 
 the products of the several acts of Thought, the 
 Concept, the Judgment, and the Syllogism, the 
 legitimate objects of Formal Logic. 1. A Con- 
 cept is a collection of attributes, united by a 
 sign, and representing a possible object of intui- 
 
OF THE MIND. 187 
 
 tion. 2. A Judgment is a combination of two 
 concepts, related to one or more Common ob- 
 jects of possible intuition. 3. A Syllogism is a 
 combination of two judgments, necessitating a 
 third judgment as the consequence of their mu- 
 tual relation. " (Mansel, Prolegomena Loyica, 
 pp. 62-9, ed. 1860.) 
 
 181. " The mental powers employed in the 
 acquisition of knowledge are probably three in 
 number. They are substantially as Professor 
 Bain has stated them (Senses and Intellect, 2d 
 ed., pp. 5, 325, etc.): 1. The Power of Discrim- 
 ination ; 2. The Power of Detecting Identity ; 
 3. The Power of Retention. We exert the first 
 power in every act of perception. Hardly can 
 we have a sensation or feeling unless we discrim- 
 inate it from something else which preceded. 
 Consciousness would almost seem to consist in 
 the break between one state of mind and the 
 next, just as an induced current of electricity 
 arises from the beginning or the ending of the 
 primary current. We are always engaged in dis- 
 crimination ; and the rudiment of thought 
 which exists in the lower animals probably con- 
 sists in their power of feeling difference and be- 
 ing agitated by it. Yet had we the power of 
 discrimination only, Science could not be created. 
 To know that one feeling differs from another 
 gives purely negative information. It cannot 
 teach us what will happen. In such a state of 
 intellect each sensation would stand out distinct 
 from every other ; there would be no tie, no 
 bridge of affinity between them." We want a 
 
188 OK THE KNOWING FACULTIES 
 
 unifying power by which the present and the fu- 
 ture may be linked to the past ; and this seems 
 to be accomplished by a different power of mind. 
 Lord Bacon has pointed out that different men 
 possess in very different degrees the powers of 
 discrimination and identification. It may be said 
 indeed that discrimination necessarily implies 
 the action of the opposite process of identifica- 
 tion ; and so it doubtless does in negative points. 
 But there is a rare property of mind which con- 
 sists in penetrating the disguise. of variety and 
 seizing the common elements of sameness ; and 
 it is this property which furnishes the true mea- 
 sure of intellect. The name of l intellect ' expresses 
 the interlacing of the general and the single, which 
 is the peculiar province of mind. (Max Miiller, 
 Lect. Sci. Lang., 2d series, Vol. II., p. 63). 
 . . Plato said of this unifying power, that if 
 he met the man who could detect the one in the 
 many, he would follow him as a god. ' ' ( Jevons, 
 The Princ. of Science, pp. 4-5, ed. 1877.) 
 
 " LAWS OF IDENTITY AND DIFFERENCE. 
 
 182. " At the base of all thought and science 
 must lie the laws which express the very nature 
 and conditions of the discriminating and identi- 
 fying powers of mind. These are the so-called 
 Fundamental Laws of Thought, usually stated as 
 follows : 
 
 1. The Law of Identity. Whatever is, is. 
 
 2. The Law of Contradiction. A thing can- 
 not both be and not be, 
 
OF THE MIKD. 189 
 
 3. The Law of Duality. A thing must 
 either be or not be. 
 
 ' i The first of these statements may perhaps be 
 regarded as a description of identity itself, if so 
 fundamental a notion can admit of description. 
 A thing at any moment is perfectly identical with 
 itself, and, if any person were unaware of the 
 meaning of the word i identity,' we could not 
 better describe it than by such an example. 
 
 " The second law points out that contradictory 
 attributes can never be joined together. The 
 same object may vary in its different parts ; here 
 it may be black, and there white ; at one time it 
 may be hard and at another time soft ; but at 
 the same time and place an attribute cannot be 
 both present and absent. Aristotle truly de- 
 scribed this law as the first of all axioms one 
 of which we need not seek for any demonstra- 
 tion. All truths cannot be proved, otherwise 
 there would be an endless chain of demonstra- 
 tion ; and it is in self-evident truths like this 
 that we find the simplest foundations. 
 
 ' ' The third of these laws completes the other 
 two. It asserts that at every step there are two 
 possible alternatives presence or absence, affir- 
 mation or negation. Hence I propose to name 
 this law the Law of Duality, for it gives to all 
 the formulae of reasoning a dual character. It 
 asserts also that between presence and absence, 
 existence and non-existence, affirmation and ne- 
 gation, there is no third alternative. As Aris- 
 totle said, there. can be no mean between oppo- 
 
190 OK THE KNOWING FACULTIES 
 
 site assertions : we must either affirm or deny." 
 (Ibid., pp. 5-6.) 
 
 183. " The primitive and essential gradation 
 of thought we have indicated to be the Judg- 
 ment. In accordance with what has been said, 
 a Judgment may be denned to be a recogni- 
 tion of the identity or non-identity between 
 any two objects presented to the Faculty of 
 Thought, As expressed in words, a Judgment 
 is called a Proposition, or in grammatical no- 
 menclature, a Sentence. 
 
 " Besides the Judgment, there are two other 
 products of thought, both derivatives from the 
 Judgment. The one is the Concept, which is 
 derived from several Judgments by an act of 
 Conceiving taking together, in other words, 
 by an act of synthesis. The other is the Rea- 
 soning, which is derived from one or more Judg- 
 ments by an act of analysis or separation. As 
 all thought is essentially a movement in Quan- 
 tity, and as variations in Quantity can be affected 
 only in the one or the other of these two direc- 
 tions, synthesis and analysis, the Concept and 
 the Reasoning are the only conceivable deriva- 
 tives from a Judgment, except such as consist 
 only in variations of form, that do not affect 
 the identity of the thought. 
 
 ' i In explication of this definition of a Judg- 
 ment, it will be necessary simply to recall what 
 has been already said in the exposition of the- 
 general nature of thought. As we have seen, 
 a judgment necessarily supposes two objects ; 
 
OF THE MIND. 191 
 
 and its essential characteristic, as an act of In- 
 telligence, consists in this : that it is a cognition 
 of this particular relation of identity or non- 
 identity between the two objects. These two 
 objects of a judgment are given to it by some 
 other faculty of the Intelligence, as of Percep- 
 tion, Intuition-, Memory, or by the Discursive 
 Faculty itself, in some previous exercise. It 
 may be some object of Perception, as Bucephalus. 
 As thus given by the Perceptive Faculty, the 
 cognition is of an object by itself, without rela- 
 tion either to other objects or to the parts of 
 the object itself. Color is not in the percep- 
 tion itself distinguished from figure ; neither 
 color nor figure from the position or the time 
 in which it is perceived ; and neither of 
 these from the useful qualities of the object. 
 All the perceptible qualities are given together 
 without distinction in the presentation itself 
 of the object. But when thus given, the 
 mind at once, and by a kind of necessity of its 
 being as essentially active and reflective, exerts 
 its activity on it, first, by apprehending it as 
 a part of a multiplicity of objects around, 
 to each of which it stands in relation, and also, 
 as a whole, containing parts in itself. This is 
 the primitive and conditional gradation in all 
 thought the apprehension of an object as a part 
 or as a whole in other words, in the relation of 
 Quantity. Simultaneously with this, it appre- 
 hends some other object of thought given to it 
 by Perception, or by some other Faculty of the 
 Intelligence, or in some previous exercise of the 
 
192 OK THE KISTOWIKG FACULTIES 
 
 Judgment, and thus comes to view the two ob- 
 jects thus given in relation to each other, as the 
 same or not the same. Its act then becomes 
 complete ; and a perfected product of thought, 
 a Judgment, is the result. Thus the second ob- 
 ject may be given in the Perception itself, as 
 black, or four-footed, and the Judgment recog- 
 nizes this color or this form as belonging to 
 Bucephalus that is, as identical with one of the 
 parts or characters that make up the whole per- 
 ception. Or the second object may be given by 
 the Regulative Faculty, or Faculty of Intuition, 
 as of Being, of Space, of Time, or other idea of 
 the proper Reason ; and then the Judgment iden- 
 tifies Bucephalus with Existence, with some part 
 of Space, of Time ; or in other words, affirms 
 Bucephalus to be, to be in such a place, at 
 such a time, and the like. The second object 
 of thought may, in like manner, be given to the 
 Judging Faculty by the Memory. We may 
 identify Bucephalus as now perceived with the 
 Bucephalus perceived yesterday ; with the black 
 color, the four-footed figure, before perceived in 
 some other object. 
 
 " The essential nature of a Judgment, thus, 
 is seen to be an identification of one object 
 with another, either totally or partially in some 
 one or in all respects. It is accordingly a rela- 
 tive cognition ; and in the relation which it in- 
 volves are necessarily contained three elements : 
 1. The object of thought identified with some 
 other. 2. The object with which it is identi- 
 fied, either in whole or in part. And, 3. The 
 
OF THE MLffD. 19*3 
 
 mental act which identifies. The first two con- 
 stitute the matter of thought, the datum ; the 
 last is the Thought itself, the identifying cogni- 
 tion the Judgment. 
 
 " To the several parts, or to different aspects 
 of the complex procedure in all Thought as 
 thus exemplified in one of its gradations the 
 Judgment Psychology has assigned distinctive 
 names, which it may not be inexpedient here to 
 recall. Inasmuch as the original datum or ob- 
 ject of thought is given in an indefinite vagueness 
 as one and undivided, and as, in order to be 
 cognized in thought, it must be viewed in rela- 
 tion to some part, it becomes necessary to loosen 
 up, to analyze or separate it as a whole into its 
 parts. This part of the process is called Analy- 
 sis. 
 
 " The next step is to select the part out of 
 the whole for separate apprehension, and to 
 draw it away, as it were, to abstract it from the 
 other parts. This part of the movement in 
 Thought is called Abstraction. The term, how- 
 ever, it is proper to add, is applied in various 
 ways by different writers or on different occasions, 
 but with the same result. Thus it may be ap- 
 plied to the mind itself ; so that in Abstraction 
 the mind, when confining its view to certain 
 parts of an object, is regarded as being abstracted 
 or drawn away from tie parts that are to be ex- 
 cluded from view ; and this, it may be observed, 
 is in strictness the most correct view. But in a 
 looser sense the term may be applied to the part 
 itself that is selected, and then such part is re- 
 
194 ON THE KNOWING FACULTIES 
 
 garded as being abstracted from the other parts. 
 Or, in the third place, it may be applied to 
 those other excluded parts themselves, and then 
 they are regarded as being abstracted or drawn 
 away either from the other parts or from the 
 mind's consideration. The result is the same 
 in any view, that one part is separated from the 
 other parts for exclusive consideration, and it is 
 therefore a matter ot indifference, so far as the 
 result is concerned, which of these different 
 views is entertained. 
 
 " When thus one part is separated from the 
 rest for exclusive consideration by the mind, the 
 act of mind in which it concentrates its notice 
 upon it is called Attention. 
 
 " In the next place, the two objects are 
 brought up and viewed face to face with each 
 other in order that their identity or non-identity 
 may be apprehended. This part of the process 
 is called Comparison, 
 
 " Finally, the last part of the complex pro- 
 cess, in which the thought is perfected by bring- 
 ing together the two objects attended to into one 
 relative cognition, is called an act of Synthesis. 
 
 1 i All Thought thus begins with an Analysis, 
 it proceeds by Abstraction, Attention, and Com- 
 parison, it ends with a Synthesis. And this is 
 to be understood in a sense more or less full 
 and complete, in modes varying with the nature 
 of the particular gradation of all the acts of 
 thought, whether in judging, conceiving, or 
 reasoning. The two essential elements of thought 
 are analysis and synthesis. With one it neces- 
 
OF THE MIND. 195 
 
 sarily begins, with the other it necessarily ends. 
 For its very function is to lead to truth, to a 
 unity in the intelligence, which supposes an un- 
 distinguished manifold as its condition, and a 
 gathering into a unity as its result. The other 
 parts of the complex process, abstraction, atten- 
 tion, and comparison, are the means by which 
 the mind passes from the multiform given in the 
 analysis to the unity in the synthesis. 
 
 " Of the two objects of thought identified in 
 a Judgment, one is necessarily viewed as the 
 primitive which is to be identified with the other, 
 or is determined by it. This so viewed primi- 
 tive or determined object is called the Subject ; 
 which may be defined to be that of which we 
 judge. The other, viewed as the determining 
 element, is called the Predicate, which may be 
 defined to be that which is judged of the subject. 
 The Subject and the Predicate make up the mat- 
 ter of thought or the datum to thought. They 
 are called the Terms of a Proposition (termini). 
 The act of thought itself which recognizes the 
 identity between the two terms is called the 
 Copula, which may be defined to be the identifi- 
 cation of two objects of thought. It was called 
 by Aristotle, in reference to the two terms, an 
 Interval." (Day, Me. of Logic, pp. 31-5, ed. 
 1868.) 
 
 184. " The Second gradation of Thought is 
 the Concept. It is derived from the primitive 
 product, the Judgment, by an act of synthesis 
 or composition. It accordingly presupposes two 
 or more Judgments, and, if a valid product of 
 
196 ON THE KNOWING FACULTIES' 
 
 Thought, can always be resolved back into them. 
 It can, in fact, be verified only by being thus re- 
 ferred back to the Judgments from which it is 
 derived. It is formed either by the synthesis of 
 the Subjects of two or more Judgments, or by 
 a synthesis of their Predicates an alternative 
 which gives rise to the two fundamental classes 
 of Concepts. It may conduce to clearness to 
 exemplify the process of forming the Concept in 
 these two ways separately. 
 
 " First, then, if we synthesize the subjects, 
 the procedure will be as follows : The Judg- 
 ments, out of which the Concept is to be formed, 
 we will assume to be Socrates is rational; 
 Cicero is rational; James is rational. By 
 uniting the subjects, we have Socrates and Cicero 
 and James, and marking the union by a single 
 term which shall embrace them all in one, we 
 will say, man, we have the union signalized in 
 language. This union of the differing subjects 
 of several propositions having a common predi- 
 cate is called a Concept ; in this case a Concept 
 in Extensive Quantity. The formula for the 
 formation of all Concepts of this class is, accord- 
 ingly : The Judgments, B is A, C is A, give the 
 Concept (B + C), or when signalized in language 
 by one term, the Concept D ; or in brief : The 
 Judgments B is A, C is A, give B + C = the Con- 
 cept D. 
 
 " The procedure in forming Concepts of the 
 other class is analogous. Here the Subject re- 
 mains the same, and the Concept arises from the 
 synthesis of the Predicates which differ. Thus, 
 
OF THE MIKD. 19? 
 
 the Predicates in the Judgments, Socrates is ra- 
 tional, Socrates is animal, being united, we have 
 rational and animal, or signalizing the union -/ 
 by a single term, we have the Concept, Man. 
 The term Man here, it will be observed, means 
 a complement of attributes, as rational, animal, 
 not, as before, of subjects, as Socrates, &c. 
 This is a concept in Comprehensive Quantity ; 
 the formula of which is : The Judgments A is 
 B, A is C, give, by synthesis of the differing 
 Predicates, the aggregate (B + C), which signal- 
 ized as one in Language is expressed by D. Or 
 the Judgments A is B, A is C, give Concept 
 (B + C) = D. 
 
 ' ' A Concept may be defined, accordingly, to 
 be a product of Thought, resulting from the 
 synthesis of the Subjects or of the Predicates in 
 several Judgments. 
 
 " The common Subject in a Predicate-Con- 
 cept, or the common Predicate in a Subject- 
 Concept, on which the Concept is formed, is 
 called its Base. 
 
 " The name, Concept, is derived from the 
 Latin word Conception, meaning something 
 taken with another. The corresponding word 
 used to denote the act of forming a Concept is 
 Conception, which is also in common discourse 
 often used to denote the product. It is used, 
 in fact, like other words of this kind, in the three- 
 fold import of faculty, act, and product. 
 
 " The Law of Identity, or as, in its fuller 
 expression, it may be denominated, the Law of 
 the Same and Different, it will have been seen, 
 
 
198 ON THE KNOWING FACULTIES 
 
 presides over this product of Thought, as over 
 the Judgment. No valid Concept can be formed, 
 unless from Judgments which have either iden- 
 tical subjects or identical predicates. The Con- 
 cept arises from the Synthesis of the different 
 under the same ; of different subjects having 
 the same predicate, or of different predicates 
 having the same subject. In other words, in the 
 Base is to be found the identifying principle 
 governing in the Concept. 
 
 " It will have been observed, moreover, from 
 the mode of its formation that a Concept is es- 
 sentially a relative cognition. It is not only 
 the result of a synthesis, not only the aggregate 
 of a plurality of Judgments, and accordingly of 
 relative cognitions, but the cognitions that are 
 brought together in this synthesis sustain a de- 
 termined and peculiar relation to one another. 
 If the Concepts be formed from the subjects of 
 the Judgments, those Judgments must have a 
 common the same predicate ; if from the pred- 
 icates, the Judgments must have the same sub- 
 ject. Concepts are thus from their very nature 
 relative cognitions, and the principle of relation 
 is in the sameness of the term of the Judgment 
 which is not synthesized into the Concept in 
 its Base. 
 
 1 ' Concepts, however, differ from Judgments, 
 as relative cognitions, in this respect : that in 
 the Judgment the relation is explicit, while in 
 the Concept it is only implied. Thus in the 
 Judgment, Man is a rational animal, the rela- 
 tion is articulately declared ; but in the Concept, 
 
OF THE MIND. 199 
 
 Man, the relation to the other term of the Judg- 
 ment from which it is derived, although real, is 
 not expressed, but only implied. The Base of 
 the Concept, although real, is not expressed. 
 
 u Still further, a Concept is essentially a one- 
 sided cognition. It is formed from but one side 
 of a Judgment, from the Subject or from the 
 Predicate. It may be regarded, indeed, as an 
 aggregate of Judgments, that is, a synthesized 
 or composite Judgment, with the single term 
 the Base, and the Copula dropped. 
 
 " A Concept, however, always implies the 
 Judgments from which it is derived ; it implies- 
 the other term, which has been dropped, but 
 which is the indispensable condition of its being 
 formed, and is, therefore, appropriately denomi- 
 nated the Base of the Concept ; and also implies 
 that this Base has been identified with each of 
 the terms which compose the Concept. 
 It will occur to the reflecting mind, on this ex- 
 position of the mode in which Concepts are 
 formed, that they are mere products of Thought, 
 aggregates of Subjects, or aggregates of Predi- 
 cates, and do not imply necessarily any exactly 
 corresponding aggregates in the reality of things. 
 How many individual subjects of Judgments 
 shall be combined, or how many predicates, are 
 questions that will be determined by such con- 
 siderations as those of extent of observation,, 
 practicability of aggregation, convenience of use, 
 the needs of occasion, and the like. The ex- 
 tent of the aggregation, therefore, varies indefi- 
 nitely with the occasions of Thought ; and it is. 
 
00 Ol$ THE KNOWING FACULTIES 
 
 not to be supposed that the constitution of things 
 around us fluctuates precisely with the fluctua- 
 tions of Thought. As the mathematical analyst, 
 in the progress of his demonstration, finds it con- 
 venient to substitute single letters or symbols to 
 denote a number of quantities in some respect 
 of like character, so Thought, for its own mani- 
 fold conveniences, often aggregates like elements 
 and signalizes them by single words. " (Day, 
 Elements of Logic , ed. 1868, pp. 62-66.) 
 
 185. " The Third gradation of Thought is 
 the Reasoning* Like the Concept, it is de- 
 rived from the Judgment. It differs from the 
 Concept in its form, as, unlike that, it retains the 
 full forms of the Judgment, and accordingly, also, 
 to a certain extent, it differs from it in the mode 
 of its derivation. It differs from the Judgment 
 proper in this respect, that it is a derivation 
 from a Judgment a traced movement of 
 Thought, supperadded to that which constitutes 
 the Judgment. It is not the derived Judgment, 
 .not the mere terminus, the point at the end of 
 the line over which the Thought has moved, but 
 the line itself as traced in the movement of the 
 Thought. When viewed as a resultant product 
 of Thought, therefore, it must be regarded as 
 the track of Thought left marked by the move- 
 ment, not the mere attained object or goal of the 
 movement, which is nothing more than a Judg- 
 ment. We are carefully to distinguish, there- 
 fore, a Reasoning from the Conclusion from the 
 Judgment which is attained by the reasoning. 
 
 .* ' A Reasoning, thus, is a derivation of a Judg- 
 
OF THE MIND. 201 
 
 ment from another Judgment or Judgments. 
 1 Reasoning is a modification from the 
 French raisonner (and this is a derivation from 
 the Latin ratio), and corresponds to ratiociatio, 
 which has indeed been immediately transferred 
 into our language under the form of ratiocina- 
 tion. Ratiocination denotes properly the pro- 
 cess, but improperly, also, the product of reason- 
 ing ; Ratiocinium marks exclusively the product. 
 The original meaning of ratio was computa- 
 tion, and from the calculation of numbers it was 
 transferred to the process of mediate comparison 
 in general. Discourse (discursus, diavoia) in- 
 dicates the operation of comparison, the running 
 backward and forward between the characters or 
 notes of objects (discurrere inter notas, diavo- 
 10 dai). The terms discourse and discursus, 
 dictvoia, are, however, often used for the reason- 
 ing process, strictly considered, and discursive is 
 even applied to denote mediate, in opposition to 
 intuitive, judgment, as is done by Milton. The 
 compound term, discourse of reason, unambig- 
 uously marks its employment in this sense. Ar- 
 gumentation is derived from argumentari, 
 which means argumentis uti ; argument again, 
 argumentum what is assumed in order to argue 
 something is properly the middle notion in a 
 reasoning that through which the conclusion is 
 established ; and by the Latin Rhetoricians it 
 was defined, * probabile invention ad faciendam- 
 fidem. ' It is often, however, applied as co-exten- 
 sive with argumentation. Inference or Illation 
 (from infero) indicates the carrying out into the 
 
202 ON THE KNOWING FACULTIES 
 
 last proposition what was virtually contained in 
 the antecedent judgments. To conclude (con- 
 cludere), again, signifies the act of connecting 
 and shutting into the last proposition the two 
 notions which stood apart in the two first. A 
 conclusion (conclusio) is usually taken, in its 
 strict or proper signification, to mean the last 
 proposition of a reasoning ; it is, sometimes, 
 however, used to express the product of the 
 whole process. To syllogize means to form syl- 
 logisms. Syllogism (avJtA&yiffjAOS) seems origi- 
 nally, like ratio, to have denoted a computa- 
 tion an adding up ; and like the greater part 
 of the technical terms of Logic in general, was 
 brorrowed by Aristotle from the mathematicians. 
 2vXXoyiGjAOS may, however, be considered 
 as expressing only what the composition of the 
 word denotes a collecting together ; for av\- 
 Xoyi^sffdai comes from avKX-eyeiv,, which 
 signifies to collect. Finally, in Latin, a syllog- 
 ism is called collectio, and to reason, colligere. 
 This refers to the act of collecting, in the conclu- 
 sion, the two notions scattered in the premises./ 
 " A Reasoning is composed of two parts the 
 original Judgment or Judgments which are the 
 original datum in the process, and the move- 
 ment of the Thought in the process. As the 
 datum is regarded as logically determining and 
 preceding, it is called the Antecedent, and the 
 other part, regarded as logically determined, or 
 following, is called the Consequent. Its proper 
 sign is therefore. These are the parts of a 
 Reasoning regarded as an Integrate Whole. 
 
OF THE MIND. 203 
 
 u The antecedent in a Reasoning may consist 
 of a single Judgment, or of a plurality of Judg- 
 ments. If it consist of but one Judgment, the 
 Reasoning is called an Immediate Reasoning ; 
 as, Man is a rational animal ; therefore, Man is 
 rational. If the antecedent consists of more 
 than one Judgment, the Reasoning is called a 
 Mediate Reasoning, or, more technically, a Syl- 
 logism." (Day, "Elements of Logic, ' ' ed. 1 868, 
 pp. 91-94.) 
 
 186. " Reason, on the other hand, has no 
 relation to the body, except as the soul's lodging 
 and instrument ; it belongs to the soul, purely 
 and abidingly, and may be exercised without 
 giving the slightest external token. Instead of 
 framing bodily organs, ... it spans the 
 sciences, sails deliciously through the heavenly 
 realms of poetic analogy, penetrates the signifi- 
 cance of things, and looks into the very mind of 
 God himself. ' ' (Grindon, Life, p. 365, third ed. , 
 London.) 
 
 187. " Thinking, as Plato has observed, is 
 but the conversation of the soul with herself ; 
 and the instrument employed is the echo of that 
 which forms the medium of communication with 
 others. To this it may be added that the no- 
 tion, as represented in language, is but the sub- 
 stitute for the notion embodied in intuition, and 
 derives all the conditions of its validity from the 
 possibility of the latter ; for language, though 
 indispensable as an instrument of thought, lends 
 itself with equal facility to every combination, 
 and thus furnishes no criterion by which we can 
 
204 ON THE NATURE OF 
 
 judge between sense and nonsense between the 
 conceivable and the inconceivable. " (Mansel, 
 Metaphysics, pp. 1671-68, ed. 1871.) 
 
 (B) ON THE NATURE OF SUBJECT-MATTER. 
 
 -188. In addition to a knowledge of mind 
 and of knowing, the teacher, engaged in the 
 discovery of Methods of Teaching, must dili- 
 gently investigate the nature of the subject-mat- 
 ter that he is to teach. 
 
 189. By nature of subject-matter is meant 
 that subtle, original, and permanent property of 
 the subject-matter, at the presence of which the 
 faculties of the mind are intuitively incited to 
 their specific activities. 
 
 190. Some of this matter lies in the world 
 that is external to the mind of man, and is 
 called material. 
 
 191. Other matter rests exclusively within 
 the ego. The mind creates it both as to its 
 matter and form. In the case of material sub- 
 ject-matter, the mind determines only the form 
 under which it exists as knowledge. In the 
 other case, the immaterial, the matter and form 
 would never exist as knowledge, or as matter for 
 knowledge, were it not for the mind. The in- 
 vestigation of this whole subject is too vast to 
 attempt to do more, at this time, than touch 
 upon two or three subjects, except in the most 
 cursory manner. The inquiry is directed towards 
 the nature of Object Teaching, a familiar ex- 
 pression, and the nature of the subject-matter of 
 
SUBJECT-MATTER. 205 
 
 mathematics, one branch of which, arithmetic, 
 forms so important an element in the lower 
 schools. 
 
 192. Object Teaching is that teaching in 
 which a knowledge of objects, or object-matter, 
 or where the subject-matters are objects is 
 the real end and purpose of the instruction. Ob- 
 ject Teaching regards a knowledge of objects as 
 an end it does not consider anything beyond 
 the objects themselves it is served fully when 
 this knowledge of facts is secured its province 
 is with the actual, which exists as individual facts 
 its subject-matter is that which addresses itself 
 exclusively to the perceptive and discriminative 
 faculties of the mind, as matter to be learned 
 for its own sake. The powers of the mind that 
 are mainly instrumental in acquisitions by the 
 learner, who is taught by Object Teaching, are 
 the perceptive, which cognize intuitively and 
 immediately ; the discriminative, which outline 
 one object from another ; and memory, which 
 retains. Whatever is purely distinctive of Object 
 Teaching is found within the above limitations. 
 It relates to the region of individual facts. 
 
 193. Wherever an abundance of facts is 
 wanted as materials for the other faculties of the 
 mind to use subsequently in constructing science, 
 Object Teaching is the way by which the ne- 
 cessities can be met. 
 
 194. But Object Teaching is only possible 
 where a knowledge of facts, as such, is to be 
 obtained, and where the materials, the matters, 
 
206 ON THE NATURE OF 
 
 of knowledge, exist as objects of perception and 
 discrimination. 
 
 195. All those ways of teaching where ob- 
 jects, as charts, maps, apparatus, pictures, are 
 used, by the teacher and pupil, not as ends of 
 knowledge unto themselves, but as helps, by 
 analogy, to acquiring knowledge of other things 
 as ends all these ways of teaching are not Ob- 
 jective, they are Illustrative. 
 
 196. Ideas in the memory are joined together 
 by the nexus of their nature, termed the Laws of 
 Association. When, by any chance, one idea is 
 brought into consciousness from unconsciousness 
 one modification reproduced the whole group 
 of ideas, related by sameness of time, space, or 
 circumstances, come flitting as flocks through 
 consciousness. Connected with this association 
 of ideas is the power of imagination, which 
 creates new mental beings, and which .seizes 
 upon analogies. These states or modes of the 
 activities make Illustrative Teaching possible. 
 
 197. Illustrations are lights set by the way- 
 side in parabolic mirrors, to illuminate obscure 
 passages they are voices which call out a wel- 
 come to him who is bewildered in the midst of 
 a mazy mass of half -obscured and obscuring 
 numbers they are guides that accompany the 
 student to reveal to him on a sudden the secret 
 labyrinths through which he may arise into the 
 upper levels of light they are the Aladdin Lamp 
 and Ring, by whose mystic power their pos- 
 sessor may be instantaneously transported into 
 
SUBJECT-MATTER. 207 
 
 the palaces of the Beautiful and the True. The 
 value of an illustration consists in its brevity, 
 its brilliancy, its pointedness, its unexpected and 
 unforeseen applicability, and its convincing force 
 of plain analogy. 
 
 4 ' Illustration is vivid elucidation ( = to make 
 more fully intelligible) by certain specific and 
 effective means, as similitudes, comparisons, ap- 
 propriate incidents or anecdotes, and the like, 
 graphic representations, and even artistic draw- 
 ings. " (Smith, Syn. Discr.) 
 
 " Analogy is often used familiarly, as if it 
 meant mere moral resemblance or similarity. 
 Strictly speaking, however, analogy implies a 
 third term, or four terms, as follows : As A is 
 to B, so is C ; or as A is to B, so is C to D. 
 Analogy, therefore, is similarity of relations. 
 When we argue from example, we argue from 
 the likeness of things ; when from analogy, we 
 argue from the likeness of their relations. If I 
 argue that, because the seed dies in the earth 
 before it springs up anew, therefore it is prob- 
 able that the human body will rise again after 
 death ; this is, as to the character of the idea, 
 a resemblance, as to the argument, an analogy ; 
 the principle being that, as the same God is the 
 author of a natural and a spiritual world, He 
 may be expected to act toward each upon similar 
 and common laws. ' ' (Ibid.) 
 
 "Analogy and Induction. There are two 
 requisites in order to every analogical argument : 
 1 . That the two or several particulars concerned 
 in the argument should be known to agree in 
 
208 ON THE MATURE OF 
 
 some one point ; for otherwise they could not be 
 referable to any one class, and there would con- 
 sequently be no basis to the subsequent inference 
 drawn in the conclusion. 2. That the conclusion 
 must be modified by a reference to the circum- 
 stances of the particular to which we argue. 
 For herein consists the essential distinction be- 
 tween an analogical and an inductive argu- 
 ment." (Fleming, Vocab Phil.} 
 
 198. "I hate set dissertations ; and, above 
 all things in the world, 'tis one of the silliest 
 things in one of them, to darken your hypothesis 
 by placing a number of tall, opake words, one 
 before another, in a right line, betwixt your 
 own and your reader's conception, when, in all 
 likelihood, if you had looked about, you might 
 have seen something standing, or hanging up, 
 which would have cleared the point at once ; 
 ' for what hindrance, hurt, or harm doth the 
 laudable desire of knowledge bring to any man, 
 if even from a sot, a pot, a fool, a stool, a win- 
 ter-mitten, a truckle for a pulley, the lid of a 
 goldsmith's crucible, an -oil-bottle, an old slipper, 
 or a cane-chair ?' I am this moment sitting 
 upon one. Will you give me leave to illustrate 
 this affair of wit and judgment, by the two 
 knobs on the top of the back of it ? they are 
 fastened on, you see, with two pegs stuck slightly 
 into two gimlet-holes, and will place what I have 
 to say in so clear a light, as to let you see through 
 the drift and meaning of my whole preface, as 
 plainly as if every point and particle of it was 
 made up of sunbeams. I enter now directly 
 
SUBJECT-MATTER. 209 
 
 upon the point. Here stands wit, and there 
 stands judgment, close beside it, just like the 
 two knobs I'm speaking of, upon the back of 
 this self -same chair on which I am sitting. You 
 see, they are the highest and most ornamental 
 parts of its frame, as wit and judgment are of 
 ours, and, like them too, indubitably both made 
 and fitted to go together, in order, as we may say 
 in all such cases of duplicated embellishment, 
 to answer one another. Now, for the sake of 
 an experiment, and for the clearer illustrating 
 this matter, let us fora moment take off one of 
 these two curious ornaments (I care not which) 
 from the point or pinnacle of the chair it now 
 stands on ; nay, don't laugh at it, but did 
 you ever see, in the whole course of your lives, 
 such a ridiculous business as this has made of it ? 
 Why, 'tis as miserable a sight as a sow with one 
 ear ; and there is just as much sense and sym- 
 metry in the one as in the other. Do, pray, get 
 off your seats, only to take a view of it. Now, 
 would any man who valued his character a straw, 
 have turned a piece of work out of his hand in such 
 a condition ? Nay, lay your hands upon your 
 hearts, and answer this plain question, Whether 
 this one single knob, which now stands here like 
 a block-head by itself, can serve any purpose 
 upon earth, but to put one in mind of the want 
 of the other ? and let me farther ask, in case 
 the chair was your own, if you would not in 
 your consciences think, rather than be as it is, 
 that it would be ten times better without any 
 knobs at all ? 
 
210 ON THE STATURE OF 
 
 " Now these two knobs, or top-ornaments of 
 the mind of man, which crown the whole entab- 
 lature, being, as I said, wit and judgment, 
 which, of all others, as I have proved it, are the 
 most needful, the most prized, the most cal- 
 amitous to be without, and consequently the hard- 
 est to come at ; for all these reasons put togeth- 
 er, there is not a mortal among us so destitute of a 
 love of good fame or feeding, or so ignorant of 
 what will do him good therein, who does not 
 wish and steadfastly resolve in his own mind, to 
 be, or to be thought at least, master of the one 
 or the other, and indeed of both of them, if the 
 thing seems any way feasible, or likely to be 
 brought to pass. ' ' (Sterne, Tristram Shandy, pp. 
 88-9, ed. 1844, Philadelphia.) 
 
 199. Illustrative Teaching is seeking some- 
 thing that bears a resemblance in form, nature, 
 or kind to the point to be learned, or taught, 
 presenting it instead of the point, and thus en- 
 abling the powers of comparison possessed by 
 the pupil to act by inference from the analogy. 
 This is a process of extending the meaning of 
 words, called sometimes " the process of analo- 
 gous or metaphorical extension of the meaning 
 of words. This change may be said, no doubt, 
 to consist in generalization, since there must 
 always be a resemblance between the new and 
 old applications of the term. But the resem- 
 blance is often one of a most distant and obscure 
 kind, such as we should call analogy rather than 
 identity. " (Jevons, El. Lessons in Logic, p. 50, 
 ed. 1878.) 
 
SUBJECT-MATTER. 211 
 
 200. Example would be something akin to 
 analogy, excepting that example may be of the 
 kind of thing itself, as well as ah example illus- 
 trating the case at issue. 
 
 201. Illustrative Teaching is often called, 
 unfortunately in conception, Objective Teaching. 
 An object can be used for but two possible pur- 
 poses in teaching : (1) To be learned, in and 
 for itself ; (2) Or to be an aid in learning some- 
 thing else. The first is Object Teaching, the 
 second is Illustrative Teaching. 
 
 202. The distinction between the province 
 of Object Teaching and that of Illustrative 
 Teaching has been indistinctly apprehended by 
 teachers. This misapprehension has led to se- 
 rious obscurity of conceptions of teaching, for 
 the expression Object Teaching has been ap- 
 plied without discrimination to all kinds of teach- 
 ing where objects were used, whatever their pur- 
 pose, whether as objects to be learned, or as ob- 
 jects to use in illustrating other points. 
 
 ' 1 The science which enlightens, and the phys- 
 ick that cures, are doubtless very useful : but 
 the pretended science that misleads, and the 
 physick that kills, are as certainly destructive. 
 Teach us, therefore, to distinguish between them. 
 . . It may be replied, as it constantly is, 
 the fault is in the physician, and not in the sci- 
 ence of medicine, which is otherwise infallible. 
 Well, well, be it so : take care, however, the 
 physick be never accompanied by the doctor : 
 for, as sure as ever they come together, there 
 will be an hundred times more to fear from the 
 
212 ON THE NATURE OF 
 
 blunders of the artist, than to hope for from the 
 efficacy of the art." (Rousseau, JEmilius, Vol. 
 L, pp. 45-6.) 
 
 203. It has already been remarked that Ob- 
 ject Teaching can be resorted to only with those 
 subjects where facts obtained by perception and 
 discrimination are desired. There are branches 
 to be taught where it is impossible, from the 
 nature of the subject-matter, to teach in this 
 way. The subject of mathematics is one that 
 has grown from a basis of definitions. The axi- 
 oms follow definitions, but they are phases of 
 conclusive reasoning, and assume things which 
 are the creations of definitions. Definitions are 
 the bases of mathematic science in its matter. 
 Axioms are the bases in its logical processes of 
 reasoning. Definitions are things which are prod- 
 ucts growing out of relations. Relations are ob- 
 jects only as they are products of the activities of 
 the faculty of Thought. Hence all mathematical 
 subjects are, from their nature, incapable of be- 
 ing taught objectively. All lines, mathematical 
 blocks, charts, astronomical apparatus, and cal- 
 culating machines, are but objects which illus- 
 trate mathematical truths, its definitions, and 
 results, as intellectual products they are not the 
 things which are learned in themselves. What 
 are called Applied Mathematics are only hypo- 
 thetical illustrations of mental creations. It is 
 also true that this science is one ' ' in whose reas- 
 onings both matter and form can be furnished 
 by the mind itself," and not one where " the 
 form alone is from the mind, the matter being 
 
SUBJECT-MATTER. 
 
 derived from experience." (Manse], Prol. Log* 
 p. 93, ed. 1860.) 
 
 204. " Abstract terms are strongly distin- 
 guished from general terms by possessing only 
 one kind of meaning ; for as they denote quali- 
 ties there is nothing which they cannot in addi- 
 tion imply. The adjective ' red ' is the name 
 of red objects, but it implies the possession by 
 them of the quality redness ; but this latter 
 term has one single meaning the quality alone. 
 Thus it arises that abstract terms are incapable 
 of plurality." (Jevons, Prin. Science, p. 27, ed. 
 1877.). . . " Numerical Abstraction consists in 
 abstracting the character of the difference from 
 which plurality arises, retaining merely the fact. 
 When I speak of three men I need not at once 
 specify the marks by which each may be known 
 from each. Those marks must exist if they are 
 really three men and not one and the same, and 
 in speaking of them as many I imply the exist- 
 ence of the requisite differences. Abstract 
 number, then, is the empty form of difference ; 
 the abstract number three asserts the existence 
 of marks without specifying their kind. Num- 
 erical abstraction is thus seen to be a different 
 process from logical abstraction, for in the latter 
 process we drop out of notice the very existence 
 of difference and plurality. . . . The ori- 
 gin of the great generality of number is now ap- 
 parent. Three sounds differ from three colours, 
 or three riders from three horses ; but they agree 
 in respect of the variety of marks by which they 
 can be discriminated. The symbols 1 -f- 1 -f- 1 are 
 
ON THE NATURE OF 
 
 thus the empty marks asserting the existence of 
 discrimination. But in dropping out of sight 
 the character of the differences we give rise to 
 new agreements on which mathematical reason- 
 ing is founded. . . . The common distinc- 
 tion between concrete and abstract number can 
 now be easily stated. In proportion as we speci- 
 fy the logical characters of the things numbered, 
 we render them concrete. In the abstract num- 
 ber three there is no statement of the points in 
 which the three objects agree ; but in three coins, 
 three men, or three horses, not only are the ob- 
 jects numbered, but their nature is restricted. 
 Concrete number thus implies the same con- 
 sciousness of difference as abstract number, but 
 it is mingled with a groundwork of similarity 
 expressed in the logical terms. There is identity 
 so far as logical terms enter ; difference so far as 
 the terms are merely numerical. The reason 
 of the important Law of Homogeneity will now 
 be apparent. This law asserts that in every 
 arithmetical calculation the logical nature of the 
 things numbered must remain unaltered. The 
 specified logical agreement of the things must 
 not be affected by the unspecified numerical 
 differences. A calculation would be palpably 
 absurd which, after commencing with length, 
 gave a result in hours. It is equally absurd, in 
 a purely arithmetical point of view, to deduce 
 areas from the calculation of lengths, masses 
 from the combination of volume and density, or 
 momenta from mass and velocity. It must re- 
 main for subsequent consideration to decide in 
 
SUBJECT-MATTER. 215 
 
 what sense one may truly say that two linear 
 feet multiplied by two linear feet give four su- 
 perficial feet ; arithmetically it is absurd, be- 
 cause there is a change of unit. As a general 
 rule we treat in each calculation only objects of 
 one nature. We do not, and cannot properly 
 add, in the same sum yards of cloth and pounds 
 of sugar. We cannot even conceive the result 
 of adding area to velocity, or length to density, 
 or weight to value. The units added must have 
 a basis of homogeneity, or must be reducible to 
 some common denominator. Nevertheless it is- 
 possible, and in fact common, to treat in one 
 complex calculation the most heterogeneous quan- 
 tities, on the condition that each kind of object 
 is kept distinct, and treated numerically only in 
 conjunction with its own kind. Different units, 
 so far as their logical differences are specified, must 
 never be substituted one for the other. (Ibid., 
 pp. 158-60.) 
 
 " Abstractly considered, Number is the measure 
 of the relation between quantities or things of the 
 same kind. We can form* no conception of the 
 absolute magnitude of any quantity, and can only 
 acquire a relative conception of it, by comparing 
 it with some other quantity of the same kind, 
 assumed as a standard of comparison. The 
 comparison is made by seeking how many times 
 the standard is contained in the quantity mea- 
 sured. The result of this comparison is a 
 number." (Davies and Peck, Diet, of Math.) 
 
 " Groups of units are what we really treat in 
 arithmetic. The number five is really 1 + 1 -f 1 
 
216 ON THE NATURE OF 
 
 + 1 + 1 , but for the sake of conciseness we sub- 
 stitute the more compact sign 5, or the name 
 five. These names being arbitrarily imposed in 
 any one manner, an infinite variety of relations 
 spring up between them which are not in the 
 least arbitrary. If we define four as 1 + 1 + 1 + 1, 
 and five as 1 + 1 + 1 + 1 + 1, then of course it 
 follows that five=four + l ; but it would be 
 equally possible to take this latter equality as a 
 definition, in which case one of the former equali- 
 ties would become an inference. It is hardly re- 
 quisite to decide how we define the names of 
 numbers, provided we remember that out of the 
 infinitely numerous relations of one number to 
 others, some one relation expressed in an equali- 
 ty must be a definition of the number in question 
 and the other relations immediately become nec- 
 essary inferences. 
 
 " In the science of number the variety of 
 classes which can be formed is altogether infinite, 
 and statements of perfect generality may be 
 made subject only to difficulty or exception at 
 the lower end of the scale. Every existing 
 number for instance belongs to the class M + 7 ; 
 that is, every number must be the sum of another 
 number and seven, except of course the first six 
 or seven numbers, negative quantities not being 
 here taken into account. Every number is the 
 half of some other, and so on. The subject of 
 generalization, as exhibited in mathematical 
 truths, is an infinitely wide one. In number 
 we are only at the first step of an extensive series 
 of generalizations. As number is general com- 
 
SUBJECT-MATTER. 217 
 
 pared with the particular things numbered, so 
 we have general symbols for numbers, and gen- 
 eral symbols for relations between undetermined 
 numbers. There is an unlimited hierarchy of 
 successive generalizations. " (Jevons, Pr. Sc., 
 pp. 167-168.) 
 
 " A large proportion of the mathematical 
 functions which are conceivable have no applica- 
 tion to the circumstances of this world. Phy- 
 sicists certainly do investigate the nature and 
 consequences of forces which nowhere exist. 
 Newton's Principia is full of such investigations. 
 In one chapter of his Mecanique, Celeste Laplace 
 indulges in a remarkable speculation as to what 
 the laws of motion would have been if momen- 
 tum, instead of varying simply as the velocity, 
 had been a more complicated function of it. 
 . Thought is not bound down to the limits 
 of what is materially existent, but is circum- 
 scribed only by those Fundamental Laws of 
 Identity, Contradiction, and Duality, which have 
 'already been laid down," (Ibid., pp. 70-45.) 
 
 205. " Mathematical Judgments may be di- 
 vided into two kinds indemonstrable or axiom- 
 atic judgments, whose necessity is self-evident ; 
 and demonstrable judgments, whose necessity 
 depends on some previous assumption. The 
 necessity of the latter is derived from that of the 
 former, so that the indemonstrable judgments 
 alone require a special examination. Under 
 this class are comprehended the axioms of geom- 
 etry, properly so-called viz., the original as- 
 sumptions concerning magnitudes in space as 
 
218 ON THE NATURE OF 
 
 such, and the propositions belonging to the fun- 
 damental operations of arithmetic addition and 
 subtraction. (Distinguish between postulates, and 
 some axioms which are logical, not geometrical 
 principles, and depend solely on the laws of 
 thought.) (Though in some things, as in num- 
 bers, besides adding and subtracting, men name 
 other operations, as multiplying and dividing, 
 yet are they the same ; for multiplication is but 
 adding together of things equal ; and division 
 but subtracting of one thing as often as we can. 
 Hobbes, Leviathan, p. L, chap. 5.) The ne- 
 cessity of these judgments results from the exist- 
 ence in the mind of the a priori forms of intui- 
 tion Space and Time. The axioms of geometry 
 are self-evident statements concerning magni- 
 tudes in space ; such as that two straight lines 
 cannot enclose a space. Their self-evidence or 
 necessity is to be explained by the circumstance 
 that the presented intuition, as well as the repre- 
 sentative thought, is derived from within, not 
 from without. For geometrical propositions are 
 primarily necessary, not as truths relating to ob- 
 jects without the mind, but as thoughts relating 
 to objects within : their necessity, as regards 
 real objects, is only secondary and hypothetical. 
 If there exist anywhere in the world two perfect 
 straight lines, those lines cannot enclose a space ; 
 but if such lines exist nowhere but in my imagi- 
 nation, it is equally true that I cannot think of 
 them as invested with the contrary attributes. 
 This necessity of thought is dependent on a cor- 
 responding necessity of intuition. The object 
 
SUBJECT-MATTER. 219 
 
 of which pure geometry treats is not dependent 
 on sensation, but sensation on it : it is a condi- 
 tion under which alone sensible experience is 
 possible ; and therefore its characteristics must 
 accompany all our thoughts concerning any pos- 
 sible object of such experience ; for, however 
 much we may abstract from the attributes of 
 this or that particular phenomenon of experience, 
 we are clearly incompetent to deprive it of those 
 conditions under which alone, from the consti- 
 tution of our minds, experience itself is possible. 
 We can perceive only as we are permitted by 
 the laws of our perceptive faculties, as we can 
 think only in accordance with the laws of the un- 
 derstanding. If, then, by a law of rny percep- 
 tive faculty, I am compelled to regard all ob- 
 jects as existing in space, the attributes which 
 are once presented to me as the properties of a 
 given portion of space, such as the pair of 
 straight lines now present to my sight or imagi- 
 nation, must necessarily be thought as existing 
 in all space and at all times. For to imagine a 
 portion of space in which such properties are 
 not found, would not be to imagine merely a 
 different combination of sensible phenomena, 
 such as continually takes place without any change 
 in the laws of sensibility : it would be to imagine 
 myself as perceiving under other conditions than 
 those to which, by a law of my being, I am sub- / 
 jected. But a condition, though potentially ex- 
 isting in the original constitution of the mind, 
 is actually manifested only in conjunction with 
 that of which it is the condition. Space, there- 
 
220 ON THE NATUKE OF 
 
 fore, and its laws, are first made known to con- 
 . sciousness on the occasion of an actual phenom- 
 enon of sense. Hence the twofold character of 
 geometrical principles : empirical, as suggested 
 in and through an act of experience ; necessary, 
 as relating to the conditions under which alone 
 such experience is possible to human faculties. 
 
 ' ' Arithmetic is related to Time as Geometry 
 to Space ; and the necessity of its propositions 
 may be explained upon similar principles. The 
 two sciences, however, present some important 
 features of distinction. Most of the proposi- 
 tions of geometry are deductive : it contains 
 very few axioms, properly so called, and its pro- 
 cesses consist in the demonstration of a multi- 
 tude of dependent propositions from the combi- 
 nation of these axioms with certain logical prin- 
 ciples of thought in general. On the other 
 hand, the fundamental operations of arithmetic 
 addition and subtraction present to us a vast 
 number of independent judgments, every one of 
 which is derived immediately from intuition, 
 and cannot, by any reasoning process, be de- 
 duced from any of the preceding ones. (Although 
 it is simpler to regard addition and subtraction 
 as independent processes, yet no result of either 
 can be derived from a preceding result of the 
 same operation. ) Pure geometry cannot advance 
 a step without demonstration, and its processes 
 are therefore all reducible to the syllogistic form. 
 Pure arithmetic contains no demonstration ; 
 and it is only when its calculus is applied to the 
 solution of particular problems that reasoning 
 
SUBJECT-MATTER. 221 
 
 takes place, and the laws of the syllogism be- 
 come applicable. It is not reasoning which tells 
 us that two and two make four ; nor, when we 
 have gained this proposition, can we in any way 
 deduce from it that two and four make six. 
 We must have recourse, in each separate case, 
 to the senses or the imagination (memory), and 
 by counting up the individual succession corre- 
 sponding to each term, intuitively perceive the 
 resulting sum. The intuition thus serves nearly 
 the same purpose as the figure in a geometrical 
 demonstration ; with the exception that, in the lat- 
 ter case, the construction is adopted to furnish pre- 
 mises to a proposed conclusion ; while in the for- 
 mer it gives us a judgment which we have no im- 
 mediate intention of applying to any further use. 
 " The intuition in the case of arithmetic is 
 furnished by the consciousness of successive 
 states of our own minds. Setting aside all other 
 characteristics of those states, save that of their 
 succession in time, we have the immediate con- 
 sciousness of one, two, three, four, etc. A 
 purely natural arithmetic would consist in carry- 
 ing on this series, with no other relation between 
 its members but that of succession, until the 
 memory became unable to continue the process. 
 The artificial methods by which calculation is fa- 
 cilitated and extended, such as that of a scale of 
 notation, in which the series recommences after 
 a certain number of members, vastly increase the 
 utility of the calculus, but do not affect its psy- 
 chological basis. To construct the science of 
 arithmetic in all its essential features, it is only 
 
222 ON THE NATURE OF 
 
 necessary that we should be conscious of a suc- 
 cession in time, and should be able to give names 
 to the several members of the series ; and since 
 in every act of consciousness we are subject to 
 the condition of succession, it is impossible in 
 any form of consciousness to represent to our- 
 selves the facts of arithmetic as other than they 
 are. 
 
 " The necessity of propositions in geometry 
 and arithmetic is thus derived from their relation 
 to the universal forms of intuition Space and 
 Time. We can suppose the possibility of be- 
 ings existing whose consciousness has no relation 
 to space or time at all. This is no more than to 
 admit the possible existence of intelligent beings 
 otherwise constituted than ourselves, and conse- 
 quently incomprehensible by us. But to sup- 
 pose the existence of geometrical figures or arith- 
 metical numbers such as those with which we 
 are now acquainted, is to suppose the existence 
 of space and time as we are now conscious of 
 them, and therefore relatively to beings whose 
 mental constitution is so far similar to our own. 
 Such a supposition necessarily carries with it all 
 the mathematical relations in which space and 
 time, as given to us, are necessarily thought. 
 For mathematical judgments strictly relate only 
 to objects of thought as existing in my mind, 
 not to distinct realities existing in relation to my 
 mind. They therefore imply no other exist- 
 ence than that of a thinking subject, modified 
 in a certain manner. Destroy this subject, or 
 change its modification, and we cannot say, as 
 
SUBJECT-MATTER. 223 
 
 in other cases, that the object may possibly exist 
 still without the subject, or may exist in a new 
 relation to a new subject ; for the object exists 
 only in and through that particular modification 
 of the subject, and, on any other supposition, is 
 annihilated altogether. Thus it is impossible to 
 suppose that a triangle can, in relation to any 
 intelligence whatever, have its angles greater or 
 less than two right angles, or that two and two 
 should not be equal to four ; though it is quite 
 possible to suppose the existence of intelligent 
 beings destitute of the idea of a triangle or of 
 the number two. This is a necessary matter 
 in the strict sense of the term ; a relation which 
 our own minds are incapable of reversing, not 
 merely' positively, in our own acts of thought, 
 but also negatively, by supposing others who 
 can do so." (Mansel, Metaphysics, pp. 226-31. 
 ed. 1871.) 
 
 206. " The main branches of mathematical 
 science were formerly stated to be arithmetic and 
 geometry, springing out of the simple notions 
 of number and space. This is too limited a de- 
 scription. Unquestionably the science of num- 
 bers, strictly and demonstratively treated, and 
 that of geometry, or the deduction of the ele- 
 mentary properties of figure from definitions 
 which are entirely exclusive of numerical consid- 
 erations, must be considered as the elementary 
 foundations, but not as the ultimate divisions, of 
 mathematics. To them we must add the science 
 of operation, or algebra in its widest sense, the 
 method of deducing from symbols which imply 
 
224: OX THE NATURE OF 
 
 operations on magnitude, and which are to be 
 used in a given manner, the consequences of the 
 fundamental definitions. The leading idea of 
 this science is operation or process, just as num- 
 ber is that of arithmetic, and space and figure of 
 geometry : it is of a more abstract and refined 
 character than the latter two, only because it does 
 not immediately address itself to the notions 
 which are formed in the common routine of life. 
 It is the most exact of the exact sciences, accord- 
 ing to the idea of their exactness which frequent- 
 ly entertained, being more nearly based upon 
 definition than either arithmetic or geometry. 
 It is true that the definitions must be such as to 
 present results which admit of application to 
 number, space, force, time, &c., or the science 
 would be useless in mathematics, commonly so 
 called ; but it is not the less true that a system 
 of methods of operation, based upon general 
 definitions, and conducted by strict logic, may 
 be made to apply either to arithmetic or geome- 
 try, according to the manner in which the gen- 
 eralities of the definition are afterwards made 
 specific.'' (English Cyclopaedia, Mathematics.) 
 207. " The methods of observation of quan- 
 tity in general are, Numeration, which is pre- 
 cise by the nature of number ; the Measurement 
 of Space and Time, which are easily made pre- 
 cise ; the Conversion of Space and Time, by 
 which each aids the measurement of the other ; 
 the Method of Repetition ; the Method of Coinci- 
 dence or Interferences. ' ' (Whewell, Nov. Org. 
 Ren. p. 145.) 
 
SUBJECT-MATTER. 225 
 
 208. The branches known as the Natural Sci- 
 ences can be taught by Object Teaching in so 
 far as facts are needed and can be observed, for 
 the things shown or observed are the immediate 
 objects to be learned. History cannot, from its 
 nature, be taught objectively, except it happen 
 that the learner can be an eyewitness of the 
 events narrated. Language and Literature can 
 be taught by Object Teaching, they being ends 
 unto themselves, and subjects of inspection. 
 Applied mathematics, being themselves illustra- 
 tions, can hardly be taught illustratively. 
 
 209. As soon as perception and determina- 
 tion have given to the mind knowledge of indi- 
 vidual facts, the power of retention holds them 
 for future use they are reproduced and repre- 
 sented in consciousness where Thought seizes 
 them, and constructs science from them. When 
 knowledge of individual objects is gained, the 
 usefulness of the objects ceases. All beyond is 
 a work of the power of Thought. Hence the 
 stages, for subject matter that will admit of it, 
 are : (1) Knowledge of facts obtained by Per- 
 ception and Discrimination, which is the prov- 
 ince of Object Teaching ; (2) The activity of 
 Thought upon this knowledge, aided as it may 
 be by Imagination. In this second stage, Ob- 
 jects are rather a hindrance if present than an 
 aid, because they are so much useless material 
 that should be put aside Perception has done 
 its work, Discrimination has separated, and now 
 the senses may slumber while Thought is rearing 
 science out of similarities and identities any 
 
226 ON THE NATURE OF 
 
 energy of attention which is diverted, at this 
 time, towards the objects themselves is so much 
 abstracted from Thought, which is thereby weak- 
 ened, and Science so much endangered, for Sci- 
 ence is not possible without Thought. 
 
 4 i A real experiment is a very valuable product 
 of the mind, requiring great knowledge to invent 
 it and great ingenuity to carry it out. 
 It may be said that a boy takes more interest in 
 the matter by seeing for himself, or by perform- 
 ing for himself, that is by working the handle 
 of the air-pump : this we admit, while we con- 
 tinue to doubt the educational value of the trans- 
 action. . . . The function of experiment, 
 properly so called, in the investigation of the 
 laws and processes of nature can hardly be unduly 
 exalted ; but it may be said of the experimenter, 
 as of the poet, that he is born and not manufac- 
 tured. " (I. Todhunter, Conflict of Studies, pp. 
 16-19.) 
 
 210. Ignorance of the province of Object 
 Teaching leads to disaster, in practice, in mental 
 discipline. This teaching addresses the attention 
 of Perception and Discrimination. Then the ob- 
 jects have served their purpose. If the knowl- 
 edge of facts which the learner has obtained be 
 not wrought up by Thought into Concepts, which 
 are general in their character and form the data 
 for Reasoning, his mind is left far short of dis- 
 cipline. For true intellectual power comes only 
 by constant exercise of Thought, and Thought 
 busies itself only with mental products. Neglect 
 of demanding maximum amounts of work for 
 
SUBJECT-MATTER. 227 
 
 the powers of Thought of pupils habituates them 
 to superficial scholarship they may be apt at 
 observing, when objects are placed before them, 
 but they will develop little power of independent 
 research, of vigorous application to thinking, or 
 of the power to generalize. The mere acquisi- 
 tion and memorizing of a number of isolated, 
 heterogeneous, or unrelated facts, is neither learn- 
 ing nor discipline, whether the facts are obtained 
 from personal observation and examination, from 
 oral statements of teachers, or gleaned from 
 books. 
 
 (c) ON DISCOVERING METHODS OF TEACHING 
 SPECIAL SUBJECTS. 
 
 211. Having outlined the powers of know- 
 ing and the nature of subject-matter, it yet re- 
 mains to investigate the Methods of Teaching, 
 when they are to be applied in the teaching of 
 any given subject. " In every Treatise upon 
 any cience two Points are indispensably re- 
 quired ; the First, that the science which is the 
 subject of it be fully explained ; the second, 
 . that plain Directions be given, how and 
 by what method such science may be attained. ' ' 
 (Longinus, On The Sublime, pp. 12, Tr. by 
 Wm. Smith, 1739, London.) It is not the 
 purpose of this discussion to develop a complete 
 Method and Mode in any subject simply to 
 present the magnitude, importance, and direction 
 in general, of Methods in special studies. To 
 discover a Method to teach any branch is no 
 
228 ON DISCOVERING METHODS OF 
 
 easy task. The exact psychological faculties to 
 be addressed are often difficult to name the 
 subject-matter must be maintained in its integrity 
 while it is manipulated into a system to suit the 
 capacities of the mind taught. This latter point 
 is all important, as it sometimes happens that 
 the truths of science are sacrificed to error when 
 they appear in Modes of Teaching. It often 
 happens that systems, in their steps or degrees 
 of advancement, do only scant justice to the 
 mind to be taught, because they are too diffuse, 
 too prolix, too narrow in their steps, or too in- 
 elastic. These faults of systems are grave ones, 
 and show the teacher uninformed concerning 
 Methods of Teaching. The subject-matter 
 should be properly divided and subdivided, but 
 never below the present attainments of the 
 learner, for mind grows from reaching out after 
 the unknown and the difficult, provided it be not 
 clouded by discouragement in the pursuit. The 
 subject-matter should be carefully freed from all 
 that is not to be learned in that lesson the 
 steps to be presented should be those which are 
 vital to the system of the subject taught. Too 
 many words and points, and too much related 
 subject-matter, distract the mind of the learner 
 so that the real and vital points are only dimly 
 apprehended. He is most fortunate in the class- 
 room who sets forth, in sharp outline, just the 
 maximum of subject-matter for his class in- 
 spiring a zeal and determination for an increased 
 power on the morrow's lesson. 
 
 212. Suppose that a teacher wishes to dis- 
 
TEACHING SPECIAL SUBJECTS. 229 
 
 cover the Method of Teaching children the pro- 
 cess of Adding Numbers. How, in practice, 
 shall he proceed ? 
 
 1. Concerning the nature of the subject-mat- 
 ter : 
 
 (a) Addition, being purely mathematical 
 in its nature, is incapable of being 
 presented by Object Teaching. 
 
 () Being capable of a hypothetical ap- 
 plication to material objects, it can be 
 taught by Illustrative Teaching. 
 
 (c) The numbers to be added together 
 are but so many forms for the aggre- 
 gate of many smaller parts, having no> 
 logical connection. 
 
 (d) The subject-matter is represented by 
 certain characters called Figures, 
 which are arbitrary in their form, and 
 have no logical connection with each 
 other. 
 
 2. Concerning the faculties of mind that are 
 primarily active in learning addition : 
 
 (a) The Perceptive faculties are required 
 to note, intuitively, the individuals 
 that are presented to them. 
 
 (b) Discrimination, or Comparison, dis- 
 tinguishes one individual in Conscious- 
 ness from another. 
 
 (c) Memory in general, or, according to* 
 Hamilton, Retentiveness (or Mem- 
 ory), Recollection (or Reproduction), 
 and Representation, preserves for fu- 
 ture use the knowledge obtained 
 
230 ON DISCOVERING METHODS OF 
 
 through Perception and Discrimina- 
 tion. 
 
 (d) The Power of Detecting Identity, or 
 the Power of Comparison, or the 
 Power of Thought, compares or iden- 
 tifies what may come within Conscious- 
 ness through Perception, with what 
 may come there through Memory. 
 
 (e) The Power of expressing Thought, or 
 Language. 
 
 3. Having discovered these principles, which 
 are the Method of Teaching addition, he pro- 
 ceeds to invent his Mode of Teaching addition. 
 This Mode may be by illustration, by telling, by 
 questioning, and the like. 
 
 213. He regards these particular points : 1. 
 To what degree of power are the faculties of these 
 children grown ? 2. Is this System of Addition 
 philosophically constructed ? 3. In what quan- 
 tity of subject-matter shall the points of the sys- 
 tem be set to these faculties ? He may write 
 out the complete lesson, as he proposes to pre- 
 sent it. This is his Mode. He may then ap- 
 pear before the class to teach. His individual- 
 ity, when presenting the subject-matter, exhibits 
 his Manner. 
 
 The only guide possible for procedure in the 
 case is the intelligence of the teacher, who now 
 invents the Mode. If there be deficiency here, 
 it will be no matter for surprise if the children 
 are poorly taught. 
 
 "When a System of subject-matter is arranged 
 in detail in Modes of Teaching it, the arrange- 
 
TEACHING SPECIAL SUBJECTS. 231 
 
 ment is called Methodical All methodical dis- 
 cussions for teaching must rest upon Methods of 
 Teaching. 
 
 214. In the foregoing procedure, the dis- 
 covering of the Method of Teaching the process 
 of discovering the faculties, and the nature of 
 the subject-matter that is to be adjusted to them, 
 comprised under (1) and (2) is the conception 
 of the Science of Teaching. 
 
 215. The Invention of the Mode of Teaching, 
 together with the Manner of exhibiting it in 
 practice, is the conception of the Art of Teach- 
 ing. 
 
 216. The Investigation of the Science and 
 the Art of Teaching constitutes the Conception 
 of the Profession of Teaching. 
 
III. 
 
 CONCLUDING REFLECTIONS. 
 
 217. Whatever qualifications of mind and 
 person the teacher may have, he is still lacking 
 in a most important element of success if he has 
 not a quick apprehension of adopting means to 
 nds. He must possess versatility of powers to 
 discover Methods of Teaching, in order to invent 
 Modes by which he shall incite to activity the 
 pupil's mind with certainty. To do this, he 
 needs a large stock of " That unacquired, un- 
 bought, untaught sagacity, which certain men 
 have by nature," called Common Sense or good 
 sense. (McCosh, Int. of Mind, p. 93, ed. 1870.) 
 " Common Sense is the spontaneous action of 
 right reason." (M. Bautain, Art of Ext. Speak- 
 ing, ed. 1871.) This ability is needed nowhere 
 more than in the school-room, and he who lacks 
 it should diligently apply himself to cultivating 
 his " good sense," if he would attain eminence 
 in the Profession of Teaching. 
 
 218. " An open-eyed and open-minded 
 physician keeps adding to his knowledge and 
 altering and widening his theories to the day of 
 his death ; there is not less to be learned in the 
 world of mind in the world of the school-room. 
 
CONCLUDING REFLECTIONS. 233 
 
 The kind of teacher who stiffens into 
 the school-master misses his opportunities, or falls 
 a victim to that arrestment of development which 
 has overtaken many school subjects, and which 
 sometimes overtakes the whole of school life.'' 
 (Meiklejohn, Inaugural Address, Bell Chair of 
 Education, p. 11, 1876, Edinburgh.) 
 
 219. " Intellectually, as well as morally, he 
 (Arnold) felt that the teacher ought himself to be 
 perpetually learning, and so constantly above the 
 level of his scholars. ' I am sure,' he said, 
 speaking of his pupils at Laleham, ' that I do 
 not judge of them or expect of them, as I should, if 
 I were not taking pains to improve my own mind. ' 
 For this reason he maintained that no school- 
 master ought to remain at his post much more 
 than fourteen or fifteen years, lest, by that time, 
 he should have fallen behind the scholarship of 
 the age ; and by his own reading and literary 
 works he endeavored constantly to act upon this 
 principle himself. 4 The dangers ' (of 
 
 falling behind), he observed, * were of various 
 kinds. One boy may acquire a contempt for the 
 information itself, which he sees possessed by a 
 man whom he feels nevertheless to be far below 
 him. Another (pupil) will fancy himself as 
 much above nearly all the world as he feels he is 
 above his own tutor, and will become self-suffi- 
 cient and scornful. A third will believe it to be 
 his duty, as a point of humility, to bring himself 
 down intellectually to a level with one whom he 
 feels bound to reverence ; and thus there have 
 been instances where the veneration of a young 
 
234 CONCLUDING REFLECTIONS. 
 
 man of ability for a teacher of small powers has 
 been like a millstone round the neck of an eagle. ' ' ' 
 (Arnold, Life of, p. 137, ed. 1870.) 
 
 220. " We may say that common sense 
 scarcely claims to provide more than rather in- 
 definite general rules, which no prudent man 
 should neglect without giving himself a reason 
 for doing so. Such reasons may either be drawn 
 from one's knowledge of some peculiarities in 
 one's nature, or from the experience of others 
 whom one has ground for believing to be more 
 like oneself than the average of mankind are. 
 For though, as we saw, there is considerable 
 risk of error in thus appropriating the experience 
 of others and in fact the expression of it will 
 sometimes appear to be as hesitating and contra- 
 dictory as the judgments of common sense we 
 may extract from it counsel sufficiently consist- 
 ent and authoritative to supplement at least 
 roughly the deficiencies of our own empirical 
 generalizations. ' ' (Sidgwick, Methods of Ethics, 
 p. 145, ed. 1874.) 
 
 221. " But many who allow the use of sys- 
 tematic principles in other things, are accustomed 
 to cry up Common-Sense as the sufficient and 
 only safe guide in Reasoning. Now by Common- 
 Sense is meant, I apprehend, (when the term is 
 used with any distinct meaning,) an exercise of 
 the judgment unaided by any Art or system of 
 rules : such an exercise as we must necessarily 
 employ in numberless cases of daily occurrence ; 
 in which, having no established principles to 
 guide us, no line of procedure, as it were, dis- 
 
CONCLUDING REFLECTIONS. 235 
 
 tinctly chalked out we must needs act on the 
 best extemporaneous conjectures we can form. 
 He who is eminently skilful in doing this, is said 
 to possess . a superior degree of Common-Sense. 
 But that Common-Sense is only our second best 
 guide that the rules of Art, if judiciously 
 framed are always desirable when they can be 
 had, is an assertion, for the truth of which I may 
 appeal to the testimony of mankind in general ; 
 which is so much the more valuable, inasmuch 
 as it may be accounted the testimony of adver- 
 saries. For the generality have a strong predi- 
 lection in favor of Common- Sense, except in 
 those points in which they, respectively, possess 
 the knowledge of a system of rules ; but in these 
 points they deride any one who trusts to unaided 
 Common-Sense. " A sailor e.g. will, perhaps, 
 despise the pretensions of medical men, and 
 prefer treating a disease by Common-Sense : but 
 he would ridicule the proposal of navigating a 
 ship by Common-Sense, without regard to the 
 maxims of nautical art. A physician, again, 
 will perhaps contemn Systems of Political- 
 Economy, of Logic, or Metaphysics, and insist 
 on the superior wisdom of trusting to Common- 
 Sense in such matters ; but he would never ap- 
 prove of trusting to Common-Sense in the treat- 
 ment of diseases. 
 
 " Neither, again, would the Architect recom- 
 mend a reliance on Common-Sense alone, in build- 
 ing, nor a Musician, in music, to the neglect of 
 those systems of rules, which, in their respective 
 arts have been deduced from scientific reason- 
 
236 CONCLUDING REFLECTIONS. 
 
 ing aided by experience. And the induction 
 might be extended to every department of prac- 
 tice. Since, therefore, each gives the preference 
 to unassisted Common- Sense only in those cases 
 where he himself has nothing else to trust to, 
 and invariably resorts to the rules of art, wher- 
 ever he possesses the knowledge of them, it is 
 plain that mankind universally bear their testi- 
 mony, though unconsciously and often unwill- 
 ingly, to the preferableness of systematic knowl- 
 edge to conjectural judgments. 
 
 " There is, however, abundant room for the 
 employment of Common-Sense in the application 
 of the system. To bring arguments out of the 
 form in which they are expressed in conversation 
 and in books, into the regular logical shape, must 
 be of course, the business of Common-Sense, 
 aided by practice, for such arguments are, by 
 supposition, not as yet within the province of 
 science." (Whately, Elements of Logic, 1859, 
 pp. xi.-xii. of Preface.) 
 
 222. " The one talent which is worth all 
 other talents put together in all human affairs is 
 the talent of judging right upon imperfect ma- 
 terials, the talent if you please of guessing 
 right. It is a talent which no rules will ever 
 teach and which even experience does not al- 
 ways give. It often coexists with a good deal 
 of slowness and dulness and with a very slight 
 power of expression. All that can be said about 
 it is, that to see things as they are, without exag- 
 geration or passion, is essential to it ; but how 
 can we see things as they are ? Simply by open- 
 
CONCLUDING REFLECTIONS. 237 
 
 ing our eyes and looking with whatever power 
 we may have. 7 ' (Stephen, Liberty, Equality, 
 Fraternity, p. 352, ed. 1874, London.) 
 
 223. " The assumed logical perfection of 
 thought bears about the same relation to the or- 
 dinary state of the human mind as the assump- 
 tion of perfectly rigid levers and perfectly flexible 
 cords bears in the action of those instruments in 
 practice. But, on the other hand, the possibility 
 of making such allowances implies that the differ- 
 ence between practice and theory is one of de- 
 gree only, and not of kind. The instrument as 
 used may not be identical with the instrument 
 as contemplated, but it must be supposed cap- 
 able of approximation to it." (Mansel, Prol. 
 Log., p. 17.) 
 
 224. " It is a common notion, or at least it 
 is implied in many common modes of speech, 
 that the thoughts, feelings, and actions of sen- 
 tient beings are not a subject of science, in the 
 same strict sense in which this is true of the ob- 
 jects of outward nature. This notion seems to 
 involve some confusion of ideas, which it is 
 necessary to begin by clearing up. Any facts 
 are fitted, in themselves, to be a subject of 
 science which follow one another according to 
 constant laws, although those laws may not have 
 been discovered, nor even be discoverable by our 
 existing resources. . . . Scientific inquiry 
 has not yet succeeded in ascertaining the order 
 of antecedence and consequence among phenom- 
 ena, so as to^be able, at least in our regions of 
 the earth, to predict them with certainty, or 
 
238 CONCLUDING REFLECTIONS. 
 
 even with a high degree of probability. . . . 
 But meteorology not only has in itself every 
 natural requisite for being, but actually is, a 
 science ; though the science is extremely imper- 
 fect. ... No one doubts that Tidology 
 (as Dr. Whewell proposes to call it) is really a 
 science. . . But circumstances of a local or casual 
 nature, such as the configuration of the bottom 
 of the ocean, the degree of confinement from 
 shores, the direction of the wind, etc. , influence, 
 in many or all places, the height and time of 
 the tide ; and a portion of these circumstances be- 
 ing either not accurately knowable, not precisely 
 measurable, or not capable of being certainly 
 foreseen, the tide in known places commonly 
 varies from the calculated result of general prin- 
 ciples by some difference that we are not able to 
 foresee- or conjecture. . . . And this is what 
 is or ought to be meant by those who speak of 
 sciences which are not exact sciences. As- 
 tronomy was once a science, without being an 
 exact science. ... It has become an exact 
 science. . . . The science of human nature 
 is of this description. It falls far short of the 
 standard of exactness now realized in Astron- 
 omy ; but there is no reason that it should not be 
 as much a science as Tidology is, or as Astronomy 
 was when its calculations had only mastered the 
 main phenomena, but not the perturbations. 
 
 " The phenomena with which this science of 
 (human) nature is conversant being the thoughts, 
 feelings, and actions of human beings, it would 
 have attained the ideal perfection of a science if 
 
CONCLUDING REFLECTIONS. 239 
 
 it enabled us to foretell how an individual would 
 think, feel, or act throughout life, with the same 
 certainty with which astronomy enables us to pre- 
 dict the places and the occultations of the heavenly 
 bodies. It need scarcely be stated that nothing 
 approaching to this can be done. The actions of 
 individuals could not be predicted with scientific 
 accuracy, were it only because we can not fore- 
 see the whole of the circumstances in which those 
 individuals will be placed. But further, even in 
 any given combination of (present) circum- 
 stances, no assertion, which is both precise and 
 universally true, can be made respecting the 
 manner in which human beings will think, feel, 
 and act. This is not, however, because every 
 person's modes of thinking, feeling, and acting 
 do not depend on causes ; nor can we doubt that 
 if, in the case of any individual, our data could 
 be complete, we even now know enough of the 
 ultimate laws by which mental phenomena are 
 determined, to enable us in many cases to pre- 
 dict, with tolerable certainty, what, in the 
 greater number of supposable combinations of 
 circumstances, his conduct or sentiments would 
 be. But the impressions and actions of human 
 beings are not solely the result of their present 
 circumstances, but the joint result of those cir- 
 cumstances and of the characters of the individ- 
 uals ; and the agencies which determine human 
 character are so numerous and diversified (noth- 
 ing which has happened to the person through- 
 out life being without its portion of influence), 
 
240 CONCLUDING REFLECTIONS. 
 
 that in the aggregate they are never in any two 
 cases exactly similar. Hence, even if our science 
 of human nature were theoretically perfect, that 
 is, if we could calculate any character as we can 
 calculate the orbit of any planet, from given data ; 
 still, as the data are never all given, nor ever 
 precisely alike in different cases, we could neither 
 make positive predictions, nor lay down univer- 
 sal propositions. 
 
 1 i Inasmuch, however, as many of those effects 
 which it is of most importance to render amena- 
 ble to human foresight and control are deter- 
 mined, like the tides, in an incomparably greater 
 degree by general causes, than by all partial causes 
 taken together ; depending in the main on those 
 circumstances and qualities which are common 
 to all mankind, or at least to large bodies of 
 them, and only in a small degree on the idiosyn- 
 crasies of organization or the peculiar history of 
 individuals ; it is evidently possible with regard 
 to all such effects, to make predictions which 
 will almost always be verified, and general pro- 
 positions which are almost always true. And 
 whenever it is sufficient to know how the great 
 majority of the human race, or of some nation 
 or class of persons, will think, feel, and act, these 
 propositions are equivalent to universal ones. 
 For the purpose of political and social science 
 this is sufficient. As we formerly remarked, an 
 approximate generalization is, in social inquiries, 
 for most practical purposes equivalent to an exact 
 one ; that which is only probable when asserted 
 
CONCLUDING REFLECTIONS. 241 
 
 of individual human beings indiscriminately se- 
 lected, being certain when affirmed of the char- 
 acter and collective conduct of masses. 
 
 " It is no disparagement, therefore, to the 
 science of Human Nature, that those of its gen- 
 eral propositions which descend sufficiently into 
 detail to serve as a foundation for predicting 
 phenomena in the concrete, are for the most part 
 only approximately true. But in order to give 
 a genuinely scientific character to the study, it 
 is indispensable that these approximate generali- 
 zations, which in themselves would amount only 
 to the lowest kind of empirical laws, should be 
 connected deductively with the laws of nature 
 from which they result ; should be resolved 
 into the properties of the causes on which the 
 phenomena depend. In other words, the science 
 of Human Nature may be said to exist in propor- 
 tion as the approximate truths, which compose 
 a practical knowledge of mankind, can be ex- 
 hibited as corollaries from the universal laws of 
 human nature on which they rest ; whereby the 
 proper limits of those approximate truths would 
 be shown, and we should be enabled to deduce 
 others for any new state of circumstances, in an- 
 ticipation of specific experience. . . . The 
 proposition now stated is the text on which are 
 based the ' Laws of Mind, ' and * Ethology, or the 
 science of the Formation of Character. ' ' ' (Mill, 
 System of Logic, pp. 586-596, 8 ed. 1874.) 
 
APPENDIX OF QUOTATIONS. 
 
 SECTION PAGE 
 
 225. Appendix A. On Method 348 
 
 226. B. OnSystem 376 
 
 227. C. On Analysis 380 
 
 228. D. On Synthesis 383 
 
 229. E. On Definition 385 
 
 230. F. On Abstraction 390 
 
 231. G. On Generalization 392 
 
 232. H. On Classification 398 
 
 233. I. On Induction 413 
 
 234. J. On Interpretation 473 
 
 235. K. On Deduction .. 478 
 
APPENDIX A. 
 
 225. EXTRACTS SHOWING THE USE OF THE 
 TERM METHOD. 
 
 1. From Hedge's Logick, ed. 1854, pp. 149- 
 150. 
 
 Method, in logick, is a proper classification and 
 arrangement of our thoughts on any subject, 
 either to facilitate the discovery of new truths, 
 or to assist us in communicating to others truths 
 already known ; or, lastly, to enable us to preserve 
 for future use the knowledge, which we have ac- 
 quired. The disposition best adapted to the in- 
 vestigation of truth is the analytick method; 
 which is therefore denominated the method of 
 invention ; and that which is best suited to the 
 communication of knowledge, is the synthetick 
 method, which for this reason has been called 
 the method of instruction. In both of these 
 methods, ideas are arranged in such order, as 
 to exhibit their mutual connexions and relations. 
 
 2. 'FromCoipipeQ'sMements of Logic, ed. 1860, 
 pp. 23-25. 
 
 Method is the order and arrangement of facts 
 to produce a certain result ; to establish new 
 truth, to investigate old, and to explain and teach 
 both. It is derived from the Greek jted'odov $ 
 
246 APPENDIX A. 
 
 which denotes the way through which we arrive 
 at a certain result. 
 
 Whatever steps are taken to make knowledge 
 profitable, to reduce theory to practice, and to 
 give clear and intelligible ideas of science, con- 
 stitute Method. The extension of the term 
 Method, it is evident, will differ according to 
 the subject to which it is applied. 
 
 The methods of investigation differ slightly 
 for the different kinds of science, but may gen- 
 erally be classified under two heads, Analysis 
 and Synthesis, of which the former is generally 
 used in the private investigation of truth, and 
 the latter for the purposes of instruction. . . . 
 We speak of the Method of a single science, 
 or a Method which is applied to all as in that 
 which leads to the Classification of the sciences. 
 In either investigation the division of Method 
 into Analysis and Synthesis, is a just one, as 
 both are used in either process. 
 
 3. From Day's Elements of Logic, ed. 1868, 
 pp. 132-133. 
 
 "Method in general is the regulated procedure 
 towards a certain end ; that is, a process governed 
 by rules, which guide us by the shortest way 
 straight towards a certain point, and guard us 
 against devious aberrations. Now the end of 
 Thought is Truth, Knowledge, Science expres- 
 sions which may here be considered as convert- 
 ible. Science, therefore, may be regarded as the 
 perfection of thought, and to the accomplishment 
 of this perfection the Methodology of Logic 
 must be accommodated and be conducive. ' ' 
 
APPENDIX A. 247 
 
 But while Science, thus, is the proper end 
 of all Thought, and Logical Method must have 
 reference to Thought as its one end, it is still to 
 be regarded only as the immediate end, which 
 may, itself, be modified and controlled by still 
 higher ends. In fact, Science or Truth may 
 have its end either in itself in the True, or 
 in the Beautiful, or in the Right and Good ; 
 and the Method of Thought will vary in some 
 respects with this specific remoter end. Still 
 further, the Method of Thought will vary with 
 the more specific ends under each of these higher 
 governing ends. We may deal with Thought for 
 the purpose of acquiring knowledge, or for the 
 purpose of communicating knowledge ; and the 
 Method requisite for the Investigation of Truth 
 will so far vary from the Method requisite for 
 the Communication of Truth. 
 
 In like manner the Method of Thought, as- 
 governed by the higher end of guiding to the 
 Beautiful, will vary specifically, as the particular 
 end is the Contemplation or the Creation of the 
 Beautiful. 
 
 So, too, we have a specific variation in the 
 Method of Thought, where the governing idea is 
 the Right or the Good, according as Subjective 
 or Objective Rectitude or Goodness is the partic- 
 ular end. 
 
 It is sufficient to point out here these modi- 
 fications of Logical Method in respect to these 
 several general ends in thinking. The full, de- 
 tailed consideration of them belongs either to 
 modified Logic or to Applied or Special Logic. 
 
248 . APPENDIX A. 
 
 Pure Logic confines itself to the domain of Truth 
 in itself Science for its own sake. 
 
 4. From Fleming's Vocabulary of Philosophy, 
 ed. 1858, pp. 316-319. 
 
 Method means the way or path by which we 
 proceed to the attainment of some object or aim. 
 In its widest acceptation, it denotes the means 
 employed to obtain some end. Every art and 
 every handicraft has its method. 
 
 Scientific or philosophical method is the march 
 which the mind follows in ascertaining or com- 
 municating truth. It is the putting of our 
 thoughts in a certain order with a view to im- 
 prove our knowledge or to convey it to others. 
 
 Method may be called, in general, the art 
 of disposing well a series of many thoughts, 
 either for the discovering truth when we are 
 ignorant of it, or for proving it to others when 
 it is already known. Thus there are two kinds 
 of method, one for discovering truth, which is 
 called analysis, or the method of resolution, and 
 which may also be called the method of inven- 
 tion ; and the other for explaining it to others 
 when we have found it, which is called synthesis, 
 or the method of composition, and which may 
 also be called the method of doctrine. (Port 
 Boy. Logic, Part IV., ch. 2.) 
 
 "Method, which is usually described as the 
 fourth part of Logic, is rather a complete prac- 
 tical Logic. It is rather a power or spirit of the 
 intellect, pervading all that it does, than its tan- 
 gible product." (Thomson, Outline of Laws 
 of Thought, sect. 119.) 
 
APPENDIX A. 249 
 
 Every department of philosophy has its own 
 proper method ; but there is a universal method 
 or science of method. This was called by Plato, 
 dialectic ; and represented as leading to the true 
 and real. (Repub., lib. vii.) It has been said 
 that the word /*0odo, as it occurs in Aris- 
 totle's Ethics, should be translated ' systems/ 
 rather than ' method.' (Paul, Analysis of Aris- 
 totle 9 s Ethics, p. 1.) But the construction of 
 a system implies method. And no one was more 
 thoroughly aware of the importance of a right 
 method than Aristotle. He has said (Metaphys. , 
 lib. ii.), u that we ought to see well what demon- 
 stration (or proof) suits each particular subject ; 
 for it would be absurd to mix together the re- 
 search of science and that of method; two 
 things, the acquisition of which offers great diffi- 
 culty." The deductive method of philosophy 
 came at once finished from his hand. And the 
 inductive method was more extensively and suc- 
 cessfully followed out by him than has been gen- 
 erally thought. 
 
 James Acontius, or Concio, as he is sometimes 
 called, was born at Trent, and came to England 
 in 1567. He published a work, De Methodo. 
 . . . According to him all knowledge de- 
 duced from a process of reasoning presupposes 
 some primitive truths, founded in the nature of 
 man, and admitted as soon as announced ; and 
 the great aim of method should be to bring these 
 primitive truths to light, that by their light we 
 may have more light. Truths obtained by the 
 
250 APPEKDIX A. 
 
 senses, and by repeated experience, become at 
 length positive and certain knowledge. 
 
 Descartes has a discourse on Method. He 
 has reduced it to four general rules. 
 
 I. To admit nothing as true of which we 
 have not a clear and distinct idea. We have a 
 clear and distinct idea of our own existence. 
 And in proportion as our idea of anything else 
 approaches to, or recedes from, the clearness of 
 this idea, it ought to be received or rejected. 
 
 II. To divide every object inquired into as 
 much as possible into its parts. Nothing is more 
 simple than the ego, or self-consciousness. In 
 proportion as the object of inquiry is simplified, 
 the evidence comes to be nearer that of self- 
 consciousness. 
 
 III. To ascend from simple ideas or cogni- 
 tions to those that are more complex. The real 
 is often complex : and to arrive at the knowledge 
 of it as a reality, we must by synthesis reunite 
 the parts which were previously separated. 
 
 IV. By careful and repeated enumeration to 
 see that all the parts are reunited. For the syn- 
 thesis will be deceitful and incomplete if it do 
 not reunite the whole, and thus give the reality. 
 
 This method begins with provisory doubt, 
 proceeds by analysis and synthesis, and ends by 
 accepting evidence in proportion as it resembles 
 the evidence of self-consciousness. 
 
 These rules are useful in all departments 
 of philosophy. But different sciences have 
 different methods suited to their objects and to 
 the end in view. 
 
APPENDIX A. 251 
 
 In prosecuting science with the view of ex- 
 tending our knowledge of it, or the limits of it, 
 we are said to follow the method of investigation 
 or inquiry, and our procedure will be chiefly in 
 the way of analysis. But in communicating 
 what is already known, we follow the method of 
 exposition or doctrines, and our procedure will 
 be chiefly in the way of synthesis. 
 
 In some sciences the principles or laws are 
 given, and the object of the science is to discover 
 the possible application of them. In these sci- 
 ences the method is deductive, as in geometry. 
 In other sciences, the facts or phenomena are 
 given, and the object of the science is to dis- 
 cover the principles or laws. In these sciences 
 the proper method is inductive, proceeding by 
 observation or experiment, as in psychology and 
 physics. The method opposed to this, and 
 which was long followed, was the constructive 
 method ; which, instead of discovering causes by 
 induction, imagined or assigned them a priori, 
 or ex hypothesij and afterwards tried to verify 
 them. This method is seductive and bold but 
 dangerous and insecure, and should be resorted 
 to with great caution. 
 
 The use of method, both in obtaining and 
 applying knowledge for ourselves, and in convey- 
 ing and communicating it to others, is great and 
 obvious. 
 
 " Marshal thy notions into a handsome meth- 
 od. One will carry twice as much weight, 
 trussed and packed up in bundles, than when it 
 lies untoward, flapping, and hanging about his 
 
252 PPEKDIX A. 
 
 shoulders." (Pleasures of Literature 12mo, 
 Lond., 1851, p. 104.) 
 
 5. From Preface of " A Brief English Gram- 
 mar on a Logical Method," by Alexander Bain, 
 
 The chief peculiarity in the plan of the pres- 
 ent work lies in anticipating the unavoidable 
 difficulties of the subject by a previous handling 
 of certain elementary notions (belonging to all 
 science), without which no one can hope to un- 
 derstand the scope or method of grammar. 
 After such preliminary explanations, I 
 make no scruple to introduce a strict mode of 
 defining the Parts of Speech. I also exemplify 
 the leading subdivisions or classes of each. 
 Moreover, I bring forward at once the equivalent 
 phrases, which, in the case of the Adverb in par- 
 ticular, are used more frequently than single 
 words. On this method, the Grammatical pars- 
 ing of a sentence directs attention forcibly to the 
 meaning. ... It (the Key) also includes a 
 large selection of additional examples, which are 
 commented on with a view to set forth still far- 
 ther the methods of parsing, and to illustrate 
 the constructions and idioms of the language. 
 
 6. From WhewelFs Novum Organon Renova- 
 tum,ed. 1858, pp. 141-144. 
 
 The name Organon was applied to the works 
 of Aristotle which treated of Logic, i.e., of the 
 method of establishing and proving knowledge, 
 and of refuting errour, by means of Syllogisms. 
 Francis Bacon, holding that this method was in- 
 sufficient for the augmentation of real knowl- 
 edge, published his Novum Organon in which he 
 
APPENDIX A. 253 
 
 proposed for that purpose methods from which 
 he promised a better success, (p. 3.) 
 
 The Methods by which the construction of 
 Science is promoted are, Methods of Observa- 
 tion, Methods of obtaining clear Ideas, and 
 Methods of Induction. 
 
 Aphorism xxvii. ... I shall, therefore, 
 attempt to resolve the Process of Discovery into 
 its parts, and to give an account as distinct as may 
 be of Rules and Methods which belong to each 
 portion of the process. 
 
 In Book II. we considered the three main 
 parts of the process by which science is con- 
 structed : namely, the Decomposition and Ob- 
 servation of Complex Facts ; the Explication of 
 our Ideal Conceptions ; and the Colligation of 
 Elementary Facts by means of those conceptions. 
 The first and last of these three steps are capable 
 of receiving additional accuracy by peculiar pro- 
 cesses. They may further the advance of science 
 in a more effectual manner, when directed by 
 special technical Methods, of which in the pres- 
 ent book we must give a brief view. In this 
 more technical form, the observation of facts in- 
 volves the Measurement of Phenomena ; and the 
 Colligation of Facts includes all arts and rules by 
 which the process of Induction can be assisted. 
 Hence we shall have here to consider Methods 
 of Observation, and Methods of Induction, us- 
 ing these phrases in the widest sense. The sec- 
 ond of the three steps above mentioned, the 
 Explication of our Conceptions, does not admit 
 of being much, assisted by methods, although 
 
 
254 APPENDIX A. 
 
 something may be done by Education and Dis- 
 cussion. 
 
 The Methods of Induction, of which we have 
 to speak, apply only to the first step in our 
 ascent from phenomena to laws of Nature ; the 
 discovery of Laws of Phenomena. A higher and 
 ulterior step remains behind, and follow in natu- 
 ral order the discovery of Laws of Phenomena ; 
 namely, the Discovery of Causes ; and this must 
 be stated as a distinct and essential process in a 
 complete view of the course of science. Again, 
 when we have thus ascended to the causes of 
 phenomena and of their laws, we can often rea- 
 son downwards from the cause so discovered ; 
 and we are thus led to suggestions of new phe- 
 nomena, or to new explanations of phenomena 
 already known. Such proceedings may be termed 
 Applications of our discoveries ; including in 
 the phrase, Verifications of our Doctrines by 
 such an application of them to observed facts. 
 
 Hence we have the following series of pro- 
 cesses concerned in the formation of science. 
 
 (1.) Decomposition of Facts ; 
 
 (2.) Measurement of Phenomena ; 
 Explication of Conceptions ; 
 Induction of Laws of Phenomena ; 
 Induction of Causes ; 
 
 ) Application of Inductive Discoveries, 
 f these six processes, the methods by which 
 the second and fourth may be assisted are here 
 our peculiar object of attention. The treat- 
 ment of these subjects in the present work must 
 necessarily be scanty and imperfect, although we 
 
APPENDIX A. 255 
 
 may perhaps be able to add something to what 
 has hitherto been systematically taught on these 
 heads. Methods of Observation and of Induc- 
 tion might of themselves form an abundant sub- 
 ject for a treatise, and hereafter probably will do 
 so, in the hands of future writers. A few re- 
 marks, offered as contributions on this subject, 
 may serve to show how extensive it is, and how 
 much more ready it now is than it ever before 
 was, for a systematic discussion. 
 
 Of the above steps of the formation of sci- 
 ence, the first, the Decomposition of Facts, has 
 already been sufficiently explained in the last 
 Book : for if we pursue it into further detail and 
 exactitude, we find that we gradually trench upon 
 some of the succeeding parts. I, therefore, pro- 
 ceed to treat of the second step, the Measure- 
 ment of Phenomena ; of Methods by which 
 this work, in its widest sense, is executed, and 
 these I shall term Methods of Observation. 
 
 7. From Bowen's Logic, ed. 1874, pp. 30-38. 
 
 Logic is the Science of the Necessary Laws of 
 Pure Thought, . . . that is, it treats of 
 Language so far only as this is the vehicle of 
 Thought. Just the reverse is true of the science 
 of Grammar, which treats primarily of Language, 
 and only secondarily of Thought. Logic might 
 be called the Grammar of Thought. . 
 Pure, or, as it is sometimes termed, Formal 
 Thought, is the mere process of thinking, irre- 
 spective of what we are thinking about. It 
 has already been said that the Acquisitive or 
 Perceptive Faculty furnishes " the Matter," while 
 
256 APPENDIX A. 
 
 the Understanding supplies " the Form," of our 
 knowledge. This distinction between Matter 
 and Form is one of considerable importance in 
 the history of philosophy. The former is the 
 crude material or the stuff of which anything 
 consists, or out of which it is made ; while the 
 latter is the peculiar shape or modification given 
 to it by the artist, whereby it has become this 
 particular thing which it is, and not something 
 else which might have been fashioned out of the 
 same substance. Thus, wood is the Matter of 
 the desk on which I am writing, whilst the Form 
 is that which entitles it to be called a desk, rather 
 than a table or a chair. Vocal sound is the 
 Matter, of speech, and articulation is its Form. 
 It is evident that these are two correlative no- 
 tions, each of which implies the other : Matter 
 cannot exist except under some Form, and there 
 cannot be any Form except of some given Mat- 
 ter. But though the two cannot actually be sep- 
 arated, the mind can consider each separately 
 through that process, called abstraction, whereby 
 the attention is wholly given to the one to the 
 exclusion of the other. We may think sepa- 
 rately of the attributes which are common to a 
 whole class of Forms, disregarding altogether, 
 for the moment, the Matter of which each of 
 them really consists. Borrowing algebraic 
 symbols, the Matter in each case may be desig- 
 nated by a letter of the alphabet, the peculiar 
 significance of which is, that it stands for any 
 Matter whatever, and not for any one in partic- 
 ular. Thus, A is B, is the Form of an affirma- 
 
APPENDIX A. 257 
 
 tive judgment, wherein A and B stand for any 
 two Concepts whatever. Hence, whatever is true 
 of the general formula, A is B, will be true also 
 of any such particular instances, as Iron is mallea- 
 ble, Trees are plants, etc., wherein the Form is 
 associated with some particular Matter. In say- 
 ing, then, that Logic is concerned only with the 
 Forms of Thought, or Pure Thought, or Thought 
 in the abstract, for all these expressions signify 
 the same thing, we mean only, that what is Ma- 
 terial in Thought is extralogical, and, as logi- 
 cians, we have nothing to do with it ; just as 
 the geometer has nothing to do with the partic- 
 ular diagram on the paper before him, except sa 
 far as it is a symbol, or universal Form, of all pos- 
 sible figures of the same general character. . . . 
 
 Again, the definition of Logic assumes that 
 the process of Thinking, like every other opera- 
 tion in nature, does not take place at random, 
 but according to certain fixed Laws or invariable 
 modes of procedure. There could be no com- 
 munication of Thought from one mind to an- 
 other, if the process of Thinking in all minds 
 were not subject to the same general rules. We 
 follow these laws for the most part unconscious- 
 ly, as a distinct recognition of them is not by 
 any means necessary for correct thinking ; just 
 so, many persons speak and write correctly 
 without any knowledge of the grammarian's 
 rules. . . . 
 
 Properly speaking, Pure Logic terminates 
 with the consideration of the three classes of 
 products namely, Concepts, Judgments, and 
 
258 APPENDIX A. 
 
 Reasonings which are the elements into which 
 all Thought is resolved. But Thought itself is 
 subsidiary to the attainment of knowledge, that 
 is, to Science. The question remains, then, 
 after we have fully treated of Concepts, Judg- 
 ments, and Reasonings, taken separately or con- 
 sidered in themselves alone, what use is to be 
 made of them, taken together, in the construc- 
 tion of Science. A full answer to this question, 
 as it would involve a study of the objects of 
 Science, that is, of the matter of the special 
 sciences, evidently falls outside of the province 
 of Logic. But a partial answer to it, regarding 
 Science in its relation, not to the objects known, 
 but to the knowing mind, may be considered as 
 a natural appendage to Logic, as it embraces the 
 conditions not merely of possible, but of perfect, 
 Thought. Such an answer is usually called the 
 Doctrine of Method, or Logical Methodology. 
 Pure Logic considers only the Necessary Laws 
 to which all Thought must conform ; the Doc- 
 trine of Method regards those rules and princi- 
 ples to which all Thought ought to conform in 
 order to obtain its end, which is the advance- 
 ment of Science. Pure Logic treats merely of 
 the elements of Thought, while Logical Method- 
 ology regards the proper arrangement of these 
 elements into an harmonious whole. All Method 
 is a well-defined progress towards some end ; 
 and the end in this case is the attainment of 
 truth. Practically speaking, the Doctrine of 
 Method is a body of rules or precepts looking to 
 the proper regulation of the Thinking Faculty 
 
QUOTATIONS ON METHOD. 259 
 
 in the pursuit of knowledge ; and, as such, it 
 necessarily lacks the precision and the demon- 
 strative certainty which are characteristic of the 
 principles of Pure Logic. The laws of Pure 
 Thought are absolute ; the merits of Perfect 
 Thought are various, and attainable in different 
 degrees, according to circumstances. 
 
 Another distinction has been taken, in this 
 science, between Pure and Applied Logic, or as 
 Sir William Hamilton prefers to call the latter, 
 Modified Logic. The former, as we have seen, 
 considers the Thinking Faculty alone, as if it 
 constituted the whole of the human mind, and 
 therefore as if its Laws and Products were unaf- 
 fected by any collateral and disturbing influences, 
 but were manifested in precisely the same man- 
 ner by different persons. It takes no account of 
 the defects and hinderances which obstruct the 
 normal action of the understanding. Modified 
 Logic, on the other hand, considers Thought as 
 it is, and not merely as it ought to be. It re- 
 gards ' i the Causes of Error and the Impediments 
 to Truth by which man is beset in the employ- 
 ment of his Faculties, and what are the means 
 of their removal." And yet it is a universal 
 science, as much so as Pure Logic ; for it 
 does not consider the Matter of Thought. . 
 . . . But Modified Logic is not properly called 
 Logic, as it is a branch of Psychology, which 
 treats of the phenomena of mind in general, and 
 not merely of the normal action and necessary 
 laws of one special faculty, the Understanding. 
 As Modified Logic, however, is nearly allied in 
 
260 QUOTATIONS OK METHOD. 
 
 purpose with the Doctrine of Method, both look- 
 ing to the same general end, the attainment of 
 truth through the proper regulation of the Think- 
 ing Faculty, the two may well be considered 
 together, under the general name of Applied 
 Logic, as a kind of supplement to the science 
 properly so called. 
 
 8. From Outlines of Ontological Science, by 
 H. N. Day, ed. 1878, pp. 123 and following. 
 
 The very conception of method involves, to- 
 gether with something that changes, a source or 
 origin from which the change begins ; an end or 
 goal in which it rests or to which it tends ; and 
 a way by which the end is reached from the be- 
 ginning. 
 
 A rational method, moreover, implies a unity 
 of nature and imposes a unity on each of 
 the fundamental elements of true method. It 
 prescribes the right movement from some single 
 source, to some single end, by some single way. 
 Its function is discharged when it indicates this 
 movement and directs it as to such single source, 
 end, and way. 
 
 We have found in all knowledge a twofold, a 
 subjective and an objective element a knowing 
 and a known. A rational method respects the 
 change in both aspects. At every stage of prog- 
 ress, in all true and right knowledge the corre- 
 spondence between these two constituents is main- 
 tained perfect and exact. The subjective con- 
 stituent increases by the growth effected through 
 exercise in a living agent ; and the objective 
 constituent increases in exact correspondence ; 
 
QUOTATIONS ON METHOD. 261 
 
 the capacity of knowing is enlarged and intensi- 
 fied as the matter known is broadened and deep- 
 ened. The view of method, however, will be 
 modified according as the one or the other of 
 these constituents is prominently regarded. We 
 conveniently distinguish, accordingly, a subjec- 
 tive and an objective method in knowl- 
 edge. . . . 
 
 The subjective method in knowledge respects- 
 the knowing subject. The source or origin here 
 is ever the knowing power or function itself at 
 each of the ever advancing stages of its progress. 
 
 The end or goal is primarily the perfection 
 of the knowing faculty, and through that the 
 perfection, according to its nature, of the whole 
 organism of which this faculty is a part ; a 
 goal ever aimed at, but never reached as a final 
 knowing, yet in each specific act of knowing 
 attained in its own proper degree and measure. 
 
 The way is by a continuous endeavor in ac- 
 cordance with the laws of thinking or knowing, in, 
 which each new measure of thinking energy at- 
 tained is made the occasion and means of a still 
 more vigorous life of thought. This is prescrib- 
 ed by the principle of adjacence ; continuousness- 
 is but progress from next to next in order of 
 proximity or adjacence. 
 
 The objective method in knowledge respects 
 the matter known. 
 
 The beginning in knowledge here is the datum 
 presented to thought. This datum must be of 
 the nature of that which can be known ; must be 
 of the nature of truth. Every fresh attainment 
 of truth adds so much to the volume of attain- 
 
262 QUOTATIONS OK METHOD. 
 
 ment which, with what is given on each succes- 
 sive occasion of thought, constitutes the datum 
 for the succeeding stage. 
 
 The objective end in knowledge is truth ac- 
 quired in its complete fulness and comprehensive- 
 ness the universe of truth ; an end never fully 
 reached, yet in its measure attained in every new 
 acquisition. 
 
 The way in objective knowledge is in unde- 
 viating course through the adjacent fields of truth, 
 from boundary through to boundary, avoiding, as 
 far as may be, under the conditions of human 
 life, skips and divisions and devious windings. 
 
 9. From Comte's Philosophy of the Sciences, 
 G. H. Lewes, London, 1853. 
 
 Atheists may therefore be regarded as the 
 most illogical of theologians, since they attempt 
 the theological problems while rejecting the only 
 suitable method, (p. 25.) 
 
 That the positive Method is the only Method 
 adapted to human capacity, the only one on which 
 truth can be found, is easily proved : on it alone 
 can prevision of phenomena depend, (p. 39.) 
 
 The present condition of science, therefore, 
 exhibits three ^lethods instead of one : hence the 
 anarchy. 
 
 To remedy the evil, all differences must cease : 
 one Method must preside, (p. 38.) 
 
 In passing from one science to another, we 
 discover the several modifications which method 
 (essentially the same in all) undergoes. 
 
 A proper knowledge of the positive method 
 can only be acquired in this way. (p. 49.) 
 
 I propose to call the relations of co-existence 
 
QUOTATIONS ON METHOD. 263 
 
 and succession, usually named Laws, by the 
 name of Methods. 
 
 Etymologically, Method is a path leading on- 
 wards, a way of transit. The Methods of Na- 
 ture would therefore express the paths along 
 which the activities of Nature travelled to results 
 (phenomena), (p. 55.) 
 
 What we call Laws are nothing but the paths, 
 or Methods, along which the Forces (of Nature) 
 move. (p. 57.) 
 
 Astronomy is more truly scientific and has at- 
 tained the highest degree of philosophical perfec- 
 tion that any science can ever pretend to, as re-' 
 spects Method, the exact reduction of all phe- 
 nomena, both in kind and in degree, to one gen- 
 eral law (solar astronomy), (p. 83.) 
 
 A law of Nature can only be discovered by In- 
 duction or Deduction. Often, however, neither 
 method is of itself sufficient, (p. 105.) 
 
 The Methods in which these masses (suns, 
 planets, etc.) move, science attempts to ascer- 
 tain ; but in Astronomy we speak of Motion, in 
 Chemistry of Combination ; both are Methods of 
 the unknown unknowable Force, (p. 113.) 
 
 The methods by which the construction of 
 science is promoted are, Methods of Observation, 
 Methods of obtaining clear Ideas, and Methods 
 of Instruction, (p. 141.) (Whewell.) 
 
 The methods of observation of quantity in 
 general are, Numeration, which is precise by the 
 nature of number : the Measurement of Space 
 and Time, by which aids the Measurement of the 
 other ; the Method of Repetition ; the Method 
 of Coincidences or Interferences. (p. 145.) 
 (Whewell.) 
 
QUOTATIONS ON SYSTEM. 
 
 APPENDIX B. 
 
 226. From Fleming Vocabulary of Philos- 
 ophy, ed. 1867. 
 
 SYSTEM is a full and connected view of all the 
 truths of some department of knowledge. An 
 organized body of truth, or truths arrange 
 under one and the same idea, which idea is as 
 the life or soul which assimilates all those truths. 
 No truth is altogether isolated. Every truth 
 has relation to some other. And we should 
 try to unite the facts of our knowledge so as to 
 see them in their several bearings. This we do 
 when we frame them into a system. To do so 
 legitimately we must begin by analysis and end 
 with synthesis. But system applies not only to 
 our knowledge, but to the objects of our knowl- 
 edge. Thus we speak of the planetary system, 
 the muscular system, the nervous system. We 
 believe that the order to which we would reduce 
 our ideas has a foundation in the nature of 
 things. And it is this belief that encourages us 
 to reduce our knowledge of things into a system- 
 atic order. The doing so is attended with many 
 advantages. At the same time a spirit of sys- 
 tematizing may be carried too far. It is only in 
 so far as it is in accordance with the order of na- 
 
QUOTATIONS OK SYSTEM. 265 
 
 ture that it can be useful or sound. Condillac 
 has a Traite des Systemes, in which he traces 
 their causes and their dangerous consequences. 
 
 SYSTEM, ECONOMY, OR CONSTITUTION. "A 
 System, Economy, or Constitution, is a one or 
 a whole, made up of several parts, but yet that 
 the several parts even considered as a whole do 
 not complete the idea, unless in the notion of the 
 whole you include the relations and respects 
 which these parts have to each other. Every 
 work, both of nature and of art, is a system ; and 
 as every particular thing, both natural and artifi- 
 cial, is for some use or purpose out of and beyond 
 itself, one may add to what has been already 
 brought into the idea of a system, its conducive- 
 ness to this one or more ends. Let us instance 
 in a watch suppose the several parts of it taken 
 to pieces, and placed apart from each other ; let 
 a man have ever so exact a notion of these several 
 parts, unless he considers the respects and relations 
 which they have to each other, he will not have 
 anything like the idea of a watch. Suppose these 
 several parts brought together and anyhow united : 
 neither will he yet, be the union ever so close, 
 have an idea which will bear any resemblance to 
 that of a watch. But let him view these several 
 parts put together, or consider them as to be put 
 together in the manner of a watch ; let him form 
 a notion of the relations which these several parts 
 have to each other all conducive in their re- 
 spective ways to this purpose, showing the hour 
 of the day ; and then he has the idea of a watch. 
 Thus it is with regard to the inward frame of 
 
66 QUOTATIONS OK SYSTEM. 
 
 man. Appetites, passions, affections, and the 
 principle of reflection, considered merely as the 
 several parts of our inward nature, do not give us 
 an idea of the system or constitution of this 
 nature ; because the constitution is formed by 
 somewhat not yet taken into consideration, 
 namely, by the relations which these several 
 parts have to each other, the chief of which is 
 the authority of reflection or conscience. It is 
 from considering the relations which the several 
 appetites and passions in the inward frame have 
 to each other, and, above all, the supremacy of 
 reflection or conscience, that we get the idea of 
 the system or constitution of human nature. 
 And from the idea itself it will as fully appear, 
 that this our nature, i.e., constitution, is adapted 
 to virtue, as from the idea of a watch it appears 
 that its nature, i.e., constitution or system, is 
 adapted to measure time." 
 
QUOTATIONS ON ANALYSIS. 
 
 APPENDIX C. 
 
 227. From Fleming's Vocabulary of Philos- 
 ophy, ed. 1867. 
 
 ANALYSIS and SYNTHESIS, or decomposition and 
 recomposition. Objects of sense and of thought 
 are presented to us in a complex state, but we can 
 only, or at least best, understand what is simple. 
 Among the varied objects of a landscape, I be- 
 hold a tree, I separate it from the other objects, 
 I examine separately its different parts trunk, 
 branches, leaves, etc., and then reuniting them 
 into one whole I form a notion of the tree. The 
 first part of this process is analysis, the second 
 is synthesis. If this must be done with an indi- 
 vidual, it is more necessary with the infinitude 
 of objects which surround us, to evolve the one 
 out of many, to recall the multitude to unity. 
 We compare objects with one another to see 
 wherein they agree ; we next, by a synthetical 
 process, infer a general law, or generalize the co- 
 incident qualities, and perform an act of induction 
 which is purely a synthetical process, though 
 commonly called analytical. Thus, from our ex- 
 perience that bodies attract within certain limits, 
 we infer that all bodies gravitate towards each 
 other. The antecedent here only says that cer- 
 
268 QUOTATIONS OK ANALYSIS. 
 
 tain bodies gravitate, the consequent says all bod- 
 ies gravitate. They are brought together by the 
 mental insertion of a third proposition, which is, 
 * i that nature is uniform. ' ' This is not the 
 product of induction, but antecedent to all in- 
 duction. The statement fully expressed is, this 
 and that body, which we know, gravitate, but 
 nature is uniform ; this and that body repre- 
 sent all bodies all bodies gravitate. It is the 
 mind which connects these things, and the pro- 
 cess is synthetical. This is the one universal 
 method in all philosophy, and different schools 
 have differed only in the way of employing it. 
 Method is the following of one thing through 
 another. Order is the following of one thing 
 after another. Analysis is real, as when a 
 chemist separates two substances. Logical, as 
 when we consider the properties of the sides and 
 angles of a triangle separately, though we can- 
 not think of a triangle without sides and angles. 
 
 The instruments of analysis are observation 
 and experiment; of synthesis, definition and 
 classification. 
 
 Take down a watch, analysis ; put it up, syn- 
 thesis. 
 
 Analysis is decomposing what is compound to 
 detect its elements. Objects may be compound, 
 as consisting of several distinct parts united, or 
 of several properties equally distinct. In the 
 former view, analysis will divide the object into 
 its parts, and present them to us successively, and 
 then the relations by which they are united. In 
 the second case, analysis will separate the dis- 
 
QUOTATION'S ON ANALYSIS. 269 
 
 tinct properties, and show the relations of every 
 kind which may be between them. 
 
 Analysis is the resolving into its constituent 
 elements of a compound heterogeneous substance. 
 Thus, water can be analyzed into oxygen and hy- 
 drogen, atmospheric air into these and azote. 
 
 Abstraction is analysis, since it is decomposi- 
 tion, but what distinguishes it is that it is exer- 
 cised upon qualities which by themselves have 
 no real existence. Classification is synthesis. 
 Induction rests upon analysis. Deduction is 
 a synthetical process. Demonstration includes 
 both. 
 
QUOTATIONS ON SYNTHESIS. 
 
 APPENDIX D. 
 
 228. From Fleming's Vocabulary of Phi- 
 losophy, ed. 1867. 
 
 SYNTHESIS " consists in assuming the causes 
 discovered and established as principles, and by 
 them explaining the phenomena proceeding from 
 them and proving the explanation. ' ' 
 
 " Every synthesis which has not started with 
 a complete analysis ends at a result which, in 
 Greek, is called hypothesis ; instead of which, if 
 synthesis has been preceded by a sufficient 
 analysis, the synthesis founded upon that anal- 
 ysis leads to a result which in Greek is called 
 system. The legitimacy of every synthesis is 
 directly owing to the exactness of analysis; 
 every system which is merely an hypothesis is a 
 vain system ; every synthesis which has not been 
 preceded by analysis is a pure imagination : but 
 at the same time every analysis which does not 
 aspire to a synthesis which may be equal to it, 
 is an analysis which halts on the way. On the 
 one hand, synthesis without analysis gives a false 
 science ; on the other hand, analysis without 
 synthesis gives an incomplete science. An in- 
 complete science is a hundred times more valu- 
 
QUOTATIONS ON SYNTHESIS. 271 
 
 able than a false science ; but neither a false 
 science nor an incomplete science is the ideal of 
 science. The ideal of science, the ideal of phi- 
 losophy, can be realized only by a method which 
 combines the two processes of analysis and 
 synthesis, " 
 
QUOTATIONS ON DEFINITION. 
 
 APPENDIX E. 
 
 229. From Fleming's Vocabulary of Philos- 
 ophy, ed. 1867. 
 
 DEFINITION (definio, to mark out limits). 
 
 " The simplest and most correct notion of a 
 definition is, a proposition declaratory of the 
 meaning of a word. ' ' 
 
 Definition signifies " laying down a bound- 
 ary ;" and is used in Logic to signify " an ex- 
 pression which explains any term so as to sepa- 
 rate it from everything else, as a boundary sep- 
 arates fields. Logicians distinguish definitions 
 into Nominal and Real. 
 
 " Definitions are called nominal, which ex- 
 plain merely the meaning of the term ; and real, 
 which explain the nature of the thing signified 
 by that term. Logic is concerned with nominal 
 definitions alone. ' ' 
 
 " By a real, in contrast to a verbal or nomi- 
 nal definition, the logicians do not intend i the 
 giving an adequate conception of the nature and 
 essence of a thing ;' that is, of a thing considered 
 in itself, and apart from the conceptions of it 
 already possessed. By verbal definition is meant 
 the more accurate determination of the significa- 
 
QUOTATIONS ON DEFINITION. 273 
 
 tion of a word ; by real the more accurate deter- 
 mination of the contents of a notion. The one 
 clears up the relation of words to notions ; the 
 other of notions to things. The substitution of 
 notional for real would, perhaps, remove the 
 ambiguity. But if we retain the term real, the 
 aim of a verbal definition being to specify the 
 thought denoted by the word, such definition 
 ought to be called notional, on the principle on 
 which the definition of a notion is called real ; 
 for this definition is the exposition of what things 
 are comprehended in a thought. ' ' 
 
 " In the sense in which nominal and real 
 definitions were distinguished by the scholastic 
 logicians, logic is concerned with real, i.e., 
 notional definitions only ; to explain the mean- 
 ing of words belongs to dictionaries or gram- 
 mars. ' ' 
 
 i 1 There is a real distinction between definitions 
 of names and what are erroneously called defini- 
 tions of things ; but it is that the latter, along 
 with the meaning of a name, covertly asserts a 
 matter of fact. This covert assertion is not a 
 definition, but a postulate. The definition is a 
 mere identical proposition, which gives informa- 
 tion only about the use of language, and from 
 which no conclusions respecting matters of fact 
 can possibly be drawn. The accompanying pos- 
 tulate, on the other hand, affirms a fact which 
 may lead to consequences of every degree of im- 
 portance. It affirms the real existence of things, 
 possessing the combination of attributes set forth 
 in the definition, and this, if true, may be foun- 
 
274 QUOTATIONS ON DEFINITION. 
 
 dation sufficient to build a whole fabric of scien- 
 tific truth." 
 
 Real definitions are divided into essential and 
 accidental. An essential definition states what 
 are regarded as the constituent parts of the es- 
 sence of that which is to be defined ; and an ac- 
 cidental definition (or description) lays down 
 what are regarded as circumstances belonging to 
 it, viz., properties or accidents, such as causes, 
 effects, &c. 
 
 " Essential definition is divided into physical 
 (natural) and logical (metaphysical) ; the phy- 
 sical definition being made by an enumeration of 
 such parts as are actually separable ; such as are 
 the hull, masts, &c. , of a i ship ' ; the root, trunk, 
 branches, bark, &c., of a 'tree.' The logical 
 definition consists of the genus and difference, 
 which are called by some the metaphysical 
 (ideal) parts ; as being not two real parts into 
 which an individual object can (as in the former 
 case), be actually divided, but only different 
 views taken (notions formed) of a class of objects, 
 by one mind. Thus a magnet would be defined 
 logically, ' an iron ore having attraction for 
 iron/ " 
 
 Accidental or descriptive definition may be 
 1 . Causal ; as when man is defined as made 
 after the image of God, and for his glory. 2. 
 Accidental ; as when he is defined to be ani- 
 mal, bipes implume. 3. Genetic; as when the 
 means by which it is made are indicated ; as, if a 
 straight line fixed at one end be drawn round by 
 the other end so as to return to itself, a circle 
 
QUOTATIONS ON DEFINITION. 275 
 
 will be described. Or, 4. Per opposition ; as, 
 when virtue is said to be flying from vice. 
 
 The rules of a good definition are : 1. That it 
 be adequate. If .it be too narrow, you explain 
 a part instead of a whole ; if too extensive, a 
 whole instead of a part. 2. That it be clearer 
 (i.e., consist of ideas less complex) than the 
 thing defined. 3. That it be in just a sufficient 
 number of proper words. Metaphorical words 
 are excluded because they are indefinite. 
 
 2. From Mill's System of Logic, pp. 105-106, 
 8 edition. 
 
 The simplest and most correct notion of a 
 Definition is, a proposition declaratory of the 
 meaning of a word ; namely, either the meaning 
 which it bears in common acceptation, or that 
 which the speaker or writer, for the particular 
 purposes of his discourse, intends to annex to it. 
 .... This form of definition is the most pre- 
 cise and least equivocal of any ; but it is not 
 brief enough, and is besides too technical for 
 common discourse. The more usual mode of de- 
 claring the connotation of a name, is to predicate 
 of it another name or names of known significa- 
 tion, which connote the same aggregation of at- 
 tributes The definition of a name, ac- 
 cording to this view of it, is the sum total of all 
 the essential propositions which can be framed 
 with that name for their subject. All proposi- 
 tions the truth of which is implied in the name, 
 all those which we are made aware of by merely 
 hearing the name, are included in the definition, 
 if complete, and may be evolved from it without 
 
276 QUOTATIONS ON DEFINITION. 
 
 the aid of any other premises ; whether the defi- 
 nition expresses them in two or three words, or 
 in a larger number. It is, therefore, not with- 
 out reason that Condillac and other writers have 
 affirmed a definition to be an analysis. To re- 
 solve any complex whole into the elements of 
 which it is compounded, is the meaning of anal- 
 ysis : and this we do when we replace one word 
 which connotes a set of attributes collectively, by 
 two or more which connote the same attributes 
 singly, or in smaller groups. 
 
QUOTATIONS ON ABSTRACTION. 
 
 APPENDIX F. 
 
 230. From Fleming's Vocabulary of Philos- 
 ophy. 
 
 ABSTRACT, ABSTRACTION (abstractio, from 
 abs traho, to draw away from. It is also called 
 separatio and resolutio) . Dobrisch observes that 
 the term abstraction is used sometimes in a psy- 
 chological, sometimes in a logical sense. In the 
 former we are said to abstract the attention from 
 certain distinctive features of objects presented. 
 In the latter, we are said to abstract certain por- 
 tions of a given concept from the remainder. 
 (Mansel.) 
 
 1 ' ABSTRACTION (Psychological)/' says Mr. 
 Stewart, " is the power of considering certain 
 qualities or attributes of an object apart from the 
 rest ; or, as I would rather choose to define it, 
 the power which the understanding has of sepa- 
 rating the combinations which are presented to 
 it." Perhaps it may be more correctly regarded 
 as a process rather than a power as a function 
 rather than a faculty. Dr. Reid has called it ' i an 
 operation of the understanding. " . . . The 
 chemist separates into their elements those bodies, 
 which are submitted to his analysis. The psy- 
 
278 QUOTATIONS ON ABSTRACTION. 
 
 chologist does the same thing mentally. ... In 
 contemplating mind, he may think of its capacity 
 of feeling without thinking of its power of activ- 
 ity, or the faculty of memory apart from any or 
 all of the other faculties with which it is al- 
 lied. 
 
 ABSTRACTION (LOGICAL), " As we have de- 
 scribed it," says Mr. Thomson (Outline of the 
 Laws of Thought p. 107), " would include three 
 separate acts ; first, an act of comparison, which 
 brings several intuitions together ; next, one of 
 reflection, which seeks for some marks which 
 they all possess, and by which they may be com- 
 bined into one group ; and last, one of general- 
 ization, which forms the new general notion or 
 conception. Kant, however, confines the name 
 of abstraction to the last of the three ; others 
 apply it to the second. It is not of much conse- 
 quence whether we enlarge or narrow the mean- 
 ing of the word, so long as we see the various 
 steps in the process. The word means a draw- 
 ing away of the common marks from all the dis- 
 tinctive marks which the single objects have. " . . 
 Mr. J. S. Mill uses the term abstract as opposed 
 to concrete. By an abstract name he means the 
 name of an attribute by a concrete name the 
 name of an object. 
 
QUOTATIONS ON GENERALIZATION. 
 
 APPENDIX G. 
 
 231. 1. From Fleming's Vocabulary of Phi- 
 losophy, ed. 1867. 
 
 Generalization ' * is the act of comprehending, 
 under a common name, several objects agreeing" 
 in some point which we abstract from each of 
 them, and which that common name serves to in- 
 dicate." 
 
 " When we are contemplating several individ- 
 uals which resemble each other in some part of 
 their nature, we can (by attending to that part 
 alone, and not to those points wherein they 
 differ) assign them one common name, which will 
 express or stand for them merely as far as they 
 all agree ; and which, of course, will be appli- 
 cable to all or any of them (which process is 
 called generalization) ; and each of these names 
 is called a common term, from its belonging to 
 them all alike ; or a predicable, because it may 
 be predicated affirmatively of them or any of 
 them." 
 
 Generalization is of two kinds classification 
 and generalization properly so called. 
 
 When we observe facts accompanied by di- 
 verse circumstances, and reduce these circum- 
 
280 QUOTATIONS ON GENERALIZATION. 
 
 stances to such as are essential and common, we 
 obtain a law. 
 
 When we observe individual objects and ar- 
 range them according to their common charac 
 ters, we obtain a class. When the characters 
 selected are such as belong essentially to the na- 
 ture of the objects, the class corresponds with 
 the law. When the character selected is not 
 natural the classification is artificial. If we were 
 to class animals into white and red, we would 
 have a classification which had no reference to 
 the laws of their nature. But if we classify them 
 as vertebrate or invertebrate, we have a classi- 
 fication founded on their organization. Artificial 
 classification is of no value in science, it is a 
 mere aid to the memory. Natural classification 
 is the foundation of all science. This is some- 
 times called generalization. It is more properly 
 classification. 
 
 The law of gravitation is exemplified in the fall 
 of a single stone to the ground. But many stones 
 and other heavy bodies must have been observed 
 to fall before the fact was generalized, and the 
 law stated. And in this process of generalizing 
 there is involved a principle which experience 
 does not furnish. Experience, how extensive 
 soever it may be, can only give the particular, yet 
 from the particular we rise to the general, and 
 affirm not only that all heavy bodies which have 
 been observed, but that all heavy bodies whether 
 they have been observed or not, gravitate. In 
 this is implied a belief that there is order in na- 
 ture, that under the same circumstances the same 
 
QUOTATIONS ON GENERALIZATION. 281 
 
 substances will present the same phenomena. 
 This is a principle furnished by reason, the pro- 
 cess founded on it embodies elements furnished 
 by experience. 
 
 The results of generalization are general no- 
 tions expressed by general terms. Objects are 
 classed according to certain properties which they 
 have in common, into genera and species. 
 Hence arose the question which caused centuries 
 of acrimonious discussion. Have genera and 
 species a real, independent existence, or are they 
 only to be found in the mind ? 
 
 The principle of generalization is, that be- 
 ings howsoever different agree or are homo- 
 geneous in some respect. 
 
 2. From Jevon's Principles of Science, pp. 
 597-599, ed. 1877. 
 
 The term generalization, as commonly used, 
 includes two processes which are of different 
 character, but are often closely associated to- 
 gether. In the first place, we generalize when 
 we .recognize even in two objects a common na- 
 ture. We cannot detect the slightest similarity 
 without opening the way to inference from one 
 case to the other. If we compare a cubical crys- 
 tal with a regular octahedron, there is little ap- 
 parent similarity ; but, as soon as we perceive that 
 either can be produced by the symmetrical modi- 
 fication of the other, we discover a groundwork of 
 similarity in the crystals, which enable us to infer 
 many things of one, because they are true of the 
 other. Our knowledge of ozone took its rise 
 from the time when the similarity of smell, at- 
 
282 QUOTATIONS ON GENERALIZATION. 
 
 tending electric sparks, strokes of lightning, and 
 the slow combustion of phosphorus, was noticed 
 by Schonbein. There was a time when the rain- 
 bow was an inexplicable phenomenon a portent, 
 like a comet, and a cause of superstitious hopes 
 and fears. But we find the true spirit of science 
 in Roger Bacon, who desires us to consider the 
 objects which present the same colours as the rain- 
 bow ; he mentions hexagonal crystals from Ire- 
 land and India, but he bids us not suppose that 
 the hexagonal form is essential, for similar colours 
 may be detected in many transparent stones. 
 Drops of water scattered by the oar in the sun, 
 the spray from a water-wheel, the dewdrops lying 
 on the grass in the summer morning, all display 
 a similar phenomenon. No sooner have we 
 grouped together these apparently diverse in- 
 stances, than we have begun to generalise, and 
 have acquired a power of applying to one in- 
 stance what we can detect of others. Even when 
 we do not apply the knowledge gained to new 
 objects, our comprehension of those already ob- 
 served is greatly strengthened and deepened by 
 learning to view them as particular cases of a 
 more general property. 
 
 A second process, to which the name of gen- 
 eralization is often given, consists in passing from 
 a fact or partial law to a multitude of unexamined 
 cases, which we believe to be subject to the same 
 conditions. Instead of merely recognising sim- 
 ilarity as it is brought before us, we predict its 
 existence before our senses can detect it, so that 
 generalisation of this kind endows us with a 
 
QUOTATIONS ON GENERALIZATION. 283 
 
 prophetic power of more or less probability. 
 Having observed that many substances assume, 
 like water and mercury, the three states of solid, 
 liquid, and gas, and having assured ourselves by 
 frequent trial that the greater the means we 
 possess of heating and cooling, the more sub- 
 stances we can vaporise and freeze, we pass con- 
 fidently in advance of fact, and assume that all 
 substances are capable of these three forms. 
 Such a generalisation was accepted by Lavoisier 
 and Laplace before many of the corroborative 
 facts now in our possession were known. The 
 reduction of a single comet beneath the sway of 
 gravity was considered sufficient indication that 
 all comets obey the same power. Few persons 
 doubted that the law of gravity extended over 
 the whole heavens ; certainly the fact that a few 
 stars out of many millions manifest the action of 
 gravity, is now held to be sufficient evidence of 
 its general extension over the visible universe 
 
QUOTATIONS ON CLASSIFICATION. 
 
 APPENDIX H. 
 
 232. 1. From Fleming's Vocabulary of Phi - 
 losophy, ed. 1858, pp. 91-92. 
 
 " Montesquieu observed very justly, that in 
 their classification of the citizens, the great 
 legislators of antiquity made the greatest display 
 of their powers, and even soared above them- 
 selves. ' ' Burke, On the French Revolution. 
 
 " A class consists of several things coming 
 under a common description. ' ' Whately, Log. , 
 b. i., 3. 
 
 " The sorting of a multitude of things into 
 parcels, for the sake of knowing them better, 
 and remembering them more easily, is classifica- 
 tion. When we attempt to classify a multitude 
 of things, we first observe some respects in 
 which they differ from each other ; for we could 
 not classify things that are entirely alike ; as, 
 for instance, a bushel of peas ; we then separate 
 things that are not alike, and bring together 
 things that are similar." Taylor, Elements of 
 Thought. 
 
 " In every act of classification, two steps must 
 be taken ; certain marks are to be selected, the 
 possession of which is to be the title to admis- 
 
QUOTATIONS OK CLASSIFICATION. 285 
 
 sion into the class, and then all the objects that 
 possess them are to be ascertained. When the 
 marks selected are really important and con- 
 nected closely with the nature and functions of 
 the thing, the classification is said to be natu- 
 ral ; where they are such as do not affect the 
 nature of the objects materially, and belong in 
 common to things the most different in their 
 main properties, it is artificial." Thomson, 
 Outline of Laws of Thought, 2d edit., p. 377. 
 
 The condition common to both modes of clas- 
 sification, is to comprehend everything and to 
 suppose nothing. But the rules for a natural 
 classification are more strict than for an artificial 
 or arbitrary one. We may classify objects arbi- 
 trarily in any point of view in which we are 
 pleased to regard them. But a natural classifi- 
 cation can only proceed according to the real 
 nature and qualities of the objects. The advan- 
 tages of classification are to give a convenient 
 form to our acquirements, and to enlarge our 
 knowledge of the relations in which different ob- 
 jects stand to one another. A good classifica- 
 tion should 1st, Rest on one principle or analo- 
 gous principles. 2d, The principle or princi- 
 ples should be of a constant and permanent char- 
 acter. 3d, It should be natural, that is, even 
 when artificial, it should not be violent or 
 forced. 4th, It should clearly and easily apply 
 to all the objects classified. 
 
 The principles on which classification rests 
 are these: 1st, of Generalization; 2d, of 
 Specification ; and 3d, of Continuity. 
 
286 QUOTATIONS ON CLASSIFICATION. 
 
 Classification proceeds upon observed resem- 
 blances. Generalization rests upon the princi- 
 ple, that the same or similar causes will produce 
 similar effects. Mill, Log., b. i., chap. 7, 4 ; 
 McCosh, Typical Forms, b. iii., chap. 1. 
 
 2. From Jevons' Elementary Lessons in Logic, 
 ed. 1878, pp. 276-286. 
 
 It may be said that the subject we are treating 
 is coextensive with the science of logic. All 
 thought, all reasoning, so far as it deals with 
 general names or general notions, may be said 
 to consist in classification. Every common 
 name or general name is the name of a class, and 
 every name of a class is a common name. 
 " Metal " is the name of one class of substantives 
 so often used in our syllogistic examples ; 
 * ' Element' ' of another class, of which the former 
 class is part. Reasoning has been plausibly rep- 
 resented to consist in affirming of the parts of a 
 class whatever may be affirmed of the whole. 
 Every law of nature which we arrive at enables 
 us to classify together a number of facts, and it 
 would hardly be too much to define logic as the 
 theory of classification. . . . Classification 
 may perhaps be best defined as the arrange- 
 ment of things, or our notions of them, accord- 
 ing to their resemblances, or identities. 
 
 Every class should so be constituted as to con- 
 tain objects exactly resembling each other in 
 certain definite qualities, which are stated in the 
 definition of the class. The more numerous and 
 extensive the resemblances which are thus indi- 
 
QUOTATIONS ON CLASSIFICATION. 28? 
 
 cated by any system of classes, the more perfect 
 and useful must that system be considered. 
 
 Mr. Mill thus describes his view of the mean- 
 ing i ' Classification is a contrivance for the best 
 possible ordering of the ideas of objects in our 
 minds ; for causing the ideas to accompany or 
 succeed one another in such a way as shall give 
 us the greatest command over our knowledge 
 already acquired, and lead most directly to the 
 acquisition of more. The general problem of 
 classification, in reference to these purposes may 
 be stated as follows : To provide that things shall 
 be thought of in such groups, and those groups 
 in such an order, as will best conduce to the re- 
 membrance, and to the ascertainment .of their 
 laws." 
 
 A collection of objects may be classified in an 
 indefinite number of ways. Any quality which 
 is possessed by some and not by others may be 
 taken as the first difference, and the groups thus 
 distinguished may be subdivided in succession by 
 any other qualities taken at will. Thus a library 
 of books might be arranged, (1) according to 
 size, (2) according to the language in which 
 they are written, (3) according to the alphabetic 
 order of their authors' names, (4) according 
 to their subjects ; and in various other ways. 
 In large libraries and in catalogues such modes 
 of arrangement are adopted and variously com- 
 bined. . . . The population of a kingdom, again, 
 may be classified in an almost endless number of 
 ways with regard to different purposes or sci- 
 ences. The population of the United Kingdom 
 
288 QUOTATIONS ON CLASSIFICATION. 
 
 may be divided according to their place of birth, 
 as English, Welsh, Scotch, Irish, Colonial -born 
 and aliens. The ethnographer would divide 
 them into Anglo-Saxons, Cymri, Gaels, Picts, 
 &c. The statist arranges them according to age ; 
 to condition, as married, unmarried, widowed, 
 etc. ; to state of body, as able, incapacitated, 
 blind, imbecile. . . . 
 
 In the natural world, again, we may mak^ va- 
 rious classifications. Plants may be arranged 
 according to the country from which they are 
 derived ; the kind of place or habitat in which 
 they flourish ; the time they live, as annual, 
 biennial, perennial ; their size, as herbs, shrubs, 
 trees ; their properties, as esculents, drugs, or 
 poisons : all these are distinct from the classifi- 
 cations which the botanist devises to represent 
 the natural affinities or relationships of plants. 
 It is thus evident that in making a classification 
 we have no one fixed method which can be ascer- 
 tained by rule, but that an indefinite number of 
 choices or alternatives are usually open to us. 
 Logic cannot in such cases do much ; and it is 
 really the work of the special sciences to investi- 
 gate the character of the classification required. 
 All that logic can do is to point out certain gen- 
 eral requirements and principles. 
 
 The first requisite of a good classification is, 
 that it should be appropriate to the purpose in 
 hand ; that is to say, the points of resemblance 
 selected to form the leading classes shall be those 
 of importance to the practical use of the classifi- 
 cation. All those things must be arranged to- 
 
QUOTATIONS ON CLASSIFICATION. 289 
 
 gether which require to be treated alike, and 
 those things must be separated which require to 
 be treated separately. ... 
 
 Another and, in a scientific point of view, 
 the most important requisite of a good classifica- 
 tion, is that it shall enable the greatest possi- 
 ble number of general assertions to be made. 
 This is the criterion, as stated by Dr. Whewell, 
 which distinguishes a natural from an artificial 
 system of classification, and we must carefully 
 dwell upon its meaning. It will be apparent 
 that a good classification is more than a mere 
 orderly arrangement ; it involves a process of 
 induction which will bring to light all the more 
 general relations which exist between the things 
 classified. An arrangement of books will gen- 
 erally be artificial ; the octavo volumes will not 
 have any common character except being of an 
 octavo size. An alphabetical arrangement of 
 names again is exceedingly appropriate and con- 
 venient to many purposes, but is artificial because 
 it allows of few or no general assertions. We 
 cannot make any general assertions whatever 
 about persons because their names happen to 
 begin with an A or a B, a P or a W. 
 
 In a classification of plants again we meet 
 with most deep and natural distinctions between 
 the great classes called Exogens, Endogens, and 
 Acrogens. . . . These are the very widest 
 classes in what is called the natural system of 
 botanical arrangement; but similar principles 
 are observed in all its minor classes. 
 
 The continual efforts of botanists are directed 
 
290 QUOTATIONS ON" CLASSIFICATION. 
 
 to bringing the great multitudes of plants to- 
 gether in species, genera, orders, classes, and in 
 various intermediate groups, so that the members 
 of each group shall have the greatest number of 
 points of mutual resemblance and the fewest 
 points of resemblance to members of other 
 groups. Thus is best fulfilled the great purpose 
 of classification, which reduces multiplicity to 
 unity, and enables us to infer of all the other 
 members of a class what we know of any one 
 member, provided we distinguish properly be- 
 tween those qualities which are likely or are 
 known to belong to the class, and those which 
 are peculiar to the individual. It is a necessary 
 condition of correct classification, as remarked by 
 Prof. Huxley, that the definition of a group 
 shall hold exactly true of all the members of a 
 group, and not of the members of any other 
 group. . . . 
 
 Natural classifications give us the deepest re- 
 semblances and relations, and may lead us ulti- 
 mately to a knowledge of the way in which the 
 varieties of things are produced. They are, 
 therefore, essential to a true science, and may al- 
 most be said to constitute the framework of the 
 science. . . . 
 
 Closely connected with the process of Classifi- 
 cation is that of abstraction. To abstract is to 
 separate the qualities common to all individuals 
 -of a group from the peculiarities of each individ- 
 ual. The notion " triangle" is the result of ab- 
 straction in so far as we can reason concerning 
 triangles, without any regard to the particular 
 
QUOTATIONS ON CLASSIFICATION. 291 
 
 size or shape of any one triangle. All classifica- 
 tion implies abstraction, for in framing and 
 defining the class I must separate the common 
 qualities from the peculiarities. When I ab- 
 stract, too, I form a general conception, or one, 
 which, generally speaking, embraces many ob- 
 jects. If, indeed, the quality abstracted is a pe- 
 culiar property of the class, or one which belongs 
 to the whole and not to any other objects, I 
 may not increase the extent of the notion, so that 
 Mr. Herbert Spencer is, perhaps, right in holding 
 that we can abstract without generalizing. 
 We often use this word generalization, and 
 the process may be defined as inferring of a whole 
 class what we know only of a part. Whenever 
 we regard the qualities of a thing as not confined 
 to that thing only but as extended to other ob- 
 jects ; when, in fact, we consider a thing only 
 as a member of a class, we are said to generalize. 
 . . . Dr. Whewell added to the superabundance 
 of terms to express the same processes when he 
 introduced the expression Colligation of facts. 
 
 Whenever two things are found to have simi- 
 lar properties so as to be placed in the same 
 class they may be said to be connected to- 
 gether. 
 
 We connect together the places of a planet as 
 it moves round the sun, when we conceive them 
 as points upon a common ellipse. Whenever 
 we thus join together previously disconnected 
 facts, by a suitable general notion or hypothesis, 
 we are said to colligate them. Dr. Whewell 
 
292 QUOTATIONS ON CLASSIFICATION. 
 
 adds that the general conceptions employed must 
 be (1) clear, and (2) appropriate ; but it may 
 well be questioned whether there is anything 
 really different in these processes from the gen- 
 eral process of natural classification which we 
 have considered. 
 
QUOTATIONS ON INDUCTION. 
 
 APPENDIX I. 
 
 233. 1. From Smith Synonyms Discrimi- 
 nated " Inference" ed. 1878. 
 
 Inference (Lat. in, and ferre, to bring) is the 
 broadest of these terms (see below), denoting any 
 process by which from one truth or fact laid down 
 or known we draw another. Inference may be 
 either by induction or deduction, and hence may 
 be probable or certain. Inference by induction 
 is more or less probable, except where all cases 
 of the kind have been collated, when it ceases, 
 strictly speaking, to be inference, and is only the 
 assigning of a common name, or stating an uni- 
 versal proposition. From having seen twenty 
 swans all white, one might infer that all swans 
 are so. This would be only a probability in it- 
 self, and, as a fact, not true. In induction we 
 observe a sufficient number of individual facts 
 or cases, and extending by analogy what is true 
 of them to others of the same class, establish a 
 general principle or law. This is the method of 
 physical science. The process of deduction is 
 the converse of this. We lay down a general 
 truth, and connect a particular case with it by 
 means of a middle term. When inference is 
 
294 QUOTATIONS OK INDUCTION. 
 
 conducted by the syllogistic process, it is Deduc- 
 tion (Lat. deducere, to draw from), which, if 
 rightly conducted, must be logically sound, 
 though not necessarily true in fact. In a chain 
 of reasoning the minor, subordinate, or less 
 fully-expressed conclusions are called inferences, 
 as distinguished from the great common infer- 
 ence or Conclusion, which terminates and estab- 
 lishes, or, as it were, shuts up (Concludere, to 
 shut) the argument. A conclusion is a proposi- 
 tion viewed relatively to others from which it has 
 been deduced. A Consequence (Lat. consequi, 
 to follow) is a conclusion regarded as admitting 
 of degrees of closeness or directness. Between 
 the first stage of any argument and any particu- 
 lar consequence several links of reasoning may 
 intervene. Hence the common phrase, * ' remote 
 consequences," as meaning results which will 
 follow sooner or later from what has been stated 
 or conceded. 
 
 2. From Day's Elements of Logic, ed. 1868, 
 p. 226. 
 
 The accepted characteristics of Induction 
 are : 
 
 (a) It is a process of Thought that is identical 
 in essential character in all those movements of 
 Intelligence which induce, which infer mediately 
 otherwise than by deduction. There is but one 
 Induction, as there is but one Deduction in all 
 Thought. 
 
 (6) It is a reasoning, being a derivative Judg- 
 ment, not a Concept ; an inference from a 
 datum, implying a new proper Judgment-Cog- 
 
QUOTATIONS ON INDUCTION. 295 
 
 nition, not a mere synthesis of subjects or of 
 predicates that is, not a Concept. 
 
 (c) It is a mediate reasoning, being derived not * 
 from a single Judgment, but from a plurality of 
 Judgments, related to each other under the rela- 
 tionship of part to complementary part in two 
 of their terms which are alike related to the 
 third or middle term as parts to a whole. 
 
 3. From Fleming's Vocabulary of Philosophy, 
 ed. 1858, pp. 252-254. 
 
 Method or Process of Induction. " It has 
 been said that Aristotle attributed the discovery 
 of induction to Socrates, deriving the word 
 from the Socratic accumulation of instances, 
 serving as antecedents to establish the requisite 
 conclusion. " Devey, Log., p. 151, note. 
 
 Induction is a kind of argument which infers, 
 respecting a whole class, what has been ascer- 
 tained respecting one or more individuals of that 
 class. Whately, Log., book ii., chap. 5, 5. 
 
 "Induction is that operation of mind by 
 which we infer that what we know to be true in 
 a particular case or cases, will be true in all cases 
 which resemble the former in certain assignable 
 respects. In other words, induction is the pro- 
 cess by which we conclude that what is true of 
 certain individuals of a class, is true of the whole 
 class, or that what is true at certain times will be 
 true under similar circumstances at all times. " 
 Mill, Log., b. iii., ch. 2, 1. 
 
 " Induction is usually denned to be the pro- 
 cess of drawing a general rule from a sufficient 
 number of particular cases ; deduction is the 
 
296 QUOTATIONS OJS INDUCTION. 
 
 converse process of proving that some property 
 belongs to the particular case from the consider- 
 ation that it belongs to the whole class in which 
 the case is found. That all bodies tend to fall 
 towards the earth is a truth which we have ob 
 tained from examining a number of bodies com- 
 ing under our notice, by induction ; if from this 
 general principle we argue that the stone we 
 throw from our hand will show the same ten- 
 dency, we adopt the deductive method. . . . 
 More exactly, we may define the inductive 
 method as the process of discovering laws and 
 rules from facts, and causes from effects ; and 
 the deductive, as the method of deriving facts 
 from laws and effects from their causes." 
 (Thomson, Outline of the Laws of Thought, 2d 
 edit., pp. 321, 323.) 
 
 According to Sir William Hamilton (Discus- 
 sions, p. 156), "Induction has been employed 
 to designate three very different operations 1. 
 The objective process of investigating particular 
 facts, as preparatory to induction, which is not 
 a process of reasoning of any kind. 2. A ma- 
 terial illation of the universal from the singular, 
 as warranted either by the general analogy of 
 nature, or the special presumptions afforded by 
 the object-matter of any real science. 3. A for- 
 mal illation of the universal from the individual, 
 as legitimated solely by the laws of thought, and 
 abstract from the conditions of this or that ' par- 
 ticular matter. ' The second of these is the in- 
 ductive method of Bacon, which proceeds by way 
 of rejections and conclusions, so as to arrive at 
 
QUOTATIONS ON INDUCTION. 297 
 
 those axioms or general laws from which we infer 
 by way of synthesis other particulars unknown 
 to us, and perhaps placed beyond reach of direct 
 examination. Aristotle's definition coincides 
 with the third, and * induction is an inference 
 drawn from all the particulars ' (Prior Analyt., 
 ii., c. 23). The second and third have been 
 confounded. But the second is not a logical pro- 
 cess at all, since the conclusion is not necessarily 
 inferrible from the premiss, for the some of the 
 antecedent does not necessarily legitimate the all 
 of the conclusion, notwithstanding that the pro- 
 cedure may be warranted by the material problem 
 of the science or the fundamental principles of 
 the human understanding. The third alone is 
 properly an induction of Logic ; for Logic does 
 not consider things, but the general forms of 
 thought under which the mind conceives them ; 
 and the logical inference is not determined by 
 any relation of casuality between the premiss 
 and the conclusion, but by the subjective relation 
 of reason and consequence as involved in the 
 thought/' 
 
 " The Baconian or Material Induction pro- 
 ceeds on the assumption of general laws in the 
 relations of physical phenomena, and endeavours, 
 by select observations and experiments, to detect 
 the law in any particular case. This, whatever 
 be its value as a general method of physical in- 
 vestigation, has no place in Formal Logic. The 
 Aristotelian or Formal Induction proceeds on 
 the assumption of general laws of thought, and 
 inquires into the instances in which, by such 
 
298 QUOTATIONS ON INDUCTION. 
 
 laws, we are necessitated to reason from an accu- 
 mulation of particular instances to an universal 
 rule." Mansel, Prolegom. Log., p. 209. 
 
 Principle of Induction. By the principle of 
 induction is meant the ground or warrant on 
 which we conclude that what has happened in 
 certain cases, which have been observed, will also 
 happen in other cases, which have not been ob- 
 served. This principle is involved in the words 
 of the wise man, Eccles. i. 9, " The thing that 
 hath been, it is that which shall be : and that 
 which is done is that which shall be done." In 
 nature there is nothing insulated. All things 
 exist in consequence of a sufficient reason, all 
 events occur according to the efficacy of proper 
 causes. In the language of Newton, Effectuum 
 naturalium ejusdem generis esedem sunt 
 causae, The same causes produce the same 
 effects. The principle of induction is an appli- 
 cation of the principle of casuality. Phenomena 
 have their proper causes, and these causes ope- 
 rate according to a fixed law. This law has been 
 expressed by saying, substance is persistent. 
 Our belief in the established order of nature is a 
 primitive judgment, according to Dr. Reid and 
 others, and the ground of all the knowledge we 
 derive from experience. According to others 
 this belief is a result or inference derived from 
 experience. 
 
 4. From Whe well's Novum Organon Reno- 
 vaium, 3d edition, 1858, p. 139 : 
 
 The Pure Mathematical Sciences can hardly 
 be called Inductive Sciences. Their principles 
 
QUOTATIONS ON INDUCTION. 299 
 
 are not obtained by Induction from Facts, but 
 are necessarily assumed in reasoning upon the 
 subject-matter which those sciences involve. 
 
 5. From English Cyclopaedia, edition 1867. 
 
 Induction (srt&y&tyri), as defined by Arch- 
 bishop Whately, is " a kind of argument which 
 infers respecting a whole class what has been as- 
 certained respecting one or more individuals of 
 that class. ' ' According to Sir William Hamilton 
 the word has been employed to designate three 
 very different operations : 1 . The objective pro- 
 cess of investigating particular facts, as prepara- 
 tory to Induction, which he observes is manifestly 
 not a process of reasoning of any kind ; 2. A ma- 
 terial illation of a universal from a singular, as 
 warranted either by the general analogy of na- 
 ture or the special presumptions afforded by the 
 object matter of any real science ; 3. A formal 
 illation of a universal from the individual, as 
 legitimated solely by the laws of thought and 
 abstracted from the conditions of any particular 
 matter. The second of these operations is the 
 inductive method of Bacon, which proceeds by 
 means of rejections and conclusions, so as to ar- 
 rive at those axioms or general laws from which 
 we may infer by way of synthesis other particu- 
 lars unknown to us, and perhaps placed beyond 
 reach of direct examination. (' Nov. Org.^ 
 i Aph.^ c. iii., c. v.) Aristotle's definition co- 
 incides with the third, and induction i i is an in- 
 ference drawn from all particulars. ' ' ( 4 Prior 
 Analy.J ii., c. xxiii.) The second and third 
 processes are improperly confounded by most 
 writers on logic, and treated as one simple and 
 
300 QUOTATIONS OK INDUCTION. 
 
 purely logical operation. But the second is not 
 a logical process at all ; since the conclusion is 
 not necessarily inferrible from the premise, for 
 the some of the antecedent does not necessarily 
 legitimate the all of the conclusion, notwithstand- 
 ing that the procedure may be warranted by the 
 material problem of the science, or the funda- 
 mental principles of the human understanding. 
 The third alone is properly an induction of logic ; 
 for logic does not consider things, but the general 
 forms of thought under which the mind conceives 
 them ; and the logical inference is not deter- 
 mined by any relation of causality between the 
 premise and conclusion, but by the subjective 
 relation of reason and consequence as involved 
 in the thought. The inductive process is exactly 
 the reverse of the deductive ; for while the latter 
 proceeds from the whole to the part, the former 
 ascends from the part to the whole : since it is 
 only under the character of a constituted or con- 
 taining whole, or as a constituent and contained 
 part, that anything can become the term of logi- 
 cal argumentation. Of these two processes, Sir 
 William Hamilton gives the following figures : 
 
 Induction. Deduction. 
 
 XYZareA. B is A. 
 
 X Y Z are whole B. X Y Z are under B. 
 
 . \ whole B is A. . . X Y Z are A. 
 
 or, or, 
 
 A contains X Y Z. A contains B. 
 
 X Y Z contains B. B contains X Y Z. 
 
 .*. A contains B. .*. A contains X Y Z. 
 This confusion of material and logical indue- 
 
QUOTATIONS ON INDUCTION. 301 
 
 tion led Gillies and others to insist on the same- 
 ness of the Baconian and Aristotelian induction ; 
 while Campbell and Dugald Stewart, who totally 
 mistook the value of all logical inference, yet 
 rightly maintained their difference. 
 
 By Aristotle, induction and deduction are 
 viewed as in certain respects similar in form ; 
 Lut in others as diametrically opposed, the latter 
 being an analysis of the whole into its parts, by 
 descending from the more general to the more 
 particular ; but the former descends by a syn- 
 thetical process from the parts to the whole. 
 The logicians, who misapprehended the nature of 
 induction, reduced it to a deductive syllogism of 
 the third form, and thereby overthrew the valid- 
 ity of all deduction itself, since the latter is only 
 possible by means of the former, which legiti- 
 mates the proposition from which its reasoniifg 
 proceeds. 
 
 Again, the Aristotelian induction was drawn 
 from all the particulars, whereas the confusion 
 which Sir W. Hamilton has pointed out gave 
 rise to a division of the inductive process into 
 perfect and imperfect, according as the enumera- 
 tion of particulars is complete or incomplete. 
 The latter gives only a probable result, whereas 
 the necessity of the conclusion is essential to all 
 logical inference, as its demonstrative stringency 
 depends upon the form of the illation, and not 
 upon the truth of the premises. It is proper to 
 add, that no one ever knew the distinction be- 
 tween the imperfect and perfect forms of the 
 conclusion better than Aristotle himself. 
 
302 QUOTATIONS ON INDUCTION. 
 
 Induction (Mathematics). The method of 
 induction, in the sense in which the word is used 
 in natural philosophy, is not known in pure 
 mathematics. There certainly are instances in 
 which a general proposition is proved by a col- 
 lection of the demonstrations of different cases, 
 which may remind the investigator of the induc- 
 tive process, or the collection of the general from 
 the particular. Such instances however must 
 not be taken as permanent, for it usually happens 
 that a general demonstration is discovered as 
 soon as attention is turned to the subject. 
 
 There is however one particular method of 
 proceeding which is extremely common in math- 
 ematical reasoning, and to which we propose to 
 give the name of successive induction. It has 
 the character of induction as defined by the logi- 
 cians, because it is really the collection of a gen- 
 eral truth from a demonstration which implies 
 the examination of every particular case ; but it 
 adds to the necessary character of induction that 
 each case depends upon one or more of those 
 which precede. 'Substituting demonstration for 
 observation, the mathematical process is truly 
 inductive. A couple of instances of the method 
 will enable the mathematical reader to recognize 
 a mode of investigation with which he is already 
 familiar. 
 
 Example 1. The sum of any number of suc- 
 cessive odd numbers, beginning from unity, is a 
 square number, namely, the square of half the 
 even number which follows the last odd number. 
 
QUOTATIONS ON INDUCTION. 303 
 
 Let this proposition be true in any one single in- 
 stance ; that is, n being some whole number, let 
 1, 3, 5 . . . . up to 2n + l put together give 
 (n-f-1) 2 . Then the next odd number being 
 2n + 3, the sum of all the odd numbers up to 
 2n + 3 will be (n+l) 2 -h 2 n + 3, or n 2 +4n+4, 
 or (n+2) 2 . But n+2 is the half of the even 
 number next following 2n+3 : consequently, 
 if the proposition be true of any one set of odd 
 numbers, it is true of one more. But it is true 
 of the first odd number 1, for this is the square 
 of half the even number next following. Conse- 
 quently, being true of 1, it is true of 1+3 ; be- 
 ing true of 1+3, it is true of 1+3+5 ; being 
 true of 1+3+5, it is true of 1 + 3+5+7, and 
 so on ad infinitum. 
 
 Example 2. The formula x n & 1 , n being a 
 whole number, is always algebraically divisible 
 by x a. 
 
 x n a n =x n a n ~ 1 x+a n - 1 x a n 
 
 =x(x n - 1 a n - 1 )+a n ~ 1 (x a) 
 In this last expression the second term a n-1 
 (x a) is obviously divisible by x a: if then 
 any one of the succession 
 
 x a, x 2 a 2 ,x 3 a 3 , x 4 a 4 , <fec. 
 be divisible by x a, so is the next. But this is 
 obviously true of the first, therefore it is true of 
 the second ; being true of the second, it is true 
 of the third ; and so on, ad infinitum. 
 
 There are cases in which the successive induc- 
 tion only brings any term within the general rule, 
 when two, three, or more of the terms immedi- 
 ately preceding are brought within it. Thus 
 
304 QUOTATIONS ON INDUCTION. 
 
 in the application of this method to the deduc- 
 tion of the well known consequence of 
 
 x H = 2 cos. 9, 
 namely, 
 
 x n H = 2 cos. n 6* 
 
 x n 
 
 it can only be shown that any one case of this 
 theorem is true, by showing that the preceding 
 two cases are true ; thus its truth, when n = 5 
 and n = 6, makes it necessarily follow when 
 n = 7. In this case the two first instances must 
 be established (when n=l by hypothesis, and 
 when n=2 by independent demonstration), 
 which two establish the third, the second and 
 third establish the fourth, and so on. 
 
 An instance of mathematical induction occurs 
 in many equations of differences, in every recur- 
 ring series, etc. 
 
 6. From Jevons' Elementary Lessons in Logic , 
 pp. 208-28, ed. 1878. 
 
 To express the difference between knowledge 
 derived deductively and that obtained induct- 
 ively the Latin phrases d priori and a pos- 
 teriori are often used. By A priori reason- 
 ing we mean argument based on truths pre- 
 viously known ; A posteriori reasoning, on 
 the contrary, proceeds to infer from the conse- 
 quences of a general truth what that gen- 
 eral truth is. Many philosophers consider that 
 the mind is naturally in possession of certain 
 
QUOTATIONS ON INDUCTION. 305 
 
 laws or truths which it must recognise in every 
 act of thought ; all such, if they exist, would be 
 d priori truths. It cannot be doubted, for in- 
 stance, that we must always recognise in thought 
 the three Primary Laws of Thought considered 
 in Lesson xiv. We have there an d priori 
 knowledge that ' ' matter cannot both have weight 
 and be without weight, ' ' or that ' ' every thing 
 must be either self-luminous or not self-lumin- 
 ous. " But there is no law of thought which 
 can oblige us to think that matter has weight, 
 and luminous ether has not weight ; that Jupiter 
 and Venus are not self-luminous, but that comets 
 are to some extent self-luminous. These are 
 facts which are no doubt necessary consequences 
 of the laws of nature and the general constitution 
 of the world ; but as we are not naturally ac- 
 quainted with all the secrets of creation, we 
 have to learn them by observation, or by the d 
 posteriori method. 
 
 It is not however usual at the present time 
 to restrict the name d priori to truths obtained 
 altogether without recourse to observation. 
 Knowledge may originally be of an d posteriori 
 origin, and yet having been long in possession, 
 and having acquired the greatest certainty, it 
 may be the ground of deductions, and may then 
 be said to give d priori knowledge. Thus it is 
 now believed by all scientific men that force 
 cannot be created or destroyed by any of the 
 processes of nature. If this be true the force 
 which disappears when a bullet strikes a target 
 must be converted into something else, and on 
 
306 QUOTATIONS OK INDUCTION. 
 
 d priori grounds we may assert that heat will be 
 the result. It is true that we might easily learn 
 the same truth d posteriori, by picking up por- 
 tions of a bullet which has just struck a target 
 and observing that they are warm. But there 
 is a great advantage in d priori knowledge ; we 
 can often apply it in cases where experiment or 
 observation would be difficult. If I lift a stone 
 and then drop it, the most delicate instruments 
 could hardly show that the stone was heated by 
 striking the earth ; yet on d priori grounds I 
 know that it must have been so, and can easily 
 calculate the amount of heat produced. Simi- 
 larly we know, without the trouble of observa- 
 tion, that the Falls of Niagara and all other 
 waterfalls produce heat. This is fairly an in- 
 stance of d priori knowledge because no one 
 that I have heard of has tried the fact or proved 
 it d posteriori; nevertheless the knowledge is 
 originally founded on the experiments of Mr. 
 Joule, who observed in certain well-chosen cases 
 how much force is equivalent to a certain amount 
 of heat. The reader, however, should take care 
 not to confuse the meaning of d priori thus ex- 
 plained with that given to the words by the phi- 
 losophers who hold the mind to be in the pos- 
 session of knowledge indepeudently of all obser- 
 vation. 
 
 It is not difficult to see that the d priori 
 method is equivalent to the synthetic method 
 considered in intension, the d posteriori method 
 of course being equivalent to the analytic 
 method. But the same difference is really ex- 
 
QUOTATIONS OX INDUCTION. 307 
 
 pressed in the words deductive and inductive ; 
 and we shall frequently need to consider it in 
 the following lessons. 
 
 PERFECT INDUCTION AND THE INDUCTIVE 
 SYLLOGISM. 
 
 WE have in previous lessons considered de- 
 ductive reasoning, which consists in combining 
 two or more general propositions synthetically, 
 and thus arriving at a conclusion which is a 
 proposition or truth of less generality than the 
 premises, that is to say, it applies to fewer indi- 
 vidual instances than the separate premises from 
 which it was inferred. When I combine the 
 general truth that " metals are good conductors 
 of heat, ' ' with the truth that i i aluminium is a 
 metal, " I am enabled by a syllogism in the mood 
 Barbara to infer that l ' aluminium is a good con- 
 ductor of heat. ' ' As this is a proposition con- 
 cerning one metal only, it is evidently less gen- 
 eral than the premise, which referred to all 
 metals whatsoever. In induction, on the con- 
 trary, we proceed from less general, or even from 
 individual facts, to more general propositions, 
 truths, or, as we shall often call them, Laws of 
 Nature. When it is known that Mercury moves 
 in an elliptic orbit round the Sun, as also Venus, 
 the Earth, Mars, Jupiter, &c., we are able to 
 arrive at the simple and general truth that " all 
 the planets move in elliptic orbits round the 
 sun." This is an example of an inductive pro- 
 cess of reasoning. 
 
 It is true that we may reason without ren- 
 
308 QUOTATIONS ON INDUCTION. 
 
 dering our conclusion either more or less general 
 than the premises, as in the following : 
 Snowdon is the highest mountain in England or 
 
 Wales. 
 
 Snowdon is not so high as Ben Nevis. 
 Therefore the highest mountain in England or 
 
 Wales is not so high as Ben Nevis. 
 Again : 
 
 Lithium is the lightest metal known. 
 Lithium is the metal indicated by one bright red 
 
 line in the spectrum.* 
 Therefore the lightest metal known is the metal 
 
 indicated by a spectrum of one bright red line. 
 
 In these examples all the propositions are 
 singular propositions, and merely assert the iden- 
 tity of singular terms, so that there is no altera- 
 tion of generality. Each conclusion applies to 
 just such an object as each of the premises applies 
 to. To this kind of reasoning the apt name of 
 Traduction has been given. 
 
 Induction is a much more difficult and more 
 important kind of reasoning process than Tra- 
 duction or even Deduction ; for it is engaged in 
 detecting the general laws or uniformities, the 
 relations of cause and effect, or in short all the 
 general truths that may be asserted concerning 
 the numberless and very diverse events that take 
 place in the natural world around us. The 
 greater part, if not, as some philosophers think, 
 the whole of our knowledge, is ultimately due to 
 inductive reasoning. The mind, it is plausibly 
 
 * Roscoe's Lessons in Elementary Chemistry, p. 199. 
 
QUOTATIONS ON INDUCTION. 309 
 
 said, is not furnished with knowledge in the 
 form of general propositions ready made and 
 stamped upon it, but is endowed with powers of 
 observation, comparison, and reasoning, which 
 are adequate, when well educated and exercised, 
 to procure knowledge of the world without us 
 and the worl 1 within the human mind. Even 
 when we argue synthetically and deductively 
 from simple ideas and truths which seem to be 
 ready in the mind, as in the case of the science 
 of geometry, it may be that we have gathered 
 those simple ideas and truths from previous ob- 
 servation or induction of an almost unconscious, 
 kind. This is a debated point upon which I 
 will not here speak positively ; but if the truth 
 be as stated, Induction will be the mode by 
 which all the materials of knowledge are brought 
 to the mind and analysed. Deduction w r ill then 
 be the almost equally important process by 
 which the knowledge thus acquired is utilised, 
 and by which new Inductions of a more compli- 
 cated character, as we shall see, are rendered 
 possible. 
 
 An Induction, that is an act of Inductive 
 reasoning, is called Perfect when all the possible 
 cases or instances to which the conclusion can 
 refer, have been examined and enumerated in the 
 premises. If, as usually happens, it is impossi- 
 ble to examine all cases, since they may occur at 
 future times or in distant parts of the earth or 
 other regions of the universe, the Induction is. 
 called Imperfect. The assertion that all the 
 months of the year are of less length than thirty- 
 
310 QUOTATIONS ON INDUCTION. 
 
 two days is derived from Perfect Induction, and 
 is a certain conclusion because the calendar is a 
 human institution, so that we know beyond 
 doubt how many months there are, and can 
 readily ascertain that each of them is less than 
 thirty-two days in length. But the assertion 
 that all the planets move in one direction round 
 the sun, from West to East, is derived from Im- 
 perfect Induction ; for it is possible that there 
 exist planets more distant than the most distant- 
 known planet Neptune, and to such a planet of 
 course the assertion would apply. 
 
 Hence it is obvious that there is a great 
 difference between Perfect and Imperfect Induc- 
 tion. The latter includes some process by 
 which we are enabled to make assertions concern- 
 ing things that we have never seen or examined 
 or even Known to exist. But it must be care- 
 fully remembered also that no Imperfect Induc- 
 tion can give a certain conclusion. It may be 
 highly probable or nearly certain that the cases 
 nnexamined will resemble those which have been 
 examined, but it can never be certain. It is 
 quite possible, for instance, that a new planet 
 might go round the sun in an opposite direction 
 to the other planets. In the case of the satel- 
 lites belonging to the planets more than one ex- 
 ception of this kind has been discovered, and 
 mistakes have constantly occurred in science 
 from expecting that all new cases would exactly 
 resemble old ones. Imperfect Induction thus 
 gives only a certain degree of probability or like- 
 lihood that all instances will agree with those 
 
QUOTATIONS ON INDUCTION. 311 
 
 examined. Perfect Induction, on the other hand, 
 gives a necessary and certain conclusion, but it 
 asserts nothing beyond what was asserted in the 
 premises. 
 
 Mr. Mill, indeed, differs from almost all other 
 logicians in holding that Perfect Induction is- 
 improperly called Induction, because it does not 
 lead to any new knowledge. He defines In- 
 duction as inference from the known to the un- 
 known, and considers the unexamined cases which 
 are apparently brought into our knowledge as the 
 only gain from the process of reasoning. Hence 
 Perfect Induction seems to him to be of no scien- 
 tific value whatever, because the conclusion is a 
 mere reassertion in a briefer form, a mere sum- 
 ming up of the premises. I may point out, how- 
 ever, that if Perfect Induction were no more 
 than a process of abbreviation it is yet of great 
 importance, and requires to be continually used 
 hi science and common life. Without it we 
 could never make a comprehensive statement, 
 but should be obliged to enumerate every partic- 
 ular. After examining the books in a library 
 and finding them to be all English books we 
 should be unable to sum up our results in the 
 one proposition, " all the books in this library 
 are English books ;" but should be required to go 
 over the list of books every time we desired to 
 make any one acquainted with the contents of 
 the library. The fact is, that the power of ex- 
 pressing a great number of particular facts in a 
 very brief space is essential to the progress of 
 science. Just as the whole science of arithmetic 
 
312 QUOTATIONS ON INDUCTION. 
 
 consists in nothing but a series of processes for 
 abbreviating addition and subtraction, and enab- 
 ling us to deal with a great number of units in a 
 very short time, so Perfect Induction is abso- 
 lutely necessary to enable us to deal with a great 
 number of particular facts in a very brief space. 
 
 It is usual to represent Perfect Induction in 
 the form of an Inductive Syllogism, as in the 
 following instance : 
 Mercury, Venus, the Earth, &c., all move round 
 
 the sun from West to East. 
 Mercury, Venus, the Earth, &c., are all the 
 
 known Planets. 
 Therefore all the known planets move round the 
 
 sun from AVest to East. 
 
 This argument is a true Perfect Induction 
 because the conclusion only makes an assertion 
 of all known planets, which excludes all refer- 
 ence to possible future discoveries ; and we may 
 suppose that all the known planets have been 
 enumerated in the premises. . . . 
 
 As another example of a Perfect Induction 
 we may take 
 
 January, February, December, each con- 
 tain less than 32 days. 
 January December are all the months of 
 
 the year. 
 Therefore all the months of the year contain less 
 
 than 32 days. 
 
 Although Sir W. Hamilton has entirely 
 rejected the notion, it seems worthy of inquiry 
 whether the Inductive Syllogism be not really of 
 the Disjunctive form of Syllogism. Thus I 
 
QUOTATIONS ON INDUCTION. 313 
 
 should be inclined to represent the last example 
 in the form : 
 
 A month of the year is either January, or 
 
 February, or March or December ; but 
 
 January has less than 32 days ; and February has 
 less than 32 days ; and so on until we come to 
 December, which has less than 32 days. 
 
 It follows clearly that a month must in any 
 case have less than 32 days ; for there are only 
 12 possible cases, and in each case this is affirm- 
 ed. The fact is that the major premise of the 
 syllogism on the last page is a compound sen- 
 tence with twelve subjects, and is therefore equi- 
 valent to twelve distinct logical propositions. 
 The minor premise is either a disjunctive propo- 
 sition, as I have represented it, or something 
 quite different from anything we have elsewhere 
 had. 
 
 From Perfect Induction we shall have to 
 pass to Imperfect Induction ; but the opinions 
 of Logicians are not in agreement as to the 
 grounds upon which we are warranted in taking 
 a part of the instances only, and concluding that 
 what is true of those is true of all. Thus if we 
 adopt the example found in many books and 
 say 
 
 This, that, and the other magnet attract iron ; 
 This, that, and the other magnet are all magnets ; 
 Therefore all magnets attract iron, 
 we evidently employ a false minor premise, be- 
 cause this, that, and the other magnet which we 
 have examined, cannot possibly be all existing 
 magnets. In whatever form we put it there 
 
314 QUOTATIONS ON INDUCTION. 
 
 must be an assumption that the magnets which 
 we have examined are a fair specimen of all 
 magnets, so that what we find in some we may 
 expect in all. Archbishop Whately con- 
 siders that this assumption should be expressed 
 in one of the premises, and he represents Induc- 
 tion as a Syllogism as follows : 
 That which belongs to this, that, and the other 
 
 magnet, belongs to all ; 
 Attracting iron belongs to this, that, and the 
 
 other ; 
 
 Therefore it belongs to all. 
 
 But though this is doubtless a correct expression 
 of the assumption made in an Imperfect Induc- 
 tion, it does not in the least explain the grounds 
 on which we are allowed to make the assump- 
 tion, and under what circumstances such an as- 
 sumption would be likely to prove true. Some 
 writers have asserted that there is a Principle 
 called the Uniformity of Nature, which enables 
 us to affirm that what has often been found to 
 be true of anything will continue to be found 
 true of the same sort of thing. It must be ob- 
 served, however, that if there be such a principle 
 it is liable to exceptions ; for many facts which 
 have held true up to a certain point have after- 
 wards been found not to be always true. Thus 
 there was a wide and unbroken induction tend- 
 ing to show that all the Satellites in the plane- 
 tary system went in one uniform direction round 
 their planets. Nevertheless the Satellites of 
 Uranus when discovered were found to move in 
 a retrograde direction, or in an opposite direction 
 
QUOTATIONS ON INDUCTION. 315 
 
 to all Satellites previously known, and the same 
 peculiarity attaches to the Satellite of Neptune 
 more lately discovered. 
 
 We may defer to the next lesson the ques- 
 tion of the varying degree of certainty which be- 
 longs to induction in the several branches of 
 knowledge. 
 
 The advanced student may consult the fol- 
 lowing with advantage : Hansel's Aldrich, Ap- 
 pendix, Notes G and H. Hamilton's Lectures 
 on Logic, Lecture xvn., and Appendix vn., On 
 Induction and Example, Vol. n., p. 358. J. S. 
 Mill's System of Logic, Book in. Chap. 2, Of 
 Inductions improperly so-called. 
 
 GEOMETKICAL AND MATHEMATICAL INDUC- 
 TION, ANALOGY AND EXAMPLE. 
 
 IT is now indispensable that we should con- 
 sider with great care upon what grounds Imper- 
 fect Induction is founded. No difficulty is en- 
 countered in Perfect Induction because all possi- 
 ble cases which can come under the general con- 
 clusion are enumerated in the premises, so that 
 in fact there is no information in the conclusion 
 which was not given in the premises. In this 
 respect the Inductive Syllogism perfectly agrees 
 with the general principles of deductive reason- 
 ing, which require that the information contain- 
 ed in the conclusion should be shown only from 
 the data, and that we should merely unfold, or 
 transform into an explicit statement what is con- 
 tained in the premises implicitly. 
 
 In Imperfect Induction the process seems to 
 
316 QUOTATIONS ON INDUCTION. 
 
 be of a wholly di fferent character, since the in- 
 stances concerning which we acquire knowledge 
 may be infinitely more numerous than those from 
 which we acquire the knowledge. Let us con- 
 sider in the first place the process of Geometrical 
 Reasoning which has a close resemblance to in- 
 ductive reasoning. When in the fifth proposi- 
 tion of the first book of Euclid we prove that 
 the angles at the base of an isosceles triangle are 
 equal to each other, it is done by taking one par- 
 ticular triangle as an example. A figure is given 
 which the reader is requested to regard as having 
 two equal sides, and it is conclusively proved 
 that if the sides be really equal then the angles 
 opposite to those sides must be equal also. But 
 Euclid says nothing about other isosceles trian- 
 gles ; he treats one single triangle as a sufficient 
 specimen of all isosceles triangles, and we are 
 asked to believe that what is true of that is true 
 of any other, whether its sides be so small as to 
 be only visible in a microscope, or so large as to 
 reach to the furthest fixed star. There may evi- 
 dently be an infinite number of isosceles trian- 
 gles as regards the length of the equal sides, and 
 each of these may be infinitely varied by increas- 
 ing or diminishing the contained angle, so that 
 the number of possi-ble isosceles triangles is infi- 
 nitely infinite ; and yet we are asked to believe 
 of this incomprehensible number of objects what 
 we have proved only of one single specimen. 
 This might seem to be the most extremely Im- 
 perfect Induction possible, and yet every one al- 
 lows that it gives us really certain knowledge. 
 
QUOTATIONS ON INDUCTION. 317 
 
 We do know with as much certainty as knowl- 
 edge can possess, that if lines be conceived as 
 drawn from the earth to two stars equally dis- 
 tant, they will make equal angles with the line 
 joining those stars ; and yet we can never have 
 tried the experiment. 
 
 The generality of this geometrical reasoning 
 evidently depends upon the certainty with which 
 we know that all isosceles triangles exactly resem- 
 ble each other. The proposition proved does 
 not in fact apply to a triangle unless it agrees 
 with our specimen in all the qualities essential to 
 the proof. The absolute length of any of the 
 sides or the absolute magnitude of the angle con- 
 tained between any of them were not points 
 upon which the proof depended they were 
 purely accidental circumstances ; hence we are 
 at perfect liberty to apply to all new cases of an 
 isosceles triangle what we learn of one case. 
 Upon a similar ground rests all the vast body of 
 certain knowledge contained in the mathematical 
 sciences not only all the geometrical truths, but 
 all general algebraical truth. It was shown, for 
 instance, in p. 58, that if a and b be two quan- 
 tities, and we multiply together their sum and 
 difference, we get the difference of the squares 
 of a and b. However often we try this it will 
 be found true ; thus if a=10 and 6=7, the prod- 
 uct of the sum and difference is 17x3 = 51 ; 
 the squares of the quantities are 10x10 or 100 
 and 7x7 or 49, the difference of which is also 
 51. But however often we tried the rule no 
 certainty would be added to it ; because when 
 
318 QUOTATIONS ON INDUCTION. 
 
 proved algebraically there was no condition 
 which restricted the result to any particular num- 
 bers, and a and b might consequently be auy 
 numbers whatever. This generality of algebraical 
 reasoning by which a property is proved of infi- 
 nite varieties of numbers at once, is one of the 
 chief advantages of algebra over arithmetic. 
 There is also in algebra a process called Mathe- 
 matical Induction or Demonstrative Induction, 
 which shows the powers of reasoning in a very 
 conspicuous way. A good example is found in 
 the following problem : If we take the first two 
 consecutive odd numbers, 1 and 3, and add them 
 together the sum is 4, or exactly twice two ; if we 
 take three such numbers l-)-3-j-5, the sum is 9 
 or exactly three times three ; if we take four, 
 namely l-|~3+5-|-7 the sum is 16, or exactly 
 four times four ; or generally, if we take any 
 given number of the series, l-[-3+5-|-7+... 
 the sum is equal to the number of the terms mul- 
 tiplied by itself. Anyone who knows a very 
 little algebra can prove that this remarkable law 
 is universally true, as follows Let n be the 
 number of terms, and assume for a moment that 
 this law is true up to n terms, thus 
 
 1+3 + 5 + 7+ ...... + (2 n 1) = n\ 
 
 Now add 2n + 1 to each side of the equation. 
 It follows that 
 
 1+3 + 5 + 7+ 
 
 = n* 
 
 But the last quantity ri* -\-2n-\-\ is just 
 
QUOTATIONS ON INDUCTION. 319 
 
 equal to (n-\-iy ; so that if the law is true for n 
 terms it is true also for n-\-l terms. We are 
 enabled to argue from each single case of the 
 law to the next case ; but we have already shown 
 that it is true of the first few cases, therefore it 
 must be true of all. By no conceivable labor 
 could a person ascertain by trial what is the sum 
 of the first billion odd numbers, and yet symbol- 
 ically or by general reasoning we know with cer- 
 tainty that they would amount to a billion bil- 
 lion, and neither more nor less even by a unit. 
 This process of Mathematical Induction is not 
 exactly the same as Geometrical Induction, be- 
 cause each case depends upon the last, but the 
 proof rests upon an equally narrow basis of ex- 
 perience, and creates knowledge of equal cer- 
 tainty and generality. 
 
 Such mathematical truths depend upon ob- 
 servation of a few cases, but they acquire cer- 
 tainty from the perception we have of the exact 
 similarity of one case to another, so that we un- 
 doubtingly believe what is true of one case to be 
 true of another. It is very instructive to con- 
 trast with these cases certain other ones where 
 there is a like ground of observation, but not 
 the same tie of similarity. It was at one time 
 believed that if any integral number were multi- 
 pled by itself, added to itself and then added 
 to 41, the result would be a prime number, that 
 is a number which could not be divided by any 
 other integral number except unity ; in symbols, 
 
 x 2 + x + 41 = prime number. 
 
320 QUOTATIONS ON INDUCTION. 
 
 This was believed solely on the ground of 
 trial, and experience, and it certainly holds for a 
 great many values of x. Thus when x is suc- 
 cessively made equal to the numbers in the first 
 line below, the expression x* -\-x-\- 41 gives the 
 values in the second line, and they are all prime 
 numbers : 
 
 0123456789 10 
 41 43 47 53 61 71 83 97 113 131 151 
 
 No reason however could be given why it 
 should always be true, and accordingly it was 
 found that the rule does not always hold true, 
 but fails when #=40. Then we have 40x40 
 _j_40-|-41=:1681, but this is clearly equal to 
 41 X40-J-41 or 41 X41, and is not a prime num- 
 ber. 
 
 In that branch of mathematics which treats 
 of the peculiar properties and kinds of numbers, 
 other propositions depending solely upon obser- 
 vation have been asserted to be always true. 
 
 z 
 
 Thus Fermat believed that 2 2 -|-l always repre- 
 sents a prime number, but could not give any 
 reason for the assertion. It holds true in fact 
 until the product reaches the large number 
 4294967297, which was found to be divisible by 
 641, so that the generality of the statement was 
 disproved. 
 
 We find then that in some cases a single in- 
 stance proves a general and certain rule, while 
 in others a very great number of instances are 
 insufficient to give any certainty at all ; all de- 
 
QUOTATIONS OK INDUCTION'. 321 
 
 pends upon the perception we have of similarity 
 or identity between one case and another. We 
 can perceive no similarity between all prime 
 numbers which assures us that because one is 
 represented by a certain formula, also another 
 is ; but we do find such similarity between the 
 sums of odd numbers, or between isosceles tri- 
 angles. 
 
 Exactly similar considerations apply to induc- 
 tions in physical science. When a chemist an- 
 alyses a few grains of water and finds that they 
 contain exactly 8 parts of oxygen and 1 of hy- 
 drogen for 9 parts of water, he feels warranted in 
 asserting that the same is true of all pure water 
 whatever be its origin, and whatever be the part 
 of the world from which it comes. But if he 
 analyse a piece of granite, or a sample of sea- 
 water from one part of the world, he does not 
 feel any confidence that it will resemble exactly 
 a piece of granite, or a sample of sea- water from 
 another part of the earth ; hence he does not 
 venture to assert of all granite or sea- water, what 
 he finds true of a single sample. Extended ex- 
 perience shows that granite is very variable in 
 composition, but that sea-water is rendered 
 pretty uniform by constant mixture of currents. 
 Nothing but experience in these cases could in- 
 form us how far we may assert safely of one 
 sample what we have ascertained of another. 
 But we have reason to believe that chemical 
 compounds are naturally fixed and invariable in 
 composition, according to Dalton's laws of com- 
 bining proportions. No d priori reasoning from 
 
322 QUOTATIONS ON INDUCTION. 
 
 the principles of thought could have told us this, 
 and we only learn it by extended experiment. 
 But having once shown it to be true with certain 
 substances we do not need to repeat the trial 
 with all other substances, because we have every 
 reason to believe that it is a natural law in which 
 all chemical substances resemble each other. It 
 is only necessary then for a single accurate anal- 
 ysis of a given fixed compound to be made in 
 order to inform us of the composition of all 
 other portions of the same substance. 
 
 It must be carefully observed however that 
 all inductions in physical science are only 
 probable, or that if certain, it is only hypotheti- 
 cal certainty they possess. Can I be absolutely 
 certain that all water contains one part of hydro- 
 gen in nine ? I am certain only on two condi- 
 tions : 
 
 1 . That this was certainly the composition of 
 the sample tried. 
 
 2. That any other substance I call water ex- 
 actly resembles that sample. 
 
 But even if the first condition be undoubtedly 
 true, 1 cannot be certain of the second. For how 
 do I know what is water except by the fact of 
 its being a transparent liquid, freezing into a 
 : solid and evaporating into steam, possessing a 
 high specific heat, and a number of other dis- 
 tinct properties ? But can I be absolutely cer- 
 tain that every liquid possessing all these proper- 
 ties is water ? Practically I can be certain, but 
 theoretically I cannot. 
 
QUOTATION'S Otf INDUCTION. 323 
 
 V. From Mill's System of Logic, pp. 125, 126 : 
 210-228, 8vo edition. 
 
 Reasoning, in the extended sense in which I 
 use the term, and in which it is synonymous 
 with Inference, is popularly said to be of two 
 kinds : reasoning from particulars to generals, 
 and reasoning from generals to particulars ; 
 the former being called Induction, the latter 
 Ratiocination or Syllogism. It will presently 
 be shown that there is a third species of rea- 
 soning, which falls under neither of these de- 
 scriptions, and which, nevertheless* is not only 
 valid, but is the foundation of both the 
 others. ... Of Induction, therefore, we 
 shall say no more at present, than that it at least 
 is, without doubt, a process of real inference. 
 The conclusion in an induction embraces more 
 than is contained in the premises. The principle 
 or law collected from particular instances, the 
 general proposition in which we embody the re- 
 sult of our experience, covers a much larger ex- 
 tent of ground than the individual experiments 
 which form its basis. A principle ascertained by 
 experience, is more than a mere summing up of 
 what has been specifically observed in the indi- 
 vidual cases which have been examined ; it is a 
 generalization grounded on those cases, and ex- 
 pressive of our belief, that what we there found 
 true is true in an indefinite number of cases 
 which we have not examined, and are never 
 likely to examine. The nature and grounds of 
 this inference, and the conditions necessary to 
 make it legitimate, will be the subject of discus- 
 
324 QUOTATIONS OK INDUCTION. 
 
 sion in the Third Book : but that such inference 
 really takes place is not susceptible of question. 
 In every induction we proceed from truths which 
 we knew, to truths which we did not know ; 
 from facts certified by observation, to facts 
 which we have not observed, and even to facts 
 not capable of being now observed ; future 
 facts, for example ; but which we do not hesi- 
 tate to believe on the sole evidence of the induc- 
 tion itself. Induction, then, is a real process of 
 Reasoning or Inference. 
 
 OF INDUCTIONS IMPROPERLY SO CALLED. 
 
 1. Induction, then, is that operation of the 
 mind, by which we infer that what we know to be 
 true in a particular case or cases, will be true in all 
 cases which resemble the former in certain assign- 
 able respects. In other words, Induction is the 
 process by which we conclude that what is true 
 of certain individuals of a class is true of the 
 whole class, or that what is true at certain times 
 will be true in similar circumstances at all times. 
 
 This definition excludes from the meaning of 
 the term Induction, various logical operations, to 
 which it is not unusual to apply that name. 
 
 Induction, as above defined, is a process of 
 inference-; it proceeds from the known to the 
 unknown ; and any operation involving no infer- 
 ence, any process in which what seems the con- 
 clusion is no wider than the premises from which 
 it is drawn, does not fall within the meaning of 
 the term. Yet in the common books of Logic 
 we find this laid down as the most perfect, in- 
 
QUOTATIONS OK INDUCTION. 325 
 
 deed the only quite perfect, form of induction. 
 In those books, every process .which sets out 
 from a less general and terminates in a more 
 general expression which admits of being stated 
 in the form, " This and that A are B, therefore 
 every A is B " is called an induction, whether 
 any thing be really concluded or not : and the 
 induction is asserted not to be perfect, unless 
 every single individual of the class A is included 
 in the antecedent, or premise : that is, unless 
 what we affirm of the class has already been as- 
 certained to be true of every individual in it, so- 
 that the nominal conclusion is not really a con- 
 clusion, but a mere re-assertion of the premises. 
 If we were to say, All the planets shine by the 
 sun's light, from observation of each separate 
 planet, or All the Apostles were Jews, because 
 this is true of Peter, Paul, John, and every other 
 apostle these, and such as these, would, in the 
 phraseology in question, be called perfect, and 
 the only perfect, Inductions. This, however, is 
 a totally different kind of induction from ours ; 
 it is not an inference from facts known to facts 
 unknown, but a mere short-hand registration of 
 facts known. The two simulated arguments 
 which we have quoted, are not generalizations ; 
 the propositions purporting to be conclusions 
 from them, are not really general propositions. 
 A general proposition is one in which the predi- 
 cate is affirmed or denied of an unlimited num- 
 ber of individuals ; namely, all, whether few or 
 many, existing or capable of existing, which pos- 
 sess the properties connoted by the subject of 
 
326 QUOTATIONS ON INDUCTION. 
 
 the proposition. i l All men are mortal ' ' does 
 not mean all now living, but all men past, pres- 
 ent, and to come. When the signification of 
 the term is limited so as to render it a name not 
 for any and every individual falling under a cer- 
 tain general description, but only for each of a 
 number of individuals, designated as such, and 
 as it were, counted off individually, the proposi- 
 tion, though it may be general in its language, 
 is no general proposition, but merely that num- 
 ber of singular propositions, written in an abridg- 
 ed character. The operation may be very use- 
 ful, as most forms of abridged notation are ; 
 but it is no part of the investigation of truth, 
 though often bearing an important part in the 
 preparation of the materials for that investiga- 
 tion. 
 
 As we may sum up a definite number of singular 
 propositions in one proposition, which will be 
 apparently, but not really, general, so we may 
 sum up a definite number of general proposi- 
 tions in one proposition, which will be apparent- 
 ly, but not really, more general. If by a sepa- 
 rate induction applied to every distinct species of 
 animals, it has been established that each pos- 
 sesses a nervous system, and we affirm thereupon 
 that all animals have a nervous system ; this looks 
 like a generalization, though as the conclusion 
 merely affirms of all what has already been af- 
 firmed of each, it seems to tell us nothing but what 
 we knew before. A distinction, however, must 
 be made. If in concluding that all animals have 
 a nervous system, we mean the same thing and 
 
QUOTATIONS ON INDUCTION. 32? 
 
 no more as if we had said " all known animals, " 
 the proposition is not general, and the process 
 by which it is arrived at is not induction. But 
 if our meaning is that the observations made of 
 the various species of animals have discovered to 
 us a law of animal nature, and that we are in a 
 condition to say that a nervous system will be 
 found even in animals yet undiscovered, this in- 
 deed is an induction ; but in this case the general 
 proposition contains more than the sum of the 
 special propositions from which it is inferred. 
 The distinction is still more forcibly brought out 
 when we consider, that if this real generalization 
 be legitimate at all, its legitimacy probably does 
 not require that we should have examined with- 
 out exception every known species. It is the 
 number and nature of the instances, and not their 
 being the whole of those which happen to be 
 known, that makes them sufficient evidence ta 
 prove a general law : while the more limited as- 
 sertion, which stops at all known animals, cannot 
 be made unless we have rigorously verified it in 
 every species. In like manner (to return to a 
 former example) we might have inferred, not that 
 all the planets, but that all planets, shine by re- 
 flected light : the former is no induction ; the 
 latter is an induction, and a bad one, being dis- 
 proved by the case of double stars self-lum- 
 inous bodies which are properly planets, since 
 they revolve round a centre. 
 
 2. There are several processes used in math- 
 ematics which require to be distinguished from 
 Induction, being not unfrequently called by that 
 
328 QUOTATIONS ON INDUCTION. 
 
 name, and being so far similar to Induction 
 properly so called, that the propositions they 
 lead to are really general propositions. For ex- 
 ample, when we have proved with respect to 
 the circle, that a straight line can not meet it in 
 more than two points, and when the same thing 
 has been successively proved of the ellipse, the 
 parabola, and the hyperbola, it may be laid 
 down as a universal property of the sections of 
 the cone. The distinction drawn in the two 
 previous examples can have no place here, there 
 being no difference between all known sections 
 of the cone and all sections, since a cone demon- 
 strably can not be intersected by a plane except 
 in one of these four lines. It would be diffi- 
 cult, therefore, to refuse to the proposition ar- 
 rived at, the name of a generalization, since 
 there is no room for any generalization beyond 
 it. But there is no induction, because there is 
 no inference : the conclusion is a mere summing 
 up of what was asserted in the various proposi- 
 tions from which it is drawn. A case some- 
 what, though not altogether, similar, is the proof 
 of a geometrical theorem by means of a diagram. 
 Whether the diagram be on paper or only in the 
 imagination, the demonstration (as formerly ob- 
 served) does not prove directly the general theo- 
 rem ; it proves only that the conclusion, which 
 the theorem asserts generally, is true of the par- 
 ticular triangle or circle exhibited in the diagram ; 
 but since we perceive that in the same way in 
 which we have proved it of that circle, it might 
 also be proved of any other circle, we gather up 
 
QUOTATIONS O:NT INDUCTION. 329 
 
 into one general expression all the singular prop- 
 ositions susceptible of being thus proved, arid 
 embody them in a universal proposition. Hav- 
 ing shown that the three angles of the triangle 
 ABC are together equal to two right angles, we 
 conclude that this is true of every other triangle, 
 not because it is true of ABC, but for the same 
 reason which proved it to be true of ABC. If 
 this were to be called Induction, an appropriate 
 name for it would be, induction by parity of rea- 
 soning. But the term can not properly belong 
 to it ; the characteristic quality of Induction is 
 wanting, since the truth obtained, though really 
 general, is not believed on the evidence of par- 
 ticular instances. We do not conclude that all 
 triangles have the property because some trian- 
 gles have, but from the ulterior demonstrative 
 evidence which was the ground of our conviction 
 in the particular instances. 
 
 There are nevertheless, in mathematics, some 
 examples of so-called Induction, in which the 
 conclusion does bear the appearance of a gener- 
 alization grounded on some of the particular 
 cases included in it. A mathematician, when he 
 has calculated a sufficient number of the terms of 
 an algebraical or arithmetical series to have ascer- 
 tained what is called the law of the series, does 
 not hesitate to fill up any number of the suc- 
 ceeding terms without repeating the calculations. 
 But I apprehend he only does so when it is appa- 
 rent from a priori considerations (which might 
 be exhibited in the form of demonstration) that 
 the mode of formation of the subsequent terms, 
 
330 QUOTATIONS OK INDUCTION. 
 
 each from that which preceded it, must be simi- 
 lar to the formation of the terms which have 
 been already calculated. And when the attempt 
 has been hazarded without the sanction of such 
 general considerations, there are instances on rec- 
 ord in which it has led to false results. 
 
 It is said that Newton discovered the binomial 
 theorem by induction ; by raising a binomial 
 successively to a certain number of powers, and 
 comparing those powers with one another until 
 he detected the relation in which the algebraic 
 formula of each power stands to the exponent of 
 that power, and to the two terms of the bino- 
 mial. The fact is not improbable : but a math- 
 ematician like Newton, who seemed to arrive per 
 saltum at principles and conclusions that ordinary 
 mathematicians only reached by a succession of 
 steps, certainly could not have performed the 
 comparison in question without being led by it 
 to the a priori ground of the law ; since any one 
 who understands sufficiently the nature of multi- 
 plication to venture upon multiplying several 
 lines of symbols at one operation, can not but 
 perceive that in raising a binomial to a power, 
 the co-efficients must depend on the laws of per- 
 mutation and combination : and as soon as this 
 is recognized, the theorem is demonstrated. 
 Indeed, when once it was seen that the law pre- 
 vailed in a few of the lower powers, its identity 
 with the law of permutation would at once sug- 
 gest the considerations which prove it to obtain 
 universally. Even, therefore, such cases as 
 these, are but examples of what I have called In- 
 
QUOTATIONS OK INDUCTION. 331 
 
 d action by parity of reasoning, that is, not really 
 Induction, because not involving inference of a 
 general proposition from particular instances. 
 
 3. There remains a third improper use of 
 the term Induction, which it is of real impor- 
 tance to clear up, because the theory of Induction 
 has been, in no ordinary degree, confused by it, 
 and because the confusion is exemplified in the 
 most recent and elaborate treatise on the induc- 
 tive philosophy which exists in our language. 
 The error in question is that of confounding a 
 mere description, by general terms, of a set of 
 observed phenomena, with an induction from 
 them. 
 
 Suppose that a phenomenon consists of parts, 
 and that these parts are only capable of being 
 observed separately, and as it were piecemeal. 
 When the observations have been made, there is 
 a convenience (amounting for many purposes to 
 a necessity) in obtaining a representation of the 
 phenomenon as a whole, by combining, or as we 
 may say, piecing these detached fragments to- 
 gether. A navigator sailing in the midst of the 
 ocean discovers land : he can not at first, or by any 
 one observation, determine whether it is a conti- 
 nent or an island ; but he coasts along it, and 
 after a few days finds himself to have sailed com- 
 pletely round it : he then pronounces it an island. 
 Now there was no particular time or place of ob- 
 servation at which he could perceive that this 
 land was entirely surrounded by water : he as- 
 certained the fact by a succession of partial ob- 
 servations, and then selected a general expression 
 
332 QUOTATIONS ON INDUCTION. 
 
 which summed up in two or three words the 
 whole of what he so observed. But is there any 
 thing of the nature of an induction in this pro- 
 cess ? Did he infer any thing that had not been 
 observed, from something else which had ? Cer- 
 tainly not. He had observed the whole of what 
 the proposition asserts. That the land in ques- 
 tion is an island, is not an inference from the 
 partial facts which the navigator saw in the 
 course of his circumnavigation ; it is the facts 
 themselves ; it is a summary of those facts ; the 
 description of a complex fact, to which those 
 simpler ones are as the parts of a whole. 
 
 Now there is, I conceive, no difference in kind 
 between this simple operation, and that by which 
 Kepler ascertained the nature of the planetary 
 orbits : and Kepler's operation, all at least that 
 was characteristic in it, was not more an induc- 
 tive act than that of our supposed navigator. 
 
 The object of Kepler was to determine the 
 real path described by each of the planets, or let 
 us say by the planet Mars (since it was of that 
 body that he first established the two of his three 
 laws which did not require a comparison of plan- 
 ets). To do this there was no other mode than 
 that of direct observation : and all which obser- 
 vation could do was to ascertain a great number 
 of the successive places of the planet ; or rather, 
 of its apparent places. That the planet occupied 
 successively all these positions, or at all events, 
 positions which produced the same impressions 
 on the eye, and that it passed from one of these 
 to another insensibly, and without any apparent 
 
QUOTATIONS ON INDUCTION. 333 
 
 breach of continuity ; thus much the senses, 
 with the aid of the proper instruments, could 
 ascertain. What Kepler did more than this, 
 was to find what sort of a curve these different 
 points would make, supposing them to be all 
 joined together. He expressed the whole series 
 of the observed places of Mars by what Dr. Whe- 
 well calls the general conception of an ellipse. 
 This operation was far from being as easy as 
 that of the navigator who expressed the series of 
 his observations on successive points of the 
 coast by the general conception of an island. 
 But it is the very same sort of operation ; and if 
 the one is not an induction but a description, 
 this must also be true of the other. 
 
 The only real induction concerned in the case, 
 consisted in inferring that because the observed 
 places of Mars were correctly represented by 
 points in an imaginary ellipse, therefore Mars 
 would continue to revolve in that same ellipse ; 
 and in concluding (before the gap had been 
 filled up by further observations) that the posi- 
 tions of the planet during the time which inter- 
 vened between two observations, must have coin- 
 cided with the intermediate points of the curve. 
 For these were facts which had not been directly 
 observed. They were inferences from the obser- 
 vations ; facts inferred, as distinguished from 
 facts seen. But these inferences were so far from 
 being a part of Kepler's philosophical operation, 
 that they had been drawn long before he was 
 born. Astronomers had long known that the 
 planets periodically returned to the same places. 
 
334 QUOTATIONS OK INDUCTION. 
 
 When this had been ascertained, there was no 
 induction left for Kepler to make, nor did he 
 make any further induction. He merely applied 
 his new conception to the facts inferred, as he 
 did to the facts observed. Knowing already that 
 the planets continued to move in the same paths ; 
 when he found that an ellipse correctly repre- 
 sented the past path, he knew that it would rep- 
 resent the future path. In finding a compen- 
 dious expression for the one set of facts, he 
 found one for the other : but he found the ex- 
 pression only, not the inference ; nor did he 
 (which is the true test of a general truth) add 
 any thing to the power of prediction already 
 possessed. 
 
 4. The descriptive operation which enables 
 a number of details to be summed up in a single 
 proposition, Dr. Whewell, by an aptly chosen 
 expression, has termed the Colligation of Facts. 
 In most of his observations concerning that men- 
 tal process I fully agree, and would gladly trans- 
 fer all that portion of his book into my own 
 pages. I only think him mistaken in setting up 
 this kind of operation, which according to the 
 old and received meaning of the term, is not in- 
 duction at all, as the type of induction generally; 
 and laying down, throughout his work, as prin- 
 ciples of induction, the principles of mere colli- 
 gation. 
 
 Dr. Whewell maintains that the general prop- 
 osition which binds together the particular 
 facts, and makes them, as it were, one fact, is 
 not the mere sum of those facts, but something 
 
QUOTATIONS ON INDUCTION". 335 
 
 more, since there is introduced a conception of 
 the mind, which did not exist in the facts them- 
 selves. " The particular facts, " says he,* " are 
 not merely brought together, but there is a new ete- 
 ment added to the combination by the very act of 
 thought by which they are combined. . . 
 When the Greeks, after long observing the mo- 
 tions of the planets, baw that these motions 
 might be rightly considered as produced by the 
 motion of one wheel revolving in the inside of an- 
 other wheel, these wheels were creations of their 
 minds, added to the facts which they perceived 
 by sense. And even if the wheels were no 
 longer supposed to be material, but were reduced 
 to mere geometrical spheres or circles, they were 
 not the less products of the mind alone some- 
 thing additional to the facts observed. The 
 same is the case in all other discoveries. The 
 facts are known, but they are insulated and un- 
 connected, till the discoverer supplies from his 
 own store a principle of connection. The pearls 
 are there, but they will not hang together till 
 some one provides the string. ' * 
 
 Let me first remark that Dr. Whewell, in this 
 passage, blends together, indiscriminately, ex- 
 amples of both the processes which I am endeav- 
 oring to distinguish from one another. When 
 the Greeks abandoned the supposition that the 
 planetary motions were produced by the revo- 
 lution of material wheels, and fell back upon the 
 idea of u mere geometrical spheres or circles/' 
 
 * Novum Orgamim Renovatum, pp. 72, 73. 
 
336 QUOTATIONS ON INDUCTION. 
 
 there was more in this change of opinion than 
 the mere substitution of an ideal curve for a 
 physical one. There was the abandonment of a 
 theory, and the replacement of it by a mere de- 
 scription. No one would think of calling the 
 doctrine of material wheels a mere description. 
 That doctrine was an attempt to point out the 
 force by which the planets were acted upon, and 
 compelled to move in their orbits. But when, 
 by a great step in philosophy, the materiality of 
 the wheels was discarded, and the geometrical 
 forms alone retained, the attempt to account for 
 the motions was given up, and what was left of 
 the theory was a mere description of the orbits. 
 The assertion that the planets were carried round 
 by wheels revolving in the inside of other 
 wheels, gave place to the proposition, that they 
 moved in the same lines which would be traced 
 by bodies so carried : which was a mere mode 
 of representing the sum of the observed facts ; 
 as Kepler's was another^ and a better mode of 
 representing the same observations. 
 
 It is true that for these simply descriptive op- 
 erations, as well as for the erroneous inductive 
 one, a conception of the mind was required. 
 The conception of an ellipse must have presented 
 itself to Kepler's mind, before he could identify 
 the planetary orbits with it. According to Dr. 
 Whewell, the conception was something added 
 to the facts. He expresses himself as if Kepler 
 had put something into the facts by his mode 
 of conceiving them. But Kepler did no such 
 thing. The "ellipse was in the facts before Kep- 
 
QUOTATIONS ON INDUCTION. 337 
 
 ler recognized it ; just as the island was an island 
 before it had been sailed round. Kepler did 
 not put what he had conceived into the facts, but 
 saw it in them. A conception implies, and cor- 
 responds to, something conceived : and though 
 the conception itself is not in the facts, but in 
 our mind, yet if it is to convey any knowledge 
 relating to them, it must be a conception of 
 something which really is in the facts, some pro- 
 perty which they actually possess, and which 
 they would manifest to our senses, if our senses- 
 were able to take cognizance of it. If, for in- 
 stance, the planet left behind it in space a visible 
 track, and if the observer were in a fixed posi- 
 tion at such a distance from the plane of the 
 orbit as would enable him to see the whole of it 
 at once, he would see it to be an ellipse ; and if 
 gifted with appropriate instruments and powers- 
 of locomotion, he could prove it to be such by 
 measuring its different dimensions. Nay, fur- 
 ther : if the track were visible, and he were so- 
 placed that he could see all parts of it in succes- 
 sion, but not all of them at once, he might be 
 able, by piecing together his successive observa- 
 tions, to discover both that it was an ellipse and 
 that the planet moved in it. The case would 
 then exactly resemble that of the navigator who- 
 discovers the land to be an island by sailing 
 round it. If the path was visible, no one I 
 think would dispute that to identify it with an 
 ellipse is to describe it : and I can not see why 
 any difference should be made by its not being 
 
338 QUOTATIONS ON INDUCTION. 
 
 directly an object of sense, when every point in it 
 is as exactly ascertained as if it were so. 
 
 Subject to the indispensable condition which 
 has just been stated, I do not conceive that the 
 part which conceptions have in the operation of 
 studying facts, has ever been overlooked or un- 
 dervalued. No one ever disputed that in order 
 to reason about any thing we must have a concep- 
 tion of it ; or that when we include a multitude 
 of things under a general expression, there is im- 
 plied in the expression a conception of something 
 common to those things. But it by no means 
 follows that the conception is necessarily pre-ex- 
 istent, or constructed by the mind out of its own 
 materials. If the facts are rightly classed under 
 the conception, it is because there is in the facts 
 themselves something of which the conception is 
 itself a copy $ and which if we can not directly 
 perceive, it is because of the limited power of 
 our organs, and not because the thing itself is not 
 there. The conception itself is often obtained 
 by abstraction from the very facts which, in Dr. 
 WhewelPs language, it is afterward called in to 
 connect. This he himself admits, when he ob- 
 serves (which he does on several occasions), how 
 great a service would be rendered to the science 
 of physiology *by the philosopher ' l who should 
 establish a precise, tenable, and consistent con- 
 ception of life." * Such a conception can only 
 he abstracted from the phenomena of life itself ; 
 from the very facts which it is put in requisition 
 
 * Jtfovum Organum Renovatum, p. 32. 
 
QUOTATIONS ON INDUCTION. 339 
 
 to connect. In other cases, no doubt, instead of 
 collecting the conception from the very phenom- 
 ena which we are attempting to colligate, we se- 
 lect it from among those which have been pre- 
 viously collected by abstraction from other facts. 
 In the instance of Kepler's laws, the latter was 
 the case. The facts being out of the reach of 
 being observed, in any such manner as would have 
 enabled the senses to identify directly the path of 
 the planet, the conception requisite for framing 
 a general description of that path could not be 
 collected by abstraction from the observations 
 themselves ; the mind had to supply hypotheti- 
 cally, from among the conceptions it had ob- 
 tained from other portions of its experience, 
 some one which would correctly represent the 
 series of the observed facts. It had to frame a 
 supposition respecting the general course of the 
 phenomenon, and ask itself, If this be the general 
 description, what will the details be ? and then 
 compare these with the details actually observed. 
 If they agreed, the hypothesis would serve for a 
 description of the phenomenon : if not, it was 
 necessarily abandoned, and another tried. It is 
 such a case as this which gives rise to the doc- 
 trine that the mind, in framing the descriptions, 
 adds something of its own which it does not find 
 in the facts. 
 
 Yet it is a fact surely, that the planet does 
 describe an ellipse ; and a fact which we could 
 see, if we had adequate visual organs and a suit- 
 able position. Not having these advantages, but 
 possessing the conception of an ellipse, or (to ex- 
 
340 QUOTATIONS OK INDUCTION. 
 
 press the meaning in less technical language) 
 knowing what an ellipse was, Kepler tried 
 whether the observed places of the planet were 
 consistent with such a path. He found they 
 were so ; and he, consequently, asserted as a 
 fact that the planet moved in an ellipse. But 
 .this fact, which Kepler did not add to, but found 
 in, the motions of the planet, namely, that it 
 occupied in succession the various points in the 
 circumference of a given ellipse, was the very 
 fact, the separate parts of which had been sepa- 
 rately observed ; it was the sum of the different 
 observations. 
 
 Having stated this fundamental difference be- 
 tween my opinion and that of Dr. Whewell, I 
 must add, that his account of the manner in 
 which a conception is selected, suitable to ex- 
 press the facts, appears to me perfectly just. 
 The experience of all thinkers will, I believe, 
 testify that the process is tentative ; that it con- 
 sists of a succession of guesses ; many being re- 
 jected, until one at last occurs fit to be chosen. 
 We know from Kepler himself that before hitting 
 upon the " conception" of an ellipse, he tried 
 nineteen other imaginary paths, which, finding 
 them inconsistent with the observations, he was 
 obliged to reject. But, as Dr. Whewell truly 
 says, the successful hypothesis, though a guess, 
 ought generally to be called, not a lucky, but a 
 skillful guess. The guesses which serve to give 
 mental unity and wholeness to a chaos of 
 scattered particulars, are accidents which rarely 
 occur to any minds but those abounding in 
 
QUOTATION'S OK INDUCTION. 341 
 
 knowledge and disciplined in intellectual combi- 
 nations. 
 
 How far this tentative method, so indispens- 
 able as a means to the colligation of facts for 
 purposes of description, admits of application to 
 Induction itself, and what functions belong to it 
 in that department, will be considered in the 
 chapter of the present Book which relates to 
 Hypotheses. On the present occasion we have 
 chiefly to distinguish this process of Colligation 
 from Induction properly so called ; and that the 
 distinction may be made clearer, it is well to ad- 
 vert to a curious and interesting remark, which 
 is as strikingly true of the former operation, as 
 it appears to me unequivocally false of the latter. 
 
 In different stages of the progress of knowledge, 
 philosophers have employed, for the colligation 
 of the same order of facts, different conceptions. 
 The early rude observations of the heavenly 
 bodies, in which minute precision was neither 
 attained nor sought, presented nothing inconsist- 
 ent with the representation of the path of a 
 planet as an exact circle, having the earth for its 
 centre. As observations increased in accuracy, 
 facts were disclosed which were not reconcilable 
 with this simple supposition : for the colligation 
 of those additional facts, the supposition was 
 varied ; and varied again and again as facts be- 
 came more numerous and precise. The earth 
 was removed from the centre to some other 
 point within the circle ; the planet was supposed 
 to revolve in a smaller circle called an epicycle, 
 round an imaginary point which revolved in a 
 
342 QUOTATIONS ON INDUCTION. 
 
 circle round the earth : in proportion as observa- 
 tion elicited fresh facts contradictory to these 
 representations, other epicycles and other eccen- 
 trics were added, producing additional complica- 
 tion ; until at last Kepler swept all these circles 
 away, and substituted the conception of an exact 
 ellipse. Even this is found not to represent with 
 complete correctness the accurate observations of 
 the present day, which disclose many slight de- 
 viations from an orbit exactly elliptical. Now 
 Dr. Whewell has remarked that these successive 
 general expressions, though apparently so con- 
 flicting, were all correct : . they all answered the 
 purpose of colligation ; they all enabled the 
 mind to represent to itself with facility, and by 
 a simultaneous glance, the whole body of facts 
 at the time ascertained : each in its turn served 
 as a correct description of the phenomena, so far 
 as the senses had up to that time taken cogni- 
 zance of them. If a necessity afterward arose 
 for discarding one of these general descriptions 
 of the planet 's orbit, and framing a different 
 imaginary line, by which to express the series of 
 observed positions, it was because a number of 
 new facts had now been added, which it was 
 necessary to combine with the old facts into one 
 general description. But this did not affect the 
 correctness of the former expression, considered 
 as a general statement of the only facts which it 
 was intended to represent. And so true is this, 
 that, as is well remarked by M. Comte, these 
 ancient generalizations, even the rudest and most 
 imperfect of them, that of uniform movement in 
 
QUOTATIONS OK INDUCTION. 343 
 
 a circle, are so far from being entirely false, 
 that they are even now habitually employed by 
 astronomers when only a rough approximation 
 to correctness is required. " L'astronomie mod- 
 erne, en detruisant sans re tour les hypotheses 
 primitives, envisagees comme lois reelles du 
 monde, a soigneusement maintenu leur valeur 
 positive et permanente, la propriete de repre- 
 senter commodement les phenomenes quand il 
 s'agit d'une premiere ebauche. Nos ressources a 
 cet egard sont me me bien plus etendues, precise- 
 ment a cause que nous ne nous faisons aucune 
 illusion sur la realite des hypotheses ; ce qui 
 nous permet d 7 employer sans scrupule, en chaque 
 cas, celle que nous jugeons la plus avantageuse. "* 
 
 Dr. Whe well's remark, therefore, is philo- 
 sophically correct. Successive expressions for 
 the colligation of observed facts, or, in other 
 words, successive descriptions of a phenomenon 
 as a whole, which has been observed only in 
 parts, may, though conflicting, be all correct as 
 far as they go. But it would surely be absurd 
 to assert this of conflicting inductions. 
 
 The scientific study of facts may be under- 
 taken for three different purposes : the simple 
 description of the facts ; their explanation ; or 
 their prediction : meaning by prediction, the de- 
 termination of the conditions under which sim- 
 ilar facts may be expected again to occur. To 
 the first of these three operations the name of 
 Induction does not properly belong : to the 
 
 * Cours de Philosophic Positive, vol. ii. , p. 202. 
 
344 QUOTATIONS OK INDUCTION. 
 
 other two it does. Now, Dr. Whe well's obser- 
 vation is true of the first alone. Considered as 
 a mere description, the circular theory of the 
 heavenly motions represents perfectly well their 
 general features : and by adding epicycles with- 
 out limit, those motions, even as now known to 
 us, might be expressed with any degree of accu- 
 racy that might be required. The elliptical 
 theory, as a mere description, would have a great 
 advantage in point of simplicity, and in the con- 
 sequent facility of conceiving it and reasoning 
 about it ; but it would not really be more true 
 than the other. Different descriptions, there- 
 fore, may be all true : but not, surely, different 
 explanations. The doctrine that the heavenly 
 bodies moved by a virtue inherent in their celes- 
 tial nature ; the doctrine that they were moved 
 l>y impact (which led to the hypothesis of vor- 
 tices as the only impelling force capable of 
 whirling bodies in circles), and the Newtonian 
 doctrine, that they are moved by the composi- 
 tion of a centripetal with an original projectile 
 force ; all these are explanations, collected by 
 real induction from supposed parallel cases ; and 
 they were all successively received by philoso- 
 phers, as scientific truths on the subject of the 
 heavenly bodies. Can it be said of these, as 
 was said of the different descriptions, that they 
 are all true as far as they go ? Is it not clear 
 that only one can be true in any degree, and 
 the other two must be altogether false ? So 
 much for explanations : let us now compare 
 different predictions : the first, that eclipses will 
 
QUOTATIONS ON INDUCTION. 345 
 
 occur when one planet or satellite is so situated 
 as to cast its shadow upon another ; the second, 
 that they will occur when some great calamity is 
 impending over mankind. Do these two doc- 
 trines only differ in the degree of their truth, as 
 expressing real facts with unequal degrees of ac- 
 curacy ? Assuredly the one is true, and the 
 other absolutely false.* 
 
 * Dr. Whewell, in his reply, contests the distinction 
 here drawn, and maintains, that not only different 
 descriptions, but different explanations of a phenom- 
 enon, may all be true. Of the three theories respect- 
 ing the motions of the heavenly bodies, he says (Phi- 
 losophy of Discovery, p. 231) : " Undoubtedly, all these 
 explanations may be true and consistent with each 
 other, and would be so if each had been followed out 
 so as to show in what manner it could be made con- 
 sistent with the facts. And this was, in reality, in a 
 great measure done. The doctrine that the heavenly- 
 bodies were moved by vortices was successfully mod- 
 ified, so that it came to coincide in its results with 
 the doctrine of an inverse-quadratic centripetal force. 
 . . . When this point was reached, the vortex was 
 merely a machinery, well or ill devised, for produc- 
 ing such a centripetal force, and therefore did not con- 
 tradict the doctrine of a centripetal force. Newton 
 himself does not appear to have been averse to ex- 
 plaining gravity by impulse. So little is it true that 
 if one theory be true the other must be false. The 
 attempt to explain gravity by the impulse of streams 
 of particles flowing through the universe in all direc- 
 tions, which I have mentioned in the Philosophy, is so 
 far from being consistent with the Newtonian theory, 
 that it is founded entirely upon it. And even with 
 regard to the doctrine, that the heavenly bodies move 
 by an inherent virtue ; if this doctrine had been main- 
 tained in any such way that it w y as brought to agree 
 
346 QUOTATIONS ON INDUCTION. 
 
 In every way, therefore, it is evident that to 
 explain induction as the colligation of facts by 
 
 with the facts, the inherent virtue must have had its 
 laws determined ; and then it would have been found 
 that the virtue had a reference to the central body ; 
 and so, the ' inherent virtue ' must have coincided in 
 its effect with the Newtonian force ; and then, the two 
 explanations would agree, except so far as the word 
 ' inherent ' was concerned. And if such a part of an 
 earlier theory as this word inherent indicates, is found 
 to be untenable, it is of course rejected in the transi- 
 tion to later and more exact theories, in Inductions 
 of this kind, as well as in what Mr. Mill calls De- 
 scriptions. There is, therefore, still no validity dis- 
 coverable in the distinction which Mr. Mill attempts to 
 draw between descriptions like Kepler's law of ellip- 
 tical orbits, and other examples of induction. ' ' 
 
 If the doctrine of vortices had meant, not that vor- 
 tices, existed but only that the planets moved in the 
 same manner as if they had been whirled by vortices ; 
 if the hypothesis had been merely a mode of repre- 
 senting the facts, not an attempt to account for them ; 
 if, in short, it had been only a Description ; it would, 
 no doubt, have been reconcilable with the Newtonian 
 theory. The vortices, however, were not a mere aid 
 to conceiving the motions of the planets, but a sup- 
 posed physical agent, actively impelling them ; a 
 . material fact, which might be true or not true, but 
 could not be both true and not true. According to 
 Descartes's theory it was true, according to Newton's 
 it was not true. Dr. Whewell probably means that 
 since the phrases, centripetal and projectile force, do 
 not declare the nature but only the direction of the 
 forces, the Newtonian theory does not absolutely 
 contradict any hypothesis which may be framed re- 
 specting the mode of their production. The New- 
 tonian theory, regarded as a mere description of the 
 planetary motions, does not ; but the Newtonian 
 theory as an explanation of them does. For in what 
 
QUOTATIONS ON INDUCTION. 347 
 
 means of appropriate conceptions, that is, con- 
 ceptions which will really express them, is to 
 
 does the explanation consist? In ascribing those 
 motions to a general law which obtains between all 
 particles of matter, and in identifying this with the 
 law by which bodies fall to the ground. If the 
 planets are kept in their orbits by a force which 
 draws the particles composing them toward every 
 other particle of matter in the solar system, they are 
 not kept in those orbits by the impulsive force of 
 certain streams of matter which whirl them round. 
 The one explanation absolutely excludes the other. 
 Either the planets are not moved by vortices, or they 
 do not move by a law common to all matter. It is 
 impossible that both opinions can be true. As well 
 might it be said that there is no contradiction be- 
 tween the assertions, that a man died because some- 
 body killed him, and that he died a natural death. 
 
 So, again, the theory that the planets move by a 
 virtue inherent in their celestial nature, is incom- 
 patible w T ith either of the two others : either that of 
 their being moved by vortices, or that which regards 
 them as moving by a property which they have in 
 common with the earth and all terrestrial bodies. 
 Dr. Whewell says that the theory of an inherent 
 virtue agrees with Newton's when the word inherent 
 is left out, which of course it would be (he says) if 
 "found to be untenable." But leave that out, and 
 where is the theory? The word inherent is the 
 theory. When that is omitted, there remains nothing 
 except that the heavenly bodies move " by a virtue," 
 i.e., by a power of some sort ; or by virtue of their 
 celestial nature, which directly contradicts the doc- 
 trine that terrestrial bodies fall by the same law. 
 
 If Dr. "Whewell is not yet satisfied, any other sub- 
 ject will serve equally well to test his doctrine. He 
 will hardly say that there is no contradiction between 
 the emission theory and the undulatory theory of 
 light ; or that there can be both one and two electric- 
 
348 QUOTATIONS ON INDUCTION. 
 
 confound mere description of the observed facts 
 with inference from those facts, and ascribe to 
 
 ities ; or that the hypothesis of the production of the 
 higher organic forms by development from the lower, 
 and the supposition of separate and successive acts of 
 creation, are quite reconcilable ; or that the theory 
 that volcanoes are fed from a central fire, and the 
 doctrines which ascribe them to chemical action at a 
 comparatively small depth below the earth's surface, 
 are consistent with one another, and all true as far as 
 they go. 
 
 If different explanations of the same fact can not 
 both be true, still less, surely, can different predic- 
 tions. Dr. Whewell quarrels (on what ground it is 
 not necessary here to consider) with the example I 
 had chosen on this point, and thinks an objection to 
 an illustration a sufficient answer to a theory. Ex- 
 amples not liable to his objection are easily found, 
 if the proposition that conflicting predictions can not 
 both be true, can be made clearer by any examples. 
 Suppose the phenomenon to be a newly-discovered 
 comet, and that one astronomer predicts its return 
 once in every 300 years another once in every 400 : 
 can they both be right ? When Columbus predicted 
 that by sailing constantly westward he should in 
 time return to the point from which he set out, while 
 others asserted that he could never do so except by 
 turning back, were both he and his opponents true 
 prophets ? Were the predictions which foretold the 
 wonders of railways and steamships, and those which 
 averred that the Atlantic could never be crossed by 
 steam navigation, nor a railway train propelled ten 
 miles an hour, both (in Dr. Whewell's words) " true, 
 and consistent with one another ?" 
 
 Dr. Whewell sees no distinction between holding 
 contradictory opinions on a question of fact, and 
 merely employing different analogies to facilitate the 
 conception of the same fact. The case of different 
 Inductions belongs to the former class, that of differ- 
 ent Descriptions to the latter. 
 
QUOTATIONS OX INDUCTION. 349 
 
 the latter what is a characteristic property of the 
 former. 
 
 There is, however, between Colligation and 
 Induction, a real correlation, which it is impor- 
 tant to conceive correctly. Colligation is not 
 always induction ; but induction is always colli- 
 gation. The assertion that the planets move in 
 ellipses, was but a mode of representing observed 
 facts ; it was but a colligation ; while the asser- 
 tion that they are drawn, or tend, toward the 
 sun, was the statement of a new fact, inferred 
 by induction. But the induction, once made, 
 accomplishes the purposes of colligation likewise. 
 It brings the same facts, which Kepler had con- 
 nected by his conception of an ellipse, under the 
 additional conception of bodies acted upon by a 
 central force, and serves, therefore, as a new 
 bond of connection for those facts ; a new prin- 
 ciple for their classification. 
 
 Further, the descriptions which are improp- 
 erly confounded with induction, are nevertheless 
 a necessary preparation for induction ; no less 
 necessary than correct observation of the facts 
 themselves. Without the previous colligation of 
 detached observations by means of one general 
 conception, we could never have obtained any 
 basis for an induction, except in the case of 
 phenomena of very limited compass. We should 
 not be able to affirm any predicates at all, of a 
 subject incapable of being observed otherwise 
 than piecemeal : much less could we extend those 
 predicates by induction to other similar subjects. 
 Induction, therefore, always presupposes, not 
 
350 QUOTATIONS OK INDUCTION. 
 
 only that the necessary observations are made 
 with the necessary accuracy, but also that the 
 results of these observations are, so far as prac- 
 ticable, connected together by general descrip- 
 tions, enabling the mind to represent to itself 
 as wholes whatever phenomena are capable of 
 being so represented. 
 
 5. Dr. Whewell has replied at some length 
 to the preceding observations, restating his opin- 
 ions, but without (as far as I can perceive) add- 
 ing any thing material to his former arguments. 
 Since, however, mine have not had the good for- 
 tune to make any impression upon him, I will 
 subjoin a few remarks, tending to show more 
 clearly in what our difference of opinion consists, 
 as well as, in some measure, to account for it. 
 
 Nearly all the definitions of induction, by 
 writers of authority, make it consist in drawing 
 inferences from known cases to unknown ; 
 affirming of a class, a predicate which has been 
 found true of some cases belonging to the class ; 
 concluding because some things have a certain 
 property, that other things which resemble them 
 have the same property or because a thing has 
 manifested a property at a certain time, that it 
 has and will have that property at other times. 
 
 It will scarcely be contended that -Kepler's 
 operation was an Induction in this sense of the 
 term. The statement, that Mars moves in an 
 elliptical orbit, was no generalization from indi- 
 vidual cases to a class of cases. Neither was it 
 an extension to all time, of what had been found 
 true at some particular time. The whole amount 
 
QUOTATIONS ON INDUCTIQN. 351 
 
 of generalization which the case admitted of, 
 was already completed, or might have been so. 
 Long before the elliptic theory was thought of, 
 it had been ascertained that the planets returned 
 periodically to the same apparent places ; the 
 series of these places was, or might have been, 
 completely determined, and the apparent course 
 of each planet marked out on the celestial globe 
 in an uninterrupted line. Kepler did not extend 
 an observed truth to other cases than those in 
 which it had been observed : he did not widen 
 the subject of the proposition which expressed 
 the observed facts. The alteration he made was 
 in the predicate. Instead of saying, the suc- 
 cessive places of Mars are so and so, he summed 
 them up in the statement, that the successive 
 places of Mars are points in an ellipse. It is 
 true, this statement, as Dr. Whewell says, was 
 not the sum of the observations merely ; it was 
 the sum of the observations seen under a new point 
 of view. * But it was not the sum of more than 
 the observations, as a real induction is. It took 
 in no cases but those which had been actually ob- 
 served, or which could have been inferred from 
 the observations before the new point of view 
 presented itself. There was not that transition 
 from known cases to unknown, which constitutes 
 Induction in the original and acknowledged 
 meaning of the term. 
 
 Old definitions, it is true, can not prevail 
 against new knowledge : and if the Keplerian 
 
 * Phil ofDiscov.,?. 256. 
 
352 QUOTATIONS ON INDUCTION. 
 
 
 
 operation, as a logical process, be really identical 
 with what takes place in acknowledged induc- 
 tion, the definition of induction ought to be so 
 widened as to take it in ; since scientific language 
 ought to adapt itself to the true relations which 
 subsist between the things it is employed to des- 
 ignate. Here then it is that I am at issue with 
 Dr. Whewell. He does think the operations 
 identical. He allows of no logical process in 
 any case of induction, other than what there was 
 in Kepler's case, namely, guessing until a guess 
 is found which tallies with the facts ; and ac- 
 cordingly, as we shall see hereafter, he rejects all 
 canons of induction, because it is not by means 
 of them that we guess. Dr. Whewell' s theory 
 of the logic of science would be very perfect if 
 it did not pass over altogether the question of 
 Proof. But in my apprehension there is such a 
 thing as proof, and inductions differ altogether 
 from descriptions in their relation to that ele- 
 ment. Induction is proof ; it is inferring some- 
 thing unobserved from something observed : it 
 requires, therefore, an appropriate test of proof ; 
 and to provide that test, is the special purpose 
 of inductive logic. When, on the contrary, we 
 merely collate known observations, and, in Dr. 
 Whew ell's phraseology, connect them by means 
 of a new conception ; if the conception does 
 serve to connect the observations, we have all 
 we want. As the proposition in which it is em- 
 bodied pretends to no other truth than what it 
 may share with many other modes of represent- 
 ing the same facts, to be consistent with the facts 
 
QUOTATIONS OK INDUCTION. 353 
 
 is all it requires : it neither needs nor admits 
 of proof ; though it may serve to prove other 
 things, inasmuch as, by placing the facts in 
 mental connection with other facts, not previ- 
 ously seen to resemble them, it assimilates the 
 case to another class of phenomena, concerning 
 which real Inductions have already been made. 
 Thus Kepler's so-called law brought the orbit of 
 Mars into the class ellipse, and by doing so, 
 proved all the properties of an ellipse to be true 
 of the orbit : but in this proof Kepler's law sup- 
 plied the minor premise, and not (as is the case 
 with real Inductions) the major. 
 
 Dr. Whewell calls nothing Induction where 
 there is not a new mental conception introduced, 
 and every thing induction where there is. But 
 this is to confound two very different things, In- 
 vention and Proof. The introduction of a new 
 conception belongs to Invention : and invention 
 may be required in any operation, but is the es- 
 sence of none. A new conception may be intro- 
 duced for descriptive purposes, and so it may for 
 inductive purposes. But it is so far from con- 
 stituting induction, that induction does not nec- 
 essarily stand in need of it. Most inductions 
 require no conception but what was present in 
 every one of the particular instances on which 
 the induction is grounded. That all men are 
 mortal is surely an inductive conclusion ; yet no 
 new conception is introduced by it. Whoever 
 knows that any man has died, has all the concep- 
 tions involved in the inductive generalization. But 
 Dr. Whewell considers the process of invention 
 
354 QUOTATIONS OX INDUCTION. 
 
 which consists in framing a new conception con- 
 sistent with the facts, to be not merely a neces- 
 sary part of all induction, but the whole of it. 
 
 The mental operation which extracts from a 
 number of detached observations certain general 
 characters in which the observed phenomena re- 
 semble one another, or resemble other known 
 facts, is what Bacon, Locke, and most subse- 
 quent metaphysicians, have understood by the 
 word Abstraction. A general expression ob- 
 tained by abstraction, connecting known facts 
 by means of common characters, but without 
 concluding from them to unknown, may, I 
 think, with strict logical correctness, be termed 
 a Description ; nor do I know in what other way 
 things can ever be described. My position, how- 
 ver, does not depend on the employment of that 
 particular word ; I am quite content to use Dr. 
 WhewelPs term Colligation, or the more gen- 
 eral phrases, ' mode of representing, or of ex- 
 pressing, phenomena : ' provided it be clearly 
 seen that the process is not Induction, but 
 something radically different. 
 
 What more may usefully be said on the subject 
 -of Colligation, or of the correlative expression 
 invented by Dr. Whewell, the Explication of 
 Conceptions, and generally on the subject of 
 ideas and mental representations as connected 
 with the study of facts, will find a more appro- 
 priate place in the Fourth Book, on the Opera- 
 tions Subsidiary to Induction : to which I must 
 refer the reader for the removal of any difficulty 
 "which the present discussion may have left. 
 
QUOTATIONS ON INDUCTION. 355 
 
 OF THE GROUND OF INDUCTION. 
 
 1. INDUCTION properly so called, as dis- 
 tinguished from those mental operations, some- 
 times, though improperly, designated by the 
 name, which I have attempted in the preceding 
 chapter to characterize, may, then, be summarily 
 defined as Generalization from Experience. It 
 consists in inferring from some individual in- 
 stances in which a phenomenon is observed to 
 occur, that it occurs in all instances of a certain 
 class ; namely, in all which resemble the former, 
 in what are regarded as the material circum- 
 stances. 
 
 In what way the material circumstances are 
 to be distinguished from those which are imma- 
 terial, or why some of the circumstances are ma- 
 terial and others not so, we are not yet ready to 
 point out. We must first observe, that there is 
 a principle implied in the very statement of what 
 Induction is ; an assumption with regard to the 
 course of nature and the order of the universe ; 
 namely, that there are such things in nature as 
 parallel cases ; that what happens once, will, 
 under a sufficient degree of similarity of circum- 
 stances, happen again, and not only again, but 
 as often as the same circumstances recur. This, 
 I say, is an assumption, involved in every case 
 of induction. And, if we consult the actual 
 course of nature, we find that the assumption is 
 warranted. The universe, so far as known to 
 us, is so constituted, that whatever is true in 
 any one case, is true in all cases of a certain de- 
 
356 QUOTATIONS ON INDUCTION. 
 
 script! on ; the only difficulty is, to find what de- 
 scription. 
 
 This universal fact, which is our warrant for 
 all inferences from experience, has been de- 
 scribed by different philosophers in different 
 forms of language : that the course of nature is 
 uniform ; that the universe is governed by gen- 
 eral laws ; and the like. One of the most usual 
 of these modes of expression, but also one of 
 the most inadequate, is that which has been 
 brought into familiar use by the metaphysicians 
 of the school of Reid and Stewart. The dispo- 
 sition of the human mind to generalize from ex- 
 perience a propensity considered by these phi- 
 losophers as an instinct of our nature they usu- 
 ally describe under some such name as " our in- 
 tuitive conviction that the future will resemble 
 the past." Now it has been well pointed out by 
 Mr. Bailey,* that (whether the tendency be or 
 not an original and ultimate element of our na- 
 ture), Time, in its modifications of past, present, 
 and future, has no concern either with the belief 
 itself, or with the grounds of it. We believe 
 that fire will burn to-morrow, because it burned 
 to-day and yesterday ; but we believe, on pre- 
 cisely the same grounds, that it burned before we 
 were born, and that it burns this very day in 
 Cochin-China. It is not from the past to the 
 future, as past and future, that we infer, but from 
 the known to the unknown ; from facts observed 
 to facts unobserved ; from what we have per- 
 
 * Essays an tJie Pursuit of Truth. 
 
QUOTATIONS ON INDUCTION. 357 
 
 ceived, or been directly conscious of, to what has 
 not come within onr experience. In this last 
 predicament is the whole region of the future ; 
 but also the vastly greater portion of the present 
 and of the past. 
 
 Whatever be the most proper mode of express- 
 ing it, the proposition that the course of nature 
 is uniform, is the fundamental principle, or gen- 
 eral axiom, of Induction. It would yet be a 
 great error to offer this large generalization as 
 any explanation of the inductive process. On the 
 contrary, I hold it to be itself an instance of in- 
 duction, and induction by no means of the most 
 obvious kind. Far from being the first induction 
 we make, it is one of the last, or at all events one 
 of those which are latest in attaining strict phil- 
 osophical accuracy. As a general maxim, indeed, 
 it has scarcely entered into the minds of any but 
 philosophers; nor even by them, as we shall have 
 many opportunities of remarking, have its extent 
 and limits been always very justly conceived. 
 The truth is, that this great generalization is itself 
 founded on prior generalizations. The obscurer 
 laws of nature were discovered by means of it, 
 but the more obvious ones must have been under- 
 stood and assented to as general truths before it 
 was ever heard of. We should never have thought 
 of affirming that all phenomena take place ac- 
 cording to general laws, if we had not first arrived, 
 in the case of a great multitude of phenomena, 
 at some knowledge of the laws themselves ; which 
 could be done no otherwise than by induction. 
 In what sense, then, can a principle, which is so 
 
358 QUOTATIONS OK INDUCTION. 
 
 far from being our earliest induction, be regarded 
 as our warrant for all the others ? In the only 
 sense, in which (as we have already seen) the 
 general propositions which we place at the head 
 of our reasonings when we throw them into syl- 
 logisms, ever really contribute to their validity. 
 As Archbishop Whately remarks, every induction 
 is a syllogism with the major premise suppress- 
 ed ; or (as I prefer expressing it) every induction 
 may be thrown into the form of a syllogism, by 
 supplying a major premise. If this be actually 
 done, the principle which we are now considering, 
 that of the uniformity of the course of nature, 
 will appear as the ultimate major premise of all 
 inductions, and will, therefore, stand to all in- 
 ductions in the relation in which, as has been 
 shown at so much length, the major proposition 
 of a syllogism always stands to the conclusion ; 
 not contributing at all to prove it, but being a 
 necessary condition of its being proved ; since no 
 conclusion is proved, for which there can not be 
 found a true major premise.* 
 
 * In the first edition a note was appended at this 
 place, containing some criticism on Archbishop's 
 Whately 's mode of conceiving the relation between 
 Syllogism and Induction. In a subsequent issue of 
 his Logic, the Archbishop made a reply to the criti- 
 cism, which induced me to cancel part of the note, 
 incorporating the remainder in the text. In a still 
 later edition, the Archbishop observes in a tone of 
 something like disapprobation, that the objections, 
 *' doubtless from their being fully answered and 
 found untenable, were silently suppressed," and that 
 hence he might appear to some of his readers to be 
 
QUOTATIONS ON INDUCTION". 359 
 
 The statement, that the uniformity of the course 
 of nature is the ultimate major premise in all cases 
 
 combating a shadow. On this latter point, the Arch- 
 bishop need give himself no uneasiness. His readers, 
 I make bold to say, will fully credit his mere affirm- 
 ation that the objections have actually been made. 
 
 But as he seems to think that what he terms the 
 suppression of the objections ought not to have been 
 made " silently," I now break that silence, and 
 state exactly what it is that I suppressed, and why. 
 I suppressed that alone which might be regarded as 
 personal criticism on the Archbishop. I had imput- 
 ed to him the having omitted to ask himself a partic- 
 ular question. I found that he had asked himself the 
 question, and could give it an answer consistent with 
 his own theory. I had also, within the compass of a 
 parenthesis, hazarded some remarks on certain general 
 characteristics of Archbishop Whately as a philoso- 
 pher. These remarks, though their tone, I hope, was 
 neither disrespectful nor arrogant, I felt, on recon- 
 sideration, that I was hardly entitled to make ; least 
 of all, when the instance which I had regarded as an 
 illustration of them, failed, as I now saw, to bear 
 them out. The real matter at the bottom of the 
 whole dispute, the different view we take of the 
 function of the major premise, remains exactly where 
 it was ; and so far was I from thinking that my 
 opinion had been fully " answered" and was "un- 
 tenable," that in the same edition in which I can- 
 celled the note, I not only enforced the opinion by 
 further arguments, but answered (though without 
 naming him) those of the Archbishop. 
 
 For not having made this statement before, I do 
 not think it needful to apologize. It would be at- 
 taching very great importance to one's smallest say- 
 ings, to think a formal retractation requisite every 
 time that one falls into an error. Nor is Archbishop 
 "Whately 's well-earned fame of so lender a quality as 
 
360 QUOTATIONS ON INDUCTION. 
 
 of induction, may be thought to require some 
 explanation. The immediate major premise in 
 every inductive argument, it certainly is not. Of 
 that, Archbishop Whately 's must be held to be the 
 correct account. The induction, " John, Peter, 
 etc., are mortal, therefore all mankind are mor- 
 tal," may, as he justly says, be thrown into a syl- 
 logism by prefixing as a major premise (what is at 
 any rate a necessary condition of the validity of 
 the argument), namely, that what is true of John 
 Peter, etc., is true of all mankind. But how 
 came we by this major premise ? It is not self- 
 evident ; nay, in all cases of unwarranted gene- 
 ralization, it is not true. How, then, is it arrived 
 at ? Necessarily either by induction or ratioci- 
 nation ; and if by induction, the process, like all 
 other inductive arguments, may be thrown into 
 the form of a syllogism. This previous syllogism 
 it is, therefore, necessary to construct. There is, 
 in the long run, only one possible construction. 
 The real proof that what is true of John, Peter, 
 etc., is true of all mankind, can only be, that a 
 different supposition would be inconsistent with 
 the uniformity which we know to exist in the 
 course of nature. Whether there would be this 
 inconsistency or not, may be a matter of long and 
 delicate inquiry ; but unless there would, we have 
 no sufficient ground for the major of the induct- 
 ive syllogism. It hence appears, that if we throw 
 the whole course of any inductive argument into 
 
 to require that in withdrawing a slight criticism on 
 him I should have been bound to offer a public 
 amende for having made it. 
 
QUOTATIONS ON INDUCTION. 361 
 
 a series of syllogisms, we shall arrive by more or 
 fewer steps at an ultimate syllogism, which will 
 have for its major premise the principle, or axi- 
 om, of the uniformity of the course of nature.* 
 It was not to be expected that in the case of 
 this axiom, any more than of other axioms, there 
 should be unanimity among thinkers with respect 
 to the grounds on which it is to be received as 
 true. I have already stated that I regard it as 
 
 * But though it is a condition of the validity of 
 every induction that there be uniformity in the course 
 of nature, it is not a necessary condition that the uni- 
 formity should pervade all nature. It is enough that 
 it pervades the particular class of phenomena to 
 which the induction relates. An induction concern- 
 ing the motions of the planets, or the properties of the 
 magnet, would not be vitiated though we were to sup- 
 pose that wind and weather are the sport of chance, 
 provided it be assumed that astronomical and mag- 
 netic phenomena are under the dominion of general 
 laws. Otherwise the early experience of mankind 
 would have rested on a very weak foundation ; for 
 in the infancy of science it could not be known that 
 all phenomena are regular in their course. 
 
 Neither would it be correct to say that every induc- 
 tion by which we infer any truth, implies the general 
 fact of imiformity as foreknown, even in reference to 
 the kind of phenomena concerned. It implies, either 
 that this general fact is already known, or that we 
 may now know it : as the conclusion, the Duke of 
 Wellington is mortal, drawn from the instances A, B, 
 and C, implies either that we have already concluded 
 all men to be mortal, or that we are now entitled to 
 do so from the same evidence. A vast amount of 
 confusion and paralogism respecting the grounds of 
 Induction would be dispelled by keeping in view 
 these simple considerations. 
 
362 QUOTATIONS OK INDUCTION. 
 
 itself a generalization from experience. Others 
 hold it to be a principle which, antecedently to 
 any verification by experience, we are compelled 
 by the constitution of our thinking faculty to as- 
 sume as true. Having so recently, and at so 
 much length, combated a similar doctrine as ap- 
 plied to the axioms of mathematics, by arguments 
 which are in a great measure applicable to the 
 present case, I shall defer the more particular 
 discussion of this controverted point in regard to 
 the fundamental axiom of induction, until a more 
 advanced period of our inquiry. At present it 
 is of more importance to understand thoroughly 
 the import of the axiom itself. For the propo- 
 sition, that the course of nature is uniform, pos- 
 sesses rather the brevity suitable to popular, than 
 the precision requisite in philosophical language : 
 its terms require to be explained, and a stricter 
 than their ordinary signification given to them, 
 before the truth of the assertion can be admitted. 
 2. Every person's consciousness assures him 
 that he does not always expect uniformity in the 
 course of events ; he does not always believe that 
 the unknown will be similar to the known, that 
 the future will resemble the past. Nobody be- 
 lieves that the succession of rain and fine weather 
 will be the same in every future year as in the 
 present. Nobody expects to have the same 
 dreams repeated every night. On the contrary, 
 every body mentions it as something extraordi- 
 nary, if the course of nature is constant, and re- 
 sembles itself, in these particulars. To look for 
 constancy where constancy is not to be expected, 
 
QUOTATIONS ON INDUCTION. 363 
 
 as for instance that a day which has once brought 
 good fortune will always be a fortunate day, is 
 justly accounted superstition. 
 
 The course of nature, in truth, is not only uni- 
 form, it is also infinitely various. Some phenom- 
 ena are always seen to recur in the very same 
 combinations in which we met with them at first; 
 others seem altogether capricious ; while some, 
 which we have been accustomed to regard as bound 
 down exclusively to a particular set of combina- 
 tions, 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 an inhabitant of Central 
 Africa, fifty years ago, no fact probably appeared 
 to rest on more uniform experience than this, 
 that all human beings are black. To Europeans, 
 not many years ago, the proposition, All swans 
 are white, appeared an equally unequivocal in- 
 stance of uniformity in the course, of nature. 
 Further experience has proved to both that they 
 were mistaken ; but they had to wait fifty centu- 
 ries for this experience. During that long time, 
 mankind believed in a uniformity of the course 
 of nature where no such uniformity really existed. 
 
 According to the notion which the ancients en- 
 tertained of induction, the foregoing were cases 
 of as legitimate inference as any inductions what- 
 ever. In these two instances, in which, the con- 
 clusion being false, the ground of inference must 
 have been insufficient, there was, nevertheless, as 
 much ground for it as this conception of induction 
 admitted of. The induction of the ancients has 
 
364 QUOTATIONS OK INDUCTION. 
 
 been well described by Bacon, under the name 
 of u Inductio per enumerationem simplicem, ubi 
 non reperitur instantia contradictoria. ' ' It con- 
 sists in ascribing the character of general truths to 
 all propositions which are true in every instance 
 that we happen to know of. This is the kind of 
 induction which is natural to the mind when un- 
 accustomed to scientific methods. The tendency, 
 which some call an instinct, and which others 
 account for by association, to infer the future 
 from the past, the known from the unknown, is 
 simply a habit of expecting that what has been 
 found true once or several times, and never yet 
 found false, will be found true again. Whether 
 the instances are few or many, conclusive or in- 
 conclusive, does not much affect the matter : 
 these are considerations which occur only on re- 
 flection ; the unprompted tendency of the mind 
 is to generalize its experience, provided this points 
 all in one direction ; provided no other experience 
 of a conflicting character comes unsought. The 
 notion of seeking it, of experimenting for it, of 
 interrogating nature (to use Bacon's expression) 
 is of much later growth. The observation of na- 
 ture, by uncultivated intellects, is purely passive : 
 they accept the facts which present themselves, 
 without taking the trouble of searching for more : 
 it is a superior mind only which asks itself what 
 facts are needed to enable it to come to a safe 
 conclusion, and then looks out for these. 
 
 But though we have always a propensity to 
 generalize from unvarying experience, we are not 
 always warranted in doing so. Before we can be 
 
QUOTATIONS ON INDUCTION. 365 
 
 at liberty to conclude that something is univers- 
 ally true because we have never known an instance 
 to the contrary, we must have reason to believe 
 that if there were in nature any instances to the 
 contrary, we should have known of them. This 
 assurance, in the great majority of cases, we can 
 not have, or can have only in a very moderate 
 degree. The possibility of having it, is the 
 foundation on which we shall see hereafter that 
 induction by simple enumeration may in some 
 remarkable cases amount practically to proof. 
 No such assurance, however, can be had, on any 
 of the ordinary subjects of scientific inquiry. 
 Popular notions are usually founded on induction 
 by simple enumeration ; in science it carries us 
 but a little way. We are forced to begin with 
 it ; we must often rely on it provisionally, in the 
 absence of means of more searching investigation. 
 But, for the accurate study of nature, we require 
 a surer and a more potent instrument. 
 
 It was, above all, by pointing out the insuf- 
 ficiency of this rude and loose conception of In- 
 duction, that Bacon merited the title so generally 
 awarded to him, of Founder of the Inductive 
 Philosophy. The value of his own contributions 
 to a more philosophical theory of the subject has 
 certainly been exaggerated. Although (along with 
 some fundamental errors) his writings contain, 
 more or less fully developed, several of the most 
 important principles of the Inductive Method, 
 physical investigation has now far outgrown the 
 Baconian conception of Induction. Moral and 
 political inquiry, indeed, are as yet far behind 
 
366 QUOTATIONS ON INDUCTION. 
 
 that conception. The current and approved 
 modes of reasoning on these subjects are still of 
 the same vicious description against which Bacon 
 protested ; the method almost exclusively em- 
 ployed by those professing to treat such matters 
 inductively, is the very inductioper enumcrationem 
 simplicem which he condemns ; and the experi- 
 ence which we hear so confidently appealed to by 
 all sects, parties, and interests, is still, in his own 
 emphatic words, mera palpatio. 
 
 3. In order to a better understanding of the 
 problem which the logician must solve if he 
 would establish a scientific theory of Induction, 
 let us compare a few cases of incorrect inductions 
 with others which are acknowledged to be legiti- 
 mate. Some, we know, which were believed for 
 centuries to be correct, were nevertheless incor- 
 rect. That all swans are white, can not have 
 been a good induction, since the conclusion has 
 turned out erroneous. The experience, however, 
 on which the conclusion rested, was genuine. 
 From the earliest records, the testimony of the 
 inhabitants of the known world was unanimous 
 on the point. The uniform experience, therefore, 
 of the inhabitants of the known world, agreeing 
 in a common result, without one known instance 
 of deviation, from that result, is not always suffi- 
 cient to establish a general conclusion. 
 
 But let us now turn to an instance apparently 
 not very dissimilar to this. Mankind were wrong, 
 it seems, in concluding that all swans were white : 
 are we also wrong, when we conclude that all 
 men's heads grow above their shoulders, and 
 
QUOTATIONS ON INDUCTION. 367 
 
 never below, in spite of the conflicting testimony 
 of the naturalist Pliny ? As there were black 
 swans, though civilized people had existed for 
 three thousand years on the earth without meet- 
 ing with them, may there not also be " men 
 whose heads do grow beneath their shoulders, ' ' 
 notwithstanding a rather less perfect unanimity 
 of negative testimony from observers ? Most 
 persons would answer No ; it was more credible 
 that a bird should vary in its color, than that men 
 should vary in the relative position of their prin- 
 cipal organs. And there is no doubt that in so 
 saying they would be right : but to say why they 
 are right, would be impossible, without entering 
 more deeply than is usually done into the true 
 theory of Induction. 
 
 Again, there are cases in which we reckon with 
 the most unfailing confidence upon uniformity, 
 and other cases in which we do not count upon it 
 at all. In some we feel complete assurance that 
 the future will resemble the past, the unknown 
 be precisely similar to the known. In others, 
 however invariable may be the result obtained 
 from the instances which have been observed, we 
 draw from them no more than a very feeble pre- 
 sumption that the like result will hold in all other 
 cases. That a straight line is the shortest dis- 
 tance between two points, we do not doubt to be 
 true even in the region of the fixed stars.* When 
 
 * In strictness, wherever the present constitution 
 of space exists ; which we have ample reason to 
 believe that it does in the reign of the fixed stars. 
 
368 QUOTATIONS ON INDUCTION. 
 
 a chemist announces the existence and properties 
 of a newly-discovered substance, if we confide in 
 his accuracy, we feel assured that the conclusions 
 he has arrived at will hold universally, though the 
 induction be founded but on a single instance. 
 We do not withhold our assent, waiting for a 
 repetition of the experiment ; or if we do, it is 
 from a doubt whether the one experiment was 
 properly made, not whether if properly made it 
 would be conclusive. Here, then, is a general law 
 of nature, inferred without hesitation from a 
 single instance ; a universal proposition from a 
 singular one. Now mark another case, and con- 
 trast it with this. Not all the instances which 
 have been observed since the beginning of the 
 world, in support of the general proposition that 
 all crows are black, would be deemed a sufficient 
 presumption of the truth of the proposition, to 
 outweigh the testimony of one unexceptionable 
 witness who should affirm that in some region of 
 the earth not fully explored, he had caught and 
 examined a crow, and had found it to be gray. 
 
 Why is a single instance, in some cases, suffi- 
 cient for a complete induction, while in others, 
 myriads of concurring instances, without a single 
 exception known or presumed, go such a very little 
 way toward establishing a universal proposition ? 
 Whoever can answer this question knows more 
 of the philosophy of logic than the wisest of the 
 ancients, and has solved the problem of induction. 
 
 (pp. 431432). What renders arithmetic the 
 type of a deductive science, is the fortunate ap- 
 plicability to it of a law so comprehensive as 
 
QUOTATIONS OX INDUCTION. 369 
 
 i i The sums of equals are equals' ' : or (to express 
 the same principle in less familiar but more char- 
 acteristic language), whatever is made up of 
 parts, is made up of the parts of those parts. 
 This truth, obvious to the senses in all cases which 
 can be fairly referred to their decision, and so 
 general as to be co- extensive with nature itself, 
 being true of all sorts of phenomena (for all ad- 
 mit of being numbered), must be considered an 
 inductive truth, or law of nature, of the highest 
 order. And every arithmetical operation is an 
 application of this law, or of other laws capable 
 of being deduced from it. This is our warrant 
 for all calculations. We believe that five and two 
 are equal to seven, on the evidence of this in- 
 ductive law, combined with the definitions of 
 those numbers. We arrive at that conclusion (as 
 all know who remember how they first learned it) 
 by adding a single unit at a time : 5+1 = 6, 
 therefore 5+1 + 1 = 6+1 = 7 ; and again 2 = 1 
 +1, therefore 
 
QUOTATIONS ON INTERPRETATION. 
 
 APPENDIX J. 
 
 234. 1. From Davies and Peck, Dictionary 
 of Mathematics. 
 
 Interpretation. [L. interpretatio, explana- 
 tion]. The process of explaining results arrived 
 at by the application of mathematical rules. 
 When, for example, an algebraic definition is 
 laid down, there is frequently some restriction 
 implied in making the definition, so that the re- 
 sult to which it leads presents more cases than can 
 be explained by it, or even than was contemplated 
 by it. Thus the abbreviation of a a, a a a, into 
 a 2 , a 3 , and the rules which spring from it, lead 
 to results of the form. 
 
 a ~ 2 , a, a*, a ~ *, etc. 
 
 These results, until interpreted, are without any 
 intelligent algebraic meaning. 
 
 When such results arise, the province of inter- 
 pretation begins ; their meaning and force are 
 investigated and explained, and the definitions 
 heretofore too narrow, are extended so as to cover 
 these and other results. 
 
 The rule to be adopted in interpreting new ex- 
 pressions obtained by applying known processes, 
 is to attribute to them such a meaning as to make 
 
QUOTATIONS ON INTERPRETATION. 371 
 
 the whole of the process true by which they were 
 obtained. For example : the formula 
 
 a m X n = a m + n 
 
 is perfectly intelligible so long as m and n are 
 whole numbers. Suppose it were required to in- 
 terpret the symbol a, that is, to give to it such 
 a meaning, that the above formula shall be true 
 in that case. Making m=0, the formula becomes 
 
 a X a n + n = n ', 
 
 hence, a = 1. Again, suppose it were required 
 to interpret the symbol a*. Make m = ^ and 
 91 = , and the formula becomes 
 
 hence, a* 6 = V, for ^a x ^ = , by definition. 
 
 Besides the application of the principles of in- 
 terpretation to the explanation of new symbols, 
 another very important application consists in 
 making suppositions upon certain arbitrary quan- 
 tities which enter formulas, and then comparing 
 the results with known facts, thus deducing new 
 truths. As an example of this method of inter- 
 pretation let us take the equation of the ellipse 
 
 and suppose x > a, finding the value of y in 
 terms of a;, we have 
 
372 QUOTATIONS ON INTERPRETATION. 
 
 from which we see that for all values of x greater 
 than a, y is imaginary. Now an imaginary 
 result indicates an impossibility in the assumption. 
 Hence, we interpret the result as indicating that 
 no point of the ellipse can lie at a greater distance 
 from its conjugate axis than the extremity of the 
 transverse axis. 
 
 In integrating the differential of a transcen- 
 dental function by an algebraic rule, a result oo is 
 reached, which is manifestly absurd, since no 
 function can be oo. We interpret this as indi- 
 cating that the rule fails in the case considered. 
 
 2. From Smith's Synonyms Discriminated. 
 
 Expound (Lat. expono) denotes sustained ex- 
 planation ; while a mere word or phrase may 
 be explained, a whole work or parts of it may 
 be expounded. Exposition is continuous crit- 
 ical explanation. Interpret (Lat. interpres, 
 an interpreter), beyond the mere sense of verbal 
 translation from one language to another, conveys 
 the idea of private or personal explanation of 
 what is capable of more than one view. Hence 
 interpretation is more arbitrary than exposition, 
 and more theoretical than explanation. Expound 
 relates only to words in series, interpretation is 
 applicable also to anything of a symbolical char- 
 acter, as to interpret a dream or a prophecy. It 
 is also, in common with explain, an application 
 to anything which may be viewed in different 
 lights, as the actions of men. In this way, to 
 explain conduct would rather be to account for 
 it ; to interpret it would be to assign motives or 
 significance to it. Explanation deals with facts, 
 interpretation with causes also. 
 
QUOTATIONS ON DEDUCTION. 
 
 APPENDIX K. 
 
 235. 1. From Fleming's Vocabulary of Phi- 
 losophy, Ed. 1858, pp. 126-7. 
 
 Deduction (from deduce, to draw from, to 
 cause to come out of,) is the mental operation 
 which consists in drawing a particular truth from 
 a general principle antecedently known. It is 
 opposed to induction, which consists in rising 
 from particular truths to the determination of 
 a general principle. Let it be proposed to prove 
 that Peter is mortal ; I know that Peter is a 
 man, and this enables me to say that all men are 
 mortal, from which affirmation I deduce that 
 Peter is mortal. 
 
 The syllogism is the form of deduction. Aris- 
 totle (Prior. Analyt.,\\b. 1, cap. 1) has defined 
 it to be " an enunciation in which certain asser- 
 tions being made, by their being true, it follows 
 necessarily, that another assertion different from 
 the first is true also. ' ' 
 
 Before we can deduce a particular truth, we 
 must be in possession of the general truth. This 
 may be acquired intuitively, as every change 
 implies a cause ; or inductively, as the volume 
 of gas is in the inverse ratio of the pressure. 
 
 Deduction, when it uses the former kind of 
 
374 QUOTATIONS ON DEDUCTION. 
 
 truths, is demonstration or science. Truths 
 drawn from the latter kind are contingent and . 
 relative, and admit of correction by increasing 
 knowledge. The principle of deduction is, that 
 things that agree with the same things agree with 
 one another. The principle of induction is, that 
 in the same circumstances, and in the same sub- 
 stances, from the same causes the same effects 
 will follow. 
 
 The mathematical and metaphysical sciences 
 are founded on deduction, the physical sciences 
 rest on induction, 
 
 2. From Day's Elements of Logic, Ed. 1868, 
 p. 105. 
 
 A Deductive Syllogism is a Mediate Reasoning 
 in which the movement of Thought is from a 
 Whole to a Part, mediated through a middle 
 term, which is, respectively, a part of that whob 
 and a whole of that part ; as, Man is mortal ; Caius 
 is a man ; therefore, Caius is mortal. 
 
 As the Deductive Syllogism is a Mediate 
 Reasoning, its datum must consist of two Judg- 
 ments, which, as given to Thought, are not of 
 course at all validated by the Reasoning. 
 
 They must be regarded consequently as only 
 assumed for the Reasoning, or must rest on evi- 
 dence foreign to it. But the movement of 
 Thought in itself may be valid, although the given 
 Judgments are false ; just as an arithmetical pro- 
 cess may be correct, although applied to unreal 
 objects. 
 
 3. From Bowen's Logic, Ed. 1874, pp. 261, 
 262. 
 
QUOTATIONS ON DEDUCTION. 375 
 
 Reasoning, however, proceeds not only in dif- 
 ferent wholes, but in different aspects of the same 
 whole. We may, it is evident, regard any whole, 
 considered as the complement of its parts, in 
 either of two ways ; for we may, on the one hand, 
 look from the whole to the parts, and reason ac- 
 cordingly downwards ; or, on the other hand, look 
 from the parts to the whole they constitute, and 
 reason accordingly upwards. The former of these 
 reasonings is called Deductive, the latter Induc- 
 tive. Deductive reasoning is founded on the 
 maxim, ' What belongs to the containing whole 
 belongs also to the contained parts ;' Induction, 
 on the contrary maxim, i What belongs to the 
 constituent parts belongs also to the constituted 
 whole.' Thus, in Deductive reasoning, the 
 whole is stated first, and what is affirmed of it is 
 affirmed of the parts it contains ; in other words, 
 a general law is laid down, and predicated of the 
 particular instances to which it applies. 
 
 In Inductive reasoning, the parts are first stated, 
 and what is predicated of them is also predicated 
 of the whole they constitute ; in other words, the 
 particular instances are first 'stated as facts, and 
 then the law they constitute is evolved. 
 
 4. From Hedge's Elements of Logick, Ed. 
 1854, pp. 118, 119. 
 
 Syllogism (= Deduction) and induction pro- 
 ceed in opposite directions. Induction . . begins 
 with individual objects, as they exist in nature, 
 and ascends by successive steps to the most 
 general truths. Syllogism (=: Deduction) begins 
 where inductions terminates. It commences with 
 
376 QUOTATIONS ON DEDUCTION. 
 
 some universal proposition, and follows back the 
 footsteps of the former process, transferring at 
 each stage the predicate of the more general to 
 the less general rank of beings ; or, in other 
 words, predicating the genus of the species, and 
 the species of the individual. 
 
 . . . Syllogism (= Deduction) is employed 
 with advantage in communicating to others, in 
 an exact and perspicuous manner, the general 
 principles of science. It may also be used with 
 success in exposing the weakness of arguments, 
 stated in loose or figurative language. But it 
 is of no service in helping us to the discovery 
 of new truths. ' ' We must know a thing first, ' ' 
 Mr. Locke observes, " and then we can prove it 
 syllogisticallj- " 
 
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 do it ; and it has proved more practically helpful in the school-room than 
 any other book ever issued. 
 
 U. A Quiz-Book on the Theory and Practice of Teaching. By A. P. 
 SOUTHWICK, author of the "Dune Question Books." 12mo, pp. 220. Price $1.00. 
 
 This is one of the six books recommended by the State Department for 
 study in preparation for State Certificates. The others are Hoose's Methods 
 ($1.00), Hughes's Mistakes (50 cts.), Fitch's Lectures ($1.00), Page's Theory and' 
 Practice ($1.25), and Swett's Methods ($1.25). We will send the six post-paid- 
 for $5.00. 
 
 5. Mistakes in Teaching. By JAMES L. HUGHES. American edition, with 
 contents and index. Cloth, 16mo, pp. 135. Price 50 cts. 
 
 More than 15,000 have been used in the county institutes of Iowa, and 
 elsewhere superintendents often choose this book for their less thoughtful 
 teachers, assured that its pungent style and chatty treatment will arrest- 
 attention and produce good results. 
 
 6 How to Secure and Eetain Attention. By JAMES L. HUGHES. 16mo y 
 cloth, pp. 97. Price 50 cts. 
 
 This touches attractively and helpfully upon the first serious difficulty 
 the teacher encounters. No young teacher should neglect these hints. 
 
 7. Primary Helps. A Kindergarten Manual for Public School Teachers. 
 By W. N. HAILMANN. 8vo, boards, pp. 58, with 15 full-page plates. Pi-ice 75 cts. 
 
 In these days, no primary teacher can afford to be ignorant of " The New 
 Education," and this is perhaps the only volume that makes kindergarten 
 principles practically available in public schools. 
 
 8. Dime Question Book, No. 4, Theoiy and Practice of Teaching. 16mo, 
 y aper, pp. 40. Price 10 cts. By A. P. SOUTHWICK. 
 
 A capital preparation for examination. 
 C. W. BARDEEN, Publisher, Syracuse, N. Y, 
 
- THE S CHO OL B ULLETIN PUBLIC A r i / 9J\ S. 
 
 The Five Great English Books, 
 
 The recognition of Teaching as a Science was much earlier in England 
 than in this country, and the five books which are there recognized as stan- 
 dards, have probably no equals in soundness and scope. Hence they are 
 usually the first books adopted by Reading Circles, and are indispensable to 
 the library of an intelligent teacher. These are : 
 
 1. Essays on Educational Reformers. By ROBERT HENRY QUICK. Cloth, 
 16mo, pp. 330. Price $1.50 ; or special edition, thinner covers, price $1.00. 
 
 This is altogether the best History of Education. " With the suggestion 
 that study should be made interesting," writes Principal Morgan, of the Rhode 
 Island State Normal School, "we most heartily agree. How this may be 
 done, the attentive reader will be helped in learning by the study of this 
 admirable book." 
 
 2. Lectures on Teaching. By J. G. FITCH. New Edition with a Preface 
 by an American Normal Teacher. Cloth, 16mo, pp. 393. Price $1.25. 
 
 This forms the proper Basis for pedagogical knowledge, beginning with 
 the teacher, the school, and the school-room, and giving the why as well aa 
 the what. We publish in our "School Room Classics" the "Art of Ques- 
 tioning," and the "Art of Securing Attention," by the same author, at 15 
 cents each. 
 
 3. Lectures on the Science ami Art of Education. By JOSEPH PAYNE. 
 Cloth, IGmo, pp. 384. Price $1.00. 
 
 The student is now ready to take up the Science of Education, which Is 
 nowhere else so brilliantly and effectively presented. The lectures are sin- 
 gularly fascinating, and the full analysis and indexes in this edition make it 
 easy to collate and compare all that the author has uttered upon any topio 
 suggested. 
 
 U. The Philosophy of Education, or the Principles and Practice of Teaching. 
 BY THOMAS TATE. Cloth, 16mo, pp. 440. Price $1.50. 
 
 This gives the application of the Science to the Art of Teaching, and is 
 without a rival in its clear presentation and abundant illustrations. The 
 tuthor is not content with giving directions. He shows by specimens of 
 ^ass-work just what should be done and may be done. 
 
 5. Introductory Tcxt-BooTc to School Education, Method and School Man- 
 By JOHN GILL. Cloth, 16mo, pp. 276. Price $1.00. 
 
 This supplements the work of all the rest by practical directions as to 
 School Management. Of the five this has had a sale equal to that of all the 
 rest combined. The teacher's greatest difficulty, his surest discomfiture if 
 he fails, is in the discipline and management of his school. That this man- 
 ual has proved of inestimable help is proved from the fact that the present 
 English edition is the 44th thousand printed. 
 
 C, W, BARDEEN, Publisher, Syracuse, N. Y. 
 
-THE SCHOOL BULLETIN" PUBLICATIONS.- 
 
 The School Eoom Classics. 
 
 Under the above title we have published a series of Monographs upon 
 Education, as follows, all 16mo, in paper, at 15 cts. each. 
 
 1. Unconscious Tuition. By Bishop HUNTINGTON. Pp. 45. 
 
 "There is probably nothing finer in the whole range of educational lit- 
 erature." Ohio Educational Monthly. 
 
 "It cannot be read without a wholesome self -weighing, and a yearning 
 which develops true character." The Schoolmaster, Chicago. 
 
 2. The Art, of Questioning. By J. G. FITCH. Pp. 36. 
 
 "Mr. Fitch is happily inside his subject, and as clear as a bell." Chris- 
 Man Register. 
 
 3. The Philosophy of School Discipline. By JOHN KENNEDY. Pp. 23. 
 "Clear and logical, and goes down to the very foundation." Utica 
 
 Herald. 
 
 k. The Art of Securing Attention. By J. G. FITCH. Pp. 43. 
 
 "Perhaps I overestimate Fitch's works, but I fail to find in the state- 
 ment of any other educational writer a juster comprehension of the needs 
 and difficulties of both teacher and pupil, or more common sense put into 
 neater, clearer style." The Student, Philadelphia. 
 
 5. Learning and Health. By B. W. RICHARDSON. Pp. 39. 
 "A timely topic ably treated." N. E. Journal of Education. 
 
 " Certainly worth many times its weight in gold." Eclectic TeacJier. 
 
 6. The New Education. By J. M. W. MEIKLEJOHN. Pp. 35. 
 
 " Absolutely the best summary we have seen of the doctrines of Froebel 
 in their present development." JV. Y. School Journal. 
 
 7. A Small Tractate of Education. By JOHN MILTON. Pp. 26. 
 
 " Far more important in the literature of the subject than the treatise 
 of Locke." Encyclopaedia Brittanica. 
 
 8. TJie School Work-Shop. By Baroness VON MARENHOLZ-BUELOTT. trans- 
 lated by Miss BLOW. Pp. 27. 
 
 "In this treatise the kindergarten view of Industrial Education receives 
 its best exemplification." N. E. Journal of Education. 
 
 9. Sex in Mind and in Education. By HENRY MAUDSLEY. Pp. 42. 
 
 " A masterly treatment of a delicate subject." N. E. Journal of Edu- 
 cation. 
 
 10. Education as Viewed by Thinkers. Pp. 47. 
 
 This contains 95 classified quotations from leading authorities of every 
 time and country, and will be of use to every writer and speaker. 
 
 11. How to Teach Natural Science in Public Schools. By WM. T. HARRIS. 
 Pp. 40. 
 
 Since this was first published in 1871 for the schools of St. Louis, it has 
 been regarded as the standard authority upon the subject, and this edition, 
 revised by the author, was prepared by the request of the Committee on 
 Physics-Teaching in 1887 of the National Association. 
 
 C. W. BARDEEN, Publisher, Syracuse, N. Y. 
 
-THE SCHOOL BULLETIN PUBLICATIONS.- 
 
 Instruction in Citizenship, 
 
 1. Civil Government for Common Schools, prepared as a manual for 
 public instruction in the State of New York. To which are appended the 
 Constitution of the State of New York as amended at the election of 1882, 
 the Constitution of the United States, and the Declaration of Independence, 
 etc., etc. By HENRY C. NORTHAM. 16mo, cloth, pp. 185. 75 cts. 
 
 Is it that this book was made because the times demanded it, or that the 
 publication of a book which made the teaching of Civil Government practi- 
 cable led to a general desire that it should be taught ? Certain it is that this 
 subject, formerly regarded as a " finishing " branch in the high school, is 
 now found on every teacher's examination-paper, and is commonly taught 
 in district schools. Equally certain is it that in the State of New York this 
 text-book is used more than all others combined. 
 
 2. A Chart of Civil Government. By CHARLES T. POOLER. Sheets 12xl8 r 
 5 cts. The same folded, in cloth covers, 25 cts. 
 
 Schools using Northam's Civil Government will find this chart of great 
 use, and those not yet ready to introduce a text-book will be able to give no 
 little valuable instruction by the charts alone. Some commissioners have 
 purchased them by the hundred and presented one to every school house in 
 the county. 
 
 8. Handbook for School Teachers and Trustees. A manual of School 
 Law for School Officers, Teachers and Parents in the State of New York. 
 By HERBERT BROWNELL. 16mo, leatherette, pp. 64. 35 cts. 
 
 This is a specification of the general subject, presenting clearly, defi- 
 nitely, and with references, important questions of School Law. Particular 
 attention is called to the chapters treating of schools under visitation of the 
 Regents a topic upon which definite information is often sought for in vain. 
 
 h. t Common School Law for Common School Teachers. A digest of the 
 provisions of statute and common law as to the relations of the Teacher to 
 the Pupil, the Parent, and the District. With 500 references to legal decis- 
 ions in 28 different States. 14th edition, wholly re-written, with references 
 to the new Code of 1888. By C. W. BARDEEN. 16mo, cloth, pp. 120. 75 cts. 
 
 This has been since 1875 the standard authority upon the teacher's rela- 
 tions, and is frequently quoted in legal decisions. The new edition is much 
 more complete than its predecessors, containing Topical Table of Contents, 
 and a minute Index. 
 
 5. Laics of New York relating to Common Schools, with comments and 
 instructions, and a digest of decisions. 8vo, leather, pp. 867. $4.00. 
 
 This is what is known as u The New Code of 1888," and contains all re- 
 visions of the State school-law to date. 
 
 6. The Powers and Duties of Officers and Teachers. By ALBERT P. MAR- 
 BLE. 16mo, paper, pp. 27. 15 cts. 
 
 A vigorous presentation in Sup't Marble's pungent style of tendencies 
 as well as facts. 
 
 7. First Principles of Political Economy. By JOSEPH ALDEN. 16mo, 
 cloth, pp. 153. 75 cts. 
 
 Ex-President Andrew D. White says of this book : " It is clear, well 
 arranged, and the best treatise for the purpose I have ever seen." 
 
 C. W. BARDEEN, Publisher, Syracuse, N. Y. 
 
* THE SCHO OL B ULLETIN PUBLZCA TIONS. 
 
 Teachers' Question Books. 
 
 1. The Regents' Questions in Arithmetic, Geography, Grammar and Spell- 
 ing from the first examination in 1866 to June 1882. (No questions of later date 
 will be printed.} Being the 11,000 Questions for the preliminary examinations 
 for admission to the University of the State of New York, prepared by the 
 Regents of the University, and participated in simultaneously by more than 
 250 academies, forming a basis for the distribution of more than a million of 
 dollars. Complete with Key. Cloth, 16mo, pp. 473. $2.00. 
 
 9. Complete. The same as above but without answers. Pp. 340. $1.00. 
 
 In the subjects named, no other Question Book can compare with this 
 either in completeness, in excellence, or in popularity. By Legislative Enact- 
 ment no lawyer can be admitted to the bar in the State of New York without 
 passing a Regents' Examination in these subjects. 
 
 3. The Dime Question Books, with full answers, notes, queries, etc. Paper, 
 pp. about 40. By A. P. SOTJTHWICK. Each 10 cts. 
 
 Elementary Series. Advanced Series. 
 
 3. Physiology. 1. Physics. 
 
 4. Theory and Practice. 2. General Literature, 
 6. U. S. History and Civil Gov't. 5. General History. 
 
 10. Algebra. 7. Astronomy. 
 
 13. American Literature. 8. Mythology. 
 
 14. Grammar. 9. Rhetoric. 
 
 15. Orthography and Etymology. 11. Botany. 
 
 18. Arithmetic. 12. ZoOlogy. 
 
 19. Physical and Political Geog. 16. Chemistry. 
 50. Reading and Punctuation. 17. Geology. 
 
 These 10 in one book. Cloth, $1.00. These 10 in one book. Cloth, $1.06. 
 Extra Volume, 21. Temperance Physiology. 
 
 The immense sale of the Regents' Questions in Arithmetic, Geography, 
 Grammar, and Spelling has led to frequent inquiry for the questions in the 
 Advanced Examinations. -4s it is not permitted to reprint these, we have had 
 prepared this series, by which the teacher need purchase books only on the 
 subjects upon which special help is needed. Frequently a $1.50 book is 
 bought for the sake of a few questions in a single study. Here, the studies 
 may be taken up one at a time, a special advantage in New York, sinct appli- 
 cants for State Certificates may nmv present themselves for examination in only 
 part of the subjects, 'and receive partial Certificates to be exchanged for full Cer- 
 tificates when all the branches have been passed. The same plan is very gener- 
 ally pursued by county superintendents and commissioners who are encour- 
 ing their teachers to prepare themselves for higher certificates. 
 
 U. Quizzism. Quirks and Quibbles from Queer Quarters. Being a Melange 
 of questions in Literature, Science, History, Biography, Mythology, Philolo- 
 gy, Geography, etc. By A. P. SOUTHWICK. 16mo, pp. 55. 25 cts. Key, $1.00. 
 
 A stimulus for home study, and invaluable for school or teachers' 
 gatherings. 
 
 5. New York State Examination Questions. Cloth, 16mo, pp. 256. 50 cts. 
 This contains all the questions given at all the New York Examinations 
 
 for State Certificates from the beginning. There are more questions and in 
 greater variety than in any other collection. It does not give answers. 
 
 6. The Common School Question Book. By ASA L. CRAIG. Cloth, 12 mo, 
 pp. 340. $1.50. We can also furnish SHAW'S National Question Book, pp. 351, 
 $1.50 ; STILLWELL'S Practical Question Book, pp. 400, $1.50 ; BROWN'S Common 
 School Examiner, pp. 371, $1.00: THOMPSON'S Teachers Examiner^ pp. 378 
 $1.50; SHERRILL'S Normal Question Book, pp. 460, $1.50. 
 
 C. W. BARDEE^, Publisher, Syracuse, N, Y. 
 
-THE SCHOOL BULLETIN PUBLICATIONS.- 
 
 Helps toward Correct Speech. 
 
 1. Verbal Pitfalls: a manual of 1500 words commonly misused, includ- 
 ing all those the use of which in any sense has been questioned by Dean. 
 Alvord, G. W. Moon, Fitzedward Hall, Archbishop Trench, Wm. C. Hodg- 
 son, W. L. Blackley, G. F. Graham, Richard Grant White, M. Schele de Vere, 
 Wm. Mathews, " Alfred Ayres," and many others. Arranged alphabetically 
 with 3000 references and quotations, and the ruling of the dictionaries. 
 By C. W. BARDEEN. 16ino, cloth, pp. 223. 75 cts. 
 
 Perhaps the happiest feature of the book is its interesting form. Some 
 hundreds of anecdotes have been gathered to illustrate the various points 
 made. These have the advantage not only of making the work entertain- 
 ing, but of fixing the point in the mind as a mere precept could not do. The 
 type indicates at a glance whether the use of a word is (1) indefensible, (2} 
 defensible but objectionable, or (3) thoroughly authorized. 
 
 *. A System of Rlietoric. By C. W. BARDEEN. 12mo, half leather, pp. 
 813. $1.75. 
 
 3. A SJwrter Course in Rhetoric. By C. W. BABDEEN. 12mo, half leather, 
 pp. 311. $1.00. 
 
 It. Outlines of Sentence Making. By C. W. BARDEEN. 12mo, cloth, pp. 
 187. 75 cts. 
 
 5. Practical PJionics. A comprehensive study of Pronunciation, form- 
 ing a complete guide to the study of elementary sounds of the English Lan- 
 guage, and containing 3,000 words of difficult pronunciation, with diacriti- 
 cal marks according to Webster's Dictionary. By E. V. DE GRAFF. 16mo, 
 cloth, pp. 108. 75 cts. 
 
 The "book before us is the latest, and in many respects the best, of the 
 manuals prepared for this purpose. The directions for teaching elementary 
 sounds are remarkably explicit and simple, and the diacritical marks a r& 
 fuller than in any other book we know of, the obscure vowels being mai kod, 
 as well as the accented ones. This manual is not like others of the kind, a 
 simple reference book. It is meant for careful study and drill, and is es- 
 pecially adapted to class use. New England Journal of Education. 
 
 6. Pocket Pronunciation Book, containing the 3,000 words of difficult 
 pronunciation, with diacritical marks according to Webster's Dictionary. 
 By E. V. DE GRAFF. 16mo, manilla, pp. 47. 15 cts. 
 
 Every vowel that can possibly be mispronounced is guarded by danger 
 signals which send one back to the phonic chart for instructions. We are 
 glad to notice that the Professor is leading a campaign against the despoil 
 ers of the vowel u ; he cannot hold communion with an educated man whose 
 third day in the week is "Toosday." Northern Christian Advocate. 
 
 7. Studies in Articulation : a study and drill-book in the Alphabetic Ele- 
 ments of the English language. Fifth thousand. By J. H. HOOSE. 16mo, 
 cloth, pp. 70. 50 cts. 
 
 This work not only analyzes each sound in the language, but gives as 
 illustrations hundreds of words commonly mispronounced. 
 
 Dr. Hoose's " Studies in Articulation " is the most useful manual of the 
 kind that I know of. It should be a text-book in every Teachers' Institute. 
 A. J. Rickoff, formerly Sujft of Schools at Cleveland and at Yonkers. 
 
 8. Hints on Teaching Orthoepy. By CHAS. T. POOLER. 16mo, paper, pp. 
 15. 10 cts. 
 
 9. Question Book of Orthography, Orthoepy, and Etymology^ with Notes, 
 Queries, etc. By ALBERT P. SOUTHWICK. 16mo, paper, pp. 40, 10 Jts. 
 
 10. Question Book of Reading and Punctuation, with Notes, Queries, etc. 
 By ALBERT P. SOUTHWICK. 16mo, paper, pp. 38. 10 cts. 
 
 C. W. BARDEEtf, Publisher, Syracuse, N. Y. 
 
THE SCHOOL BULLETIN PUBLICATIONS. 
 
 Helps in Language Teaching. 
 
 1. Normal Language Lessons : being the instruction in Grammar given 
 at the Cortland State Normal School. By Prof. S. J. SORNBERGER. 16mo, 
 boards, pp. 81. 50 cts. 
 
 Whatever text-book the teacher uses, or if he uses no text-book at all, 
 he will find this manual of great assistance. Its classification is simple, its 
 definitions are careful, its tabular analyses are complete, and Us reference by 
 page to ail the best autJiors makes it invaluable. 
 
 2. Exercises in English Syntax. By A. G. BUGBEE. 16mo, leatherette, 
 pp. 87. 35 cts. 
 
 This differs from other handbooks of sentences for class-drill in that it 
 does not print wrong sentences to be corrected, a practice now generally 
 condemned, because incorrect forms should never be put before the child's 
 eye : but leaves blanks in the sentence to be filled by the pupil from a 
 choice of expressions given, thus calling in the most effective way to right 
 usage and its reasons. It is of especial assistance in preparation for Re- 
 gents' examinations, which always include much work of this kind. Send 
 for special circular with specimen sentences, and recommendations. 
 
 8. The Regents' Questions in Grammar, from the beginning to June, 
 1882. By DANIEL J. PRATT, Assistant Secretary. 16mo, manilla, pp. 109. 
 25 cts. 
 
 This unequalled series of questions is recognized throughout the country 
 as the best drill-book ever made, and the only satisfactory preparation for 
 examination. 
 
 An edition of these Questions, with complete answers, and references to the 
 grammars of Brown, Murray, Greene, Clark, Kerl, Quackenbos, Weld & 
 Quackenbos, Hart-, Fowler, Swinton, Reed & Kellogg, and Whitney, will be 
 sent post-paid to any address on receipt of One Dollar. It contains 198 
 pages, and is handsomely bound in cloth. 
 
 U. Dime Question Book No. lit, Grammar. By ALBERT P. SOUTHWICK. 
 KJmo, paper, pp. 35. 10 cts. 
 
 This is one of the best books in a deservedly popular series, giving full 
 answers to every question, with notes, queries, etc. Conductor John Ken- 
 nedy says: " The bad question book fosters cram; the good one suggests 
 study. Mr. Southwick's system is good. It is happy and nourishing. I 
 hope you may sell a million of them." 
 
 5. The Diacritical Speller. A practical course of exercises in Spelling 
 and Pronunciation. By C. R. BALES. 8vo, boards, pp. 68. 50 cts. 
 
 This work is novel even in a field so thoroughly worked as spelling. Its 
 striking features are conciseness and simplicity. The pupil is not drilled 
 upon what all pupils know, but only upon what most pupils fail in. The 
 collections of words are made with great skill, and the pupil who uses this 
 book is not likely to say Toosday or Reuler. The selection of test-words is 
 particularly happy, and the exercises in synonyms will afford material for 
 many a spare ten minutes. California Teacher. 
 
 6. An Aid to English Grammar; designed principally for Teachers. 
 By ASHER P. STARKWEATHER. IGmo, boards, pp. 230. 75 cts. 
 
 This is a grammar aid book on a wholly original plan. It is simply a 
 collection of words which are used as two or more parts of speech, with 
 illustrative sentences to show their correct use. School Herald, Chicago. 
 
 C, W. BAItDEEN, Publisher, Syracuse, N. Y. 
 
-THE SCiIOOL BULLETIN PUBLICATIONS.- 
 
 Helps in Teaching Literature. 
 
 1. A Series of Questions in English and American Literature, prepared 
 for class drill and private study by MARY F. HENDRICK, teacher in the State 
 Normal School, Cortland, N. Y. 16mo, boards, pages 100, interleaved. 35 cts. 
 
 This edition is especially prepared for taking notes in the literature 
 class, and may be used in connection with any text-book or under any in- 
 struction. 
 
 2. Early English Literature, from the Lay of Beowulf to Edmund Spen- 
 ser. By WM. B. HARLOW, instructor in the High School, Syracuse, N. Y. 
 16mo, cloth, pp. 138. 75 cts. 
 
 This handsome volume gives copious extracts from all leading authors, 
 of sufficient length to afford a fair taste of their style, while its biographical 
 and critical notes give it rare value. 
 
 3. Dime Question Book No. 2, General Literature, and No. 13, American, 
 Literature. By ALBERT P; SOUTHWICK. 16mo, paper, pp. 35, 39. 10 cts. each. 
 
 These are among the most interesting books in the series, abounding in 
 allusion and suggestion, as well as giving full answers to every question. 
 They afford a capital drill, and should be used in every class as a prepara- 
 tion for examination. 
 
 h. How to Obtain the Greatest Value from a Book. By the Rev. R. W. 
 LOWRIE. 8vo, pp. 12. 25 cts. 
 
 No one can read this essay without pleasure and profit. 
 
 5. The Art of Questioning. By JOSHUA G. FITCH. 16mo, paper, pp. 36. 
 15 cts. 
 
 Mr. Fitch, one of Her Majesty's inspectors of schools, now recognized as 
 the ablest of English writers on education, owed his early reputation to this 
 address, the practical helpfulness of which is everywhere acknowledged. 
 
 6. The Art of Securing Attention. By JOSHUA G. FITCH. 16mo, paper, 
 pp. 43. 15 cts. 
 
 The Maryland School Journal well says: " It is itself an exemplification 
 of the problem discussed, for the first page fixes the attention so that the 
 reader never wearies, till he comes to the last and then wishes that the end 
 had not come so soon." 
 
 7. The Elocutionist's Annual, comprising new and popular Readings, 
 Recitations, Declamations, Dialogues, Tableaux, etc., etc. Compiled oy 
 Mrs. J. W. SHOEMAKER. Paper, 16mo, pp. 200. 12 Numbers. Price of each, 
 30 cts. 
 
 Though primarily designed for classes in elocution, the character of the 
 selections is so high that any of these volumes may be used with profit in a 
 literature class. 
 
 S. The Bible in the Public Schools. Paper, 24mo, 2 vols., pp. 214, 28. 
 50 cts. 
 
 These volumes contain the most important arguments, decisions, and 
 addresses connected with the celebrated contest in Cincinnati, 1869. 
 
 C. W. BARDEEN, Publisher, Syracuse, N. Y, 
 
-THE SCHOOL BULLETIN PUBLICATIONS.- 
 
 Helps in t Teaching History. 
 
 1. A Thousand Questions in Ame?*ican History. 16mo, cloth, pp. 347. 
 Price $1.00. 
 
 This work has been prepared by an eminent teacher for use in his own 
 school one of the largest in the State. It shows rare breadth of view and 
 discrimination, dealing not merely with events but with causes, and with th 
 side-issues that have so much to do with determining the destiny of a nation. 
 
 2 . Helps in Fixing tlie Facts of Amei^ican History. By HENRY C. NOR- 
 THAM. 16mo, cloth, pp. 298. Price $1.00. < ^ 
 
 Here all facts are presented in groups. The . L exington. _ 
 key-word to the Revolution, for instance, is I independence. >^ 
 LIBERTY, as shown in the accompanying table B urgoyne's Surrender. 1 
 of Key-Words and in like manner the events of E vacuation. 
 the late civil war are kept chronologically dis- R etribution. 
 tinct by the key-words SLAVES FREED. Chart T reason, f 
 ^"o. 1 indicates by stars the years in each decade Y orktown. v 
 from 1492 to 1789, in which the most remarkable events occured, while tht 
 colored chart No. 2 arranges the events in twelve groups. 
 
 5. Topics and References in American History, with numerousSearoh 
 Questions. By GEO. A. WILLIAMS. IGmo, leatherette, pp. 50. 50 cts. 
 
 This is a book of immediate practical value to every teacher. The refer- 
 ences are largely to the lighter and more interesting illustrations of history, 
 of a kind to arouse the- thought of pupils by giving vivid conceptions of th 
 events narrated. By dividing these references among the members of a class, 
 the history recitation may be made the most delightful of the day. 
 
 U. Dime Question Books, No. 5, General History, and No. 6, United States 
 History and Civil Government. By ALBERT P. SOUTHWICK. 16mo, paper, pp. 
 37, 32. 10 cts. each. , 
 
 5. Outlines and Questions in United States History. By C. B. Van Win. 
 16mo, paper, pp. 40, and folding Map. 15 cts. 
 
 The outgrowth of four years' practical work in the school-room with 
 map prepared by a pupil as a suggestive model. 
 
 6. Tablet of American History, with Map of the United States on the 
 back. By RTJFUS BLANCHARD. Heavy paper, mounted on rollers, 3^ by 5 
 feet. Price, express paid, $3.00. 
 
 The demand for a colored chart to hang upon the wall and thus catck 
 the often-lifted eye of the pupil, has led to the preparation of this chart by 
 an experienced author. The events of the four centuries are grouped in 
 parallel belts of different colors, and upon the corners and sides are names 
 of the States and Territories, with their etymology, etc., history of political 
 parties, portraits of all the Presidents, Coats of Arms of all the States, etc. 
 The map is engraved expressly for this chart by Rand & McNally, is colored 
 both by States and by counties, and gives all the latest railroads, the new ar- 
 rangement of time-lines, showing where the hour changes, etc. 
 
 C, W, BATODEEN, Publisher, Syracuse, N. Y, 
 
-THE SCHOOL BULLETIN PUBLICATIONS,- 
 
 Music in the School Eoom. 
 
 1. The Song Budget. A collections of Songs and Music for Educational 
 Gatherings. By E. V. DE GRAFF. Small 4to, paper, pp. 76. 15 cts. 
 
 This book owes its popularity to two causes : 
 
 (1) It gives a great deal for the money. 
 
 (2) The songs are not only numerous (107), but they are the standard favor- 
 ites of the last fifty years. 
 
 This is why the book contains more music that will be used than any other 
 book published. For in all other books that we know of, two-thirds of the 
 tunes are written by the compilers, who are of course partial to their own 
 productions. Sup't De Graff wrote no songs of his own, but gathered those 
 which his long experience as a conductor of teachers' institutes had shown 
 him to be the most generally familiar and pleasing. 
 
 In fact, the success of this book has been due to the fact that only those 
 songs were admitted that have proved to be universal favorites. This in- 
 volved a large original outlay, as much as fifty dollars having been paid for 
 the right to use a single song. But the best were taken, wherever they 
 could be found and at whatever cost, and the result is a school singing-book 
 of popularity unexampled. For instance, a single firm in Cleveland, Ohio, 
 J. R. Holcomb & Co., had purchased of us up to Feb. 15, 1888, no less than 
 9730 copies, 4500 within the last six months, besides 2100 of the School Eoom 
 Chorus. 
 
 2. TJi-e School Room Choru,s. A collection of Two Hundred Songs for 
 Public and Private Schools, compiled by E. V. DE GRAFF. Small, 4to, boards, 
 pp. 148. 35 cts. 
 
 This is an enlarged edition of the Song Budget, with twice the number 
 of songs. The plates of the last edition are so arranged that it is identical 
 with the Song Budget as far as page 68, so that both books can be used to- 
 gether. The Budget and Chorus are particularly adapted for Teachers' Asso- 
 ciations and Institutes. At these prices eveiy meeting of teachers can be sup- 
 plied with one or the other, while the fact that the tunes are standard 
 favorites makes it easy for any audience to join in the singing at sight 
 
 3. The Diadem of ScJiool Songs : containing Songs and Music for all 
 grades of Schools, a new system of Instruction in the elements of Music, 
 and a Manual of Directions for the use of Teachers. By WM. TILLINGHAST. 
 Small, 4to, boards, pp. 160. 50 cts. 
 
 This book, of which Dr. French, the veteran institute-instructor was 
 associate author, gives an exceedingly simple and practical system of in- 
 struction, as well as a valuable collection of songs. 
 
 h. Half a Hundred Songs, for the School-Room and Home. By HATTIE 
 S. RUSSELL. 16mo, boards, pp. 103. 35 cts. 
 
 These songs are all original, but without music. 
 
 5. The School Vocalist ; containing a thorough system of elementary 
 instruction in Vocal Music, with Practical Exercises, Songs, Hymns, Chants, 
 &c., adapted to the use or Schools and Academies. By E. LOCKE, and S. 
 NOURSE. Oblong, boards, pp. 160. Price 50 cts. 
 
 6. The School Melodist. A Song Book for School and Home. By E. 
 LOCKE and S. NOURSE. Oblong, boards, pp. 160. Price 50 cts. 
 
 7. The Song Life, for Sunday Schools, etc., illustrating in song the 
 journey of Christiana and her children to the Celestial City. Small 4to 
 boards, pp. 176. Price 50 cts. 
 
 Nos. 5, 6, and 7 are books that have had their day, but of which we have 
 a few hundred copies of each on hand. These we will sell at 10 cts. each ; 
 if to go by mail, 6 cts. each extra. They contain much good music. 
 
 C. W. BARDEEN, Publisher, Syracuse, N. Y. 
 
-THE SCHOOL BULLETIN PUBLICATIONS.- 
 
 Arithmetic by the Grube Method. 
 
 1. First Steps among Figures. A drill book in the Fundamental Rules 
 of Arithmetic. By LEVI N. BEEBE. Cloth, 16mo, 3 editions. Pupils 1 Edi- 
 tion, pp. 140, 45 cts. Oral Edition, pp. 139, 50 cts. TeacJiers' Edition, includ- 
 ing all in both the others, with additional parallel matter, Index, and Key, 
 pp. 326, SI. 00. 
 
 These books give the only practical exposition of the Grube MetJwd, now 
 generally admitted to produce the best results with beginners. It has been 
 used ten years in the primary schools of such cities as Norwich, Conn., and 
 Auburn, N. Y., and for many years every student in the Albany State Normal 
 School has been directed to purchase a copy to take with him for his subse- 
 quent use in teaching. 
 
 From a multitude of testimonials we copy the following : 
 
 44 We are still successfully using Beebe's First Steps. It has many admi- 
 rable qualities." Svp't N. L. Bishop, Norwich, Conn. 
 
 44 I think it especially excellent for a system of graded schools, where 
 uniformity of teaching is essential. It develops in practical shape an idea 
 that I have long sustained as to the proper method of teaching arithmetic." 
 Supt B. B. Snow, Auburn, N. Y. 
 
 44 1 have recommended Beebe's First Steps as the best work in primary 
 arithmetic. . . . The book is received with much favor, and is very helpful 
 to me in my work. " Prof. A. N. Husted, State Normal School, Albany, N. Y. 
 
 44 1 am much pleased with the book, and wish every primary teacher to 
 have a copy." Sup't J. M. Frost, Hudson, N. Y. 
 
 "By vote of the Board of Education a copy of the Teachers' Edition 
 was placed on the desk of every primary teacher in the city. Sup't Edward 
 Smith, Syracuse, N. Y. 
 
 44 1 consider Beebe's First Steps the best work of the kind that I have 
 ever seen, and I take every opportunity to recommend it." Mary L. Sutliff, 
 Haiku, Maid, Hawaian Islands^ Feb. 9, 1888. 
 
 2 The Pestalozzian Series of Arithmetics. Teachers' Manual and First- 
 Year Text-Book for pupils in the first grade. Based upon Pestalozzi's 
 method of teaching Elementary Number. By JAMES H. HOOSE. Boards, 
 16mo, 2 editions. Pupils' Edition, pp. 156, 35 cts. Teacher's Edition, contain- 
 ing the former, with additional matter, pp. 217, 50 cts. 
 
 This is a practical exposition of the Pestalozzian Method, and has met with 
 great success not only in the Cortland Normal School, where it was first 
 developed, but in many other leading schools, as at Gloversville, Babylon, 
 etc. It is diametrically opposed to the GrubS Method, and good teachers 
 should be familiar with both, that they may choose intelligently between 
 them. 
 
 5. Lessons in Number, as given in a Pestalozzian School, Cheam Surrey. 
 The Master-s Manual By C. REINER. 16mo, pp. 224. $1.50. 
 
 This work was prepared in 1835 under the supervision of Dr. C Mayo in 
 the first English Pestalozzian school, and has particular value as represent- 
 ing directly the educational methods of the great reformer. 
 
 C. W. BARDEEN, Publisher, Syracuse, N. Y. 
 
-THE SCHOOL BULLETIN PUBLICATIONS.- 
 
 Useful Appliances in Arithmetic. 
 
 1. The Word Method in Number. A series of 45 Cards, on which are 
 printed all the possible Combinations of Two Figures. In box. By H. R. 
 SANFORD, Institute Canductor. Size 3*4 x 6 inches. Price 50 cts. 
 
 These cards need only to be seen, as the principle is familiar and ac- 
 cepted. The type, in written figures, is large enough to be seen across the 
 room, and the combination on one side is given in reversed order on the 
 other, so that as the teacher holds the card before him he knows the figures 
 presented to the class. The pupil is taught to look upon the combination 
 4-f9 as itself 13, not as "4 and 9 are 13," just as he looks upon DOG as an 
 entire word, not as D-O-G. Success is certain if new combinations are in- 
 troduced only after those already given are thoroughly learned. Reviews 
 should be constant. 
 
 2. A Fractional Apparatus. By W. W. DAVIS. A box of eight wooden 
 balls, three and one-half inches in diameter, seven of which are sawn into 
 2, 3, 4, G, 8, 9, and 12 parts respectively, while the eighth is left a sphere. 
 Price $4 00. 
 
 With this apparatus every principle and rule can be developed, and the 
 pupils can be led to deduce rules for themselves. 
 
 Many other expedients are resorted to, but they are all objectionable. 
 Suppose a teacher takes a stick and breaks it in the middle, will the pupil 
 perceive two halves of a stick or two sticks? In teaching fractions object- 
 ively, that should be taken for unity from which if a part is taken unity is 
 destroyed. This is not the case with a stick or cube. Apples are objection- 
 able for three reasons ; first because they cannot always be obtained ; sec- 
 ond because they are perishable ; and third, because the attention of the 
 pupils is diverted by a desire to know whether they are sweet or sour, etc. 
 Nor can the teacher readily saw wooden balls into divisions even enough for 
 the purpose designed, the charm of this method being the exact presentation 
 to the pupil's eye of the fact illustrated. 
 
 3. A Manual of Suggestions for Teaching Fractions especially designed 
 for accompanying the above apparatus. By W. W. DAVIS. Paper, 12mo, 
 pp. 43. 25 cts. 
 
 This accompanying manual gives probably the best arrangement of th 
 subject into sixty lessons ever made, with practical suggestions which all 
 teachers will find valuable. 
 
 h. Cube Eoot Blocks, carried to Three Places. In box. $1.00. 
 
 Our blocks are unusually large, the inner cube being two inches, and th 
 additions each one-half inch wide. 
 
 5. Numeral Frame, with 100 balls, $1.25 ; with 144 balls, $1.50. 
 
 "Initiate children to arithmetic by means of the ball f rime alone, there- 
 by making their elementary instruction a simple and natui al exten sion of 
 their own daily observation," says Laurie, in his standard book on Primary 
 Instruction (p. 112), and as he leaves the subject of arithmetic, he adds this 
 note (p. 117), as if in fear he had not been sufficiently emphatic : 
 
 " The teaching of arithmetic should be begun earlier than is customary, 
 and always with the ball-frame.'" 
 
 C. W. BABI>EEN, Publisher, Syracuse, IT. Y, 
 
-1*ttE SCHOOL BULLETIN PUBLICATIONS.- 
 
 Maps, Charts and Globes. 
 
 1. Johnston s Watt Naps These are of three sizes, 27x33 inches, costing 
 $2.50 each; 40x48 costing $5.00 each; and 63x72, costing $10.00 each. 
 
 The Common School Series includes (ct) Hemispheres, (b) North America, 
 (e) South America , (rf)United States, (e) Europe, (/) Asia, (?) Africa. Others 
 sometimes substituted or added are (h) World, Mercator's Projection, (i) 
 Eastern Hemiphere, (&) Western Hemisphere. 
 
 We can furnish also in the 40x48 size: (/) England, (rri) France, (n) Italy, 
 (o) Spain, ( p) Central America, (q) Orbis Veteribus Notus, (r) Italia Antiqua, 
 ($) Grecia Antiqua, (t) Asia Minor, (n) Orbis Romanus, (to) De Bello Gallico, 
 (x) Canaan and Palestine, (y) Bible Countries, (z) United States, historical, 
 showing at a glance when and whence each portion of its territory was de- 
 riveda very valuable map in history classes. 
 
 All these maps are engraved on copper, and printed in permanent oil 
 colors. All are cloth-mounted, on rollers. Spring rollers are added at an 
 extra cost of $1.00, $1.50, and $2.50 respectively. 
 
 We offer a special consignment of T. Ruddinian Johnston's maps 40x48, 
 in sets only, including Hemispheres, North America, South America, United 
 States, political, United States, historical, Europe, Asia, and Africa, 8 maps, 
 regular price $40.00, at $15.00 per set. They were prepared for a firm in the 
 west who have been obliged to discontinue the business, and were sent to 
 us by the Johnston Co. with instruction to close them out at once. Hence 
 the unparallelled price, which applies enly to this 100 sets. 
 
 8. Bulletin Map of the United States. Paper, on rollers, 3^>x5 ft., with 
 Blanchard's chart of the United States History upon the back. $3.00. 
 
 This is colored both by States and by Counties and gives correctly the 
 new time lines. 
 
 U Map of New York State, colored both by Counties and by Towns, 
 2fx3 ft. on rollers. Paper, $1.00; Cloth, $2.00. 
 
 5. Adams's Large Map of New Yoc*k State, 61x66 inches. Cloth, on rollers, 
 $10.00; on spring rollers, $12.00. We ire now the sole proprietors of this 
 latest and best map, and can hereafter fill all orders promptly. 
 
 6. Dissected Map of New York, s?irn into Counties. 75 cts. 
 
 7. Dissected Map of the United Stales, sawn into States. 75 cts. 
 
 8. Chart of Life Series of Physiology Charts. 23x27 inches, four in num- 
 ber, including one to show the effec'a of alcohol on the system. These show 
 every organ, life-size and in place. Per set, $10.00; on spring rollers, $12.50. 
 
 9. EclcharVs Anatomical Charts consisting of 12 double plates, with 
 more than 100 distinct and separate figures. Per set, $15.00. 
 
 10. Keadin g Charts of all kinds. Appleton's, $12.50; Monroe's Complete, 
 $10.00. Monroe's Abridged, $6.00, eft}. 
 
 The School Bulletin Globe. Whi?e we keep a dozen styles always in stock, 
 we recommend this especially beep-vise: 1. It is 12 or 6 inches in diameter. 2. 
 It has a low and heavy Bronzed Iron Frame. Its axis is adjustable. 4. 
 It shows an entire Hemisphere. 5. Its Meridian is movable. 6. Its map is 
 Johnston's. 7. It is shipped to an} address at Fifteen Dollars for a 12-incb. 
 r Five Dollars for 6-inch size. 8. VERY GLOBE is GUARANTEED TO BB ABSO 
 
 LUTELY PERFECT (14) 
 
 C. W. BARDEEX, Publisher, Syracuse, N. Y* 
 
THE SCHOOL BUIXETISr PUBLICATIONS.- 
 
 Blackboard Material. 
 
 No feature of the school-room is of more vital importance to the health 
 of scholars and teachers than the Blackboard. If it be gray or greasy the 
 amount of chalk used fills the air with dust, which produces catarrhal and 
 bronchial difficulties, and yet makes so faint a mark that the children's 
 eyes are permanently injured. Choice should be made among the following 
 materials. 
 
 1. Solid Slate. This is durable, but costs from 30 to 50 cts. a square foot, 
 is noisy, not black enough in color, and unhealthful because there is com- 
 monly used upon it the softest crayon. Where solid slate is already in, we 
 recommend the Slate Pencil Crayon, as the only preventive of serious disease. 
 
 But it is better to put either upon the plastered wall, or upon the wall 
 covered with manilla paper, or upon wooden boards, one of the following 
 preparations. 
 
 . Agalite Slating. This is the cheapest of all, may be sent by mail, and 
 usually gives fair satisfaction. Price, post-paid, for box to cover 400 feet, 
 one coat, $6.00; 200 feet, $8 25; 100 feet, $1.75; 50 feet, $1.00. We furnish the 
 Black Diamond or Silicate Slating at the same price, but it can be sent only 
 by express. 
 
 5. Slate Pencil Slating. This remarkable preparation does away alto- 
 gether with chalk-dust, having sufficient grit to take a distinct mark from a 
 slate-pencil. Soft crayon should never be used upon it, unless it is first rubbed 
 down to smoother surface. It is a pure alcohol slating, and therefore dura- 
 ble. Price per gallon, covering 600 ft., one coat, $10.00; quarts, $2.75; pints 
 $1.50. 
 
 In many schools using the Slate Pencil Slating, the State Normal at 
 Potsdam, for instance, Faber's slate-pencils have taken the place of crayon. 
 In other schools hard crayon, like Alpha H, is used. 
 
 U. Hornstone Slating. This is new, and altogether the best in the market, 
 making a really stone surface which is yet absolutely black. There is no 
 waste of chalk, even with soft crayon, while the Alpha H produces a 
 beautifully clear mark. It contains no oil or grease, and grows harder with 
 age. It is put on with a paint-brush, and adheres to any material, so that 
 it may be put on walls, boards, paper, or any other smooth surface. Price 
 $8.00 per gallon, covering 200 feet with four coats. It is somewhat expen- 
 sive, and must be put on with care; but when properly finished it is a delight 
 to the eye. 
 
 Sup't Smith, of Syracuse, says: "Your Ilornstone Slating is now in use 
 in four of our buildings, and I have no hesitation in saying that it is superior 
 to solid slate or to any other blackboard surface I ever saw." Principal 
 Miner, of Skaneateles, says: " Its very smooth surface saves crayon and les- 
 sens the amount of chalk-dust in the room I do not hesitate to say that 
 it is the best board I ever used." 
 
 Cheney's Dustless Erasers work well on any of the boards named. 
 Price 10 cts. each, $1.00 a dozen. The School Bulletin Erasers are made ot 
 the closest and best felt, and are very durable. Price 15 cts. each, $1.50 a 
 dozen. Specimen of either by mail for 15 cts. Alpha Crayon, M or II, 75 
 cts. a box. Ordinary While Crayon, 15 cts. a box. Colored Crayon^ 75 cts. a 
 box. Slate Pencil Crayon, for solid slate, 50 cts. a box. (13) 
 
 C. W. BAKDEEN, Publisher, Syracuse, N. Y. 
 
THE 8 CH O PL JJ ULLE'l 'IN PUBLIC A Tl ONS.- 
 
 School Kecords and Reports, 
 
 1. The Bulletin Class Register. Designed by EDWARD SMITH, Superin- 
 tendent of Schools, Syracuse, N. X". Press-board cover. Three Sizes, (a) 6x7, 
 for terms of twenty weeks; (6) 5x7, for terms of fourteen weeks. When not 
 otherwise specified this size is always sent. Pp. 48. Each 25 cts. (c), like (&) 
 but with one half more (72) pages. Each 35 cts. 
 
 This register gives lines on each of 12 pages for 29 names, and by a nar- 
 row leaf-puts opposite these names blanks for one entry each day for either 
 14 or 20 weeks, as desired, with additional lines for summary, examina- 
 tions, and remarks. Nothing can be more simple, compact, and neat, where 
 it is desired simply to keep a record of attendance, deportment, and class- 
 standing. It is used in nearly two-thirds of the union schools of New York. 
 
 . The Peabody Class Record, No. 1, with 3 blanks to each scholar each 
 day for a year. Boards 4^x9J, pp. 100, &1.00. No. 2, with 5 blanks to each 
 scholar, 8x11, $1.50. Like No. 1, but gives 3 or 5 blanks each day. 
 
 8. Ryan's School Record, 112 blanks to a sheet, per dozen sheets, 50 cts. 
 
 h. Keller's Monthly Report Card, to be returned with signature of parent 
 or guardian, card-board 2%x4, per hundred, $1.00. 
 
 5. Babcock's Excelsior Grading Blanks, manilla, 3x5, with blanks on both 
 sides. Comprising (a) Report Cards; (6) Grade Certificates for each of 9 
 grades; (c) High School Certificate (double size). Price of (a) and (b) $1.00 a 
 hundred; of (c) $1.50 a hundred. 
 
 6. Shaw's Scholar's Register, for each Week, with Abstract for the Term. 
 Paper, 5x7, pp. 16. Per dozen, 50 cts. Each pupil keeps his own record. 
 
 7. Jackson's Class Record Cards. Per set of 90 white and 10 colored 
 cards, with hints, 50 cts. Only imp&fect recitations need be marked. 
 
 8. Aids to School Discipline, containing 80 Certificates, 120 Checks, 200 
 Cards, 100 Single and Half Merits. Per box, $1.25. Supplied separately per 
 hundred: Half Merits, 15 cts., Cards, 15 cts., Checks, 50 cts., Certificates, 50 cts. 
 
 The use of millions of these Aids, with the unqualified approval of teach- 
 ers, parents, and pupils, is assurance that they are doing great good. 
 
 They save time by avoiding the drudgery of Record keeping and Reports. 
 
 They abolish all notions of "partiality" by determining the pupil's 
 standing with mathematical precision. 
 
 They naturally and invariably awaken a lively paternal interest, for the 
 pupil takes home with him the witness of his daily conduct and progress. 
 
 They are neat in design, printed in bright colors. The Certificates are 
 prizes which children will cherish. The Single Merits and Half Merits are 
 printed on heavy card board, the Cards and Checks on heavy paper, and both 
 may be used many times hence the system is cheap, as well as more atr 
 tractive than any other to young children. 
 
 9. Mottoes for the School-Room. By A. W. EDSON, State Agent of Massa- 
 chusetts. Per set of 12 on heavy colored card-board 7x4 inches, printed OH 
 both sides, $1.00, post-paid, $1.10. 
 
 These mottoes are "Never too Late," " Above all, be Useful," "Dare to 
 Say No," " God Bless our School," "Avoid Anger," "Be Good, Do Good," 
 " Think, Speak, Act the Truth," "Fear to Do Wrong," "Misspent Time is 
 
 First of Others," " Dare to Do Right," " Order is Heaven's First Law," "A 
 Will Makes a Way," "Study to Learn," "Hold Fast to Honor," "God 
 Sees Me." (12) 
 
 C. W. BARDEEN, Publisher, Syracuse, N. Y. 
 
-THE SCHOOL BULLETIN PUBLICATIONS.- 
 
 Official Question Books. 
 
 1. The New York State Examination Questions from the beginning to 
 the present date. Cloth, IGmo, pp. 274, 50 cts. 
 
 These annual examinations, only by which can State Certificates be ob- 
 tained in New York, have a reputation all over the country for excellence 
 and comprehensiveness. The subjects are as follows : 
 
 Arithmetic, Grammar, Physics, Geography, 
 
 Book-Keeping, Composition, Chemistry, Civil Government, 
 Algebra, Rhetoric, Geology, Astronomy, 
 
 Geometry, Literature, Botany, Methods, 
 
 Drawing, History, ZoClogy, School Economy, 
 
 Penmanship, Latin, Physiology, School Law. 
 
 No answers are published, except in the following special volume. 
 #. Dime Question Book on Book-Keeping* containing all the questions in 
 that subject given at the first 15 New York Examinations for State Certifi- 
 cates, ivithfull Answers, Solutions, and Forms. Paper, 16mo, pp. 31, 10 cts. 
 
 8. The Uniform Examination Questions. By voluntary adoption of the 
 113 School-Commissioners of the State of New York, certificates are now 
 given only on examinations held under these questionSj which are issued 
 sealed from the State Department. They are published in the School Bulle- 
 tin of the following dates, ivith Complete Official Answers', price of each, 
 10 cts. 
 
 June, 1888, School Law, 34 Questions and Answers. 
 July, 1888, Arithmetic, 167 
 Aug., 1888, Geography, 385 
 Oct., 1888, Grammar, 328 
 Nov., 1888, Physiology, 250 
 Dec., 1888, Am. History, 301 
 U. The Civil Service Question Book. Cloth, 16mo, pp. 282, $1.50. 
 42,000 places are now filled exclusively by appointments dependent on 
 examinations. No favoritism is possible. You do not need the influence of 
 Congressman or of politician. You have only to learn when the next ex- 
 amination is held, apply for the necessary papers, present yourself, and 
 answer the questions asked. The appointments are made from those who 
 stand highest, and are open to women as well as to men. All the particu- 
 lars as to these examinations, the places and dates where held, and how to 
 apply, are here given with 943 specimen questions in Arithmetic, 575 specimen 
 questions in Geography, 400 specimen questions in English Syntax, 100 each 
 in Amencan History and Civil Government, with full treatises on Book-Keep- 
 ing and on Letter- Writing. To prepare for competition for places at $1,000 
 and higher these subjects and these only are required. Any one who can 
 answer the questions here given, to all of which full and complete ansioers are 
 tdded, is ready to enter the next examination. 
 
 Hon JOHN B. RILEY, Chief Examiner, State of New York, July 10, 1888, 
 says : " I am pleased with your Civil Service Question Book. It will not only 
 be of service to those intending to try the Civil Service examinations, but 
 teachers or others who are obliged to prepare questions for examinations in 
 the common English branches will find it a great convenience.'* 
 
 The N. E. Journal of Education says, Aug. 23, 1888 : " It is rarely that any 
 fcook can be found with so many valuable and so few unimportant questions." 
 
 OTHER QUESTION BOOKS. 
 
 5. The Common School Question Book. By ASA L. CRAIG. Cloth, 12mo, 
 pp. 340. $1.50. SHAW'S National Question Book, pp. 351, $1.50 : STILLWELL'S 
 Practical Question Book, pp. 400, $1.50 ; BROWN'S Common School Examiner, 
 pp. 371, $1.00 ; THOMPSON'S TeacJier's Examiner, pp. 378, $1.50 ; SHERRILL'S 
 Normal Question Book, pp. 400, $1.50. 
 
 C. W. BARDEEN, Publisher, Syracuse, N. Y. 
 
Mei 
 Mai 
 
 -[Hemispheres', N. Am., S'. Am., Europe, AMU, jij-nvu, ^.^.^ ,t7. S. 3 00 
 
 Historical, (Jolniston's) 40x48, cloth, each 5 00 
 
 Dissected M aps. United States sawn into States 75 
 
 The same, New York State sawn into Counties 75 
 
 Michael (O. S.) Algebra for Beginners. Cloth, 16mo, pp. 120 75 
 
 Miller (Warner.) Education as a Dep't of Government. Paper, 8vo, pp. 12. 15 
 Mills (C. D. B.) The Tree of Mythology: its Growth and Fruitage; Gene- 
 sis of the Nursery Tale, Laws of Folk Lore, etc. Cloth, 8vo, large 
 
 paper, top edge gilt. Pp. 281 3 00 
 
 Milton (John) A Small Tractate of Education. Paper, 16mo, pp. 26 15 
 
 Mottoes for *.he School Room. Per set of 24, 12 cards, 7x14 1 00 
 
 Natural History of the State of New York. 26 volumes 4to. 
 
 -f Reports on the Cabinet of Natural History 35 volumes, 8vo, and 4to. 
 
 Write for information as to the above. 
 
 New York State Examination Questions. Cloth, 16mo, pp. 256 50 
 
 The Questions in BooK-Keeping, with Answers. Paper, IGmo, pp . 81 10 
 
 Northam (Henry C.) Civil Government. Cloth, 16mo, pp. 185.... 75 
 
 Fixing the "icts of American History. Cloth, 12mo, pp. 300 75 
 
 Conversati* I Lessons Leading to Geography. 16mo, pp. 39 25 
 
 Northend (Chas.) Memory Selections. Three series. Each 25 
 
 Northrop (B. G.) High Schools. Paper,8vo, pp. 26 25 
 
 Northrup (A. J.) Camps and Tramps in the Adirondaclts. 16mo, pp. 302." 
 
 Paper, 50 cents; in Cloth 1 25 
 
 Number Lessons. On card -board, 7x11, after the Grube Method 10 
 
 Payne (Joseph.) Lectures on the Art of Education. Cloth, 16mo, pp. 281.. 1 00 
 
 Pardon (Emma L.) Oral Instruction in Geography. Paper, 16mo, pp. 29 15 
 
 Payne (W. H.) A Short History of Education. Cloth, 16mo, pp. 105.... 50 
 
 Pedagogical Biography. 16mo, paper, each 15 
 
 I. The Jesuits, Ascham, Montaigne, Ratich, Milton. 
 II. John Amos Comenius. III. John Locke. 
 IV. Jean Jacques Rousseau. V. John Bernard Basedow. 
 VI. Joseph Jacotot. VII. John Henry Pestalozzi. 
 
 Perez (B.) The First Three Tears of Childhood. With an introduction by 
 
 Prof . Sully. Cloth, 12mo, pp. 294 " 150 
 
 Periodicals. The School Bulletin. Monthly, 16 pp., 10x14. Per year 1 00 
 
 Bound Vols. I-XIV. Cloth, 200pp., each 2 00 
 
 The School Room. Bound volumes I- V. Each 150 
 
 Phillips (Philip.) Song Life. Oblong, boards, pp. 176 50 
 
 Pooler (Chas. T.) Chart of Civil Government. Cloth 25 
 
 TheSame, in sheets 12x18. per hundred 5 00 
 
 Hints on Teaching Orthoepy. Paper, 12mo, pp. 15 10 
 
 Postage-Stamp P7iofo0rapfrs. Taken from photograph of any size. Per 100. 1 50 
 Quick (R. H.) Essays on Educational Reformers. Cloth, 12mo, pp., 831 .... 1 50 
 
 * Regents' Examination Paper. Six styles. Per ream, $1.75 to 2 50 
 
 Regents' Examination Record. Cards, per hundred 50 
 
 The same on sheets 5 to page, 72 pages for 720 scholars, bound 2 50 
 
 The same on sheet 5 to page, 144 pages for 1440 scholars, bound 3 00 
 
 Regents' Examination Syllabus, published two months before each ex- 
 amination in American and in English History only, on the special topic 
 
 given. Paper, 8vo, pp 4-6, per dozen , each subject 50 
 
 Regents' Questions. To June, 1882. (No later are printed}. Eleven Editions. 
 
 1. Complete with Key. The Regents' Questions from the first exam- 
 ination in 1866. Cloth, 16mo, pp. 476 200 
 
 2. Complete. The same as the above but without the answers. Pp. 333. 1 00 
 
 3. Arithmetic. The 1,293 questions in Arithmetic. Pp.93 25 
 
 4. Key to A rithmetic, Answers to the above. Manilla, 16mo, pp. 20. ... 25 
 
 5. Thousand Regents 1 Questions in Arithmetic. Card-board 1 00 
 
 6. Geography, The 1,987 questions in Geography. Pp.70 25 
 
 7. Key to Geography. Answers to the above. Manilla, I6mo, pp. 36 25 
 
 8. Grammar. The 2,976 questions in Grammar. Manilla, 16mo, pp. 109 25 
 
 9. Grammar and Key. Cloth, 16mo, pp. 198 1 00 
 
 11. Key to Grammar. Manilla, 16mo, pp. 88 25 
 
 10. Spelling. The 4,800 words given in Spelling. Manilla, 16mo, pp. 61 . 
 Richardson (B. W.) -Learning and Health. Paper. 16mo. pp. 39 15 
 
C. W. BARDEEN, PUBLI 
 
 Roe (Martha.) A Work in Number. 
 
 Roget (P.M.) Thesaurus of English Wo\ 
 
 Ryan (G. W.) School Record. 56 blan, 
 
 Sanford (H. K.) The Word Method in i\ umber. Per box of 45 cards., 50 
 
 School Room Classics. 11 vols. Paper, 16mo, pp. about 40 15 
 
 I. Huntington's Unconscious Tuition. 
 II. Fitch's Art of Questioning. 
 
 III. Kennedy's Philosophy of School 
 
 Discipline. 
 
 IV. Fitch's Art of Securing Attention. 
 V. Richardson's Learning and Health. 
 
 VI. Meikeljolm's New Education. 
 
 Shaw's Scholar 's Reg ister, Paper, 5x7, pp. 16. P^r dozen 50 
 
 Sheeley (Aaron) Anecdotes and Humors of School Life. 12mo, pp* 350 150 
 
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