Jevons Hill. 
 

 
 THE 
 
 ELEMENTS OF LOGIC, 
 
 A TEXT-BOOK 
 
 FOR SCHOOLS AND COLLEGES; 
 
 THE ELEMENTARY LESSONS IN LOGIC. 
 
 BY 
 
 W. STANLEY JEVONS, LL.D., F.R.S., 
 
 LATE PROFESSOR OF LOGIC IN OWENS COLLEGE, MANCHESTBK. 
 
 RECAST BY 
 DAVID J. HILL, LL.D:, 
 
 U'RKSIDKNT OP THE UNIVERSITY OP ROCHESTER, AND AUTHOR OP HILL'i 
 RHETORICAL SEKIES AND THE ELEMENTS OF PSYCHOLOGY. 
 
 NEW YORK . CINCINNATI . CHICAGO 
 
 AMERICAN BOOK COMPANY 
 
 X
 
 PRESIDENT HILL'S TEXT-BOOKS 
 
 ttt. 
 
 THE ELEMENTS OF RHETORIC 
 AND COMPOSITION. 
 
 ad. 
 
 THE SCIENCE OF RHETORIC. 
 
 30- 
 THE ELEMENTS OF LOGIC. 
 
 Copyright, 188.3, h SheleUm &* Co.
 
 ''^^''^ 'i^ J 'i^ '1^ '1^ 
 
 B"5r OTHB ElDITOIt. 
 
 Although there are many elementary works on 
 Logic, it has been for a long time felt that there is 
 no text-book that precisely meets the wants of our 
 colleges and normal schools. The nearest approach to 
 the desideratum is the "Elementary Lessons in Logic" 
 which constitutes the substance of this book. Its 
 merits are its fresh treatment of the subject, its ful- 
 ness and felicity of illustration, its clearness and vigor 
 of style, its recognition of the logical methods of 
 science as a part of Logic, and its comprehensive pre- 
 sentation of recent views on the subject of reasoning. 
 It was designed by its author, Professor W. Stanley 
 Jevons, as a hand-book for students in the English 
 Universities. It is this alone that has stood in the 
 way of its general adoption as a text-book in this 
 country, for the methods of study in England and 
 America are essential'iy difffirent. In England the 
 student reads under the direci,Ion of a Tutor and thus 
 prepares himself for a public examination. In America 
 daily i-ecitations on the topical plan are almost univer-
 
 nr PREFACE. 
 
 sal in the study of this subject. Although Professoi 
 Jevoiis divided his work into Lessons, these bore no 
 relation to the amount usually assigned for a daily les- 
 son, and so failed to provide that distribution of the 
 matter that is desirable for the class-room. It is also a 
 defect of this method of dividing a subject that it fails 
 to present the logical relations of parts and the organic 
 unity of the whole. But the chief defect of the original 
 work, as a text-book for classes using the topical 
 method, is the want of an exact analysis of the topics 
 and a discrimination of that which is essential and 
 should be firmly fixed in tiie memory, from that which 
 is merely explanatory and illustrative and needs only to 
 be carefully read and comprehended. The amount o{ 
 illustration is superabundant in some cases, and tends 
 to distnict the mind and render it less attentive to 
 gteat principles than is consistent with a firm grasp of 
 such a science. The amount of matter in the book, 
 unless a part be subordinated, is too great to be 
 mastcrod in the single term that is usually given to the 
 gtudy even in the highest grade of schools in this 
 country. 
 
 The publishers have been led to believe from the rep- 
 resentations of professors of Logic who have had exten- 
 sive exi>crien('o in teaching the science, that a recjisting 
 of Professor Jevons' work, with special reference to the 
 diflBculties enumenited above, would render it in every 
 respect adapted to meet the confessed demand for a 
 thorough txt-book on this subject. It would have 
 been most desirable if Professor Jevons himself might 
 have recast the book with these considerations in mind, 
 but that was rendered impossible by his sudden death
 
 PBEFAOB. t 
 
 by disowning. In attempting to adapt this admirable 
 treatise to the needs of American students, I have 
 sought to make the following changes : 
 
 1. To introduce a complete and precise Analysis, 
 and to distribute the text in such a manner as to 
 render the method and arrangement of the book as 
 lucid as possible. 
 
 2. To give prominence to cardinal principles and 
 important doctrines by stating them in large type, 
 while matter that is simplj* explanatory and illustrative 
 is subordinated by being thrown into smaller type. 
 
 3. To impart to the treatment of Inductive Logic 
 more system and co-ordination than are found in the 
 original work. 
 
 4. To give unity to the treatment of the subject by 
 placing the discussion of Recent Logical Views at the 
 end of the text, instead of near the middle of the book, 
 thus avoiding a break in the continuity of the better 
 established doctrines of the science. 
 
 5. To facilitate reviews by placing at the end of 
 each section a summary of the topics treated of in 
 that section. 
 
 6. To impart some information concerning writers 
 on Logic named in the text, of whom the average 
 student cannot be presumed to have any exact knowl- 
 edge. This information is inserted in the Index and 
 Glossary under the names of the writers referred to. 
 
 I have for the most part retained the language of the 
 author, only adding where addition seemed to be 
 necessary to clearness. Such errors and infelicities of 
 expression as I have noticed, I have corrected. The
 
 Vl PREFACE. 
 
 singular clearness of Professor Jevons's mind, however, 
 has rendered the occurrence of these infrequent. 
 
 Although the opinion of teachers may vary upon this 
 point, the plan of requiring a close reproduction of the 
 text in large print, with questioning upon the matter 
 in the small 'type, will probably commend itself in 
 practice. In the review the parts in small type might 
 be omitted. Questions for examinations are inserted 
 at the end of the book. 
 
 In the hope that the work as recast may be found 
 useful to teachers and students, this revision is offered 
 to the public. 
 
 The Editob.
 
 A SKETCH 
 
 OF 
 
 THE AUTHOR'S LIFE. 
 
 WILLIAM STANLEY JEVONS was bom in Liverpool, in 
 September, 1835. His father, Thomas Jevons, was an iron mer- 
 chant, and bis mother was a daughter of William Roscoe, the 
 banker and historian. 
 
 Having obtained his early education at the High School of 
 Liverpool and at the Mechanics' Institution, at the age of sixteen 
 he entered University College, London. There he became so 
 distinguished in mathematics and chemistry that at the age of 
 nineteen, while still an undergraduate, he was invited to a posi- 
 tion in the Sydney Mint, Australia. He accepted this appoint- 
 ment, but after five years' residence in Australia, he returned to 
 London, completed his course of study and took the Master's 
 degree. He attained the highest honors in Logic, Moral Phil- 
 osophy and Political EJconomy. 
 
 In 1863 Jevons began his work as a teacher in Owens College, 
 Manchester, and three years later was elected Professor of the 
 three studies in which he especially excelled. After ten years of 
 distinguished service at Manchester, during which period he won 
 an extended reputation as a writer, Professor Jevons felt the 
 burden of his varied duties to be too heavy for him and accepted
 
 viii AUTHOR'S LIFE. 
 
 the chair of Political FJconomy in University College, London. 
 Even the duties of tliis j)osition, tliougli not extensive, became 
 opprffisive to liiin witli hcaltli that liad grown uncertain, and in 
 ibe winter of 1880-1 he retired to private life. 
 
 Ui8 life was terminated by an accident on the 13th of August, 
 1882, while bathing at Galley Hill, on the Sussex coast. The 
 precise cause of his death in the water is not known, but it is 
 8uppo8?d that in his feeble health he was not able to resist the 
 nervous shock caused by the excitement of bathing, and being 
 disabled he was drowned. 
 
 As a writer Professor Jevons was remarkably fertile. In 
 addition to the present work, he produced on the subject of logic 
 three notable books. A work entitled " Pure Ix)gic" was pub- 
 lished in 1864. "The Substitution of Similars" (1869) was an 
 attempt to simplify all reasoning by referring it to a single 
 ])rinciplo more comj)rehensive than Aristotle's dicta. "The 
 Principles of Science" (1874) was, in eflFect, the application of 
 this principle to the details of scientific method, and anex[)OBition 
 of the fundamental postulates on which all human science rests. 
 Both works have called forth considerable controversy, but the 
 latt'r in particular has been useful in the direction of scientific 
 rr8onlnp. More recently Professor Jevons has reviewed with 
 m-archin^r eriticisrn the logical work of the late John Stuart Mill. 
 Referring to h.n treatises on l.rf)gic and his review of Mill, the 
 " Rrvue Philoflophique" nays: " His great work ' The Principles 
 of S<-ienre " and hi.s recent iK)lemic against the Logic of Stuart 
 Mill have given him a (ii>^tiiiguished rank among English 
 logirianft." The name notice also a<lds that " the elementary 
 workfl cf Stanley Jevonn have Ixjcome classic." 
 
 We cannot prf)i.erly rlosf this sketch without a brief reference 
 to PmfeHwr J.vons' works on Political Rconomy. to which he 
 devot4>d many of hitt l)est yMrH. The most popular of these are
 
 AUTHOR'S LIFE. IX 
 
 The " ITieory of Political Economy " (1871), an attempt to present 
 the subject under a mathematical form ; " Money and the Mecb 
 anism of Exchange " (1875), a more popular presentation of th 
 subject, being a contribution to the International Scientific 
 Series ; and " The Primer of Political Economy " (1878), a greatly 
 simplified introduction to the subject. A more special and 
 technical production is the work on " The Coal Question." 
 
 " As a man," says the Editor of the English periodical Mind, 
 " Jevons was most lovable. Of a shy and retiring disposi- 
 tion, he never mixed much in general society, but he bad a 
 geniality of nature and sweetness of temper, with a ready help- 
 fulness, which secured him an inner circle of most devoted 
 friends. With so firm a grasp as he had of his own convictions 
 and opinions, he was admirable for the spirit in which he courted 
 and welcomed criticism." 
 
 In recognition of his attainments Professor Jevons was made 
 a Fellow of the Royal Society, and the honorary degree o{ 
 Doctor of Laws was conferred upon him by the University 
 of Edinburgh. The highest authorities in Europe accord to him 
 "an assured reputation as an original thinker and writer in tha 
 two departments of Logic and Political Economy." 
 
 Tbs Eoitob.
 
 INTRODUCTION. 
 
 PASB 
 
 1. Definition OF Logic 1 
 
 2. Natuke of a Law of Thought 2 
 
 8. A Science of Thought Possible , , . . . 8 
 
 4. Distinction between Fobm and Matter 5 
 
 5. Logic a General Science 6 
 
 6. The Particular Sciences, Special Logics. 6 
 
 7. Logic both a Science and an Art 7 
 
 8. The Usefulness of Logic 8 
 
 9. Analysis of an Argument 9 
 
 10. Theories of the Real Subject-matter of IjOgic. ... 10 
 
 11. The Three Logical Operations of Mind 18 
 
 12. Method of Treatment 16 
 
 OHAPTEB I 
 
 TERMS. 
 
 SECTION . THE VARIOUS KINDS OF TERMS 
 
 1. The Meaning of ' Term" Explained 17 
 
 2. CATEGORBaJATIC AND SyNCATEGOREMATIC WoRDS 18 
 
 B. Singular Terms 20 
 
 4 General Terms 20 
 
 6. Collective Terms 21 
 
 8. Ooncrkths and Abstract Terms 2S
 
 Ili ANALYSIS. 
 
 7 PoemvK and Negativk Terms 24 
 
 8. Tkiv \TiVK Tkums ..26 
 
 9. Uelative AND Absolute Tbbms 27 
 
 10. SOMMARY 28 
 
 SECTION II. THE AMBIGUITY OF TERMS. 
 
 1. Importance of Avoiding Ambiguity 80 
 
 2. Univocal and Equivocai, Terms 81 
 
 8. Knn AND Causes OK Ambiguity 88 
 
 SECTION III. EXTENSION AND INTENSION. 
 
 1. IlCPORTANCB OF UNDimSTANDINO THIS DOUBLE MEAN- 
 
 ING 39 
 
 2. Meaning of Extension and Intension 39 
 
 8. Various Forms of Expressing Extension and Inten- 
 sion 41 
 
 4. The Variation of Extension and Intension 42 
 
 6. TiiK Law OF Variation 42 
 
 8. CONNOTATivE and Non-connotative Terms 43 
 
 SECTION IV.-THE GROWTH OF LANGUAGE, 
 
 1 TnF- Two Principal Processes of Growth 46 
 
 '^. (Iknkuai.izvtion 47 
 
 3. Specialization 50 
 
 A Dksynonymizatiov 51 
 
 5. Mktaphoukai, Extension of Meaning 52 
 
 B OrKMN ok THE MkNTAI. ViK'ABULARY 53 
 
 7. The Fertility ok Hoot woriw 54 
 
 SECTION V -rHE PERFFCT AND THE IMPERFECT 
 KNOWLEDGE OF TERMS. 
 
 1. Statement of the Qi:ehtion 66 
 
 2. Scheme ok DisTiNcrioNs 56 
 
 S. The Intuitive and Svmkolic Methods Compared 02
 
 ANALYSIS. XIU 
 
 CHAPTER II. 
 PROPOSITIONS. 
 
 SECTION I. THE KINDS OF PROPOSITIONS. 
 
 FAOB 
 
 1. Meaning op " Proposition " Explained 64 
 
 2. Analysis of a Proposition 65 
 
 3. Categorical and Conditional Propositions 66 
 
 4. The Quantity and Quality of Propositions 67 
 
 5. Aristotle's View of Quantity 68 
 
 6. Names op the Four Propositions 70 
 
 7. Variations from the Logical Form 71 
 
 8. The Modality of Propositions 73 
 
 SECTION II. THE OPPOSITION OF PROPOSITIONS. 
 
 1. The Four Propositions Explained 75 
 
 3. The Distribution of Terms 79 
 
 3. Tablk of Results 80 
 
 4. Relations of the Four Propositions 80 
 
 5. The Scheme of Opposition 83 
 
 6. The Laws of Opposition 83 
 
 7. The Conditions of Opposition . . 84 
 
 8. The Matter of Propositions 85 
 
 SECTION III. CONVERSION AND IMMEDIATE 
 INFERENCE. 
 
 1. The Nature of Inference 86 
 
 2. Conversion of Propositions 87 
 
 3. Immediate Inference 90
 
 xiT ANALYSIS. 
 
 SECTION IV. THE LOGICAL ANALYSIS OF SEN- 
 TENCES, 
 
 FAsa 
 
 1. Relation of Logic to this Topic 93 
 
 2. The Gkammatical and the Looical Predicate 94 
 
 8 The Plurality of Propositions in a Sentence 95 
 
 4. Complex Sentences 96 
 
 5. Modes of Exuibitino Constroction 99 
 
 CHAPTER III. 
 SYLLOGISMS. 
 
 SECTION I THE LAWS OF THOUGHT. 
 
 1. The Statement of tiik Primary Laws of Thought. . 104 
 
 2. Explanation of tiik Laws 105 
 
 8. The Canons ok SyLi,<xiisM 108 
 
 4. TuK .VxioMH OF Mathematics 110 
 
 6. Aristotle's Dicta Ill 
 
 SECTION II. -THE RULES OF THE SYLLOGISM. 
 
 1. The Definition OF "Syllogism" 118 
 
 2. The Mf.antno OK " MiDDLK Term" 114 
 
 8. The Uhk of MmDi.E Tkum in Syllogism 114 
 
 4. Statkmknt ok thk Rulp;8 of Syllogism 115 
 
 5 Explanation (/F the Rm.Ks 116 
 
 SECTION III. THE MOODS AND FIGURES OF 
 THE SYLLOGISM. 
 
 1. Expi.anation ok " Moods" 124 
 
 2 The Ncmbek ok Valid Moods 125 
 
 8. Explanation of ' Figures " 187
 
 ANALYSIS. XV 
 
 PASS 
 
 4. Thb Valid Moods in the Different Figures 128 
 
 5. Conclusions Proved in the Different Figures 130 
 
 SECTION IV. THE REDUCTION OF SYLLOGISMS. 
 
 1. The Mnemonic Verses 183 
 
 2. Explanation of the Mnemonic Verses 184 
 
 3. Conclusions from Particular Premises 139 
 
 SECTION v. IRREGULAR AND COMPOUND 
 SYLLOGISMS. 
 
 1. The Irregular Mode of Expressing Inferences 141 
 
 2. Explanation of " Enthymeme " 142 
 
 3. Prosyllogisms and Episyllogisms 144 
 
 4 Sorites 145 
 
 5. Syllogisms in Extension and in Intension 148 
 
 SECTION VI. CONDITIONAL SYLLOGISMS. 
 
 1. Classification op Propositions 149 
 
 2. Antecedent and Consequent 150 
 
 3. Kinds of Hypothetical Syllogisms 151 
 
 4 The Rule for Hypothetical Syllogisms 152 
 
 5. The Reduction of Hypothetical to Categorical 
 
 Syllogisms 153 
 
 6. Fallacies in Hypothetical Syllogisms 155 
 
 7. Disjunctive Syllogisms 156 
 
 8. Thb Dilemma 158 
 
 CHAPTEE IV. 
 FALLACIES. 
 
 SECTION I. LOGICAL FALLACIES. 
 
 1. Classification of Logical Fallacies 162 
 
 2. The Fallacy of Equivocation 163 
 
 3. The Fallacy of Amphibology 164
 
 tfl AKALYSSS. 
 
 rMB 
 
 4 The Fallacy of Compositiok 1<>5 
 
 5. The Fallacy ok Division 16* 
 
 6. The Fallacy of Accident 167 
 
 7 Tu* Fallacy of the Figuke of Speech 168 
 
 SECTION ll.~MATERIAL FALUCIES. 
 
 1. The Ci.A98rFiCATi0N op Matekial Fallacies 169 
 
 2. The Fallacy of Accidknt and its Converse 169 
 
 3. The Fallacy of Irrelevant Conclusion , 171 
 
 4. The Fallacy of Petitio Principii 173 
 
 5. The Fallacy of the Consequent. 175 
 
 6. The Fallacy of False Cause 175 
 
 7. The Fallacy of Many Questions 176 
 
 CHAPTER V. 
 INDUCTION. 
 
 SECTION I. THE INDUCTIVE SYLLOGISM. 
 
 1. Induction and DFa>ucTioN Contrasted 178 
 
 2. Exi'LAS ation ok Traduction 179 
 
 8. iMrOKTANCB ok INDUCTION 180 
 
 4. Pekkfxt AND Impkrke<t Induction 181 
 
 6 The Dikkerknck between Pkrfect and Imperfect 
 
 iNin-i-noN 181 
 
 6. The Pkrki-xt Inductivk Syllooism 183 
 
 7. The Peukeit Induc-iivk Svi,i,(oism Disjunctive 184 
 
 8 The iMrKUKWT Inductive Svlix)()I8m 184 
 
 8. The Fund \mkntal AS8UMITION OF Induction 185 
 
 SECTION II. THE FORMS OF INDUCTION. 
 
 1 The CnARArTEu of the Data 187 
 
 8. Spbcial Kinds ok Induction 196
 
 NALYSIS. Xfii 
 
 CHAPTER VI. 
 METHOD. 
 
 SECTION I. INDUCTIVE METHOD. 
 
 tAoa 
 
 1. The Search for Facts 201 
 
 2. The Rule for Observation 206 
 
 8. The Uses of Hypothesis and Theory 208 
 
 4. Definitions of Teums Employed in Investigation. . . 212 
 
 5. Canons op Induction 215 
 
 SECTION II. DEDUCTIVE METHOD. 
 
 1. The Predicables 227 
 
 2. Logical Divisions 234 
 
 8. Dichotomy, or Exhaustive Division 236 
 
 4. Definition 238 
 
 6. Classification 240 
 
 6. Requisites op a Good Classification 242 
 
 7. Denomination 245 
 
 SECTION III. COMPLETE METHOD. 
 
 1. Empirical and Rational Knowledge 249 
 
 2. The Elements of Complete Method 251 
 
 8. The Nature of Explanation 264 
 
 4. Pascal on Method 257 
 
 6. Descartes on Method 263 
 
 CHAPTER VII. 
 RECENT LOGICAL VIEWS 
 
 SECTION I. THE QUANTIFICATION OF THE PREDICATE 
 
 1. Meaning of the Expression %if^ 
 
 2. Conversion with a Quantified Predicate 364
 
 Zriil ANALYSIS. 
 
 8. The Rule for Conversion 266 
 
 4 Number ok Propositions with a Quantified Predi- 
 cate 266 
 
 6. Number of Syllogk-^ms with Quantified Predicate. 268 
 
 6. Hamilton's Notation 268 
 
 7. Hamilton's Canon op the Stllogism 270 
 
 SECTION II. BOOLE'S SYSTEM OF LOGIC. 
 
 1. The Difficultt of Dr. Boole's Statement 272 
 
 2. Application of the Law of Excluded Middle 273 
 
 8. Application of the Law of Contradiction 274 
 
 4. Universality of the Method. 275 
 
 5. Comparative Excellence of the System 27? 
 
 6. Thb Logical Abacus and the Logical Machine 280 
 
 Questions AND Exercises 283 
 
 biDKZ ANDULOWABT 314
 
 1. Definition of Logic. 
 
 Logic may be most briefly defined as the Science of 
 Reasoning. It is more commonly defined, however, as 
 the Science of the Laws of Thought, and some lo- 
 gicians think it desirable to specify still more accurately 
 that it is the Science of the Formal, or of the Necessary 
 Laws of Though^t. Before these definitions can be of 
 any real use to us we must come to a clear understand- 
 ing as to the meaning of the expressions ; and it will 
 probably appear that there is no great difference be- 
 tween them. 
 
 The name of logic is derived from the common Greek word 
 ^6yo^, whicli usually. means toord, or the sign and outward mani- 
 festation of any inward thought. But the same word was also 
 used to denote the inward thought or reasoning of which words 
 are the expression, and it is thus, probably, that later Greek 
 writers on reasoning, were led to call their science i-iari^firi 
 XoyiKTJ, or logical science ; also -ex^'V ^.oyiKij, or logical art. The 
 adjective XoyiKrj, being used alone, soon came to be the name of 
 the science, just as Mathematic, Rhetoric, and other names 
 ending in " ic " were originally adjectives, but have been con- 
 Terted into substantivea
 
 INTRODUOTION. 
 
 3. Nature of a l..au of Thought. 
 
 By a Law of Thought we mean a certain uniformitj 
 or agrcenunt wliicli exists and must exist in the modes 
 in which all persons think and reason, so long as they 
 do not make what we call mistakes, or fall into self- 
 contradiction and fallacy. The laws of thought are 
 natural laws with which we have no power to interfere, 
 and which are, of course, not to be in any way confused 
 with the artificial laws of a country, which are invented 
 by men and can be altered by them. Every science is 
 occu{)ied in detecting and describing the natural laws 
 which aro inflexibly observed by the objects treated in 
 the science. 
 
 The science of astronomy investigates the uniform or similar 
 way in which tlie heavenly IkkHos, and, in fact, all material sub- 
 Btancee, tend to fall towards each other, as a stone falls towarda 
 the earth, or to move round each other under the influence ol 
 this U'ndency. Tlie universal law of gravitation is thus th** 
 natural law of uniformity treated in physical astronomy. 
 
 In chemistry tlie law of equivalent proportions describes the 
 well ascertained fact that each chemical substance enters into 
 combination with every other chemical substance only in certain 
 definite proportions; as when exactly eight parts by weight of 
 oiyg(!n unite with one part of hydrogen to form water, or 
 sixti'en parts of oxygen and six parts of carbon unite to form 
 cjirbonic acid in the ordinary burning of a flame or fira 
 Whenever we can detect uniformities, or similarities, we so 
 far create science and arrive at natural laws. But there may 
 be and are, many things so fickle, complicated, and uncertain, 
 that we can never be sure we have detected laws that they will 
 uniformly ol)ey ; ir such cases no science, in the proper sense of 
 tlie word, is i)<)ssible. There is no such thing, for instance, as a 
 n-al aricnrc of human charact*r, because tl.e human mind is too 
 variable and complicated a subject of investigation. There are
 
 nrrnoDucTion'. 3 
 
 no two penons so much alike that you may be sure of one acting 
 in all circumstances as the other would ; it thus becomes impossi- 
 ble to arrange persons in classes so that all who are in the same 
 class shall act uniformly in the same manner in any given cir 
 jumstances. 
 
 3. A Science of Thought Possible. 
 
 There is a science of human reason, or thought, apart 
 from the many other acts of mind which belong to human 
 character, because there are modes in which all persons 
 do uniformly think and reason, and must think and 
 reason. Thus, if two things are identical with a third 
 common thing, they are identical with each other. 
 This is a law of thought of a very simple and obvious 
 character, and we may observe concerning it : 
 
 (1) That all people think in accordance with it, 
 and agree that they do so as soon as they understand its 
 meaning. 
 
 (2) That they think in accordance with it whatever 
 may be the subject about which they are thinking. 
 
 Thus, if the things considered are 
 
 London, 
 
 The Metropolis, 
 
 The most populous city in Great Britain, 
 
 since "the Metropolis is identical with London," and "London 
 is identical with the most populous city in Great Britain," it 
 follows, necessarily, in all minds, that " the Metropolis is identi- 
 cal with the most populous city in Great Britain." 
 Again, if we compare the three following things 
 
 Iron, 
 
 The most useful metal. 
 
 The cheapest metal, 
 
 And it be allowed that " The most useful metal is Iron," and
 
 4 INTRODUCTION. 
 
 "Iron is the cheapest metal," it follows, necessarily, in all 
 minds, that " the most useful metal is the cheapest." We here 
 have two examples of the general truth, that things identical 
 with the same thing are identical with each other; and this, we 
 may say, is a general or necessary form of thought and reasoning. 
 Compare, again, the following three things: 
 
 The earth, 
 
 Planets, 
 
 Bodies revolving in elliptic orbits. 
 
 We cannot say, as before, that " the earth is identical with the 
 planets ; " it is identical only with one of the planets, and we 
 therefore say that "it is a planet." Similarly we may say that 
 " the planets are bodies revolving in ellipti" orbits," but only a 
 part of the whole number so revolving. Nevertheless, it follows 
 that if the earth is among the planets, and the planets among 
 bodies revolving in elliptic orbits, then the earth is among the 
 latter. 
 
 A very elementary knowledge of cheraistiy enables UB to 
 argue similarly concerning the following: 
 
 Iron, 
 
 Metals, 
 
 Elementary substances. 
 
 Iron is one of the metals, and metals are elements or simple 
 undecomposable substances, in the sense of being among them 
 or a part of them, but not as composing the whole. It follows, 
 nec<-8.sarily, that "Iron is one of the elementary substances." 
 We have had, then, two examples of a fixed and necessary form 
 of th()Uj;ht, which is necessary and true, whatever the things 
 may l)e to which it is a|)plied. The form of argument may be 
 expressed in several different ways, and we shall have to con- 
 sider it minutely in the lessons on the syllogism. We may 
 express it, for instance, by saying that " part of a part is part 
 of the whole." Iron is part of the class of metals, which is part 
 of the class of elements hence iron is part of the class of 
 elements.
 
 HTTBODUOnON. 
 
 4. Distinction between Form and Matter. 
 
 In order to apprehend the meaning of the expression, 
 " the necessary forms of thought," we must distinguish 
 between form and matter. A 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. Just as we thus famiharly recognize 
 the difference of form and substance in common tangi- 
 ble things, so we may observe in Logic, that the form 
 of an argument is one thing, quite distinct from the 
 various subjects or matter which may be treated in that 
 form. 
 
 We may almost exhibit to the eye the form of reasoning t 
 which belong our two latter arguments, as follows : 
 
 (Y) 
 
 (3i)....is....(Z) 
 
 If within the three pairs of brackets, marked respectively X, 
 T and Z, we place three names, such that the one in place of X 
 may be said to come under that in Y. and that in Y under that 
 in Z, then it necessarily follows that the lirst cX) comes under 
 the last (Z).
 
 uttboduction. 
 
 5. IiOgric a General Science. 
 
 Logic, then, is the science occupied in ascertaining 
 and descnbing all the general forms of thought which 
 we must employ so long as we reason validly. These 
 forms are very numerous, although the principles on 
 which they are constructed are few and simple. It will 
 hence appear that logic is the most general of all the 
 sciences. Its aid must be more often required than the 
 aid of any other science, because all the particular 
 sciences treat portions only of existing things, and 
 create very different and often unconnected branches of 
 knowledge. But logic treats of those principles and 
 forms of thought which must be employed in every 
 branch of knowledge. It treats of the very origin and 
 foundations of knowledge itself ; and though it is true 
 that the logical method employed in one science may 
 differ somewhat from that employed in another science, 
 yet, whatever the particular form may be, it must be 
 logical, and must conform to the laws of thought. 
 There is, in short, something in which all sciences must 
 be similar ; to which they must conform so long as they 
 maintnin what is true and self-consistent; and the 
 work of logic is to explain this common basis of all 
 Bcience. 
 
 6. The Particular Sciences, Special Logics. 
 
 One name which has been given to Logic, namely, 
 the Science of Sciences, very aptly describes the all 
 exten.sivc power of logical principles. The cultivators 
 of 8i)ocial branches of knowledge appear to have been 
 *"ully aware of the allegiance they owe to the highest of
 
 INTBODUOTION. 7 
 
 the sciences, for they have usually given names imply, 
 ing this allegiance. The very name of logic occurs aa 
 part of nearly all the names recently adopted for the 
 sciences, which are often vulgarly called the "ologies," 
 but are really the " logics," the " o " being only a con- 
 necting vowel or part of the previous word. Thus, 
 geology is logic applied to explain the formation of the 
 earth's crust ; biology is logic apphed to the phenomena 
 of life ; psychology is logic applied to the nature of the 
 mind ; and the same is the case with physiology, ento- 
 mology, zoology, teratology, morphology, anthropology, 
 theology, ecclesiology, thalattology, and the rest.* Each 
 science is thus distinctly confessed to be a special logic. 
 
 7. Logic both a Science and an Art. 
 
 Much discussion of a somewhat trifling character has 
 arisen upon the question whether Logic should be con- 
 sidered a science only, an art only, op both at the 
 same time. Sir W. Hamilton has even taken the 
 trouble to classify almost all the writers on logic ac- 
 cording as they held one opinion or the other. But it 
 seems substantially correct and sufficient to say, that 
 logic is a science in so far as it merely investigates the 
 necessary principles and forms of thought, and thus 
 teaches us to understand in what correct thinking con- 
 sists ; but that it becomes an art when it is occupied ir 
 framing rules to assist persons in detecting false reason- 
 ing. 
 
 * Except Philology, which is diflferently formed, and means the love or 
 study of words; the name of Uxis science, if formed upon the same pUn, 
 would be logolog^
 
 t nrTRODucnoy. 
 
 A science teaches us to know and an art to do, and all tb 
 
 moie perfect sciences lead to the creation of corresponding usefui 
 arta. Astronomy is the foundation of the art of navigation on the 
 ocean, as well as of the arrangement of the calendar and chronol- 
 ogy. Physiology is the basis of the art of medicine, and chemistry 
 is the l)asis of many useful arts. Logic has similarly been con- 
 sidered as the basis of an art of correct reasoning or investigation 
 which should teach the true method to be observed in all 
 sciences. The celebrated British logician, Duns Scotus, who 
 lived in the 13th century, and called logic the Science of 
 Sciences, called it also the Art of Arts, expressing fully its 
 pro-eminonce. Others have thus defined it " Logic is the art 
 of directing the reason aright in acquiring the knowledge of 
 things, for the instruction both of ourselves and others." Dr. 
 Isaac Watts, adopting this view of logic, called his well-known 
 work " The Art of Thinking." 
 
 It may be fairly said, however, that Logic has more the form 
 of a science than of an art, for this reason ail persons 
 necessarily acquire the faculty and habit of reasoning long before 
 ^hey even know the name of logic. This they do by the natural 
 exertion of the powers of mind, or by constant but unconscious 
 imitation of others. They thus observe correctly, but uncon- 
 sciously, the principles of the science in all very simple cases. 
 But the contradictory opinions and absurd fallacies which are 
 put forth by uneducated persons show that this unaided exercise 
 of mind is not to be trusted when the subject of discussion 
 presents any difficulty or complexity. 
 
 8. The UneAiliiess of liogic. 
 
 The study of logic, then, cannot be useless. It not 
 only explains the principles on which every one has 
 often reasoned correctly before, but points out the 
 dangtrs which exist of erroneous argument. The 
 reasoner thus becomes consciously a correct reasoner 
 and learns consriously to avoid the snares of fallacy. 
 To say that men can reason well without logical science
 
 nrrRODUoTioN. 9 
 
 I's about as trne as to say that they can live healthily 
 without medicine. So they can as long as they are 
 healthy ; and so can reasoners do without the science of 
 leasoning as long as they do reason correctly ; but how 
 many are there that can do so ? As well might a man 
 claim to be immortal in his body as infallible in his 
 mind. 
 
 And if it be requisite to say a few words in defence 
 of Logic as an art, because circumstances in the past 
 history of the science have given rise to misapprehen- 
 sion, can it be necessary to say anything in its praise 
 as a science? Whatever there is that is great in science 
 or in art or in literature, it is the work of intellect. In 
 bodily form man is kindred with the brutes, and in his 
 perishable part he is but matter. It is the possession of 
 conscious intellect, the power of reasoning by general 
 notions, that raises him above all else upon the earth ; 
 and who can say that the nature and procedure of this 
 intellect is not almost the highest and most interesting 
 subject of study in which we can engage ? In vain 
 would any one deny the truth of the favorite aphorism 
 of Sir "W. Hamilton 
 
 In the world theee is nothing great but man. 
 In man there is nothing great but mind. 
 
 9. Analysis of an Argument. 
 
 It has been explained that Logic is the Science of 
 Reasoning, or the Science of those Necessary Laws of 
 Thought which must be observed if we are to argue 
 consistently with ourselves and avoid self-contradiction. 
 Argument or reasoning, therefore, is the strictly proper
 
 10 UPTBOD POTION. 
 
 subject before ns. But the most convenient and usual 
 mode of studying logic is to consider first the compo* 
 nent parts of which any argument must be made up 
 Just as an architect must be acquainted with the ma- 
 terials of a building, or a mechanic with the materials 
 of a machine, before he can pretend to be acquainted 
 with its constniction, so the materials and instruments 
 with which we must operate in reasoning are suitably 
 described before we proceed to the actual forms of 
 argument. 
 If we examine a simple argument such as this 
 
 Iron is a metal. 
 Every metal is an element, 
 Therefore Iron is an element, 
 
 we see that it is made up of three statements or asser- 
 tions, and that each of these contains, besides minor 
 words, two nouns substantive or names of things, and 
 the verb " is." In short, two names, or terms, when 
 connected by a verb, make up an assertion or proposi- 
 tion ; and three sucli propositions make up an argument, 
 culled in this case a syllogism. Hence it is natural and 
 convenient fii*st to describe terms, as the simplest parts; 
 next to proceed to the nature and varieties of proposi- 
 tions constructed out of them, and then we shall be in 
 A position to treat of the syllogism as a whole. Such, 
 accordingly, are the three parts of logical doctrine. 
 
 10. Theories of the Ileal Subject-iiiattcr of 
 
 Bnt though we may sjiy that the three parts of logic 
 are oonrerned with terms, propositions, and syllogisms.
 
 INTRODUCTION. 11 
 
 it may be said, with equal or greater truth, that th 
 acts of mind indicated by those forms of language are 
 the real subject of our consideration. The opinions, 
 or rather, perhaps, the expressions, of logicians have 
 varied on this point. Archbishop Whately says dis 
 tinctly that logic is entirely conversant about language ; 
 Sir W. Hamilton, Mr. Mausel, and most other logicians 
 treat it as concerned with the acts or states of mind 
 indicated by the words ; while Mr. J. S. Mill goes back 
 to the things themselves concerning which we argue. 
 Is the subject of logic, then, language, thought, or ob- 
 jects ? The simplest and truest answer is to say that it 
 treats, in a certain sense, of all three. Inasmuch as no 
 reasoning process can be explained or communicated to 
 another person without words, we are practically limited 
 to such reasoning as is reduced to the form of language. 
 Hence we shall always be concerned with words, but 
 only so far as they are the instruments for recording 
 and referring to our. thoughts. The grammarian also 
 treats of language, but he treats it as language merely, 
 and his science terminates with the description and ex- 
 planation of the forms, varieties, and relations of 
 words. Logic also treats of language, but only as the 
 necessary index to the action of mind. 
 
 Again, so long as we think correctly, we must think of thinpfs 
 as they are. The state of mind within us must correspond to 
 the state of things without us, whenever an opportunity ariseg 
 for comparing them. It is impossible and inconceivable that iron 
 should prove not to be an elementary substance, if it be a metal, 
 and every metal be an element. We cannot suppose, and there 
 is no reason to suppose, that by the constitution of the mind we 
 are obliged to think of things differently from the manner in 
 which they are. If, then, we may assume that things really
 
 IB nfTRODuonou. 
 
 agree or differ, according as by correct logical thought we are In- 
 duced to believe they will, it does not seem that the views of the 
 logiciana named are irreconcileable. We treat of things so fai 
 jb they are the objects of tliought, and we treat of language so 
 far as it is the embodiment of thought. If the learner will bear 
 this explanation in mind, he will be saved from some perplexity 
 when he proceeds to read different works on logic, and finds them 
 to vary exceedingly in the mode of treatment, or at least of ex- 
 pression. 
 
 1 1. The Three Logical Operations of Mind. 
 
 If, when reduced to language, there be three parts of 
 logic, terms, propositions, and syllogisms, there must be 
 as many different kinds of thought or operations of 
 mind. These are usually called 
 
 (1) Simple apprehension. 
 
 (2) Judgment 
 
 (3) Reasoning, or discourse. 
 
 (I) Simple Apprehension is the act of mind by 
 which we merely btcome aware of something, or have 
 an idea or impression of it brought into the mind. The 
 adjective simple means apart from other things, and 
 apprehension the taking hold by the mind. Thus the 
 name or term iron instantuneonsly makes the mind 
 think of a strong and very useful metal, but does not 
 tell us anything about it, or compare it with any thing 
 else. The words .?, Jupiter, Sirius, St. J'auVs Cathe- 
 drnl, arc also terms which call up into the mind certain 
 well-known objects, which dwell in our recollection even 
 when thoy arc not present to our senses. In fact, the 
 use of a term, such as those ^iven as examples, is 
 merely as u substitute for the exhibition of the actual 
 thingH named.
 
 INTBODUCnON. 18 
 
 (2) Judgment is a different action of mind, and con. 
 sists in comparing together two notions or ideas of ob- 
 jects derived from simple apprehension, so as to ascer. 
 tain whether they agree or differ. It is evident, there- 
 fore, that we cannot judge or compare unless we are con- 
 scious of two things, or have the notions of two things 
 in the mind at the same time. Thus, if I compare Jupiter 
 and Sirius, I first simply apprehend each of them ; but, 
 bringing them into comparison, I observe that they 
 agree in being small, bright, shining bodies, which rise 
 and set and move round the heavens with apparently 
 equal speed. By minute examination, however, I no 
 tice that Sirius gives a twinkling or intermittent light, 
 whereas Jupiter shines steadily. More prolonged oVj- 
 servation shows that Jupiter and Sirius do not really 
 move with equal and regular speed, but that the former 
 changes its position upon the heavens from night to 
 night in no very simple manner. If the comparison be 
 extended to others of the heavenly bodies which are ap- 
 prehended or seen at the same time, I shall find that 
 there are a multitude of stars which agree with Sirius 
 in giving a twinkling light and in remaining perfectly 
 fixed in relative position to each other, whereas two or 
 three other bodies may be seen which resemble Jupiter 
 in giving a steady light, and also in changing their 
 place from night to night among the fixed stars. I 
 have now by the action of judgment formed in my mind 
 the general notion op concept of fixed stars, by bringing 
 together mentally a number of objects which agree ; 
 while from several other objects I have formed the gen- 
 eral notion of planets. Comparing the two general 
 notions together, I find that they do not possess the
 
 14 INTRODUCTIOK. 
 
 same qualities or appearances, which I state in the 
 pro|)08ition, " Planets are not fixed stars." 
 
 The expression " General Notion " is introduced as if the 
 learner were fully acquainted with it. But though philosophers 
 have, for more than two thousand years, constantly used the ex- 
 pressions, general notion, idea, conception, concept, etc., they 
 have never succeeded in agreeing exactly as to the meaning of 
 the terms One class of philosophers, called Nominalists, say 
 that it is all a matter of names, and that when we join together 
 Jupiter, Mars, Saturn, Venus, etc., and call them planets, the 
 common name is the bond between them in our minds. Others, 
 called Realists, liave asserted that, besides these particular 
 planets, there is really something which combines the proj^erties 
 Cfjmraon to them all, without any of the differences of size, 
 'olor, or motion wliicli distinguish them. Every one allows in 
 the present day, however, that nothing can physically exist cor- 
 re8fK>nding to a general notion, because it must exist here or 
 there, of this size or of that size, and, therefore, it would be on 
 particular planet, and not any i>lanet whatever. The Nominal- 
 /Hts, too, seem e<iually wronjjf, because language, to be of any use, 
 must denote something, and must correspond, as we have seen, 
 to acts of mind. If then proper names raise up in our minds the 
 imaircs of particular things, like Jupiter, etc., general names 
 should raise up general notions. 
 
 The true opinion sejiins to be that of the philosophers called 
 Conceptualists, who say that the general notion is the knowledge 
 In the mind of th! common properties or resemblances of the 
 things embrac(!<l under the notion. Thus, the notion planet 
 really means the consciousness in anybody's mind that there are 
 c'rtain heavenly Ixxlies which agree in giving a steady light and 
 In moving alxiut the heavens differently from the fixtnl stars. It 
 hould Ix! adde<l, however, that there are many, including Sir W. 
 Hamilton, who would Im- counted as Nominalists, and who yet 
 hold that with the general name is associated a consciousness of 
 the retH;mhlance existing l)etween the things denoted by it. 
 Ik'tween this form of the doctrine and conceptualism it is not 
 easy t<> dniw a ])r(HM8f! distinction, and the subject is of too d 
 Itttable a cliaracter to be pursued in this work.
 
 INTRODUCTION". 15 
 
 (3) Reasoning, or Discourse, may be defined as 
 the progress of the miud from one or more given propo- 
 sitions to a proposition different from those given. 
 Those propositions from which we argue are called 
 Premises, and that which is drawn from them is called 
 the Conclusion. The latter is said to follow, to he con- 
 cluded, inferred, or collected from them; and the 
 premises are so called because they are put forward, or 
 at the beginning (Latin prm^ before, and mitto, I seii^ 
 or put). The essence of the process consists in gather- 
 ing the truth that is contained in the premises when 
 joined together, and carrying it with us into the con- 
 clusion, where it is embodied in a new proposition or 
 assertion. We extract out of the premises all the in- 
 formation which is useful for the purpose in view and 
 this is the whole which reasoning accomplishes. 
 
 It will appear in the course of our study that the whole of 
 logic, and the whole of any science, consists in so arranging the 
 individual things we meet in general notions or classes, and in 
 giving them appropriate general names or terms, that our 
 knowledge of them may be made as simple and general as 
 possible. Every general notion that as properly formed admits 
 of the statement of general laws or truths ; thus of the planets 
 we may affirm that they move in elliptic orbits round the sun 
 from west to east ; that they shine with the reflected light of the 
 sun ; and so on. Of the fixed stars we may affirm that they 
 shine with their own proper light; that they are incomparably 
 more distant than the planets; and so on. The whole of reason- 
 ing will be found to arise from this faculty of judgment, which 
 enables us to discover and affirm that a large number of objects 
 have similar properties, so that whatever is known of some may 
 be inferred and asserted of others. 
 
 It is in the application of such knowledge that we employ the 
 third act of mind called discourse or reasoning, by which from 
 certain judgments we are enabled, without any new reference to
 
 16 INTRODUCTION. 
 
 the real objects, to form a new judgment. If we know that iron 
 comas under the general notion of metal, and that this notion 
 comes under the still wider notion of element, then, without 
 furtlier examination of iron, we know that it is a simple unde- 
 composable substance called by chemists an element. Or if 
 from one source of infonnation we learn that Neptune is a 
 planet, and from another that planets move in elliptic orbits, we 
 can join tliese two portions of knowledge together in the mind, 
 80 ax to elicit the truth that Neptune moves in an elliptic orbit. 
 
 * 12. Method of Treatment. 
 
 Simple apprehension is expressed in terms, judgment 
 in j^ropositions, and reasoning in syllogisms. The dis- 
 cussion of these needs to be supplemented by the 
 examination of fallacies and induction, some account of 
 logical method, and a view of recent logical theoriea 
 Oui chapters, therefore, will be as follows : 
 
 1. 
 
 Terms. 
 
 2. 
 
 I'l'oposlfions, 
 
 3. 
 
 Sf/f/of/isms. 
 
 4. 
 
 Fallacies. 
 
 5. 
 
 Induction. 
 
 6. 
 
 Mrf/iod. 
 
 7. 
 
 Recent Logical Views,
 
 LOGIC. 
 
 CHAPTER I. 
 TERMS. 
 
 In the treatment of Terms we shall find it convenient 
 to consider: (1) The Various Kiiid.s of Terms; 
 (2) The Ambiffuity of Terms; (3) The Two- 
 fold Meaning of Terms, in Extension and In- 
 tension ; (4) The Growth of Lanf/aaf/e ; and 
 (5) The Perfect and the Imperfect Know- 
 ledge of Terms, The discussion of these topics 
 will occupy tiie following sections. 
 
 SECTION I. 
 
 THE VARIOUS KINDS OF TERMS, 
 
 1. The Meaning- of "Term" Explained. 
 
 It has been explained that every assertion or state- 
 ment expresses the agreement or difference of two 
 things, or of two general notions. In putting the 
 assertion or statement into words, we must accordingly 
 have words suitable for drawing the attention of the 
 mind to the things which are compared, as well as 
 words indicating the result of the comparison, that is 
 to say, the fact whether they agree or differ. The 
 words by which we point out the things or classes of 
 things in question are called Terms, and the words 
 denoting the compaiison are said to form the Copula.
 
 18 TERMS. 
 
 Hence a complete assertion or statement consists ot 
 two terms and a copula, and when thus expressed it 
 forms a Proposition. Thus in the proposition *' Dic- 
 tionaries are useful books," the two terms are diction- 
 aries and useful books ; the copula is the verb are, and 
 expresses a certain agreement of the class dictionaries 
 with the class of useful books consisting in the fact 
 that the class of dictionaries forms part of the chiss of 
 useful books. In this ease each term consists of only 
 one or two words, but any number of words may be 
 required to describe the notions or classes compared 
 together. In the proposition " the angles at the base 
 of an isosceles triangle are equal to each other," the 
 first term re({uires nine words for its expression, and 
 the second term, four words (equal to each other); and 
 there is no limit to the number of words which may \ 
 employed in the formation of a term. 
 
 A Term is so called because it forms one end (Latin, terminut) 
 of a proposition, and strictly speaking it is a term only so long as 
 it stands in the proposition. But we commonly speak of a term 
 or a name mesming any noun, substantive or adjective, or any 
 combination of words denoting an object of thought, whether 
 that be, a.s we shall shortly see, an individual thing, a group of 
 things, a quality of things, or a group of qualities. It would be 
 imiK)88ible to define a name or term better than has been done by 
 Iloblx'S : " A name is u word taken at pleasure to sf^rve for a 
 mark, which may raise in our mind a thought like to some 
 thought which w(! liad l)ef()re, and which, being pronounced to 
 otljers, may be to them a sign of what thought the Bi)eaker had 
 before in his mind." 
 
 2. CatORoreinatic and Syiicategorematic Words. 
 
 Though every t<>rm or name consists of words, it Is 
 not every word which can form a name by itself. W
 
 TARIOUS KINDS OF TERMS. 19 
 
 cannot properly say " Not is agreeable " or " Probably 
 is not true;" nothing can be asserted of a preposition, 
 an adverb, and certain other parts of speech, except 
 indeed that they are prepositions, adverbs, etc. No 
 pai't of speech except a noun substantive, or a group of 
 words used as a noun substantive, can form the subject 
 or first term of a proposition, and nothing but a noun 
 substantive, an adjective, the equivalent of an adjec- 
 tive, or a verb, can form the second term or predicate 
 of a proposition. It may indeed be questioned whether 
 an adjective can ever form a term alone ; thus in " Dic- 
 tionaries are useful," it may be said that the substan- 
 tive things or hooks is understood in the predicate, 
 the complete sentence being " Dictionaries are useful 
 hooks ; " but as this is a disputed point we will assume 
 that words are divided into two kinds in the following 
 manner : 
 
 (1) Words which stand, or appear to stand, alone as 
 complete terms, namely the substantive and adjective, 
 and certain parts of a verb, are called Categorematic 
 words, (from the Greek word KarT/yopt'to), to assert or 
 predicate. 
 
 (2) Those parts of speech, on the other hand, such 
 as prepositions, adverbs, conjunctions, etc., which can 
 only form parts of names or terms, are called Syncate- 
 gorematic words, because they must be used loiih other 
 words in order to compose terms (Greek ovv, with, and 
 KUTTj-yopeo)). Of syncategorematic words we need not 
 take further notice except so far as they form part of 
 categorematic terms.
 
 20 TERMS. 
 
 3. Sinjiriilai' Terms. 
 
 Terms are distinguished into singular or individual, 
 and general or common terms, this being a very obvious 
 division, but one of much importance. A Singular 
 term is one which can denote only a single object, so 
 long at least as it is used in exactly the same meaning ; 
 thus the Emperor of the French, the Atlantic Ocean, 
 St. Paul's, William Shakspeare, the most precious of 
 metals, are singular terms. All proper names belong 
 to this class ; for though John Jones is the name 
 of many men, yet it is used not as moaning a7iy of 
 these men, but some single man it has, in short, a 
 different meaning in each case, just as London in 
 England, has no connection in meaning with London 
 HI Canada. 
 
 4. General Terms. 
 
 General terms are applicable in the same sense 
 equally to any one of an indefinite number of objects 
 which resemble each other in certain qualities. Thus 
 vietal is a general name because it may be applied 
 indifferently to gold, silver, copper, tin, aluminium, 
 or any of about fifty known substances. It is not the 
 name of any one of these more than any other, and it 
 is in fact apjilied to any substance which possesses 
 metallic lustre, which cannot be decomposed, and 
 which has certain other qualities easily recognized by 
 chemists. Nor is tlie number of substances in the 
 class restricted ; for as new kinds of metal are from 
 time to time discovered they are added to the class. 
 A (rain, while Mars, Jupiter, Saturn, etc., are singular
 
 VARIOUS KINDS OF TERMS. %\ 
 
 terms, since each can denote only a single planet, Ihe 
 term planet is a general one, being applicable to as 
 many bodies as may be discovered to revolve round the 
 sun as the earth does. 
 
 5. Collective Terms. 
 
 We must carefully avoid any confusion between 
 general and collective terms. By a collective term we 
 mean the name of a number of things when all joined 
 together as one whole ; like the soldiers of a regimeiit, 
 the men of a jury, the crew of a vessel ; thus a coll( c- 
 tive term is the name of all, but not of each. A genei-al 
 term, on the other hand, is the name of a number of 
 things, but of each of them separately, or, to use t!ie 
 technical expression, distributively. Soldier, jurymau, 
 sailor, are the general names which may belong to John 
 Jones, Thomas BroAvn, etc., but we cannot say that 
 John Jones is a regiment, Thomas Brown a jury, and 
 so on. The distinction is exceedingly obvious when thus 
 pointed out, but it may present itself in more obscure 
 forms, and is then likely to produce erroneous reason- 
 ing. It is easy to see that we must not divide terms 
 into those which are general and those which are col- 
 lective, because it will often happen that the same term 
 is both general and collective, according as it is regard- 
 ed. Thus, library is collective as regards the books in 
 it, but is general as regards the great number of differ- 
 ent libraries, private or public, which exist. 
 
 Re^ment is a collective term as regards the soldiers wliish 
 compose it, but greneral a^ regards the hundred different re^- 
 ments. the Coldstream Guards, the Highland regiment, the
 
 23 TERMS. 
 
 Welsh Fusiliers, and the rest, which compose the British stand- 
 ing armv. Army, again, is a collective whole, as being composed 
 of a number of regiments organized together. Year is collective 
 as regards the months, weeks, or days of which it consists, but is 
 general as being the name either of 1869 or 1870, or any period 
 marked by a revolution of the earth round the sun. 
 
 We have not always in the English language sufficient means 
 of distinguishing wnveniently between tlie general and collec- 
 tive use of terms. In Latin this distinctive use was exactly 
 expressed by omnes, meaning all distributively, and cuncti 
 meaning all taken together, a contracted form of ronjuncti 
 (joine<l together). In English all men may mean any mun or all 
 men together. Even the more exact word every is sometimes 
 misused, as in the old proverb, " Every little makes a mickle," 
 where it is obvious that every little portion cannot by itself make 
 much, but only when joined to other little portions. 
 
 6. Concrete and Abstract Terms. 
 
 An important distinction between terras is that of 
 concrete terms and abstract terms; and it cannot oe 
 better described than in tlie words of Mr. Mill, by say- 
 ing that a concrete name is the name of a thing, the 
 abstract name is the name of a quality, attribute, or 
 circumst^ince of a thing. Thus red house is the name 
 of a physically-existing thing, and is concrete ; redness 
 is the name of one quality of the house, and is abstract. 
 The word aljstract means drawn from (Latin, abstrac- 
 tus, from absfrahere, to dniw away from), and indi- 
 cates tliat the quality redness is thought of in the mind 
 apart from all the other qualities which belong to the 
 red house, or other red object. But though we can 
 think of a quality by itself, we cannot suppose that the 
 quality can exist physically apart from the matter in 
 which it ig manifest to us. Redness means either a
 
 TARIOUS KINDS OF TERMS. 3S 
 
 notion in the mind, or it means that in red objecta 
 which excitee the notion. 
 
 The learner should carefully observe that adjectives are con- 
 crete, not abstract. If we say that & lx)ok is useful, it is to the 
 book we apply the adjective useful, and usefulness is the abstract 
 noun which denotes the quality ; similarly, the adjectives equal, 
 grateful, reverent, rational, are the names of thinjfs, and the 
 corresponding abstract noons are equality, gratitude, reverence, 
 rationality. 
 
 It is a good exercise to try to discover pairs of correspond- 
 ing concrete and abstract names; thus animal has animality; 
 miser, miserliness ; old, agedness, or old age ; substance, sub- 
 stantiality ; soap, soapiness; shrub, shrubbiness ; and so on. But 
 it by no means follows that an abstract word exists for each con- 
 crete ; table hardly has an abstract tabularity ; and though ink 
 has inkiness, we should not find the abstract of pen. It is by 
 the accidents of the history of language that we do or do not 
 possess abstract names ; and there is a constant tendency to 
 invent new abstract words in the progress of time and science. 
 
 Unfortunately concrete and abstract names are frequently 
 confused, and it is by no means always easy to distinguish the 
 meanings. Thus relation properly is the abstract name for the 
 position of two people or things to each other, and those people 
 are properly called relatives (Latin, relativus, one who is related). 
 But we constantly speak now of relations, meaning the persons 
 themselves ; and when we want to indicate the abstract relation 
 they have to each other we have to invent a new abstract name 
 relationship. Nation has long been a concrete term, though from 
 its form it was probably abstract at first ; but so far does the 
 abuse of language now go, especially in newspaper writing, that 
 we hear of a nationality meaning a nation, although of course if 
 nation is the concrete, nationality ought to be the abstract, 
 meaning the quality of being a nation. Similarly, action, inten- 
 tion, extension, conception, and a multitude of other properly 
 abstract names, are used confusedly for the corresponding con- 
 crete, namely, act, intent, extent, concept, etc. Production it 
 properly the condition or 8ta.te of a person who is producing or
 
 24 TBBMS. 
 
 drawing something forth ; but it has now become confused witli 
 that which is produced, so that we constantly talk of the produc- 
 tions of a country, meaning the products. The logical terms, 
 Projjosition, Deduction, Induction Syllogism, are all properly 
 abstract words, but are used concretely for a Proposition, a De- 
 duction, an Induction, a Syllogism ; and it must be allowed that 
 logicians are nearly as bad as other people in confusing abstract 
 and concrete terms. Much injury is done to language by this 
 abuse. 
 
 7. Positive and Negative Terms. 
 
 Another very obvious division of terms is between 
 those which are positive, and those which are negative. 
 The difference is usually described by saying that posi- 
 tive terms signify the existence or possession of a 
 quality, as in grateful, metallic, organic, etc., while 
 the eorresj)onding negatives signify the absence of the 
 same qualities as in ungrateful, non-metallic, inorganic. 
 The negative terms may be adjectives as above, or sub- 
 stantives, concrete or abstract ; thus ingratitude, in- 
 equality, inconvenience, are abstract negative terms; 
 and individuals, uncquals, etc., are concrete negatives. 
 We usually consider as negative terms any which have 
 a negative prefix such as not, non, un, in, etc. ; but 
 there are a great many terms which serve as negatives 
 without possessing any mark of their negative charac- 
 ter. Darkness is the negative of light or lightness, 
 since it means the absence of light ; compound is the 
 negative of element, since we should give the name of 
 compound to whatever can be decomposed, and element 
 is what cannot l)e decomposed ; theoretically speaking 
 every term has its corresponding negative, but it by no 
 means follows that language furnishes the term ready-
 
 VABIOUS KINDS OF TERMS. 25 
 
 made. Thus table has the corresponding adjective tab- 
 ular, but there is no similar negative untabular ; one 
 man may be called a bookworm, but there is no nega- 
 tive for those who are not bookworms, because no need 
 of the expression has been felt. A constant process of 
 invention of new negative terms goes on more rapidly 
 perhaps than is desirable, for when an idea is not 
 often referred to it is better to express it by a phrase 
 than add to the length of the dictionary by a new- 
 created word. 
 
 It would eeem that in many cases a negative term implies the 
 presence of some distinct quality or fact. Thus inconvenience 
 doubtless implies the absence of convenience , but also the pres 
 ence of positive trouble or pain occasioned thereby. Unhappi 
 ness is a negative term, but precisely the same notion is 
 expressed by the positive term misery. The negrative of healthy 
 is unhealthy, but the positive term sickly serves equally well. 
 It thus appears to be more a matter of accident than anything 
 else whether a positive or negative term is used to express any 
 particular notion. All that we can really say is that every posi 
 tive term necessarily implies the existence of a corresponding 
 negative term, which may be the name of all those things to 
 which the positive name cannot be applied. Whether this term 
 has been invented or not is an accident of language ; its existence 
 may be assumed in logic. 
 
 The reader may be cautioned against supposing that every 
 term appearing to be of a negative character on account of 
 possessing a negative prefix is really so. The participle unloosed 
 certainly appears to be the negative of loosed ; but the two words 
 mean exactly the same thing, the prefix vn not being really the 
 negative ; inmluable, again, means not what is devoid of value, 
 but what is so valuable that the value cannot be measured ; and 
 a shameless action can equally be called by the positive 
 term, a shameful action. Other instances might no doubt be 
 found. 
 
 Great care should be taken to avoid confusing terms which
 
 26 TEBMS. 
 
 expresB the presence or absence of a quality with those whicl 
 describe its degree. Lens is not tin- uegative of greater because 
 there is a third alternative, equal. The true negative of greater 
 is not-greater, and this is equivalent to either equal or less. So it 
 may be said that dmigreeable is not the simple negative of agree- 
 able, because there may be things which are neither one nor the 
 other, but are indifferent to us. It veould not be easy to say ofl&^ 
 hand whether every action which is not honest is dishonest, oi 
 wliother there may not be actions of an intermediate character. 
 The rule is that wherever the question is one of degree or quan 
 tity a medium is possible, and tlie subject belongs rather to the 
 science of quantity than to simple logic ; where the question is 
 one of the presence or absence of a quality, there cannot be more 
 than two alternatives, accf>rding to one of the Primary Laws of 
 Thought, which we will consider in Chap. Ill, Sec. I. In the 
 case of quantity we may call tlie extreme terms opposites ; thus 
 less 19 the opposite of greater, disagreeable of agreeable ; in th 
 case of mere negation we may call the terms negatives or con- 
 tradictories, and it is really indifferent in a logical point or 
 view which of a pair of contradictory terms we regard as the 
 positive and which as the negative. Each is the negative of the 
 other. 
 
 8. Privative Terms. 
 
 Logicians have distinguished from simple negative 
 terms a chiss of terms called privative, such as blind, 
 dead, etc. Such terms express that a thing has been 
 i;;nye(/ of a quality which it before possessed, or was 
 capable of possessing, or usually does possess. A man 
 may be born blind, so that he never did see, but he 
 {assesses the organs wliicii would have enabled him to 
 see except for some accident. A stone or a tree could 
 not have had the faculty of seeing under any circum- 
 stances. No mineral substance can jiroperly be said to 
 die or to be dead, because it was incapable of life ; but
 
 VARIOUS KINDS OF TERMS. 27 
 
 it may be called uncrystallized because it might havf 
 been in the form of a crystal. Hence we apply a 
 privative term to anything which has not a quality 
 which it was capable of having; we apply a negative 
 term to anything which has not and could not have the 
 quality. It is doubtful however whether this distinc- 
 tion can be properly carried out, and it is not of very 
 much importance. 
 
 9. Relative and Absolute Terms. 
 
 It is further usual to divide terms according as they 
 are relative or absolute, that is, non-relative. The 
 adjective absolute means whatever is " loosed from con- 
 nection with anything else " (Latin ah, from, and 
 solutus, loosed) ; whereas relative means that which is 
 carried in thought, at least, into connection with some- 
 thing else. Hence a relative term denotes an object 
 which cannot be thought of without reference to some 
 other object, or as part of a larger whole. A father 
 cannot be thought of but in relation to a child, a 
 monarch in relation to a subject, a shepherd in relation 
 to a flock; thus father, monarch, and shepherd are 
 relative terms, while child, subject, and flock are the 
 correlatives (Latin con, with, and relativus), or those 
 objects which are necessarily joined in thought with 
 the original objects. The very meaning, in fact, of 
 father is that he has a child, of monarch that he has 
 subjects, and of shepherd that he has a flock. As 
 examples of terms which have no apparent relation to 
 anything else, I may mention water, gas, tree. There 
 does not seem to me to be anything so habitually asso- 
 ciated with water that we must think of it as part of
 
 38 TERMS. 
 
 the same idea, and gas, tree, and a multitude of othei 
 terms also denote objects wiiich have no remarkable or 
 permanent relations such as would entitle the terras to 
 be called relatives. They may therefore be considered 
 absolute or non-relative terms. 
 
 The fact, however, is that everything must really have rela- 
 tions to something else, the water to the elements of whicli it is 
 comix)sed, the j^as to the coal from which it is manufactured, 
 the tree to the soil in wiiich it is rooted. By the very laws of 
 thought, again, no thing or class of things can be thougiit of but 
 by separatin^^ them from otlier existing things from which they 
 differ. I cannot use the term mortal without at once separating 
 all exi.-<ting or conctnvable things into the two groups mortal and 
 immartal ; motal, element, organic substance, and every other 
 term that could be mention(;d, Avould necessarily imply the 
 existence of a correlative negative term, non metallic, compound, 
 inorganic substance, and in this respect therefore every term is 
 undoubtedly relative. Logicians, however, have been content to 
 consider as relativi; terms those only which imply some peculiar 
 and striking kind of relation arising from position in time or 
 space, from connection of cause and effect, etc.; and it is in this 
 special sense therefore the student must use tlie distinction, 
 
 10. Summary. 
 
 The most important varieties of terms having been 
 explained, it is desirable that the learner should acquire 
 a complete familiarity with them by employing the exer- 
 cises at the end of the book. The learner is to deter 
 mine concerning each of the terms there given: 
 
 1. ff'ht'fhcr it is a ratef/oreniatic or a Hyncategore- 
 
 iimfie ivortl. 
 
 2. Whcfhrr it in a f/fuernl or a ninf/ulnr term, 
 .'{. H'/trfhf'r it is collrrtive or distributive. 
 
 rf. H'ftet/iMr it in concrete or abtttract.
 
 VARIOUS KINDS OF TERMS. 89 
 
 5, Whether it is positive, or negative^ or priva* 
 
 tive, 
 
 6, Whether it is relative or absolute. 
 
 It will be fully pointed out in the next section that most 
 terms have more than one meaninj? ; and as the one meaning 
 may be general and the other singular, the one concrete and the 
 other abstract, and so on, it is absolutely necessary that the 
 learner should first of all choose one precise meaning of the 
 term which he is examining. And in answering the que^stions 
 proposed it is desirable he should specify the way in which he 
 regards it. Taking the word sovereign, we may first select the 
 meaning in which it is equivalent to monarch ; this is a general 
 term in so far as it is the name of any one of many nionarchs 
 living or dead, but it is singular as regards the inhabitant^ of any 
 one country. It is clearly categorematic, concrete, and positive 
 and obviously relative to the subjects of the monarch. 
 
 Read Mr. Mill's chapter on Names, System of Logic, Book I, 
 chap. 2. 
 
 In this section on " Various Kinds of Terms/' 
 we have considered: 
 
 1. The Meaning of ** Term,'* 
 
 2. CVf tegoretn atic and Syncatcyoreniatic Wordt 
 
 3. Siiif/ufar Terms. 
 4-. General Terms. 
 
 5. Collective Terms. 
 
 6. Concrete and Abstract Terms. 
 
 7. Positive and Negative Terms. 
 
 8. Privative Terms. 
 
 9. Relative and Absolute Terms,
 
 so TE&MS. 
 
 SECTION IL 
 
 THE AMBIGUITY OF TERMS. 
 
 1. Importance of Avoiding Ambiguity. 
 
 There is no part of Logic which is more really useful 
 than that which treats of the ambiguity of terms, that 
 is, of the uncertainty and variety of meanings belong- 
 ing to words. Nothing indeed can be of more impor- 
 tance to the attainment of correct habits of thinking 
 and reasoning than a thorough acquaintance with the 
 great imperfections of language. Comparatively few 
 terms have one single clear meaning and one meaning 
 only, and whenever two or more meanings are uncon- 
 sciously confused together, we inevitably commit a 
 logical fallacy. If, for instance, a person should argue 
 that ' i)uni.shment is an evil," and according to the 
 principles of morality " no evil is to be allowea even with 
 the purpose of doing good," we might not at the first 
 moment see how to avoid the conclusion that " no pun- 
 ishments should be allowed," because they cause evil. 
 A little reflection will show that the word evil is here 
 used in two totally different senses ; in the first case it 
 means physical evil or pain ; in the second, moral evil ; 
 and because moral evil is never to be committed, it does 
 not follow that physical evils are never to be inflicted, 
 for they are often the very means of preventing moral 
 
 3Yil. 
 
 Another very plausible fallacy which has often ben put 
 forth in various forms is as follows: "A thoroujrhly l)enevolent 
 man cannot ijossibly refuse to relieve the poor, and since a per- 
 son wIkj cannot ix)88ibly act otherwise than he does can claim n
 
 THE AMBIOFITT OP TEBlCa 81 
 
 merit for Wa actions, it follows that a thoroughly benevolent man 
 can claim no merit for his actions." According to tliis Icind o/ 
 argument a man would have less merit in proportion as he waa 
 more virtuous, so as to feel greater and greater difSculty in act- 
 ing wrongly. That the conclusion is fallacious every one must 
 feel certain ; but the cause of the fallacy can only be detected by 
 observing that the words cannot possibly have a double meaning, 
 in the first case referring to the influence of moral motives or 
 good character, and in the second to circumstances entirely be- 
 yond a person's control ; as, for instance, the compulsion of the 
 laws, the want of money, the absence of personal liberty. The 
 more a person studies the subtle variations in the meaning of 
 common words, the more he will be convinced of the dangerous 
 nature of the tools he has to use in all communications and argu- 
 ments. Hence the learner should give much attention to the 
 contents of this section. 
 
 2. Univocal and Equivocal Terms. 
 
 Terms are said to be univocal when tliey can suggest 
 to the mind no more than one single definite meaning. 
 They are called equivocal or ambiguous when they have 
 two or more different meanings. It will be observed, 
 however, that a term is not equivocal because it can be 
 applied to many objects when it is applied in the same 
 sense or meaning to those different objects. Thus 
 cathedral is the name of St. Paul's, the York Minster, 
 and the principal churches of Salisbury, Wells, Lincoln 
 and a number of other cities, but it is not ambiguous, 
 because all these are only various instances of the same 
 meaning ; they are all objects of the same description 
 or kind. The word cathedral is probably univocal or 
 of one logical meaning only. The word church, on the 
 other hand, is equivocal, laecause it sometimes meana 
 the building in which religious worship is performed,
 
 82 TBBH8. 
 
 so'netimes the body of persons who belong to one sect 
 or jiersua^ion, and assemble in churches. Sometimes 
 also the church means the body of the clergy as distin- 
 guished from the laity ; hence there is a clear differ- 
 ence in the sense or meaning with which the word is 
 used at different times. 
 
 Instances of univocal terms are to be found chiefly in technical 
 an<l scientific language. Steam engine, gasometer, railway train, 
 permanent way, and multitudes of such technical names denot- 
 in|^ distinct common objects, are sufficiently univocal. In com- 
 mon life the names penny, mantelpiece, teacup, bread and butter, 
 have a sufficiently definite and single meaning. So also in chem- 
 istry, oxygen, hydrogen, sulphate of- copper, alumina, lithia, and 
 thi>u8!inds of other terms, are very precise, the words themselvea 
 having often been invented in very recent years, and the mean- 
 ings exactly fixed and maintained invarialile. Every science 
 ha.s, or ouglit to have, a series of terms equally precise and cer- 
 tain in meaning. Tlie names of individual objects, buildinjrs, 
 ev.-nts, or persons, apfain, are usually quite certain and clear 
 as Julius Caesar, VMllian) the Conqueror, the first Napoleon. 
 Saint Peter's, VVestmiuster Abbey, the Great Exhibition of 1851 
 an 1 so on. 
 
 But however numerous may be the univocal terms which can 
 b! adduced, still the eepiivocal terms are astonishingly common. 
 Tliey include most of the nouns and adjectives which are in 
 habitual use in the ordinary intercourse of life. They are called 
 ambiguous from the Latin verb amhigo, to wander, hesitate, or 
 be in doubt ; or a(;ain homonymous, from the Greek o^or, like, 
 and oioua, name. Whenever a ]>er8on uses equivocal words in 
 Buch a way as to confuse the different meanings and fall into 
 error, he may be said to commit the fallacy of Equivocation in 
 the logical moaning of the name (see Cliapter IV) ; but in com- 
 mon life a person is not said to equivocate unless he uses wordi 
 cons'iously and docpitfully in a manner calculated to producer 
 ooufiuiou of the true and apparent meanings.
 
 THE AMBIGUITY OF TERMS. 88 
 
 3. Kinds and Causes of Ambig^iity. 
 
 Following Dr. Watts in classifying equivocal words, 
 we may distinguish three classes according as they are 
 
 1. Equivocal in sound only. 
 
 2. Equivocal in spelling only. 
 
 3. Equivocal in both sound and spelling. 
 
 The first two classes are comparatively speaking of very 
 slight importance, and do not often give rise to serious 
 error. They produce what we should cull trivial mis- 
 takes. Thus we may confuse, when spoken only, the 
 words right, wright, and rite (ceremony); also the words 
 rein, rain and reign, might and mite, etc. Owing 
 partly to defects of pronunciation mistakes are not 
 unknown between the four words air, hair, har.e and 
 heir. 
 
 Words equivocal in spelling but not in sound are 
 such as tear (a drop), and tear pronounced tare, mean- 
 ing a rent in cloth ; or lead, the metal, and lead, as in 
 following the lead of another person. As little more 
 than momentary misapprehension, however, can arise 
 from such resembhiuce of words, we shall pass at once 
 to the class of words equivocal both in sound and spell- 
 ing. These I shall separate into three groups accord 
 ing as the equivocation arises 
 
 1. From the accidental confusion of different words. 
 
 2. From the transfer of meaning by the association 
 
 of ideas. 
 
 3. From the logical transfer of meaning to analogous 
 
 objects.
 
 34 TERMS. 
 
 (1) U'jder the first class we place a certain numbei 
 of curious but hardly important cases in which ambi< 
 guity lias arisen from tiie confusion of entirely diiferent 
 .vords, derived fi'om different languages or from differ- 
 ent roots of the same language, but which have in the 
 course of time assumed the same sound and spelUng. 
 Thus the word mean denotes either that which is 
 medium or mediocre, from the French moyen and the 
 Latin medius, connected with the Anglo-Saxon mid, 
 or middle; or it denotes what is low-minded and base 
 being then derived from the Anglo-Saxon Gemcene, 
 which means ' that belonging to the moene or many," 
 whatever in short is vulgar. The verb to man can 
 hardly be confused with the adjective mean, but it 
 comes from a third distinct root, probably connected 
 with the Sanscrit verb, to think. 
 
 As other instances of this casual ambij^ty, I may mention 
 rent, a money payment, from the French rente {rendre, to return), 
 or a tear, the result of the action of rending, this word being of 
 Anglo-Saxon origin and one of the numerous class beginning in 
 r or wr, which imitate more or less perfectly the sound of the 
 action which they denote. Pound, from the Latin pondus, a 
 weiglit, is confused with pound, in the sense of a village pinfold 
 for cattle, derived from the Saxon pyndan, to pen up. Fell, a 
 mountain, is a perfectly distinct word from feV, a skin or hid6; 
 and pnhe, a throb or beating, and ptiUe, peas, l^eans, or potage, 
 thougli ])ot}i derived from the Greek or Latin, are probably quite 
 anconnecte<l words. It is curious that gin, in the meaning of 
 trap or machine, is a contracted form of engine, and when denot- 
 ing the spirituous licjuor is a corruption of Geneva, the place 
 where the spirit was first made. 
 
 Certain important cases of confusion have been detected in 
 grammar, as between the numeral one, derived from an Aryan 
 mot, through the Lntin nniiM, and the indeterminate pronoun, 
 one (a in " om ought to do one's duty "), which is really a corrupt
 
 THE AMBIGUITT OF TERMS. M 
 
 form of the French word homme or man. The Gennans to th> 
 present day use man in this sense, as in man sagt, i. e. one says, 
 
 (2) By far the largest part of equivocal words have 
 become so by a transfer of the meaning from the thing 
 originally denoted by the word to some other thing 
 habitually connected with it so as to become closely 
 associated in thought. Thus, in Parliamentary Ian 
 guage, the House means either the chamber in whic! 
 the members meet, or it means the body of members 
 who happen to be assembled in it at any time. Simi- 
 larly, the word church originally denoted the building 
 {KvpiaKov^ the Lord's House) in which any religious 
 worshippers assemble, but it has thence derived a 
 variety of meanings ; it may mean a particular body of 
 worshippers accustomed to assemble in any one place, 
 in which sense it is used in Acts xiv. 23 ; or it means 
 any body of persons holding the same opinions and 
 connected in one organization, as in the Anglican, or 
 Greek, or Roman Catholic Church ; it is also sometimes 
 used so as to include the laity as well as the clergy; 
 but more generally perhaps the clergy and religious 
 authorities of any sect or country are so strongly asso- 
 ciated with the act of worship as to be often called the 
 church par excellence. It is quite evident, moreover, 
 that the word entirely differs in meaning according as 
 it is used by a member of the Anglican, Greek, Roman 
 Catholic, Scotch Presbyterian, or any other existing 
 church. 
 
 The word foot has suffered several curiou-s but very evident 
 transfers of meaning. Originally it denoted the foot of a man 
 or an animal, and is probably connected in a remote manner with 
 the Latin pea, pedis, and the Greek tzov^, nodoQ ; but since tht
 
 36 TERMS. 
 
 length of the foot is naturally employed as a rude measure oi 
 length, it came to be applied to a fixed measure of length ; and 
 as the foot is at the liottom of the body the name was extended 
 by analogy to the foot of a mountain, or the feet of a table ; by a 
 further extension, any position, plan, reason, or argument on 
 which we place ourselves and rely, is called the foot or footing. 
 The same word also denotes soldiers who fight uixjn their feet, 
 or infantry, and the measured part of a verse having a definite 
 length. That these very diflerent meanings are naturally con- 
 nected with the original meaning is evident from the fact that 
 the Latin and Greek words for foot are subject to exactly similar 
 series of ambiguities. 
 
 It would be a longf task to trace out completely the various 
 and often contradictory meanings of the word fellow. Originally 
 a fellow was wh&tfuUows aaother, that is a companion; thus it 
 came to mean the other of a pair, as one shoe is the fellow of the 
 otlier, or simply an equal, as when we say that Shakespeare 
 " liatli not a fellow." From the simple meaning of companion 
 again it Ofjmes to denote vaguely a person, as in the question 
 " What fellow is that? " but then there is a curious confusion of 
 depreciatory and endearing power in the word ; when a man is 
 called a mere fellow, or simjjly a fellow in a particular tone of 
 voice, the name is one of severe contempt; alter the tone of 
 voice of the connected words in the least degree, and it becomes 
 one of the most sweet and endearing appellations, as wiien we 
 speak of a dear or good fellow. We may still add the technical 
 meanings of the name as applied in the case of a Fellow of a 
 College, or of a learned society. 
 
 Another good instance of the gro^vth of a number of different 
 meanings from a single root is found in the word post. Origi- 
 nally a post was something po^Yerf, or placed firmly in the ground 
 s'lch as an upright piece of wood or stone ; such meaning stiU 
 remains in the cases of a lamp post, a gate post, signal post, etc 
 As a pimt would often be usikI to mark a fixed spot of ground, na 
 in a mile-post, it came to mean the fixed or appointed place 
 wlien^ the f)08t was plac<>d. as in a military post, the post of dan- 
 ger or honor, etc. The fixed places where horses were kept in 
 readinnsH to facilitate rapid travelling during the timee of ths
 
 THE AMBIGUITY OF TEEMS. 87 
 
 Roman empire were thus called posts, and thence the whcl 
 system of arrangement for the conveyance of persons or news 
 c&vae to he c&Ued the posts. The name has retained an exactly 
 similar meaning to the jiresent day in most parts of Europe, and 
 we still use it in post-chaise, post-boy, post-horse and postillion. 
 A system of post conveyance for letters having been organized 
 for about two centuries in England and other countries, this is 
 perhaps the meaning most closely associated with the word post 
 at present, and a number of expressions have thus arisen, smh 
 as post-office, postage, postal-guide, postman, postmaster, postal- 
 telegraph, etc. Curiously enough we now have iron letter-post* 
 in which the word post is restored exactly to its original meaning 
 Although the words described abo\-e were Eelected on account 
 of the curious variety of their meauinprs, I do not hesitate 1o 
 assert that the majority of common nouns possess various 
 meanings in greater or less number. Dr. Watts, in his Logu'.. 
 suggests that the words book, bible, fish, house, and elephant, are 
 univocal terms, but the reader would easily detect ambiguities 
 in each of them. Thus fish bears a very different meaning ia 
 natural historj'^ from what it does in the mouths of uiiscientifio 
 persons, who include under it not only true fishes, but shell-fisK 
 or molliisca, and the cetacea, such as whales and seals, in short 
 all swimming animals, whether they have the character of tru'3 
 fish or not. Elephant, in a stationer's or bookseller's shop, means 
 a large kind of paper instead of a large animal. Bible some 
 times means any particular copy of the Bible, sometimes the 
 collection of works constituting the Holy Scriptures. The word 
 man is singularly ambiguous ; sometimes it denotes man as 
 distinguished from woman ; at other times it is certainly used to 
 include both sexes ; and in certain recent election cases lawyers 
 were unable to decide whether the word man as used in the 
 Reform Act of 1867 ought or ought not to be interpreted so as to 
 include women. On other occasions man is used to denote an 
 adult male as distinguished from a boy, and it also often denotes 
 one who is emphatically a man as possessing a masculine char 
 acter. Occasionally it is used in the same way as groom, for a 
 servant, as in tho y>roverb, ''Like master, like man." At other 
 times it stands specially for a husband.
 
 B8 TEKMS. 
 
 (3) Among ambiguous words we must, thirdly, di 
 tiaguish those which derive their various meanings in 
 ft somewhat differeut manner, namely by analogy or 
 real resemblance. When we speak of a sweet taste, a 
 Bweet flower, a sweet tune, a sweet landscape, a sweet 
 face, a sweet poem, it is evident that we apply one and 
 the same word to very different things ; such a con- 
 crete thing as lump-sugar can hardly be compared 
 directly with such an intellectual existence as Tenny- 
 son's May Qtieeji. Nevertheless if the word sweet is to 
 be considered ambiguous, it is in a different way from 
 those we have before considered, because all the things 
 are called sweet on account of a peculiar pleasure which 
 they }ield, which cannot be described otherwise than 
 by comparison with sugar. 
 
 In a similar way, we describe a pain as sharp, a disappoint- 
 ment as bitter, a person's temper as sour, the future as bright or 
 gloomy, an acliievement as brilliant ; all these adjectives imply- 
 ing com|)arison with bodily sensations of the simplest kind. 
 The adjective brilliant is derived from the French briUer, to 
 glitter or SDarkle ; and this meaning it fully retains when we 
 speak of a brilliant diamond, a brilliant star, etc. By what a 
 subtle analopry is it that we speak of a brilliant position, a 
 brilliant achievement, brilliant talents, brilliant style I We 
 cannot speak of a clear explanation. Indefatigable perseverance, 
 perspicuous style, or sore calamity, without employing in each 
 of these expressions a double analogy to physical impressions, 
 actions, or I'vents. It will be shown in the fourth section tliat 
 to this process we owe the creation of all names connected with 
 mental feelings or exiQtencef 
 
 Reafl Watts' Logic, Cliapter IV. 
 
 'cke's Eiiitfiy on the Human U''^derttanding, Book III 
 Chapters IX and X.
 
 EXTENSION AND INTENSION. 89 
 
 In this section, on tlie Ambiguity of Terms, we 
 iiave considered: 
 
 1. Importance of Avoiding Ambiguity. 
 
 2. Univocal and Equivocal Terms. 
 
 3. Kinds and Causes of Ambiguity, 
 
 SECTIOIT in, 
 
 EXTENSION AND INTENSION. 
 
 1. Importance of Understanding this Double 
 Meaning. 
 
 There is no part of the doctrines of Logic more 
 necessary to be understood than the twofold meaning 
 of terms in extension and intension. The learner who 
 acquires a thorough apprehension of the difference of 
 these meanings, and learns to bear it always in mind, 
 will experience but little further difficulty in the study 
 of Logic. 
 
 2. Meaning of Extension and Intension. 
 
 The meaning of a term in extension consists of the 
 objects to which the term may be applied ; its meaning 
 in intension consists of the qualities which are necessa- 
 rily possessed by objects bearing that name. A simple 
 example will make this distinction most apparent. 
 What is the meaning of the name "metal"? The first 
 and most obvious answer is that metal means either 
 gold, or silver, or iron, or copper, or aluminium, or 
 some other of the 48 substances known to chemists,
 
 ad TERMS. 
 
 and considered to have a metallic nature. These eub- 
 Btances then form the plain and common meaning of 
 the name, which is the meaning in extension. But if 
 it be asked why the name is applied to all these sub- 
 stances and the.se only, the answer must be Because 
 they possess certain qualities which belong to the nature 
 of metal. We cannot, therefore, know to what sub- 
 stances we may apply the name, or to what we may not, 
 unless we know the qualities which are indispensable to 
 the character of a metal. Now chemists hiy these down 
 to be somewhat as follows: (1) A metal must be an 
 element or simjile substance incapable of decomposition 
 or separation into simpler substances by any known 
 means. (2) It must be a good conductor of heat and 
 electricity. (3) It must possess a great and peculiar 
 reflective power known as metallic lustre.* 
 
 These properties are common to all metals, or nearly 
 all metals, and are what mark out and distinguish a 
 metal from other substances. Hence they form in a 
 certain way the meaning of the name metal, the mean- 
 ing in intension, as it is called, to distinguish it from 
 tiie former kind of meaning. 
 
 In a similar manner almost any other common name has a 
 double meaning. " Stonnisliip " denotes in extension the Great 
 Eastern, the Persia, the Himalaya, or any one of the thousands 
 of steamships existing or which have existed ; in intension it 
 means " II vessel propelled by steam-power." Monarch is the 
 name of Queen Victoria. Victor Fmmanucl, Louis Na|X)leon, or 
 any one of a considerable number of persons who rule singlj 
 
 It ).< flonbtfnlly tnio that all molnls posoofS molalllc liif tre. and chcmifti! 
 woulfl fltid It very difficult to give niiy roiifixlcut oxpl.'innlinn of their use 
 r>t tho name ; hat the statementB in the text are Buflicienll^ true to furniBh ac 
 example.
 
 EXTENSION AND INTENSION. 41 
 
 over countries ; the persons themselves form the meaning in 
 extension ; the quality of ruling alone forms the intensive mean- 
 ing of the name. Animal is the name iu extension of any one of 
 billions of existing creatures and of indefinitely greater numbers 
 of other creatures that have existed or will exist ; in intension it 
 implies in all those creatures the existence of a certain animal 
 life and sense, or at least the power of digesting food and ezert 
 ing force, which are the marks of animal nature. 
 
 3. Forms of Expressing Exteusiou and Intension, 
 
 It is desirable to state here that this distinction of 
 extension and intension has been explained by logicians 
 under various forms of expression. It is the peculiar 
 misfortune of the science of logic to have a superfluity 
 of names or synonyms for the same idea. Thus the 
 intension of a term is synonymous with its comprehen- 
 sion, or connotation, or depth ; while the extension is 
 synonymous with the denotation or breadth. This may 
 be most clearly stated in the form of a scheme : 
 
 The extension, extent, The intension, intent, 
 
 breadth, denotation, do- depth, connotation, or im- 
 
 main, sphere or application plication of & name con- 
 
 of a name consists of the sists of the qualities the 
 
 individual things to which possession of which by those 
 
 the name applies. things is implied. 
 
 Of these words, denotation and connotation are employed 
 chiefly by Mr. J. S. Mill among modern logical writers, and are 
 very apt for the purpose. To denote is to luark down, and tlie 
 name marks the things to which it may be applied or affixed; 
 thus metal denotes gold, silver, copper, etc. To connote is to 
 mark nlovg with (Latin con, together; notnre, to mark), and the 
 connotation accordingly consists of the qualities before described, 
 the possession of which is implied by the use of the name metal
 
 iS TEBM6. 
 
 4. The Variation of Extension and Intension. 
 
 When we compare different but related terms we maj 
 observe that they differ in the quantity of their exten- 
 sion and intension. Thus the term element has a 
 greater extension of meaning than metal, because it 
 includes in its meaning all metals and other substances 
 as well. But it has at the same time less intension of 
 meaning ; for among the qualities of a metallic substance 
 must be found the qualities of an element, besides the 
 other qualities peculiar to a metal. If again we com- 
 pare the terms metal and malleable ?netal, it is apparen: 
 that the latter term does not include the metals anti- 
 mony, arsenic, and bismuth, which are brittle sub- 
 stances. Hence malleable Tnetal is a term of narrower 
 meaning in extension than metal ; but it has also 
 deeper meaning in intension, because it connotes or 
 implies the quality of malleability in addition to the 
 general (qualities of a metal. White malleable metal is 
 again a narrower term in extension because it does not 
 include gold and copper; and I can go on narrowing 
 the meaning by the use of qualifying adjectives until 
 only a single metal should be denoted by the term. 
 
 6. Tlie Law of Variation. 
 
 The learner will now see clearly that a general law of 
 great importance connects the quantity of extension 
 and the quantity of intension, viz. As the intension of 
 a term is increased the extension is decreased. It 
 must not be supposed, indeed, that there is any exact 
 proportion Ixjtween the degree in which one meaning
 
 EXTENSION AND INTENSION. iS 
 
 IS increased and the other decreased. Thus if we join 
 the adjective red to metal we narrow the meaning much 
 more than if we join the adjective ivhile, for there are 
 at least twelve times as many white metals as red. 
 Again, the term white man includes a considerable 
 fraction of the meaning of the term man as regards 
 extension, but the term blind man only a small frac- 
 tion of the meaning. Thus it is obvious that in 
 increasing the intension of a term we may decrease the 
 extension in any degree. 
 
 In understanding this law we must carefully discriminate the 
 cases where there is only an apparent increase of the intension 
 of a term, from those where the increase is real. If I add the 
 term elementary to metal, I shall not really alter the extension 
 of meaning, for all the metals are elements ; and the elementary 
 metals are neither more nor less numerous than the metals. But 
 then the intension of the term is really unaltered at the same 
 lime ; for the quality of an element is really found among the 
 qualities of metal, and it is superfluous to specify it over again. 
 A quality which belongs invariably to the whole of a class of 
 things is commonly called a property of the class, and we cannot 
 qualify or restrict a term by its own property. 
 
 6. Connotative and Nou-connotative Terms. 
 
 This is a convenient place to notice a distinction 
 between terms into those which are connotative and 
 those which are non-connotative, the latter consisting 
 of the terms which simply denote things without imply- 
 ing any knowledge of their qualities. 
 
 As Mr. Mill considers this distinction to be one of great 
 importame, it will be well to quote his own words : 
 
 " A non- connotative term is one which signifies a subject only, 
 or an attribute only. A connotative term is one which denotes a
 
 14 TBRMS. 
 
 subject, and implies an attribute. Bj a subject is here meuit 
 anything wliicli possesses attributes. Tlius John, or London, or 
 England, are names wliich signify a subjict only. Whiteness, 
 lengtli, virtue, signify an attribute only. None of these names, 
 tiierefore, are connotative. But white, long, virtuous, are conno- 
 tative. Tiie word white denotes all white tilings, as snow, paper, 
 the foam of the sen, etc., and implies, or, as it was termed by the 
 schoolmen, amnotes the attribute whiteness. The word white is 
 not predicated of the attribute, but of the subjects, snow, etc. ; 
 but when we predicate it of tliem, we imply, or connote, that thi 
 attribute wliiteness i)elong8 to them 
 
 "All concrete general names are connotative. The word 
 man, for exami)le, denotes Peter, James, John, and an indefinite 
 number of other individuals, of whom, taken as a class, it is 
 the name. But it is applied to tliem, because they possess, and 
 
 to signify that they possess, certain attributes What we call 
 
 men, are tlie subjects, the individual Styles and Nokes ; not the 
 qualities by which their lunnanity is constituted. The name, 
 therefore, is said to signify the sulyects directly, the attributes 
 indirectly ; it denotes the subjects, and implies, or involves, or 
 indicates, or, as wo shall say iienceforth, connotes, the attri- 
 bu*es. It is a connotative name 
 
 'Proper names are not connotative: they denote the indl 
 viduals who arc called by them ; but they do not indicate or im- 
 ply any attributes as belonging to those individuals. When we 
 name a child by the name Paul, or a dog by the name Csesar, 
 these nan^s are simply marks us<'d to enable those individuals 
 to be made subjects of discourse. It may be said, indeed, that 
 we must have had some reason for giving them those names 
 rather than any others ; and this is true ; but the name, once 
 given, is independent of the reason. A man may have been 
 named John, because that was the name of his father; a town 
 may have been named Dartmouth, because it is situated at the 
 month of tlie Dart. But it is no part of the signification of th 
 word John, that the father of the person so called bore the samo 
 name ; nor even of the word Dartmouth, to be situated at tlie 
 mouth of the Dart. If sand should choke up the mouth of the 
 river, or an earthquake cliange its course, or remove it to a dis-
 
 EXTENSION AND INTENSION. 46 
 
 tance from the town, the name of the town would not nece88arU;f 
 be changed. " * 
 
 I quote this in Mr. Mill's own words, because though it ex- 
 presses most clearly the view accepted by Mr. Mill aud manj 
 others, it is nevertheless probabty erroneous. The counotation 
 of[a name is conlused with the etymological meauiug, or the cir 
 cumstances which caused it to be affixed to a thing. Surely no 
 one who uses the name England, and knows what it denotes, can 
 be ignorant of the peculiar qualities and circumstances of the 
 country, and these form the connotation of the term. To any 
 one who knows the town Dartmouth the name must imply the 
 possession of the circumstances by which that town is character- 
 ized at the present time. If the river Dart should be destroyed 
 or removed, the town would so far be altered, aud the siguitica 
 tion of the name changed. The name would no longer denote a 
 town situated on the Dart, but one which was foi^merly situated 
 on the Dart, and it would be by a mere historical accident that the 
 form of the name did not appear suitable to the town. So again 
 any proper name, such as John Smith, is almost without uuaniug 
 until we know the John Smith in question. It is true that the 
 name alone connotes the fact that he is a Teuton, and is a male; 
 but, so soon as we know the exact individual it denotes, the 
 name surely implies, also, the peculiar features, form, and charac- 
 ter, of that individual. In fact, as it is only by the peculiar 
 qualities, features, or circumstances of a tiling, that we can 
 ever recognize it, no name could have any fixed meaning unless 
 we attached to it, mentally at least, such a definition of the kind 
 of thing denoted by it, that we should know whether any given 
 thing was denoted by it or not. If the name of John Smith does 
 not suggest to my mind the qualities of John Smith, how shall I 
 know him when I meet him ? for he certainly does not bear lu8 
 name written upon his brow. 
 
 Abstract names, on the other hand, can hardly possess conno- 
 tation at all, for as they already denote the attributes or qualities 
 of something, there is nothing left which can form the connota- 
 tion of the name. Mr. Mill, indeed, thinks that abstract names 
 
 * System of Logic, Vol. I, p. 31, sixth editisn. Book I, Chp. H
 
 46 TEBMS. 
 
 may often be conaidered connotative, as when the name /auA 
 connotes the attribute of hurtfulness as belonging to fault. But 
 if fault is a true abstract word at all 1 should regard hurtfulnesa 
 as a part of its denotation ; I am inclined to think that faultineu 
 is the abstract name, and that fault is generally used concretely 
 as the name of a particular action or thing that is faulty, or \k>& 
 Besses faultiness. But the subject cannot be prop>erly discussed 
 here, and the reader should note Mr. Mill's opinion that abstract 
 names are usually non-conuotative, but may be connotative in 
 some cases. 
 The subject of Extension and Intension may be pursued in 
 
 Hamilton's Lectures on Logic, Lect. Vlll. ; or in Thom 
 
 son's Laws of Thought, Sections 48 to 52. 
 
 In this section, ou xtensiou and Intension, we 
 have considered : 
 
 1. Tlie Importance of Understanding this Double 
 
 Meaning. 
 
 2. The Meaning of Extension and Intension. 
 
 3. Ttie Forms of Ejcjrressing Extension and In- 
 
 tension. 
 
 4. Ttie Variation of Extension and Intension, 
 6. The Lmv of Variation. 
 
 6. Connotative and Non-connotative Terms, 
 
 SECTION lY. 
 
 THE GROWTH OF LANGUAGE. 
 
 1. The Two Principal Processes of Growth. 
 
 Words, we have seen, become equivocal in at least 
 throe different ways by the accidental confusion of 
 different words, by the change of meaning of a word 
 by its habitual association with other things than its 
 original meaning, and by analogical transfer to objects 
 of % similar nature. We must, however, consider some*
 
 THE GROWTH OF LANGUAGE. 47 
 
 what more closely certain changes in language wliich 
 arise out of the last cause, and which are in constant 
 progress. We can almost trace, in fact, the way in 
 which language is created and extended, and the sub- 
 ject is to the logician one of a higlily instructive and 
 important character. There are two great and con- 
 trary processes which modify language, as follows : 
 
 (1) Generalization, by which a name comes to be 
 applied to a wider class of objects than before, so that 
 the extension of its meaning is increased, and the in- 
 tension diminished. 
 
 (2) Specialization, by which a name comes to be 
 restricted to a narrower class, the extension being de- 
 creased and the intension increased. 
 
 2. Generalization. 
 
 The first change arises in the most obvious manner, 
 from our detecting a resemblance between a new object, 
 which is without a name, and some well-known object. 
 To express the resemblance we are instinctively led to 
 apply the old name to the new object. Thus we are 
 well acquainted with glass, and, if we meet any sub- 
 stance having the same glassy nature and appearance, 
 we shall be apt at once to call it a kind of glass ; should 
 we often meet with this new kind of glass it would 
 probably come to share the name equally with the old 
 and original kind of glass. The word coal has under- 
 gone a change of this kind ; originally it was the name 
 of charked or charred wood, which was the principal 
 kind of fuel used five hundred years ago. As mineral 
 coal came into use it took the name from the former 
 fuel, which it resembled more nearly than anything 
 else, but was at first distinguished as sea-coal or pit-
 
 48 TEBMS. 
 
 coal. Being now far the more common of the two, it 
 
 has taken the simple name, and we distinguish charred 
 wood as charcoal. Paper has undergone a like change ; 
 originally denoting the papyrus used in the Roman 
 empire, it was translerred to the new writing material 
 made of cotton or linen rags, which was introduced at 
 a qnite uncertain period. The word character is inter- 
 esting on account of its logical employment ; the Greek 
 XapaKTfip denoted strictly a tool for engraving, but it 
 became transferred by association to the marks or letters 
 engraved with it, and this meaning is still retained by 
 the word when we speak of Greek characters, Arabic 
 characters, i. e., figures or letters. But inasmuch as 
 objects often have natural marks, signs, or tokens, 
 which may indicate them as well as artificial characters, 
 the name was generalized, and now means any peculiar 
 or distinctive mark or quality by which an object is 
 easily recognized. 
 
 Changes of this kind are usually effected bj no particular per- 
 son and witli no distinct purpose, but by a sort of unconsciout 
 instinct in a number of pcPHons using the name. In the language 
 of science, liowever, changes are often made purposely, and 
 wiih a clear ai)prelien8ion of the generalization implied. Thus 
 $oap in ordinary life is ap[)lied only to a comi)Ound of soda or 
 pota.sh with fat ; but chemists have i)ur|K>sely extended the name 
 so as to include any cf)inpound of a metallic salt with a fatty sub- 
 stance. Accordingly there are such things as lime soap and lead- 
 noap, which latt(;r is employed in making common diichyloo 
 ])laster. Alcuhol at fir.st denoted tlie product of ordinary fermen- 
 tation commonly called sjnrits of wine, but chemists having dis 
 covered that many f)ther substances had a theoretical composition 
 closely resembling 8|)irit8 of wine, the name was adopted for the 
 whole cla.ss, and a long enumeration of different kinds of alco- 
 hols will Ik; found in Dr. llo3co(!'s lessons on chemistry. Thtr
 
 IHB CmOWTH OF LANGUAGE. 49 
 
 Dumber of known alcohols is likewise subject to indefinite increase 
 by tlie progress of discovery. Every one of the chemical terms 
 acid, alkali, metal, alloy, earth, ether, oil, gas, salt, may be 
 ihown to have undergoue great generalizations. In othet 
 Bcieuces there is hardly a less supply of instances. A lena 
 originally meant a lenticular shaped or double convex piece of 
 glass, that being the kind of glass most frequently used by 
 opticians. But as glasses of other shapes came to be used along 
 with lenses, the name was extended to concave or even to per- 
 fectly flat piec.!S of glass. The words lever, plane, cone, cylinder, 
 arc, conic section, curve, prism, magnet, pendulum, ray, light, and 
 many others, have been similarly generalized. 
 
 In common language we may observe that even proper or 
 singular names are often generalized, as when in the time of 
 Cicero a good actor was called a Roscius after an actor of pre. 
 eminent talent. The name Caesar was adoi)tcd by the successor 
 of Julius Caesar as an official name of the emperor, with which it 
 gradually became synonymous, so that in the present day the 
 Kaisers of Austria and the Czars oi Russia both take their title 
 from Caesar. Even the abstract name Caesarism has been formed 
 to express a kind of imperial system as established by Caesar 
 The celebrated tower built by a king of Egypt on the island a 
 Pharos, at the entrance of the harbor of Alexandria, has caused 
 lighthouses to be called phares in French, and pharos in obsolete 
 English. From the celebrated Roman General Quintus Fabius 
 Maximus any one who avoids bringing a contest to a crisis is said 
 to pursue a Fabian policy. 
 
 In science also singular names are often extended, as when 
 the fixed stars are called distant suns, or the compan''^ns of 
 Jupiter are called his moons. ]t is indeed one theory, and a 
 probable one, that all general names were created by the process 
 nf generalization going on in the early ages of human progress. 
 As the comprehension of general notions requires higher intellect 
 than the apprehension of singular and concrete things, it seems 
 natural that names should at first denote individual objects, and 
 should afterwards be extended to classes. We have a glimpse 
 of this process in the case of the Australian natives who had 
 been accustomed to call a large dog Cadli, but when horses wer^
 
 50 TERMS. 
 
 first introdaced into the country they adopted this name as th 
 neatest description of u horse. A very similar incident is re- 
 lated by Captain Cook of the natives of Otaheite. It may be ob 
 jected, however, that a certain process of judgment must have 
 been exerted before the suitability of a name to a particular 
 thing could have been i)erceived, and it may be c<^nsidered 
 probable that specialization as well as generalization must have 
 acted in the earliest origin of language much as it does at 
 present. 
 
 3. Specialization. 
 
 Si>ecializatiou is an exactly opposite process to gener- 
 alization and is almost equally important. It consists 
 in narrowing the extension of meaning of a general 
 name, so that it comes to be the name only of an 
 individual or a minor part of the original class. It is 
 thus we are furnished with the requisite names for a 
 multitude of new implements, occupations and ideas 
 with which we deal in advancing civilization. The 
 name physician is derived from the Greek (pvatKoc, 
 natural, and (pvaiq, nature, so that it properly means 
 one who has studied nature, especially the nature of 
 the human body. It has become restricted, however, 
 to those who use this knowledge for medical })urposes, 
 and tlie investigators of natural science have been 
 obliged to adopt the new name physicist. The name 
 naturalist has been similarly restricted to those who 
 study animated nature. The name surgeon originally 
 lueant handicraftsman, beingacorru])tion o^chirurgeon, 
 lerived from the Greek ;^poi;pyof, hand- worker. It 
 nas long been 8|)ecialized, however, to those who per- 
 form the mechanical parts of the sanatory art. 
 
 Tiantruage abounds with other examples. Minister originally 
 meant a servant, or one who acted as a minor of another. Not*
 
 THB aROWTH OF LANQUAQB. 51 
 
 it often means specially the most important man in the kingdom 
 A chancellor was a clerk or even a door-keeper who sat in a placa 
 separated by bars or canceUi in the offices of tiie Roman em- 
 peror's palace ; now it is always the name of a high or even the 
 highest dignitary. Peer was an equal (Latin, Par), and we still 
 sjMjak of being tried by our peers ; but now, by the strange acci- 
 dents of language, it means the few who are superior to the rest 
 of the Queen's subjects in rank. Deacon, Bishop, Clerk, Queen, 
 Captain, General, are all words which have undergone a like 
 process of specialization. In such words as telegraph, rail, 
 signal, station, and many words relating to new inventions, we 
 may trace the progress of change in a lifetime. 
 
 4. Desynonyniization, 
 
 One effect of the process of specialization is very soon 
 to create a difference between any two words which 
 happen from some reason to be synonymous. Two or 
 more words are said to be synonymous (from the Greek 
 avv, with, and ovofia, name) when they have the same 
 meaning, as in the case, perhaps, of teaclier and in- 
 structor, similarity and resemblance, beginning and 
 commencement, sameness and identity, hypothesis and 
 supposition, intension and comprehension. But the 
 fact is that words commonly called synonymous are 
 seldom perfectly so, and there are almost always 
 shades of difference in meaning or use, which are ex- 
 plained in such works as Crabb's Englixh S>/no?ii/ms. 
 A process called by Coleridge desynonymization, and by 
 Herbert Spencer differentiation, is always going on, 
 which tends to specialize one of a pair of synonymous 
 words to one meaning and the other to another. Thus 
 wave and billow originally meant exactly the same 
 physical effect, but poets have now appropriated the 
 word " billow," whereas wave is used chiefly m practicu
 
 52 TERMS. 
 
 and scientific matters. Undulation is a third synonym, 
 which will probably become the sole scientific term for 
 a wave in course of time. Cab was originally a mere 
 abbreviation of cabriolet, and therefore of similar mean- 
 ing, but it is now specialized to mean almost exclusively 
 a hackney cab. In America car is becoming restricted 
 to the meaning of a railway car. 
 
 It may be remarked that to possess a great number of syn- 
 onymous terms is a logical defect in a language, since we 
 acquire the habit of using them indifferently without being sure 
 that they are not subject to ambiguities and obscure differences 
 of meaning. The English language is especially subject to the 
 inconvenience of having a complete series of words derived from 
 Greek or Latin roots nearly synonymous with other words of 
 Baion or French origin. The same statement may, in fact, be 
 put into Saxon or classical English ; and we often, as Whately 
 has well remarked, seem to prove a statement by merely repro- 
 ducing it in altered language. The rlietorical power of the 
 language may be increased by the copiousness and variety of 
 diction, but pitfalls are thus prepared for all kinds of fallacies. 
 
 5. Metaphorical Kxtension of Meaning'. 
 
 In addition to the effects of generalization and speci- 
 alization, vast additions and changes are made in lan- 
 guage by the process of 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 resemblance is often one of a moat 
 distant and obscure kind, such as we should call analogy 
 rather than identity. All words used metaphorically, 
 or as similitudes, are cases of this process of extension. 
 The name metaphor is derived from the Greek wordi
 
 IKE QEOWTH OF LANGUAGE. 51 
 
 fterdy over, and (pepeiv, to carry ; and expresses appar- 
 ently the transference of a word from its ordinary to a 
 peculiar purpose. Thus the old simiUtude of a ruler to 
 the pilot of a vessel gives rise to many metaphors, as in 
 speaking of the prime minister being at the helm of 
 the state. The word governor, and all its derivatives, 
 is, in fact, one result of this metaphor, being merely a 
 corrupt form of gubernator, steersman. 
 
 The words compass, polestar, ensign, anchor, and many others 
 connected with navigation, are constantly used in a metapliorical 
 manner. From tlie use of horses and Imnting we derive another 
 sei of metaphors ; as, in talking the reins of government, over- 
 turning the government, taking the bit between the teeth, the 
 government whip, being heavily weighted, etc. No doubt it 
 might be shown that every other important occupation of life has 
 furnished its corresponding stock of metaphors. 
 
 6. Origin of the Mental Vocabulary. 
 
 This process, besides going on consciously at the 
 present day, must have acted throughout tiie history of 
 language, and we owe to it almost all, or probably all, 
 the words expressive of refined mental or spiritual ideas. 
 The very word spirif, now the most refined and imma- 
 terial of ideas, is but the Latin spirifus, a gentle breeze 
 or breathing ; and inspiration, esprit, or "wdt, and many 
 other words, are due to this metaphor. It is truly 
 curious, however, that almost all the words in different 
 languages denoting mind or soul imply the same 
 analogy to breath. Thus, soul is from the Gothic root 
 denoting a strong wind or storm ; the Latin words 
 animus and ani7na are supposed to be connected with 
 the Greek avmoq, wind ; V'^%'7 is certainly derived froa;
 
 64 TEBMS. 
 
 xbvxt^, to blow ; irvevfia, air or breath, is used in the 
 New Testament for Spiritual Being; and our word 
 ghost has a similar origin. 
 
 Almost all the terms employed in mental philosophy or 
 metaphysics, to denote actions or phenomena of mind, are ulti- 
 mat 'ly derived from metaphors. Apprehension is the putting 
 forward of the hand to take anything ; compreliension is the 
 taking of things together in a handful ; extension is the spread- 
 ing out; intention, the bending to; explication, the unfolding; 
 application, the folding to; conception, the taking up together; 
 relation, the carrying back ; experience is the thoroughly going 
 through a thing ; difference is the carrying apart ; deliberatioa 
 the weighing out ; interruption, the breaking between ; proposi- 
 tioa the placing before ; intuition, the seeing into ; and the list 
 might be almost indefinitely extended. Our English name for 
 reason, the understanding, obviously contains some physica* 
 metaphor which has n<jt been fully explained ; with the Latia 
 intellect there is also a metaphor; 
 
 Every sense gives rise to words of refined meaning ; sapience^ 
 taste, insipidity, gout, are derived from the sense of taste ; saga, 
 city, from the dog's extraordinary ix)wer of smell ; but as the 
 sense of sight is by far the most acute and intellectual, it gives 
 rise to the larger part of language ; clearness, lucidity, obscurity, 
 haziness, perspicuity, and inuumerable other expressions, ar* 
 derived from this sense, 
 
 7. The Fertility of Root-words. 
 
 It is truly astonishing to notice the power which 
 language possesses by the processes of generalization, 
 3{)ecialization, and metaphor, to create many words 
 from one single root. Prof. Max Miiller has given h 
 remarkable instance of this in the case of the root 
 spec, which means sir//if, and appears in the Aryan lan- 
 guages, as in the Sanscrit spas, the Qreek oKenTOfuUf
 
 THE GROWTH OF LANOUAOE. H 
 
 with transposition of consonants, in the Latin specio, 
 and even in the English spy. 
 
 The following is an incomplete list of the words developed 
 from this one root ; species, special, especial, specimen, spice, 
 spicy, specious, speciality, sijecific, specialization, specie (gold, or 
 silver), spectre, specification, spectacle, spectator, spectral, spec- 
 trum, speculum, specular, speculation. The same root also enters 
 into composition with various prefixes ; and we thus obtain a 
 series of words, suspect, aspect, circums[x?ct, expect, inspect, 
 prospect, respect, retrospect, introspection, conspicuous, perspi- 
 cuity, perspective ; with each of which, again, a number of de- 
 rivatives is connected. Thus, from suspect, we derive suspicioa 
 Buspicable, suspicions, suspiciously, suspiciousness. I have esti- 
 mated that there are in all at least 246 words, employed at some 
 period or other in the English language, which undoubt(?dly 
 oome from the one root spec 
 
 J. S. Mill's Logic, Book IV, Chap. V, " On the Natural History 
 
 of the Variations in the Meanings of Terms." 
 Archbishop Trench, On the Study of Words. 
 Max Mliller, Lectures on the Science of Language. 
 Whitney's Life and Growth of Language. 
 
 In this section, on "The Growth of Lan 
 guage,'* we have considered : 
 
 1. The Two Principal Processes of Growtli. 
 
 2. Generalization. 
 
 3. Specialization. 
 
 4. Desynonytnization. 
 
 6. Metaphorical Extension of Meaninp* 
 
 6. Orif/in of the Mental Vocabulary. 
 
 7. The Fertility of Root-words,
 
 S rEBMS. 
 
 SECTION Y. 
 
 THE PERFECT AND THE IMPERFECT 
 KNOWLEDGE OF TERMS. 
 
 1. Statement of the Question. 
 
 In treating of Terms it is necessary that we should 
 clearly understand what a perfect notion of the mean- 
 ing of a term requires. When a name such as monarch, 
 or civilization, or autonomy is used, it refers the mind 
 to some thing or some idea, and we ought, if possible, 
 to obtain a perfect knowledge of the thing or idea be- 
 fore we use the word. In what does this perfect knowl- 
 edge consist ? What are its necessary characters ? 
 
 This is a question which the celebrated mathematician and 
 philosojiher Leibnitz attempted to answer in a small treatise or 
 tract first published in the year 1684. This tract has been the 
 basis of what is given on the subject in several recent works 
 on Logic, and a complete translation of the tract has been 
 appended by Mr. Baynes to his translation of the Port Royal 
 Logic. As the remarks of Leibnitz himself are not always easy 
 to understand, I will not confine myself to his exact words, but 
 will endeavor to give the simplest possibln statement of his views, 
 according as they have been interpreted by Dr. Thomson or Sir 
 W. Hamilton. 
 
 2. Scheme of DiHtlnctlone. 
 
 Knowledge is either obscure or clear; either oori' 
 ftjsed or distinct ; eitlier adequate or inadequate ; and 
 lastly, either symbolical or intuitive. Perfect knowledge 
 must be clear, distinct, adequate and intuitive ; if it
 
 KNOWLBDGE OF TEBM8. 67 
 
 fails in any of these respects it is more or less fmper 
 feet. We may, therefore, classify knowledge as in the 
 roUowmg scheme : 
 
 Knowledge 
 
 Clear Obscure 
 
 Distinct Confused 
 
 - ' 
 
 Adequate Inadequate 
 
 Intuitive Symbolical 
 
 Perfect. Imperfect. 
 
 (1) Clear and Obscure Knowledge Distinguished. 
 
 A notion, that is to say our knowledge of a thing, 
 is obscure when it does not enable us to recognize 
 the thing again and discriminate it from all other 
 things. We have a clear notion of a rose and of most 
 common flowers because we can recognize them with 
 certainty, and do not confuse them with each other. 
 Also we have a clear notion of any of our intimate 
 friends or persons whom we habitually meet, because 
 we recognize them whenever we see them with the 
 utmost certainty and without hesitation. 
 
 It is said that a shepherd acquires by practice a clear notion of 
 each sheep of his flock, so as to enable him to single out any one 
 separately, and a keeper of hounds learns the name and character 
 of each hound, while other persons have only an obscure idea of 
 the hounds generally, and could not discriminate one from the 
 other. But the geologist cannot give a clear idea of what sand- 
 stone, conglomerate, or schist, or slate, or traj) rock consists, be- 
 cause diflferent rocks vary infinitely in degree and character, and 
 it is often barely possible to say whether a rock is sandstone ol
 
 58 TERMS. 
 
 conglomerate, schist or slate, and so on. In the lower forms ol 
 life the naturalist hardly has a clear notion of animal life, as diS' 
 tlnguished from vegetable life ; it is often diflBciilt to decidfl 
 whether a protophyte should be claesed with animals or plants. 
 
 (2) Distinct and Confused Knowledge Distinguished. 
 
 Clear knowledge, again, is confused, when we cannot 
 distinguish the parts and qualities of the thing known, 
 and can only recognize it as a whole. Though any one 
 instantly knows a friend, and could discriminate him 
 trom all other persons, yet he would generally find it 
 impossible to say how he knows him, or by what 
 marks. He could not describe his figure or features, 
 but in the very roughest manner. A person unpractised 
 in drawing, who attempts to delineate even such a 
 familiar object as a horse or cow, soon finds that he has 
 but a confused notion of its form, while an artist has a 
 distinct idea of the form of every limb. The chemist 
 lias a distinct as well as a clear notion of gold and silver, 
 for he can not only tell Avith certainty whether any 
 metal is really gold or silver, but he can specify and 
 describe exactly the qualities by which he knows it; 
 and could, if necessary, mention a great many other 
 qualities as well. 
 
 We have a very distinct notion of a chess-board, because 
 we know it consists of 64 square spaces; and all our ideas oi 
 geometrical figures, such as triangles, circles, parallelograms, 
 squares, pentagons, hexagons, etc., are or ought to b perfectly 
 -listinct. But when we talk of a conntitvtwnal (jorernment, or a 
 tivUized nation, we have only the vagufst idea of what we mean. 
 We cannot say exactly what is requisite to make a government 
 constitutional, without including also governments which we do 
 not Intend tf> include; and so of civiliztnl nations; these tern?s 
 have neither distinct nor clear meanings.
 
 KNOWLEDGE OF TEBM8. 69 
 
 (t is to be remarked that no simple idea, such as that uf red 
 u.ior, can be distinct in the meaning here intended, l)ecau8e no- 
 bod/ can analyze red color, or describe to another person wliat 
 It is. A person who has been blind from birth cannot be made 
 to conceive it ; and it is only by bringing an actual red object 
 before the eye that we can define its character. The same is 
 generally true of all simple sensations, whether tastes, smells, 
 colors, or sounds; these, then, may be clearly known, but not 
 distinctly, in the meaning which Leibnitz gives to this word. 
 
 (3) Adequate and Inadequate Knowledge Distin- 
 guished. To explain the ditferencc wliieh Leibnitz 
 intended to denote by the names adequate aud inade- 
 quate, is not easy. He says, " When everything which 
 enters into a distinct notion is distinctly known, or 
 when the last analysis is reached, the knowledge is 
 adequate, of which I scarcely know whether a perfect 
 example can be offered the knowledge of numbers, 
 however, approaches near to it." 
 
 To have adequate knowledge of things, then, we 
 must not only distinguish the parts which make up 
 our notion of a thing, but the parts which make up 
 those parts. For instance, we might be said to have 
 an adequate notion of a chess-board, because we know 
 it to be made up of 64 squares, and we know each 
 of those squares distinctly, because each is made 
 up of 4 equal right lines, joined at right angles. 
 Nevertheless, we cannot be said to have a distinct 
 notion of a straight line, because we cannot well 
 define it, or resolve it into anything simpler. To 
 be completely adequate, our knowledge ought to ad- 
 mit of analysis after analysis ad ttiflnitum, so that 
 adequate knowledge would be impossible. But, as Dr
 
 60 TERMS. 
 
 Thomson remarks, we may consider any knowledge 
 adequate which carries the analysis sufficiently far for 
 the purpose in view. 
 
 A nieclianist, for instance, has adequate knowled^ of a 
 .nachine, if he not only knows its several wheels and parts, but 
 the purposes, materials, forms, and actions of those parts ; pro- 
 vided, again, that he knows all the mechanical properties of 
 the materials, and the geometrical properties of the forms which 
 may influence the working of the machine. But he is not ex. 
 pected to go on still further and explain why iron or wood of a 
 particular quality is strong or brittle, why oil acts as a lubricator, 
 or on what axioms the principles of mechanical forces are 
 founded. 
 
 (4) Intuitive and Symbolical Knowledge Distin* 
 guished. Lastly, we must notice the very important 
 distinction of symbolical and intuitive knowledge. 
 From the original meaning of the word, intuitive 
 would denote that which we gain by seeing (Latin, 
 intuenr, to look at), and any knowledge which we have 
 directly through ihe senses, or by immediate communi- 
 cation to the mind, is called intuitive. Thus we may 
 learn intuitively what a square or a hexagon is, but 
 hardly what a chiliagon or figure of 1000 sides is. 
 
 We could not tell the difference by sight of a figure 
 of 1000 sides and a figure of 1001 sides. Nor can we 
 imagine any such figure completely before the mind. 
 It is known to us only by name or symbolically. 
 A.11 large numbers, such as those which state the 
 velocity of light (180,000 miles per second), the dis- 
 tance of the sun (91,000.000 miles), and the like, are 
 known to us only by symbols, and they are beyond oui 
 powers of imagination-
 
 KNOWLEDGE OF TERMS. 61 
 
 In arithmetic and algebra we are chiefly occupied 
 urith symbolical knowledge only, since it is not neces- 
 sary in working a long arithmetical question or an alge- 
 braical problem that we should realize to ourselves at 
 each step the meaning of the numbers and symbols. 
 We learn from algebra that if we multiply together the 
 gum and difference of two quantities we get the differ- 
 ence of the squares ; as in symbols 
 
 {a + b) {a-b) = a^ I^: 
 
 which is readily seen to be true, as follows 
 
 a -h ft 
 
 a^ -\- ab 
 
 o2 + 52. 
 
 In the above we act darkly or symbolically, using the 
 letters a and b according to certain fixed rules, withoui 
 knowing or caring what they mean ; and whatever 
 meaning we afterwards give to a and b we may be sure 
 the process holds good, and that the conclusion is true 
 without going over the steps again. 
 
 But in geometry, we argue by intuitive perception of 
 the truth of each step, because we actually employ a 
 representation in the mind of the figures in question, 
 and satisfy ourselves that the requisite properties are 
 really possessed by the figures. Thus the algebraical 
 truth shown above in symbols may be easily jiroved to 
 hold true of lines and rectangles contained under those 
 lines, as a corollary of the 5th Prop, of Euclid's Second 
 Book.
 
 ftB TEBXBi. 
 
 3, The Intuitive and Symbolic Methods Com- 
 pared. 
 
 Much might be said concerning the comparative ad- 
 vantages of the intuitive and symbolical methods. The 
 latter is usually much the less laborious, and gives the 
 most widely applicable answers; but the symbolical 
 seldom or never gives the same command and compre- 
 hension of the subject as the intuitive method. Hence 
 the study of geometry is always indispensable in educa- 
 tion, although the same truths are often more readily 
 proved by algebra. It is the peculiar glory of Newton 
 that he was able to explain the motions of the heavenly 
 bodies by the geometric or intuitive method; whereas 
 the greatest of his successors, such as Lagrange or 
 Laplace, have treated these motions by the aid of 
 symbols. 
 
 What 18 true of matiiematical subjects may be an- 
 plied to all kinds of reasoning ; for words are symbols 
 as much as A, B, G, or ar, y, z, and it is possible to 
 argue with words without any consciousness of tneir 
 meaning. Thus if I say that "selenium is a dyad 
 element, and a dyad element is one capable of repkcing 
 two e({uivalents of hydrogen," no one ignorant of 
 chemistry will be able to attach any meaning to these 
 terms, and yet any one will be able to conclude that 
 "selenium is capable of replacing two equivalents of 
 hydrogen." Such a person argues in a purely symboli- 
 cal manner. Similarly, whenever in common life wo 
 use words, without having in mind at the moment the 
 full and precise meanmg of the words, we possess sym- 
 bolical knowledge only.
 
 KNO"VfLEDGB OF TERMS. 63 
 
 There is no worse habit for a student or reader to acquire 
 than that of accepting words Instead of a knowledge of things. 
 It is perhaps worse than useless to read a work on natural history 
 about Infusoria, Foraminifera, Rotifera and the like, if thise 
 names do not convey clear images to the mind. Nor can a 
 student who has not witnessed experiments, and examined the 
 substances with his own eyes, derive any considerable advantage 
 from works on chemistry and natural philosophy, where he will 
 meet with hundreds of new terms which would be to liim mere 
 empty and confusing signs. Un this account we should lose no 
 opportunity of acquainting ourselves, by means of our senses, 
 with the forms, proj)erties and changes of things, in order that 
 the language we employ may, as far as possible, be employed 
 intuitively, and we may be saved from the absurdities and falla- 
 cies into which we might otherwise fall. We should observe, in 
 short, the advice of Bacon Ipsis consueseere rebus to accustom 
 ourselves to things themselves. 
 
 Hamilton's Lectures on Logic, Lect. IX. 
 
 Baynes' Port Royal Logic. Part I, Chap. IX, and Appendix. 
 
 In this section, on "The Perfect and the Im- 
 perfect Knowledge of Terms," we have con- 
 sidered : 
 
 1. The Statement of the Question. 
 
 2. The Scheme of JJistinction.s. 
 
 3. The Intuitive and Symbolic Methods Com.* 
 
 pared.
 
 CHAPTEB Ih 
 PROPOSITIONS. 
 
 The treatment of Propositions will involve a con 
 sideration of the foUoYi^ing topics : (1) Tlie Kinds 
 of Propositions; (2) The Opposition of 
 Propositions; (3) Conversion and Imme- 
 diate Inference ; and (4) The Logical Anal- 
 ysis of Sentences* These topics will be treated in 
 separate sections. 
 
 8BCTI0IT ! 
 
 THE KINDS OF PROPOSITIONS. 
 
 1. Meauingr of " Proposition '* Explained. 
 
 A term standing alone is not capable of expressing 
 truth ; it merely refers the mind to some object or 
 class of objects, about which something may be affirmed 
 or denied, but about which the term itself does not 
 affirm or deny anything. "Sun," **air," ''table," 
 suggest to every mind objects of thought, but we can- 
 not say that ''sun is true," or "air is mistaken," or 
 "table is false." We must join words or terms into 
 sentences or propositions before they can express those 
 reasoning juitions of the mind to which truth or falsity 
 may be attributed. " The sun is bright," " the air is 
 fresh," " the table is unsteady," are statements which 
 may be true or may be false, but we can certainly 
 entertain tlic question of their truth in any circum- 
 Btances. Now aa the logical term was defined to be
 
 KINDS OF PEOP08ITION8. 66 
 
 any combination of words expressing an act of simple 
 apprehension, so a logical proposition is any combina- 
 tion of words expressing an a<;t of judgment. The 
 proposition is, in short, the result of an act of judg- 
 ment reduced to the form of language. 
 
 What tlie logician calls a proposition the grammarian calls a 
 sentence. But though every proposition is a sentence, it is not 
 to be supposed that every sentence is a proposition. Tliere are 
 in fact several liinds of sentences more or less distinct from a 
 proposition, such as a Sentence Interrogative or Question, a Sen- 
 tence Imperative or a Command, a Sentence Optative, which ex- 
 presses a wish, and an Exclamatory Sentence, which expresses 
 an emotion of wonder or surprise. These kinds of sentence 
 may possibly be reduced, by a more or less indirect mode of 
 expression, to the form of a Sentence Indicative, which is the 
 grammatical name for a proposition ; but until this be done they 
 have no proper place in Logic, or at least no place wliich logicians 
 have hitherto sufficiently explained. 
 
 2. Analysis of a Proposition. 
 
 The name proposition is derived from the Latin 
 words pro, before, and pono, I place, and means the 
 laying or placing before any person the result of an act 
 of judgment. Now every act of judgment or compari- 
 son must involve the two things brought into compari- 
 son, and every proposition will naturally consist of three 
 parts the two terms, or names, denoting the things 
 compared, and the copula, or verb, indicating the con- 
 nection between them, as it was ascertained in the act 
 of judgment. Thus the proposition, ' Gold is a yellow 
 substance," expresses an agreement between gold and 
 certain other substances previously called yellow in re- 
 gard to their color. Gold and yellow substance are 
 evidently the two terms, and is the copula.
 
 66 PROPOSITIONS. 
 
 It is always usual to call the first terra of a proposi- 
 tion the subject, since it denotes the underlying matter, 
 as it were (Latin, suh, under, and jadum, laid) about 
 which something is asserted. The second term is 
 called the predicate, which simply means that which is 
 affirmed or asserted. 
 
 This name is derived from the Latin proedXeare, to assert, 
 wlience comes the French name predkuteur, corrupted into our 
 preacher. This Latin verb is not to be confused with the some- 
 what similar one predlcere, which has the entirely different 
 meaning to predict or foretell. I much suspect that newspaper 
 writers and others, who pedantically use the verb " to predicate," 
 sometimes fall into this confusion, and really mean io predict, but 
 it is in any case desirable that a purely technical term like predi- 
 cate should not be needlessly introduced into common language, 
 when there are so many other good words which migiit be used. 
 This and all other technical scientific terms should be kept to 
 their proi)er scientific use, and the neglect of this rule injures at 
 once the lanf^uage of common life and the language of science. 
 
 3. Categorical and Conditional Propositions. 
 
 Propositions are distinguished into two kinds, accord- 
 ing as they make a statement conditionally or uncondi- 
 tionally. Thus the proposition, "If metals are heated 
 they are softened," is conditional, since it does not 
 make an assertion concerning metals generally, but 
 only in the circumstances when they become heated. 
 Any circumstance which must be granted or supposed 
 before the assertion becomes applicable is a condition. 
 Conditional propositions are of tvvo kinds, Hypothetical 
 and Disjunctive, but their consideration will be best 
 deferred to a subsequent chapter. Uncou'litional prop- 
 ositions are those with wLich we shall for some time
 
 KINDS OF PROPOSITIONS. 67 
 
 be solely concerned, and these are usually called Cate- 
 gorical propositions, from the Greek verb KarTjyopta 
 {kategoreo, to assert or affirm). 
 
 The following diagram will conveniently represent 
 the classification of sentences and propositions as far as 
 we have yet proceeded : 
 
 ' Indicative = Prop, -i p^H^^f^?^A J Hypothetical. 
 Interrogative < ^^^^^^^^^"^^{sjunctive. 
 
 Imperative 
 Optative 
 . Exclamatory 
 
 4. The Quality and Quantity of Propositions. 
 
 It is now necessary to consider carefully the several 
 kinds of categorical propositions. They are classified 
 according to quality and according to quantity. As 
 regards quality they are either affirmative or negative ; 
 as regards quantity they are either universal or par- 
 ticular. 
 
 An affirmative proposition is one which asserts a cer- 
 tain agreement between the subject and predicate, so 
 that the qualities or attributes of the predicate belong 
 to the subject. The proposition, ''gold is a yellow 
 substance," states such an agreement of gold with other 
 yellow substances, that we know it to have the color 
 yellow, as well as whatever qualities are implied in the 
 name substance. A negative proposition, on the other 
 hand, asserts a difference or discrepancy, so that some 
 at least of the qualities of the predicate do not belong 
 to the subject. "Gold is not easily fusible" denies that 
 the quality of being easily fused belongs to gold. 
 
 Propositions are again dividixl according to quantity
 
 68 PROPOSITIONS. 
 
 into universal and particular propositions. If the prop- 
 osition affirms the predicate to belong to the whole of 
 the subject, it is an universal proposition, as in the ex- 
 ample "all metals are elements," which affirms that 
 the quality of being undecomposable or of being simple 
 in nature is true of all metals. But if we say " some 
 metals are brittle," l,he quality of brittleness is affirmed 
 only of some indefinite portion of the metals, and there 
 is nothing in the proposition to make us sure that any 
 cjertain metal is brittle. This is a particular proposition. 
 
 The name particular being derived from the diminutive of the 
 Latin para would naturally signify a small part, but in logic it 
 must be carefully interpreted as signifying any part, from the 
 smallest fraction up to nearly the whole. Particular propositions 
 do not include cases where a predicate is affirmed of the whole or 
 of none of the subject, but they include any between these 
 limits. We may accordingly count among particular proposi- 
 tions all such as the following : 
 
 A very few metals are less dense than water. 
 
 Most elements are metals. 
 
 Many of the planets are comparatively small bodies. 
 
 Not a few distinguished men have had distinguished sons. 
 
 The reader must carefully notice the somewhat subtle point 
 explained further on, that the particular proposition though as- 
 serting the predicate only of a part of the subject, does not deny 
 it to be true of tlie whole. 
 
 5. Aristotle^s View of Quantity. 
 
 Aristotle considered that there were altogether four 
 kinds of proposition as regards quantity, namely 
 
 ( Universal. 
 _, Particular. 
 
 Proposition i j^j^g^iar. 
 
 Indefinite.
 
 KINDS OF PROPOSITIONS. 69 
 
 The singular proposition is one which has a singular 
 term for its subject, as in 
 
 Socrates was very wise. 
 London is a vast city. 
 
 But we may fairly consider that a singular proposi- 
 tion is an universal one; for it clearly refers to the 
 whole of the subject, which in this case is a single 
 individual thing. 
 
 Indefinite or indesignate propositions are those which 
 are devoid of any mark of quantity whatever, so that 
 the form of words gives us no mode of judging whether 
 the predicate is applicable to the whole or only part of 
 the subject. Metals are useful, Comets are subject to 
 the law of gravitation, are indefinite propositions. In 
 reality, however, such propositions have no distinct 
 place in logic at all, and the logician cannot properly 
 treat them until the true and precise meaning is made 
 apparent. 
 
 Tlie predicate must be true either of the whole or of part of 
 the subject, so that tlie propt)sition, as it stauds. is clearly incom 
 plete ; but if we attempt to remedy this and supply the marks of 
 quantity, we overstep the proper boundaries of logic and assume 
 ourselves to be acquainted with the sulyect matter or science of 
 which the proposition treats. We may safely take the preceding 
 examples to mean " some metals are useful " and " all comets are 
 subject to tlie law of gravitation," but not on logical grounds. 
 Hence we may strike out of logic altogether the class of indefinite 
 propositions, on the understandiu'a: tliat they must be rendered 
 definite before we treat them. In the following sections we shall 
 frequently use propositions in tlie indefinite form as examples, on 
 the understanding that where no sign of quantity ap[x'ars, the 
 universal quantity is to be assumed. It is probable that wherever 
 a terra is used alone, it ought to be interpreted as meaning the 
 whole of its class. But however this may be, we need not recogf
 
 W PROPOSITIONS. 
 
 nize the indefinite proposition as a distinct kind ; and singulai 
 propositions having been resolved into universals, there remain 
 only the two kinds, Universal and Particular. 
 
 6. Names of the Four Propositions. 
 
 Remembering now tnat there are two kinds of prop- 
 osition as regards quality, and two as regards quantity, 
 we shall be able to form altogether four varieties, 
 thus : 
 
 Proposition > 
 
 Universalj^^'T^^^ ? 
 
 ( Negative E 
 
 Particular i Affirmative I 
 
 i-articuiar < ^^ ^^^.^ q 
 
 The vowel letters placed at the rignc nand are sym- 
 bols or abbreviated names, which are always used to 
 denote the four kinds of proposition ; and there will be 
 no difficulty in remembering their meaning: if we ob- 
 serve A and I occur in the Latin verb affirmo, I affirm, 
 and E and in nego, I deny. 
 
 There will generally be no difficulty in referring to its proper 
 class any proposition that we meet with in writings. Tbe mark 
 of universality usually consists of some adjectix'e of quantity, 
 such as nil, every, each, any, the w?iole ; but whenever the predi- 
 cate Is clearly intended to apply to the whole of the subject we 
 may treat the proposition as universal. The signs of a particu- 
 lar proposition are the adjectives of quantity, some, certain; a few, 
 many, most, or such others as dearly indicate part at hast. 
 
 The neiHrative proposition is known by the adverbial particle 
 not being joined to tbo copula; but in the proposition E, that is 
 the universal nej?ative, we frequently use the particle no or none 
 prefixed to the subject. Tlius, " no metals are compound," "none 
 of tlic ancients were acquainted with the laws of motion," are 
 familiar forms of the universal negative.
 
 KIKDS OF PROPOSITIONS. 71 
 
 The student must always be prepared too to meet with mis- 
 leading or ambiguous forms of expression. Thus the proposition, 
 "all the metals are not denser than water," might be taken as E 
 or O, according as we interpret it to mean " no metals are denser 
 than water," or " not all the metals," etc., the last of course being 
 the true sense. The little arijective/ew is very subject to a subtle 
 ambiguity of this kind ; for if I say "few books are at once 
 learned and amusing." I may fairly be taken to assert that a few 
 'boohs certainly are so, but what I really mean to draw attention 
 to is my belief that " the greater number of books are not at once 
 learned and amusing." A proposition of this kind is generally 
 to be classed rather as O than I. The word some is subject to 
 an exactly similar ambiguity between some but not all, and some 
 at least, it may be all ; the latter appears to be the correct inter- 
 pretation, as shown in the following section (p. 77). 
 
 As propositions are met with in ordinary language they are 
 subject to various inversions and changes of the simple logical 
 form. 
 
 (1) It is not uncommon, especially in poetry, to find the predi- 
 cate placed first, for the sake of emphasis or variety ; as in 
 " Blessed are the merciful ; " " Comes something down with even- 
 tide :" " Great is Diana of the Ephesians." There is usually no 
 diflBculty in detecting such an inversion of tlie terms, and the 
 sentence must then be reduced to the regular order before being 
 treated in logic. 
 
 (2) The subject may sometimes be mistaken for the predicate 
 when it is described a relative clause, standing at the end of the 
 sentence, as in " no one is free who is enslaved by his appetites." 
 Here free is evidently the predicate, although it stands in the 
 middle of the sentence, and " one who is enslaved by his appe- 
 tites " is the real subject. This proposition is evidently of the 
 form E. 
 
 7. Variations from the Logical Form. 
 
 Propositions are also expressed in various modes 
 differing from the simple logical order, and some of the 
 different kinds which arise must be noticed.
 
 78 PROPOSITIONS. 
 
 (1) Exclusive propositions contain some words, snch 
 as only, alo7ie, none but, which limit the predicate to 
 the subject Thus, in "elements alone are metals," we 
 are informed that the predicate "metal" cannot be 
 applied to anything except "elements," but we are not 
 to understand that "all elements are metals." The 
 same meaning is expressed by " none but elements are 
 metals;" or, again, by "all that arc not elements are 
 not metals;" and this wc jhall sec in the next lesson is 
 really equivalent to "all metals are elements." Argu- 
 ments which appear fallacious at first sight will often 
 be found correct when they contain exclusive proposi- 
 tions and these are properly interpreted. 
 
 (2) Exceptive propositions affirm a predicate of all 
 the subject with the exception of certain defined cases, 
 to which, as is implied, the predicate does not belong. 
 Thus, " all the planets, except Venus and Mercury, are 
 beyond the earth's orbit," is a proposition evidently 
 equivalent to two, viz., that Venus and Mercury are 
 not beyond the earth's orbit, but that the rest are. If 
 the exceptions are not actually specified by name an 
 exceptive proposition must often be treated as a partic- 
 ular one. For if I say "all the planets in our system 
 except one agree with Bode's law," and do not give the 
 name of that one exception, the reader cannot, on the 
 ground of the proposition, assert of any planet positively 
 that it does agree with Bode's law. 
 
 (3) Explicative op essential propositions are so called 
 because they merely affirm of their subject a predicate 
 which is known to belong to it by all who can define 
 the subject. Such propositions merely unfold what is 
 already contained in the subject "A parallelogram
 
 KINDS OF PROPOSITIONS. 73 
 
 has four sides and four angles," is an explicative 
 or essential proposition. " London, which is the capi- 
 tal of England, is the largest city of Europe," contains 
 two propositions ; of which one merely directs our at- 
 tention to a fact which all may be supposed to knoW; 
 viz., that London is the capital of England. 
 
 (4) Ampliative propositions, ^n the other hand, join 
 a new predicate to the subject. Thus to those who do 
 not know the comparative sizes of cities in Europe, the 
 last example contains an ampliative proposition. The 
 gi'eater number of propositions are of this kind. 
 
 (5) Tautologous or Truistic propositions are those 
 which merely affirm the subject of itself, and give no 
 information whatever ; as in, "whatever is, is;" "what 
 I have written, I have written." 
 
 It is no part of formal Logic to teach us how to interpret the 
 meanings of sentences as we meet them in writings ; this is 
 rather the work of the grammarian and philologist. Logic treats 
 of the relations of the different propositions, and the inferences 
 which can be drawn from them ; but it is nevertheless desirable 
 that the reader should acquire some familiarity witli the real 
 logical meaning of conventional or peculiar forms of expression, 
 and a number of examples will be found at the end of the book, 
 ivhich the learner is requested to classify and treat as directed. 
 
 8. The Modality of Propositions. 
 
 In addition to the distinctions already noticed it has 
 long been usual to distinguish propositions as they are 
 pure or modal. The pure proposition simply asserts 
 that the predicate does or does not belong to the sub- 
 ject, while the modal proposition states this cum modo. 
 or with an intimation of the mode or manner in which 
 the predicate belongs to the subject. The presence of
 
 74 PROPOSITIONS. 
 
 any adverb of time, place, manner, degree, etc., or any 
 expression equivalent to an adverb, confers modality on 
 a proposition. " Error is always in haste ; " " justice is 
 ever equal; "a perfect man ought always to be con- 
 quering himself," are examples of modal propositions 
 in this acceptation of the name. 
 
 Other logicians, however, have adopted a different view, and 
 treat modality as consisting in the degree of certainty or pro- 
 bability with which a judgment is made and asserted. Thus, 
 we may say, " an equilateral triangle is necessarily equiangular ; " 
 " men are generally trustworthy; " "a falling barometer probably 
 indicates a coming storm ; " "Aristotle's lost treatises may possibly 
 be recovered ; " and all these assertions are made with a different 
 degree of certainty or modality. Dr. Thomson is no doubt right 
 in holding that the modality does not aff(>ct the copula of the 
 proposition, and the subject could only be properly treated in a 
 work on Probable Reasoning. 
 
 Many logicians have also divided propositions according as they 
 are true or false, and it might well seem to be a distinction of 
 importance. Nevertheless, it is wholly beyond the province of 
 the logician to consider whether a proposition is true or not 
 in itself; all that he has to determine is the comjjarative truth 
 of propositions that is, whether one proposition is true when 
 another is. Strictly speakinpr, logic has nothing to do with a 
 proposition by itself; it i.s only in converting or transmuting 
 certain propositions into certain others that the work of reason- 
 ing consists, and the truth of the concliisit)n is only so far in 
 question as it follows from the truMi of what we shall call the 
 premises. It is the duty of the special sciences each in its own 
 sphere to det<;rmino what arc true propositions and what are 
 false, and logic would be but another name for the whole of 
 knowledge could it take this duty on itself. 
 
 See Mr. Mill's System of Logic, Book I. Chap. IV, which gener- 
 ally asrrees with what \a given above. Cliapters V and VI 
 contain Mr. Mill's views on the Nature and Import of Prop-
 
 OPPOSITION OF PBOPOSITIONS EXPLAINED. 75 
 
 ositionR, which subject may be further studied in Mr. Mill's 
 Examination of Sir W. Hamilton's Philosophy, Ciiap. XVIII; 
 Hamilton's L ctures on Logic, No. XIII ; and Mansel's Pro- 
 legomena Logica, Chap. II ; but the subject is too metaphy- 
 sical in character to be treated in this work. 
 
 In this Section, on "Tlie Kinds of Propositions," 
 we have considered: 
 
 1. Tlie Meaning of the Word " Proposition." 
 
 2. The A null/sis of a Proposition. 
 
 3. The Catef/orical and Conditional Propositions. 
 
 4. The Qn(dity and Quantity of Propositions, 
 6. Aristotle\s View of Qaantity, 
 
 6. Names of the Four Propositions. 
 
 7. Variations from the Lof/ical Porni, 
 
 8. The Modality of Pro2>ositions. 
 
 SECTION IL 
 THE OPPOSITION OF PROPOSITIONS. 
 
 1. The Four Propositions Explained. 
 
 We have ascertained that four distinct kinds of prop- 
 ositions are recognized by logicians, the Universal 
 affirmative, the Particular affirmative, the Universal 
 negative, and the Particular negative, commonly indi- 
 cated by the symbols A, E, I, O. It is now desirable to 
 compare together somewhat minutely the meaning and 
 use of propositions of these various kinds, so that we 
 may clearly learn how the truth of one will affect the 
 truth of others, or how the same truth may be thrown 
 into various forms of expression.
 
 76 PROPOSITIONS. 
 
 (1) The universal affirmative proposition A expresses 
 the fact that the thing or chiss of things denoted by the 
 subject is included in, and forms part of the class of 
 things denoted by the predicate. Thus "all metals are 
 elements " means tliat metals form a part of the class of 
 elements, but not the whole. As there are altogether 63 
 known elements, of which 48 are metals, we cannot say 
 that all elements are metals. The proposition itself 
 does not tell us anything about elements in general ; it 
 is not, in fact, concerned with elements, metals being 
 the subject about which it gives us information. This 
 is best indicated by a kind of diagram, first used by the 
 celebrated mathematician Euler, in his letters to a 
 German princess. In Fig. 1, the metals are supposed 
 
 Fig. 1. 
 
 to be enclosed in the small circle somewhat as sheep 
 might be in a pinfold, this circle containing all the 
 metals and nothing else. The greater circle is sup- 
 posed to contain in a similar manner all the elements 
 and nothing else. Now as the small circle is wholly 
 within the larger one, it follows that all the metals 
 must be counted as elements, but of the part of the 
 elements outside the circle of metals we know nothing 
 from tho pror)osition. 
 
 (2) The particular affirmative proposition I exactl)
 
 OPPOSITION OF PROPOSITIONS EXPLAINED. 7? 
 
 resembles A in meaning, except that only part of the 
 subject is brought into question. When I say that 
 "some metals are brittle," I mean that of a collection of 
 all the dijfferent metals a few at least might be picked 
 out which would be found to be brittle ; but the word 
 some is exceedingly indefinite, showing neither the 
 exact number of brittle metals, nor how we are to 
 know them from the others, unless indeed by trying 
 whether they are brittle. This proposition will be 
 properly represented in Euler's mode by two intersect- 
 ing circles, one supposed to enclose all metals, and the 
 other all brittle substances. The mere fact of the two 
 
 Fig. 2. 
 
 circles intersecting proves that some part of one class 
 must coincide with some part of the other class, which 
 is what the proposition is intended to express. Con- 
 cerning the portions of the circles which do not overlap, 
 the proposition tells us nothing. 
 
 (3) The universal negative proposition E denies the 
 existence of any agreement or coincidence between the 
 subject and predicate. Thus from " no metals are com- 
 pound substances," we learn that no metal is to be 
 found among compound substances, and it follows 
 necessarily that no compound substance can be found 
 among the metals. For were there a compound sub-
 
 78 PROPOSITIONS. 
 
 Stance among the metals, there would evidently be one 
 metal at least among the compound substances. This 
 entire oeparation in thought of the two classes is well 
 eKovn in Euler's method by two disconnected circles. 
 
 Fig. a 
 
 (4) The particular negative proposition O excludes a 
 ^urt of the subject from tbe predicate. Wben I say 
 some metals are not brittle, I intentionally refer only to 
 a part of the metals, and exclude them from the class 
 of brittle substances ; but I cannot help at the same 
 time referring to the whole of the brittle substances. 
 If the metals in question coincided with any part of 
 the brittle substances they could not be said to be 
 excluded from the class. To exclude a thing from any 
 space, as from a particular chamber of a house, it must 
 not merely be removed from some part, but from any 
 part, or from the whole of that space or chamber. 
 Euler's diagram for this proposition may be constructed 
 in the same manner as for the proposition I as follows* 
 
 Fia. 4. 
 
 It is apparent that though part of the metals fall intc
 
 OPPOSITION OF PEOPOSITIONS EXPLAINED. 79 
 
 the circle of brittle substances, yet the remaining por- 
 tion are excluded from any part of the predicate. 
 
 2. The Distribution of Terms. 
 
 The learner will easily see that the proposition E is 
 distinguished from A and I, by the fact that it gives us 
 some information concerning the ivhole of the predicate, 
 because we learn that none of the objects included in 
 the predicate can be found among those included iu 
 the subject. The aflBrmative propositions, on the other 
 hand, warranted us in holding that the objects denoted 
 by tlie subject, or some particular part of them, were 
 included in the predicate, but they give us no ivarrani 
 for saying that any specified part of the predicate is in 
 the subject. Because we merely know that a substance 
 is an element, we do not learn from the proposition 
 *'all metals are elements" whether it is metal or not. 
 And from the proposition " some metals are brittle," we 
 certainly cannot ascertain whether any })articular brittle, 
 substance is a metal. We must seek the information 
 from other sources. But from " no metals are com- 
 pounds" we learn of any compound substance that it 
 is not a metal, as well as of a metal that it is not a 
 compound substance. The particular negative O dis- 
 tributes its predicate, but not its subject, for in saying 
 some metals are not brittle, I exclude some metals from 
 the whole class of brittle substances. 
 
 The important difference above explained is expressed 
 in technical language by saying that the proposition E 
 distributes its predicate, whereas the affirmative proposi- 
 tions A and I do not distribute their predicates. B^ 
 distribution of a term is simply meant taking it nniver-
 
 80 
 
 pROPOsinoiirs. 
 
 nally, or referring to all parts of it ; and as the validity 
 of any argument or syllogism will usually depend upon 
 the sufficient distribution of the terms occurring in it, 
 too much attention cannot be paid to this point. 
 
 Judging from the examples we have had, it will be 
 seen that the universal affirmative distributes its sub- 
 ject, but not its predicate; for it gives us some infor- 
 mation concerning all metals, but not all elements. The 
 particular affirmative distributes neither subject nor 
 predicate ; for we do not learn anything from our ex- 
 ample concerning all metals nor concerning all brittle 
 substances. The universal negative distributes both 
 subject and predicate, for we learn something of all 
 metals and also of all compound suistancen. The par- 
 ticular negative distributes its predicate, but not its sub- 
 ject, for it excludes the subject from the whole of the 
 predicate. 
 
 2. Table of Results! 
 
 We may state the results at which we have now 
 arrived in the following form : 
 
 o i 
 
 Universal 
 
 I Affirmative A. 
 j Negative E. 
 
 Subject. 
 
 Distributeil. 
 Distributed. 
 
 Predicate. 
 
 Undistributed 
 Distributed. 
 
 r) J- 1 j Affirmative I. Undistributed. Undistributed, 
 ^articular ^ j^gjfative 0. Undistributed. Distributed. 
 
 4. Relations of the Four Propositions. 
 
 We shall now discover with great ease the relations 
 of the four pro])osition8, each to each, that is to say, 
 the way in which they are opposed to each other. It 
 it obvious that the truth of one proposition interferes
 
 OPPOSITION OF PROPOSITIONS EXPLAINED. 81 
 
 more or less completely with the truth of anothei 
 proposition having the same subject and predicate. If 
 "all metals are elements," it is impossible that ''some 
 metals are not elements/' and still more palpably im- 
 possible, so to say, that " no metals should be elements." 
 The proposition A, then, is inconsistent with both E and 
 ; and, vice versa, E and are inconsistent with A. 
 Similarly, E is inconsistent with A and I. But this im- 
 portant difference must be noted, that if A be false, O 
 is necessarily true, but E may or may not be true. If 
 it is not true that "all men are sincere," it follows 
 that "some men are not sincere," but it does not in 
 the least follow that "no men are sincere." This dif- 
 ference is expressed by saying that A and are contra- 
 dictory propositions, whereas A and E are called con- 
 trary propositions. It is plain that A and E, as in "al! 
 men are sincere" and "no men arc sincere,'* represent 
 the utmost possible contrariety of circumstances. In 
 order to prove the falsity of A, it is sufficient to estab- 
 lish the truth of 0, and it is superfluous, even if pos- 
 sible, to prove E; similarly E is disproved by proving I, 
 and it is superfluous to prove A. Any person who 
 asserts a universal proposition, either A or E, lays him- 
 self under the necessity of explaining away or disprov- 
 ing every single exception brought against it. 
 
 An opponent may always restrict liiniself to the much easier 
 task of finding instances which apparently or truly contradict the 
 universality of the statement, luit if he takes upon himself to 
 aflBrm the direct contrary, he is himself open to easy attack. 
 Were it to be asserted, for instance, tiiat "All Christians are 
 more moral than Pagans," it would be easy to adduce examples 
 showing that " Some Christians are not more moral than 
 P*gang," but it would be absurd to suppose that it would b
 
 8t PBOPOSITIONa 
 
 necessary to go to the contrary extreme, and show that "Nt 
 Christians are more moral than Pagans." In short A is suffi- 
 ciently and best disproved by 0, and E by I. It will be easily 
 apparent that, vice versa, is disproved by A, and I by E ; nor is 
 there, indeed, any other mode at all of disproving these particu- 
 lar propositions. 
 
 When we compare together the propositions I and 
 we find that tbey are in a certain sense contrary in 
 nature, one being affirmative and the other negative, 
 but that they are still consistent with each other. It is 
 true both that "Some metals are brittle," for instance 
 Antimony, Bismuth and Arsenic ; but it is also true 
 that "Some metals are not bnttle." And the reader 
 will observe that when I affirm "Some metals are 
 elements," there is nothing in this to prevent the truth 
 of "Some metals are not elements," although on other 
 grounds we know that this is not true. The proposi- 
 tions I and are called subcontraries each of the other, 
 the name connoting a less degree of contrariety than 
 exists between A and E. 
 
 As regards the relation of A to I and E to 0, it is 
 plain that the truth of the universal includes and 
 necessitates the truth of the particular. What may be 
 affirmed or denied of all parts of a class may certainly 
 be affirmed or denied similarly of some part of the 
 class. From the truth of the particular we have no 
 right to infer either the truth or falsity of the universal 
 of the same finality. These pairs of propositions are 
 called subalterns, i. e., one under the other (Latin suh 
 under, and al/er the oth. - of two), or we may say more 
 exactly that I and are lespectively the suhaUernateS 
 of A and E, each of which is a suhalternana.
 
 OPPOSITION OF PE0P08ITI0NS EXPLAINED. 83 
 
 5. The Scheme of Oppositiou. 
 
 The relations of the propositions just described are 
 all clearly shown in the following scheme : 
 
 A Contraries E 
 
 
 
 r 
 
 I 
 
 ^^ .^^ 
 
 ('if ^^n 
 
 S!^' '"% 
 
 
 
 . Subcontraries , 
 
 03 
 
 6. The Laws of Opposition. 
 
 It is so highly important to apprehend completely 
 and readily the consistency or opposition of proposi- 
 tions, that I will put the matter in another form. Tak- 
 ing any two propositions having the same subject and 
 predicate, they must come under one of the following 
 statements : 
 
 1. Of contradictory propositions, one must be true 
 and one false. 
 
 2. Of contrary propositions, both cannot be true, 
 and both may be false. 
 
 3. Of subcontrary propositions, one only can be false, 
 and both may be true. 
 
 4. Of subalterns, the particular is true if the univer- 
 sal be true ; but the universal may or may not be true 
 when the particular is true.
 
 M PBOPOSITIOKa 
 
 7> The Conditions of Opposition. 
 
 1 put the same matter in yet aaother form in th 
 following table, which shows how the truth of each oi 
 A, E, I, and 0, affects the truth of each of the others. 
 
 
 A 
 
 E 
 
 1 
 
 
 
 
 is 
 
 is 
 
 is 
 
 is 
 
 If A be true 
 
 true 
 
 false 
 
 true 
 
 false. 
 
 i< C i( it 
 
 false 
 
 true 
 
 false 
 
 true. 
 
 it 1 (( (( 
 
 doubtful 
 
 false 
 
 true 
 
 doubtfuL 
 
 tt Q <( 
 
 false 
 
 doubtful doubtful 
 
 true. 
 
 It will be evident that from the affirmation of uni- 
 versals more information is derived than from the 
 affirmation of particulars. It follows that more infor- 
 mation can be derived from the denial of particulars 
 than from the denial of universals, that is to say, there 
 are less cases left doubtful^ as in the above table. 
 
 The learner may well be cautioned, however, afjrainst an am- 
 biguity which has misled some even of the most eminent lo- 
 gicians. In particular pro|K)sitions the adjective some is to be 
 carefully interpreted as some, and there may or may not he more 
 or all. Were we to interpret it as some, not more nor all, then it 
 would really give to the proposition the force of I and com- 
 bined. If 1 say " some men are sincere," I must not be taken as 
 Imjilying that "some men are not sincere;" I must be under- 
 stood to predicate sincerity of some men, leaving the character ol 
 the remainder wholly unaffected. It follows from this that, 
 when I deny the truth of a particular, I must not be imderstood 
 as implyinj? the trutli of the universal of the same quality. To 
 deny the truth of " some men are mortal " might seem very 
 natural, on the ground that not some but all men are mortal ; but 
 then the projKjsition denied would really be oto men are not 
 mortal, i. c. not I. Hence when I deny that "some men ara
 
 OPPOSITIOir TO PROPOSITIOITS EXPLAINID. 8A 
 
 tmmortal " I mean that ** do men are immortal ; " and when I 
 deny that " some men are not mortal," I mean that " all men are 
 inortaL" 
 
 8. The Matter of Propositions. 
 
 It has long been usual to compare propositions as re- 
 gards the quality of the subject matter to which they 
 refer, and what is technically called the matter was dis- 
 tinguished into three kinds, necessary, contingent, and 
 impossible. Necessary matter consists of any subject 
 in which the proposition A may be affirmed ; impossible 
 in which E may be affirmed. Any subject or branch of 
 knowledge in wliich universal statements cannot usually 
 be made is called contingent matter, and it implies the 
 truth of I and O. Thus "comets are subject to gravi- 
 tation," though an indefinite or indesignate proposition, 
 may be interpreted as A, because it refers to a part of 
 natural science where such general laws obtain. But 
 "men are sincere" would be properly interpreted as 
 particular or I, because the matter is clearly contingent. 
 The truth of the following statements is evident : 
 
 In necessary matter A and I are true ; E and false. 
 
 In contingent matter I and are true ; A and E false. 
 
 In impossible matter E and O are true ; A and I false. 
 
 In reality, however, this part of logical doctrine is 
 thoroughly illogical, because in treating a proposition 
 we have no right, as already explained, to assume 
 ourselves acquainted with the science to which it re- 
 fers. Our duty is to elicit the exact consequences of 
 any statements given to us. We must learn in logic to 
 transform information in every possible way, but not to 
 add extraneous facts.
 
 W PROposrnoira. 
 
 In this section, on "Tlie Opposition of Proposi- 
 tions," we have considered : 
 
 1. The Explanation of the Four Propositions, 
 
 2. Tfie Distribution of Terms, 
 
 3. The Table of Results, 
 
 4. The Itelations of the Four Propositions, 
 
 6. The Scheme of Opposition. 
 O. The Laws of Opposition. 
 
 7. The Conditions of Opposition, 
 
 8. The Matter of Propositions, 
 
 SECTION III. 
 
 CONVERSION AND IMMEDIATE INFERENCE. 
 1. The Nature of Inference. 
 
 We are said to infer wheuever we draw one truth 
 from another truth, or pass from one proposition to 
 another. As Sir W. Hamilton siiys, Inference is "the 
 carrying out into the last proposition what was virtually 
 contained in the antecedent judgments." The true 
 sphere of the science of logic indeed is to teach the prin- 
 ciples on which this act of inference must be })erformed, 
 and all the previous consideration of terms and propo- 
 sitions i-i only useful or pertinent so far as it assists us 
 to under-itand the processes of inference. We have to 
 consider in succession all the modes in which the same 
 information may be moulded into different forms of 
 expression often implying results of an a])parently 
 different character. Logi<Mans are not agreed exactly 
 as to what we may include under the name Inference, 
 and what we should not. All would allow that there
 
 OONVERSION AND INFERENCE 87 
 
 is an act of inference when we see drops of water on 
 the ground and believe that it has rained. This is a 
 somewhat comphcated act of inference, which we shall 
 consider later under the subject of Induction. Few or 
 none would say that there is an act of inference in 
 passing from " The Duke of Cambridge is Commander- 
 in-chief," to ''The Commander-in-chief is the Duke of 
 Cambridge." But without paying much regard to the 
 name of the process I shall in this section point out all 
 the ways in which we can from a single proposition of 
 the forms A, E, I or 0, pass to another proposition. 
 
 2. Conversion of Propositions. 
 
 We are said to convert a proposition when we trans- 
 pose its subject and predicate ; but in order that the 
 converse or converted proposition shall be inferred from 
 the convertend, or that which was to be converted, we 
 must observe two rules (1) the quality of the proposi- 
 tion (affirmative or negative) must be preserved, and 
 (2) no term must be distributed in the Converse unless 
 it was distributed in the Convertend. 
 
 (1) Conversion by Limitation. If in "all metals are 
 elements" we were simply to transpose the terms, thus 
 ''all elements are metals," we imply a certain knowl- 
 edge about all elements, whereas it has been clearly 
 shown that the predicate of A is undistributed, and that 
 the convertend does not really give us any information 
 concerning all elements. All that we can infer is that 
 "some elements are metals;" this converse proposi- 
 tion agrees with the rule, and the process by which we 
 thus pass from A to I is called Conversion by Limitation, 
 or Per accidens.
 
 B8 pROPOsiTioire. 
 
 ('/-) Simple Conversion. When the converse is a 
 proposition of exactly the same form as the convertend 
 the process is called simple conversion. Thus from 
 **some metals are brittle substances " I can infer "some 
 brittle substances are metals," as all the terms are here 
 undistributed. Thus I is simply converted into I. 
 
 Again, from "no metals are compounds," I can pass 
 directly to " no compounds are metals," because these 
 propositions are both in E, and all the terms are there- 
 fore distributed. Euler's diagram (p. 73, Fig. 3) clearly 
 shows, that if all the metals are separated from all the 
 compounds, all the compounds are necessarily separated 
 from all the metals. The proposition E is then simply 
 converted into E. 
 
 (3) Conversion by Negation. But in attempting to 
 convert the proposition we encounter a peculiar 
 difficulty, because its subject is undistributed ; and yet 
 the subject should become by conversion the predicate 
 of a negative proposition, which distributes its predi- 
 cate. Take for example the proposition, "some exist- 
 ing things are not material substances." By direct 
 conversion this would become "all material substances 
 are not existing things;" which is evidently absurd. 
 The fallacy arises from existing thiriys l)eing distributed 
 in the converse, whereas it is particular in the conver- 
 tend ; and the rules of the Aristotelian logic prevent us 
 from inserting the sign of particular quantity before 
 the predicate. The converse would be equally untrue 
 and fallacious were we to make the subject particular, 
 as in "some material substances are not existing 
 things." We must conclude, then, that the proposi- 
 tion O cannot be treated either by simple conversion qi
 
 CONVERSION AND INFERENCE. 89 
 
 conversion by limitation. It is requisite to apply a new 
 process, which may be called Conversion by Negation, 
 and which consists in first changing the convertend 
 into an affirmative proposition, and then converting it 
 simply. If we attach the negation to the predicate 
 instead of to the copula, the proposition becomes " some 
 existing things are immaterial substances," and, con- 
 verting simply, we have "some immaterial substances 
 are existing things," which may truly be inferred from 
 the convertend. The proposition O, then, is only to 
 be converted by this exceptional method of negation. 
 
 (4) Contpapositive Conversion. Another process of 
 conversion can be applied to the proposition A, and is 
 known as conversion by contraposition. From ''all 
 metals are elements," it necessarily follows that " all 
 not-elements arc not metals." If this be not at the 
 first moment apparent, a little reflection will render it 
 so, and from Fig.* 5 we see that if all the metals be 
 
 Fig 5 
 
 among the elements, whatever is not element, or out- 
 side the circle of elements, must also be outside the 
 circle of metals. 
 
 We may also prove the truth of the contrapositive proposi- 
 tion in this way. If what is not-element should be metal, then it
 
 00 PEOPosiTioira. 
 
 must be an element by the original proposition, or it must be at onct 
 an element and not an element ; which is impossible according 
 to the Primary Laws of 'I'houglit (Chap. Ill, Sect. I), since noth- 
 ing can botli have and not have the same property. It follows 
 tliat what is uot-element must be not-metal. 
 
 Mistakes may readily be committed in contrapositive conver- 
 sion^ from a cause which will be more apparent in Chapter VIL 
 We are very liable to infer from a proposition of the fona "all 
 metals are elements," that all not-metals are not elements, which 
 is not only a false statement in itself, but is not in the least 
 warranted by the original proposition. In Fig. 5, it is apparent 
 that because a thing lies outside the circle of metals, it does not 
 necessarily lie outside the circle of elements, which is wider than 
 that of metals. Nevertheless the mistake is often made in com- 
 mon life ; and the learner will do well to remember that the pra 
 cess of conversion by contraposition consists only in taking the 
 negative of the predicate of the proposition A, as a new subject, 
 and afiSrming of it universally the negative of the old subject. 
 
 Contrapositive conversion cannot be applied to the particu- 
 lar propositions I and at all, nor to the proposition E, in that 
 form ; but we may change E into A by attaching the negation to 
 the predicate, and then the process can be applied. Thus " no 
 men are perfect," may be changed into "all men are not per- 
 fect, i.e., "are imperfect," and then we infer by contraposition 
 "all not-imperfect beings are not-men," But not imperfect is 
 really the same as perfect, so that our new proposition is 
 really equivalent to "all |)erfect beings are not men," or "no 
 perfect l)eings are men," (E) the simple converse of the origina] 
 proposition. 
 
 3. Immediate Inference. 
 
 There remain to be described certain deductioni 
 which may be drawn from a proposition without con 
 verting its terms. They may be called immediate in- 
 ferences, and have been very clearly described by Arch 
 bishop Thomson.
 
 CONVERSION AND INFERENCE. 91 
 
 (1) Immediate Inference by Privative Conceptioi! 
 
 consists in passing from any ailinnative proposition to a 
 negative proposition implied in it, or equivalent to it, 
 or vice versa, in passing from a negative proposition to 
 Its corresponding affirmative. 
 
 The following table contains a proposition of each kind changed 
 by pnvate conception into an equivalent proposition 
 
 j A all metals are elements. 
 ^ E no metals are compounds, 
 j E no men are perfect. 
 l A all men are imperfect. 
 j I some men are trustworthy. 
 \ some men are not untrustworthy. 
 ( some men are not trustworthy. 
 { I some men are untrustworthy. 
 
 The truth of any of the above can be clearly illustrated by 
 diagrams ; thus it will be apparent that if the whole circle ot 
 metals lies inside the circle of elements, no part can lie outside 
 of that circle or among the compounds. Any of the above prop- 
 ositions may be converted, but the results will generally be such 
 as we have already obtained. Tlius the simple converse of " no 
 metals are compounds " is " nc compounds are metals," or " no 
 not-elements are metals," the contra positive of " all metals are 
 elements." From the last example we get also by simple con- 
 version, " some untrustworthy beings are men," which is obvi- 
 ously the converse by negation, as before explained. Applying 
 this kind of conversion to "some men are not untrustwortliy," 
 we have " some not-untrustworthy beings are men." Lastly, 
 from " all men are imperfect " we may obtain through conversion 
 by limitation, " some imperfect beings are men." 
 
 (2) Immediate Inference by Added Determinants 
 
 consists in joining some adjective or similar qualificar 
 tion both to the subject and predicate of a proposition, 
 so as to render the meaning of each term narrower or 
 better determined. Provided that no other alteration
 
 M PROPOSITIONS. 
 
 18 made, the truth of the new proposition necessariii 
 follows from the truth of the original in almost all 
 
 cases. 
 
 From " all metals are elements," we may thus infer that " all 
 jrery heavy metals are very heavy elements." From "a comet is 
 a material body " we infer " a visible comet is a visible material 
 body." But if we apply this kind of inference too boldly we 
 may meet with lailacious and absurd results. Thus, from " all 
 kings are men," we might infer "all incompetent kings are 
 incompetent men ;" but it does not at all follow tliat those who 
 are incompetent as kings would be incomjietent in other posi- 
 tions. In this case and many others the qualifying adjective is 
 liable to bear different meanings in the subject and predicate, 
 but the inference will only be true of necessity when the mean- 
 ing is exactly the same in each case With comparative terme 
 this kind of inference will seldom be applicable ; thus from " a 
 cottage is a building," we cannot infer "a huge cottage is a huge 
 building," sibx^c a cottage may be large when compared with 
 other cottages, but not with buildings generally. 
 
 (3) Immediate Inference by Complex Conception is 
 
 closely similar to the last, and consists in employing the 
 subject and predicate of a proposition as parts of a 
 more complex system. 
 
 From " all metals are elements," I can pass to " a mixture of 
 netals is a mixture of elements " From "a horse is a quadruped" 
 I infer "the skeleton of a horse is the skeleton of a quadruped." 
 But here again the reader must beware of applying the process 
 where the new complex conception has a different meaning in 
 the suijject and predicate. Thus, from " all Protestants are 
 Christians," it does not follow that "a majority of Protestants 
 are a majority of Christians," nor that " tlie most excellent of the 
 Protestants is the most excellent of the Christians." 
 
 The student is recommended to render himself familiar 
 with all the transformations of propositions, or immediate
 
 A.NALTSIS OF SENTENCES. 93 
 
 inlerences described in this lesson ; and copious examples are 
 fumishe>l for the purpose. It is a good exercise to throw the 
 same proposition through a series of changes, so tliat it comes 
 out in its original form at last, and thus proves the truth of all 
 the intermediate changes; but should conversion by limitation 
 have been used, the original tniversal proposition cannot be 
 regained, but only the particular proposition corresponding 
 to it. 
 On Immediate Inference, Archbishop Thomson, Outline of t/ie 
 Laws of Thought, Sections 85-92. 
 
 In this section, on ** Conversion and Immediate 
 Inference,** we have considered : 
 
 1. The Nature of Inference, 
 
 2. Conversion. 
 
 3. Innnediate Inference. 
 
 SBGTION lY. 
 
 THE LOGICAL ANALYSIS OF SENTENCES 
 
 1. Relation of Logic to this Topic. 
 
 Propositions as they are usually to be found in 
 written or spoken compositions seldom exhibit the 
 simple form, the conjunction of a subject, copula, and 
 predicate, which we have seen to be the proper logical 
 construction. Not only is the copula often confused 
 with the predicate, but several propositions may be 
 combined into one grammatical sentence. For a full 
 account of the analysis of sentences I shall refer to 
 several excellent little worls devoted to the subject ; 
 but I will here attempt to give a sketch of the various 
 ways in which a sentence ma-' be constructed.
 
 9i PE0P0SITI0N8. 
 
 2. The Grammatical and the Logical Predicate. 
 
 So often is the copula united to the predicate in 
 ordinary language, that the grammarian treats the 
 proposition as composed of only two parts, the subject 
 and predicate, or verb. Thus the proposition, " The sun 
 rises," apparently contains nothing but a subject " the 
 sun," and a predicate "rises;" but the proposition is 
 really equivalent to " the sun is rising," in which the 
 copula is distinctly shown. We shall, therefore, con- 
 sider the verb or grammatical predicate as containing 
 both copula and logical predicate. In Latin one single 
 word may combine all the three parts of the proposition, 
 as in swm, "I am ;" and the celebrated exclamation of 
 Caesar, Veni, vidi, vici, "I came, I saw, I conquered," 
 contains three distinct and complete propositions in 
 three words. These peculiar cases only arise, however, 
 from the parts of the proposition having been blended 
 together and disguised in one word ; and in the Latin 
 sum, the letter m is a relic of the pronoun me, which is 
 the real subject of the proposition. If we had a perfect 
 acquamtance with the Giammar of any language it 
 would probably not contradict the logical view of a 
 sentence, but would perha])s explain how the several 
 parts of the complete proposition had become blended 
 and apparently lost, just as the words ivill and not art 
 blended in the colloquial "I wont." 
 
 8. The Plurality of Propositions in a Sentence. 
 
 A grammatical sentence may contain any number of 
 distinct propositions, which admit of being separated
 
 ANALYSIS OP SENTENCES. 95 
 
 but which are combined together for the sake of 
 brevity. In the sentence, 
 
 "Art is long and Time is fleeting,** 
 
 there are two distinct subjects, Art and Time, and two 
 predicates, ''long" and "fleeting," so that we have 
 simply two propositions connected by the conjunction 
 ind. We may have, however, several distinct subjects 
 with one and the same predicate ; as in 
 
 " Thirty days hath September, 
 April, June, and November." 
 
 In this well-known couplet the predicate " having 
 thirty days " is placed first for the sake of emphasis, 
 and there are four subjects, September, April, etc., of 
 each of which it is affirmed. Hence these lines really 
 contain four distinct propositions. 
 
 Again, there may be one subject with a plurality of 
 predicates, so that several different propositions are 
 asserted without the repetition of the subject and 
 copula. Thus the sentence 
 
 ''Nitrogen is a colorless, tasteless, inodorous gas, 
 slightly lighter than air," contains one subject only. 
 Nitrogen, but four or five predicates ; it is plainly 
 equivalent to "Nitrogen is colorless," "Nitrogen is 
 tasteless," "Nitrogen is a gas," and so on. 
 
 Lastly, we may have several subjects and several 
 predicates all combined in the same sentence, and with 
 only one copula, so that each predicate is asserted of 
 each subject; and a great number of distinct proposi- 
 tions are condensed into one brief sentence. Thus in 
 the sentence, " Iron. Copper, f-^ad and Zinc are abun-
 
 M PROPOSITIONS, 
 
 dant, cheap and useful metals," we have evidently four 
 subjects, and we may be said to have four predicates, 
 "abundant," "cheap," "useful," and "metal." Ah 
 there is nothing to prevent our applying each predicate 
 to each subject the sentence really contains 16 distinct 
 propositions in only 11 words; thus "Iron is abun- 
 dant," "Iron is cheap," "Copper is abundant," "Cop- 
 per is cheap," and so on. In the curious sentence : 
 
 " Hearts, tongues, figures, scribes, bards, poets, can- 
 not think, speak, cast, write, sing, number, his love to 
 Antony,"* Shakspeare has united six subjects and six 
 predicates, or verbs, so that there are, strictly speaking, 
 six times six or thirty-six propositions. 
 
 In all the cases above noticed the sentence is said to be com- 
 pound, and tlie distinct proj)08itions combined together are saia 
 to be co-ordinate with each other, that is of the same order or 
 kind, because they do not depend upon each other, or in any way 
 affect each other's truth. The abundance, cheapness, or utility 
 of iron need not be stated in tlie same sentence witli the qualities 
 of copper, lead or zinc ; but as the predicates happen to be the 
 same, considerable trouble in speuking or writing is saved by 
 putting as many suiyects as possible to the same set of predi- 
 cates. It is truly said that brevity is the soul of wit, and one of 
 the great arts of composition consists in condensing as many 
 statements as yKissible into the fewest words, so long as the 
 meaning is not confused thereby. 
 
 4. Complex Seutences. 
 
 Propositions are, however, combined in a totally 
 different manner when one proposition forms a part of 
 the subject or predicate of the other. Thus in tha 
 
 Antony and Cleopatra, Aci III, Sec. 4.
 
 AKALTSIS OF SENTENCES. 97 
 
 sentence, "The man who is upright need not feai 
 accusation," there are two verbs, and two propositions, 
 but one of these only describes the subject of tlie other; 
 "who is upright" evidently restricts the application of 
 the predicate " need not fear accusation" to a part ot 
 the class "man." The meaning of the whole sentence 
 might be expressed in the form 
 
 "The upright man need not fear accusation." 
 
 A.nd it is clearly seen that the clause or apparent prop- 
 osition is substituted for an adjective. Such a clause 
 or proposition is called subordinate, because it merely 
 assists in the formation of the principal sentence, and 
 has no meaning apart from it ; and any sentence con- 
 taining a subordinate clause is said to be complex. 
 Almost any part of a sentence may thus be replaced by 
 a subordinate clause. Thus in " Oxygen and Nitrogen 
 are the gases which form the largest part of the at- 
 mosphere," there is a subordinate clause making part 
 of the predicate, and the meaning might be expressed 
 nearly as well in this way, "Oxygen and Nitn^gen are 
 the gases forming the largest part of the atmosphere." 
 
 In the case of a modal proposition, or one which states the 
 manner in which the predicate belongs to the subject, the mode 
 may be expressed either by an adverb, or by a subordinate 
 clause. "As a man lives so he dies" is such a proposition; for 
 it means, " a man dies as he lives," and " as he lives" is equiva- 
 lent to an adverb ; if he lives well, he dies well ; if he lives 
 badly, he dies badly. Adverbs or adverbial chuis-s may also 
 specify the time, place, or any other circumstance concerned in 
 the truth of the main proposition. 
 
 Assuming the learner to be acquainted with the grammatic*.'
 
 98 PROPOSITIONS. 
 
 terms ased, we may thus state the parts of which the most 
 complex sentence must consist. 
 
 The subject may consist of 
 
 1. A noun ; as m " The Queen reigns. " 
 
 2. A pronoun ; as in " She reigns." 
 
 3. An adjective converted into a noun ; as in " Whites are 
 ticilized." 
 
 4 A gerund ; as " Seeing is believing." 
 
 5. An infinitive ; as " To see is to believe." 
 
 6. A subordinate clause; as " Who falls from virtue is lost. 
 The subject may be qualified or restricted by combining with 
 
 It an attribute which may be expressed in any of the following 
 ways: 
 
 1. An adjective ; as " Fresh air is wholesome." 
 
 2. A participle ; as " Falling stars are often seen." 
 
 3. A noun used as an adjective ; as ''Iron ships are now mnch 
 employed." 
 
 4. A noun and preposition; as "ships of iron are now much 
 employed." 
 
 5. A possessive case ; as " Chatham's son was the great minister 
 Pitt" 
 
 6. A noon m apposition ; as " The Metropolis London m the 
 most populous of cities." 
 
 7. A prerund or dative infinitive ; as, " The desire to go abroad 
 is common in Englishmen." 
 
 The predicate consists almost always of a verb, which often 
 has some object or qualifying words ; thus it may be 
 
 1. A simple tense of a comiilete verb ; as " The sun rises." 
 
 2. A compound tense ; as " The sun has risen. ' 
 
 3. An incomplete verb and complement ; as " The sea appears 
 rough." 
 
 4 The verb "to be" and an adjective; as "Time is fleeting." 
 
 5. A verb with an object ; as " Warmth nwltn ice." 
 
 6. A verb with an adverbial ; as " The snow falls thickly." 
 
 The object of a verb is usually a noun or pronoun, but any 
 other of the six kinds of expressions which may serve as a sub 
 iect laay sJso serve as an object
 
 ANALYSIS OF SENTENCES. 99 
 
 The adverbial qualifying a verb and expressing the manner, 
 time, place, or other circumstance affecting the proposition may 
 be 
 
 1. An adverb ; as " The days pass slowly." 
 
 2. A noun and preposition ; as " The resolution was passed by 
 a large majority." 
 
 3. An absolute phrase ; as " The snow melts, tJie sun ha/ting 
 risen." 
 
 4. A dative infinitive ; as " She stoops to conquer." 
 
 5. Any phrase equivalent to an adverb; as "The dividends 
 are paid twice a year." 
 
 5,. Modes of Exhibiting Construction. 
 
 Various modes of exhibiting the construction of sen- 
 tences by symbols and names for the several parts have 
 been invented ; but I believe that by far the simplest 
 and most efficient mode is to exhibit the construction 
 in the form of a diagram. Any two or more parts of a 
 sentence which are co-ordinate with each other, or bear 
 the same relation to any otlier part, are written along- 
 side each other, and coupled together by a bracket; 
 thus the diagram, 
 
 Iron 
 Copper 
 Lead 
 Zinc 
 
 > are < 
 
 abundant, 
 cheap, 
 useful 
 metals, 
 
 clearly shows that there are four co-ordinate subjects, 
 and four co-ordinate predicates in the example pre- 
 viously taken. 
 
 Whenever one part of a sentence is subordinate to 
 another part it may be connected with it by a line 
 drawn in any convenient direction. Thus the analysis 
 of the following sentence is readily sliown by the dia- 
 gram below it :
 
 100 PEOPOSITIONS. 
 
 " No one who is a lover of money, a lover of pleasure, 
 and a lover of glory, is likewise a lover of mankind ; 
 but only he who is a lover of virtue." 
 
 i a lover of money, 
 who is < a lover of pleasure, 
 I ( a lover of glory. 
 
 1 1 t a lover of mankind, 
 
 who is a lover of virtue. 
 We see that the sentence is both compound and com- 
 plex, that is to say it contains two principal co-ordinate 
 propositions with a common predicate, "a lover of 
 mankind." The first proposition is negative and its 
 subject is described by three subordinate clauses, while 
 the second proposition is affirmative and has one sub- 
 ordinate clause. 
 
 Tlie learner may be helped by the analysis of a few sentences, 
 of which the first consists of some remarkably complex lines 
 from a poem of Burbidge : 
 
 " He who metes, as we should mete, 
 Could we His insight use, shall most approve, 
 Not that which fills most space in earthly eyes, 
 But what though Time scarce note it as he flies 
 Fills, like this little daisy at my feet, 
 Its function best of diligence in love." 
 
 which fills most space in earthly eyes 
 
 I 1 
 
 He shall most approve j g;;*^ jj^ j,,,^ ^^ 
 
 who metes its function of like this little 
 
 ' i ,j , diligence in daisy at my 
 
 as we should mete j^^^ Jp^^;' 
 
 could we His insight use. though Tl^e scan^note it 
 
 I 
 as he fiiea
 
 ANALYSIS OF SENTENCES. 101 
 
 " Most sweet it is with unuplifted eyes 
 
 To pace the ground, if path there be or none, 
 
 While a fair region round the traveler lies 
 
 Wliich he forbears again to look upon ; 
 
 Pleased rather with some soft ideal scene, 
 
 The work of fancy, or some happy tone 
 
 Of meditation slipping in between, 
 
 The beauty c milng, and the beauty gone." 
 
 WORDSWOKTH. 
 
 It is most sweet 
 
 I 
 To pace the ground 
 
 with unuplifted if path while a fair region 
 
 "'^'^^ there 1^^ round the I 
 
 { or none traveler lies | 
 
 which (region) he (the traveler) forbears to look upon 
 
 I ( some soft ideal scene 
 
 pleased J i 1 
 
 rather with j the work of fancy 
 
 ( or some happy tone of meditation 
 
 slipping in between the beauty coming 
 and the beauty gone. 
 
 In the above sentence there is evidently one subject, " to pace 
 the ground," which by means of the pronoun tt. is connected with 
 the predicate most sweet. The main part of the sentence, however, 
 consists of three adverbials, expressing the manner and surround- 
 ing circumstances, and the third adverbial is developed in a very 
 complicated manner. The sentence is not compound, but is 
 complex on account of four subordinate propositions. 
 
 In the following sentence tliL^re is strictly but one principal 
 proposition, "We find." but this is only a mode of introducing 
 the true purjxjrt of the sentence, " the two classes of intellectual 
 operations have much that is different, much that is common." 
 
 " When the notions with which men are conversant in the 
 common course of life, which give meaning to their familiar 
 language rtnd which give employment to tlieir hourly thoughts, 
 are compared with the ideas on which exact science is founded,
 
 102 
 
 PROPOSITIONS. 
 
 we find, that the two classes of intellectual operations have 
 
 much that is different, much that is common." 
 
 we find that the two classes (* f ) 
 
 I of intellectual ( much that is different 
 
 I operations have } much that is common 
 
 When the notions * are compared i 
 
 which give 
 meaning 
 to their 
 familiar 
 language 
 
 with the ideas f 
 
 which give 
 
 employ- | 
 
 ment to on which 
 
 their hourly exact science is 
 
 thoughts founded. 
 
 with which 
 men are 
 conversant 
 in the 
 common 
 course 
 of life 
 
 Here the two classes form a collective term, and have two co- 
 ordinate predicates rendering the sentence so far a compound one. 
 The greater part of the sentence, however, consists of a compli- 
 cated subordinate sentence of the nature of an adverbial, express- 
 ing the time or occasion when this is found to be the case. 
 As a last example we take the sentence given below : 
 "The law of gravitation, the most universal truth at which 
 human reason has yet arrived, expresses not merely the general 
 fact of the mutual attraction of all matter ; not merely the vague 
 statement that its influence decreases as the distance increases, 
 but the exact numerical rate at which that decrease takes place ; 
 so that when its amount is known at any one distance it may be 
 exactly calculated for any other. " 
 
 at which human reason has yet arrived 
 
 the most universal truth 
 I 
 The law of gravitation expresses 
 
 not merely the 
 general fact 
 
 of the mutual 
 
 attraction of all 
 
 matter 
 
 not merely the 
 vague statement 
 
 that its influence 
 decreases 
 
 I 
 
 as the distance 
 
 increases 
 
 but the exact 
 numerical rate 
 
 I 
 
 at which that 
 
 decrease takeo 
 
 place 
 
 so that its amount may be calculated for any other distance 
 
 I 
 when it is known at any one distance.
 
 ANALYSIS OF SENTENCES. 103 
 
 W. S. Dalgleish's Orammatical Ancdym, or J. D. Morell's 
 
 Analysis of Sentences. 
 Alexander Bain's English Composition and Rhetoric, pp. 91-117, 
 
 treats of construction of sentences. 
 
 In this section, on "The Logical Analysis of 
 Sentences," we have considered: 
 
 1. The Relation of Logic to this Topic. 
 
 2. Tfie Gratntnatical and the Logical Predicate, 
 
 3. The Plurality of Propositions in a Sentence, 
 4r. Complex Sentences. 
 
 6. Modes of Exhibiting Construction,
 
 CHAPTER HI. 
 SYLLOG ISMS. 
 
 The subject of Syllogisms will be considered 
 under the following divisions : (1) The Laws of 
 Thonffht; (2) The Rules of the Syllogisni; 
 (3) The Moods and Fiffures of the Syllo- 
 yisni; (4) The Meductiou of Syllogisms; 
 
 (5) Irreyiilar and Compound Syllogisms; 
 
 (6) Conditional Syllogisms, 
 
 SECTION I, 
 THE LAWS OF THOUGHT. 
 
 1. The Statement of the Primary Laws of 
 Thought. 
 
 Before proceeding to examine the structure of the 
 Syllogism and the rules that govern it, it is desirable 
 that the learner should give a careful attention to the 
 very simple laws of thought on which all reasoning 
 must ultimately depend. These laws describe the very 
 simplest truths, in which all people must agree, and 
 which at the same time apply to all notions which we 
 can conceive. It is impossible to think correctly and 
 avoid evident self-contradiction unless we observe what 
 are called tlie Three Primary Laws of Thought, which 
 may be stated as follows :
 
 LAWS OF THOUGHT. 106 
 
 1. The Law of Identity. Whatever is, is. 
 
 2. The Law of Contradiction. Nothing can both be 
 
 and not be. 
 
 3. The Law of Excluded Middle. Everything must 
 
 either be or not be. 
 
 Though these laws when thus stated may seem absurdly 
 obvious, and were ridiculed by Locke and others on that account, 
 students are seldom able to see at first their full meaning and 
 importance. All arguments may be explained when these self- 
 evident laws are granted ; and it is not too much to say that the 
 whole of logic will be plain to those who will constantly use 
 these laws as the key. 
 
 2. Explanation of the Laws. 
 
 (1.) Law of Identity. The first of the laws may be 
 regarded as the best definition we can give of identity 
 or sameness. Could any one be ignorant of the mean- 
 ing of the word Identity, it would be sufficient to in- 
 form him that everything is identical with itself. 
 
 (2.) Law of Contradiction. The second law, how- 
 ever, is one which requires more consideration. Its 
 meaning is that nothing can have at the same time and 
 at the same place contradictory and inconsistent quali- 
 ties. A piece of paper may be blackened in one part. 
 while it is white in other parts ; or it may be white at 
 one time, and afterwards become black; but we cannot 
 conceive that it should be both white and black at the 
 same place and time. A door after being open may l)e 
 shut, but it cannot at once be shut and open. Water 
 may feel warm to one hand and cold to another hand, 
 but it cannot be both warm and cold to the same 
 hand. No quality can both be present and absent at
 
 106 SYLLOGISMS. 
 
 the same time ; and this seems to be the most simple 
 and general truth which we can assert of all things. It 
 is the very nature of existence that a thing cannot be 
 otherwise than it is ; and it may be safely said that all 
 fallacy and error arise from unwittingly reasoning in a 
 way inconsistent with this law. All statements or in- 
 ferences which imply a combination of contradictory 
 qualities must be taken as impossible and false, and the 
 breaking of this law is the mark of their being false. 
 It can easily be shown that if Iron be a metal, and 
 every metal an element, Iron must be an element or it 
 can be nothing at all, since it would combine qualities 
 which are inconsistent. 
 
 (3) The Law of Excluded Middle is much less self- 
 evident than either of the two preceding ones, and the 
 learner will not perhaps see at the first moment that it 
 is equally important and necessary with them. Its 
 meaning may be best explained by saying that it is im- 
 possible to mention any thinfi and any qnalUy or cir- 
 cumstance, without allowing that the quality op circum- 
 stance either belongs to the thing or does not belong. 
 The name of the law expresses the fact that there is no 
 third or middle course ; the answer must be Yes or No. 
 Let the thing be rock and the quality hard; then rock 
 must be either hard or not-hard. Gold must be either 
 white or not white; a line must be either straight or 
 not straight ; an action must be either virtuous or not 
 virtuous. Indeed, when we know nothing of the terms 
 used we may nevertheless make assertions concerning 
 them in accordance with this law. The learner may 
 not know, and in fact chemists may not really know 
 with certainty, whether vanadium is a metal or not a
 
 LAWS OF THOUGHT. 107 
 
 metal, but any one knows that it must be one or the 
 other. Some learners may not know what a cycloid is, 
 or what an isochronous curve is ; but they must know 
 that a cycloid is either an isochronous curve or it is 
 not an isochronous curve. 
 
 This law of excluded middle is not so evident but that plausible 
 objections may be suggested to it. Rock, it may be urged, is 
 not always either hard or soft, for it may be half-way between, 
 a little hard and a little soft at the same time. This objection 
 points to a distinction which is of great logical importance, and 
 when neglected often leads to fallacy. The law of excluded 
 middle affirmed nothing about hard and soft, but only referred to 
 hard and not-hard ; if the reader chooses to substitute soft for 
 not-hard he falls into a serious confusion between opposite terms 
 and contradictory terms. It is quite possible that a thing may 
 be neither hard nor soft, being halfway between; but in that 
 case it cannot be fairly called hard, so that the law holds true. 
 Similarly water must be either warm or not-warm, but it does 
 not follow that it must be warm or cold. The alternative not- 
 warm evidently includes all cases in which it is cold besides 
 cases where it is of a medium temperature, so that we should call 
 it neither warm nor cold. We must thus carefully distinguish 
 questions of degree or quantity from those of simple logical 
 fact. In cases where a thing or quality may exist to a greater or 
 less extent there are many alternatives. Warm water, for in- 
 stance, may have any temperature from 70 perhaps up to 120'. 
 Exactly the same question occurs in cases of geometrical reason- 
 ing ; for Euclid in his Elements frequently argues from the self- 
 evident truth that any line must be either gre.-iter than, equal to, 
 or less than any other line. While there are only two alternatives 
 to choose from in logic there are three in Mathematics ; thus one 
 line, compared with another, may be 
 
 ! greater greater ) j^^ 
 
 not greater. . j ; ; ; '^^^^ \ Mathematics. 
 
 Another and even more plausible objection may be raised to
 
 108 SYLLOGISMS. 
 
 the third law of thought in this way. Virtue being the thing 
 proi)()sed, and triangular the quality, the Law oi Excludeti 
 Middle euablea us at once to assert that virtue is either triangula? 
 or not triaiijjular. At first sight it might seem false and absurd 
 to say that an immaterial notion such as virtue should be either 
 triangular or not, because it has nothing in common with those 
 material substances occupying space to wliich the notion of figure 
 belongs. But the absurdity would arise, not from any falseness 
 in the law, but from misinterpretation of the expression not- 
 triangular. If in saying that a thing is "not triangular" we are 
 taken to imply that it has some figure though not a triangular 
 figure, then of course the expression cannot be applied to virtue 
 or anything immaterial. In strict logic, however, no such im- 
 plied meaning is to be allowed, and not-triangular will include 
 both things which iiave figure other than triangular, as well as 
 things wiiich have not the properties of figure at all ; and it is 
 in the latter meaning that it is applicable to an immaterial thing 
 
 3. The Canons of Syllogism. 
 
 These three laws then being universally and neces- 
 sarily true to whatever things they are applied, become 
 the foundation of reasoning. All acts of reasoning 
 proceed from certain judgments, and the act of judg- 
 ment consists in comparing two things or ideas together 
 and discovering whether they agree or differ, that is to 
 say whether they are identical in any qualities. The 
 laws of thought inform us of the very nature of this 
 identity with which all thought is concerned. But in 
 the operation of discourse or reasoning we need certain 
 additional laws, or axioms, or self-evident truths, which 
 may be thus stated : 
 
 1. Ttoo terms agreeing with one and the same third 
 term agree wi/h each other. 
 9. Two terms of which one agrees and the other doet
 
 LA.WS OF THOUGHT. IM 
 
 noi agree with one and the same third term, do not agret 
 with eacli other. 
 
 3. Two terms both disagreeing with one and the sanu 
 third term may or may not agree ivith each other. 
 
 These self-evideut truths are commonly called the 
 Canons or Fundamental Principles of Syllogism. 
 
 They are true, whatever may be the kind of agreement in 
 question. The example we formerly used (p. 3) of the aj^ree- 
 ment of the terms " Most useful metai " and " cheapest metal " 
 with the third common term '* Iron," was but au instance of the 
 first Canon, and the agreement consisted in complete identity. 
 In the case of the " Earth," the " Planets," and " Bodies revolv- 
 ing in elliptic orbits," the agreement was less complete, because 
 the Earth is only one of many Planets, and the Planets only a 
 email portion of all the heavenly bodies, such as Satellitea 
 Comets, Meteors, and Double-Stars which revolve in such orbita 
 
 The second of the Canons applies to cases where there is di 
 agreement or difference, as in the following example : 
 
 Venus is a planet. 
 
 Planets are not self-luminous. 
 
 Therefore Venus is not selflumlnona 
 
 The first ol these propositions states a certain agreement to 
 xist between Venus and planet, just as in the previous case of 
 the Earth, but the second proposition states a disatjreement 1)e 
 tween Planet and self luminous bodies; hence we infer a dis- 
 agreement between Venus and self luminous body. But the 
 (earner will carefully observe that /rom tiM disagree ments ire can 
 never infer anything. If the following were put forth as au 
 argument it would be evidently absurd : 
 
 Sirtus is not a planet. 
 Planets are not self-luminous. 
 Therefore Sirius is not self-luminou* 
 
 %)th the premises or propositions given are true, and yet thi
 
 110 SYLLOGISMS. 
 
 conclasion is false, for all the fixed stars are self-laTninotrit, h 
 shine by their own light. This illustrates the third Canon. 
 
 4. The Axioms of Mathematics. 
 
 Self-evident rules, of an exactly similar nature tfi 
 these three Canons, are the basis of all mathematical 
 reasoning, and are usually called axioms. Euclid's first 
 axiom is that "Things which are equal to the samo 
 thing are equal to one another;" and whether we 
 apply it to the length of lines, the magnitude of angles, 
 areas, solids, numbers, degrees, or anything else which 
 admits of being equal or unequal, it holds true. Thuf 
 if the lines A and B are each equal to (7 it is evider:1 
 ihat each is equal to the other. 
 
 A 
 
 B 
 
 E. 
 
 Euclid does not give axioms correspondmg to the 
 second and third Canons, but they are really used in 
 Geometry. Thus if A is equal to B, but D is not 
 equal to B, it follows that A is not equal to D, or 
 things of which one is equal, but the other unequal to 
 the same third thing, are unequal to each other. Lastly, 
 A and E are two lines both unequal to D and un- 
 equal to each other, whereas A and B are two lines both 
 unequal to D but equal to each other; thus we plainly 
 3ee that *' two things both unequal to the same thing 
 may or may not be equal to each other." 
 
 Prom what prectsdes it will be apparent that all reasoning ra-
 
 LAWS OF THOUGHT. Ill 
 
 quires tht there should be one agreement at least; if there 
 
 be iwo agi-eements we may reason to a third agreement ; if there 
 be oue agreement and one difference we may reason to a second 
 diflference ; but if there be two differences only we cannot reason 
 to an/ conclusion whatever. These self-evident principles will 
 in thu next Lesson serve to explain some of the rules of the 
 Syllogism. 
 
 5. Aristotle's Dicta. 
 
 Logicians, however, have not confined themselvas to 
 the use of these Canons, but have often put the same 
 truth into a different form in axioms known as the 
 Dicta de omni et nullo of Aristotle. This celebrated 
 Latin phrase means "Statements concerning all and 
 none," and the axiom, or rather pair of axioms, is 
 usually given in the following words : 
 
 Whatever is predicated of a term distributed^ lohetlier 
 affirmatively or negatively, may he predicated in like 
 maimer of everything contained under it. 
 Or more briefly: 
 
 What pertains to the higher class pertains also to the 
 lower. 
 
 This merely means, in untechnical language, that what may 
 be said of all tlie tilings of any sort or kind may be said of any 
 one or any part of those things ; and, secondly, what may be 
 denied of all the things in a class may be denied of any one or 
 any part of them. Whatever may be said of " All planets " may 
 be said of Venus, the Earth, Ju]iter, or any other planet ; and, 
 as they may all be said to revolve in elliptic orbits, it follows 
 that this may be asserted of Venus, the Earth, Jupiter, or any 
 other planet. Similarly, according to the negative part of the 
 Dicta, we may deny that the planets are self luminous, and know- 
 ing that Jupiter is a planet may deny that Jupiter is self-lumi- 
 nous. A little reflection would show that the affirmative Dictum 
 is really the first of the Canons in a less complete and general 
 form, and that the negative Dictuna is similarly the second
 
 1 12 SYLLOGISMS. 
 
 Canon. These Dicta, in fact, only apply to sucli cases of agree 
 went between terms as consist in one being the name of a smaller 
 class, and another of the larger class containing it. Logicians 
 have for the most part strangely overlooked the important cases 
 in which one term agrees with another to the extent of being 
 identical with it ; but this is a subject which we cannot fitly dis- 
 cuss here at any length. It is treated in my little work called The 
 Substitution of Similars* 
 
 Some logicians have held that in addition to the three laws 
 which are called the Primary Laws of Tljought, there is a fourth 
 called " The Principle or Law of Sufficient Reason." It was 
 stated by Leibnitz in the following words : 
 
 " Nothing happens without a reasfm why it should be so rather 
 than otherwise. For instance, if there be a pair of scales in every 
 respect exactly alike on each side and with exactly equal weights 
 in each scale, it must remain motionless and in equilibrium, be- 
 cause there is no reason why one side should go down more than 
 the other. It is certainly a fundamental assumption in mechani 
 cal science that if a body is acted upon by two perfectly equal 
 ibrces in diflFerent directions it will move equally between them, 
 because there is no reason why it should move more to one side 
 than the other. Mr. Mansel, Sir W. Hamilton and others consider, 
 however, that this law has no place in logic, even if it can be 
 held self-evident at all ; and the question which appears open to 
 doubt need not be discussed here. 
 
 I have so freely used the word axiom in this lesson that it is 
 desirable to clear up its meaning as far as jiossible. Philosophers 
 do not perfectly agree about its derivation or exact meaning, but 
 it certainly comes from the verb uiinu, which is render*^, to think 
 toortky. It generally denotf^s a self evident truth of so simple a 
 character that it must be assumed to be true, and, as it cannot 
 be proved by any simpler proposition, must itself be taken as the 
 basis of reasoning. In mathematics it is clearly used in this 
 iense. 
 
 See Hamilton's Lectures on Logic, Lectures 5 and 6. 
 Macmillan A Co.. 1869.
 
 LAWS OF THOIJQHT. 113 
 
 In this Section, on "Tiie Laws of Thought," we 
 have considered: 
 
 1. SUitenient of the PHiuary Laws of Thought, 
 
 2. The Explanation of tfie Laws. 
 
 3. The Canons of the Syllogism. 
 
 4. The Axioms of Mathematics. 
 
 5. Aristotle^s I>lcta 
 
 SEGTIOH n, 
 
 THE RULES OF THE SYLLOGISM. 
 
 1. The Definition of "Syllogism." 
 
 Syllogism is the common name for mediate inference, 
 or inference bj a medium or middle term, and is to be 
 
 distinguislied from the process of immediate inference, 
 or inference which is performed without the use of any 
 third or middle term. 
 
 The name Syllogism means the joining together in 
 thought of two propositions, and is derived from the 
 Greek words avv, with, and Xoyoq, thought or reason. 
 It is thus exactly the equivalent of the word Computa- 
 tion, which means thinking together, (Latin con, to- 
 gether, puto, to think), or reckoning. lu a syllogism 
 we so unite in thought two premises, or propositions 
 put forward, that we are enabled to draw from them or 
 infer, by means of the middle term they contain, a 
 third proposition called the conclusion. SyUogism may 
 thus be defined as the act of thought by which from 
 two given propositions we proceed to a third proposi-
 
 114 SYLLOGISMS. 
 
 tion, the truth of which 'necessarily follows from 
 the truth of these given propositions. When the 
 argument is fully expressed in language it is usual to 
 call it concretely a syllogism. 
 
 2. The Meaning of "Middle Term." 
 
 We are in the habit of employing a middle term, oi 
 medium, whenever we are prevented from comparing 
 two things together directly, but can compare each 
 of them with a certain third thing. We cannot com- 
 pare the sizes of two halls by placing one in the other, 
 but we can measure each by a foot-rule or other suit- 
 able measure, which forms a common measure, and 
 enables us to ascertain with any necessary degree of 
 accuracy their relative dimensions. If we have two 
 quantities of cotton goods and want to compare them, it 
 is not necessary to bring the whole of one portion to 
 the other, but a sample is cut off, which represents 
 exactly the quality of one portion, and, according as 
 this sample does or does not agree with the other por- 
 tion, so must the two portions of goods agree or differ. 
 
 3. The Use of Middle Term in Syllogism. 
 
 The use of a middle term in syllogism is closely 
 parallel to what it is in the above instances, but not 
 exactly the same. Suppose, as an example, that we 
 wish to ascertain whether or not " Whales are vivipa- 
 rous," and that we had not an opportunity of observ- 
 ing the fact directly ; we could yet show it to be so ii 
 we knew that " whales are mammalian animals," and 
 that "all mammalian animals are viviparous." It 
 would follow that " whales are viviparous ; " and so
 
 LAWS OF THOUGHT. 115 
 
 far as the inference is concerned it does not mattei 
 what is the meaning we attribute to the words vivip 
 arous and mammalian. In this caee " mammaliai 
 animal " is the middle term. 
 
 4. Statement of the Rules of the Syllogism, 
 
 The special rules of the syllogism are founded upou 
 the Laws of Thought and the Canons considered in the 
 previous section. They serve to inform us exactly 
 under what circumstances one proposition can be in- 
 ferred from two other propositions, and are eight in 
 number, as follows : 
 
 1. Every syllogism has three and only three terms. 
 These terms are called the major term, the minor 
 
 term, and the middle term. 
 
 2. Every syllogism contains three, and only three 
 propositions. 
 
 These propositions are called the major premise, the 
 minor premise, and the conclusion. 
 
 3. The middle term must be distributed once at least, 
 and must not be ambiguous. 
 
 4. iVb term must be distributed in the conclusion 
 which was not distributed i7i one of the premises. 
 
 5. From negative premises nothing can be inferred. 
 
 6. If one 'premise be negative, the conclusion must be 
 negative ; and vice versa, to prove a negative conclusion 
 one of the premises must be fiegative. 
 
 From the above rules may be deduced two subordi- 
 nate rules, which it will nevertlieless be convenient to 
 state at once. 
 
 7. From tiuo particular premises no conclusion can h 
 drawn.
 
 116 SYLLOGISMS. 
 
 8. If one premise he particular, the conclusion must 
 ie particular. 
 
 All these rules are of such extreme importance tuat it will be 
 desirable for the student not only to acquire a perfect comprehen- 
 sion of their meaning and truth, but to commit them to memory. 
 During the remainder of this section we shall consider theii 
 meaning and force, 
 
 5. Explanation of the Rules. 
 
 The following is a detailed explanation of each of the 
 rules already stated : 
 
 (1) The First Rule. As the syllogism consists in 
 compariflg two terms by means of a middle term, there 
 cannot of course be less than three terms, nor can there 
 be more ; for if there were four terms, say A, B, C, D, 
 and we compared A with B and G with D, we should 
 either have no common medium at all between A and 
 Z>, or we should require a second syllogism, so as first 
 to compare A and Cwith -B, and then A and D with 0. 
 
 The middle term may always be known by the fact 
 that it does not occur in the conclusion. The major 
 term is always the predicate of the conclusion, and the 
 minor term the subject. These terms are thus called 
 because in the universal aflBrmative proposition (A) the 
 predicate is necessarily a wider or greater or major 
 term than the subject ; thus in "all men are mortals," 
 the predicate includes all other animals as well as men, 
 and is obviously a major term or wider term than men. 
 
 (2) The Second Rule. The syllogism necessarily 
 consists of a premise called the major premise, in which 
 the maior and middle terma are compared together ; of
 
 LAWS OF THOUOm. 117 
 
 a minor premise which similarly compares the minor 
 and middle terms ; and of a conclusion, which contains 
 the major and minor terms only. In a strictly correct 
 syllogism the major premise always stands before the 
 minor premise, but in ordinary writing and speaking 
 this rule is seldom observed ; and that premise which 
 contains the major term still continues to be the major 
 premise, whatever may be its position. 
 
 (3) The third rule is a very important one, because 
 many fallacies arise from its neglect. By the middle 
 term being distributed once at least, we mean (see p. 
 79) that the whole of it must be referred to universally 
 in one premise, if not both. The two propositions 
 
 All Frenchmen are Europeans, 
 
 All Russians are Europeans, 
 do not distribute the middle term at all, because they 
 are both aflBrmative propositions, which have (p. 80) 
 undistributed predicates. It is apparent that French- 
 men are one part of Europeans, and Russians another 
 part, as shown in Enter's method in Fig. 6, so that 
 
 Fig. 6. 
 
 there is no real middle term. Those propositions would 
 equally allow of Russians being or not being French-
 
 118 SYLLOGISMS. 
 
 men ; for whether the two interior circles overlap or 
 not they are equally within the larger circle of Euro- 
 peans. Again, the two propositions 
 
 All Frenchmen are Europeans, 
 All Parisians are Europeans, 
 
 do not enable us to infer that all Parisians are French- 
 men. For though we know of course that all Parisians 
 
 Pig. 7. 
 
 are included among Frenchmen, the premises would 
 allow of their being placed anywhere within the circle 
 of Europeans. We see in this instance that the prem- 
 ises and conclusion of an apparent argument may all be 
 true and yet the argument may be fallacious 
 
 The part of the third rule which refers to an ambiguous middle 
 term hardly requires explanation. It has been stated (Chap. I, 
 Sect. 2.) that an ambiguous term is one which has two different 
 meanings, implying different connotations, and it is really equiv- 
 alent to two different terms wliich happen to have the same form 
 of spelling, so that they are readily mistaken for each other. 
 Thus if we were to argue that because "all metals are elements 
 and brass is metal, therefore it is an element," we should be 
 oommitting a fallacy by using the middle term metal in two dif-
 
 LAWS OF THOUGHT. 119 
 
 ferent senses, in one of which it means the pure simple sub- 
 stances known to chemists as metals, and in the other a mixture 
 of metals commonly called metal in the arts, but known to 
 chemists by the name alloy. In many examples which may be 
 found in logical books the ambiguity of the middle term is ex- 
 ceedingly obvious, but the reader should always be prepared to 
 meet with cases where exceedingly subtle and difficult cases of 
 ambiguity occur. Thus it might be argued that ' ' what is right 
 should be enforced by law, and that charity is right and should 
 therefore be enforced by the law." Here it is evident that rigJit 
 is applied in one case to what the conscience approves, and in an- 
 other case to what public opinion holds to be necessary for the 
 good of society. 
 
 (4) The fourth rule forbids us to distribute a term in 
 the conclusion unless it was distributed in the premises. 
 As the sole object of the syllogism is to prove the con- 
 clusion by the premises, it is obvious that we must not 
 make a statement concerning anything unless that 
 thing was mentioned in the premises, in a way warrant- 
 ing the statement. Thus if we were to argue that 
 " because many nations are capable of self-government 
 and tliat nations capable of self-government should not 
 receive laws from a despotic government, therefore no 
 nation should receive laws from a despotic govern- 
 ment," we should be clearly exceeding the contents of 
 our premises. The minor term, many nations, was 
 particular in the minor premise, and must not be made 
 universal in the conclusion. The premises do not. 
 warrant a statement concerning anything but the mayiy 
 nations capable of self-government. The above argu- 
 ment would therefore be fallacious and would be tech- 
 nically called an illicit process of the minor term, mean- 
 ing that we have improperly treated the minor term.
 
 120 SYLLOGISMS. 
 
 Such a breach of the fourth rule as is described above 
 is exceedingly easy to detect, and is therefore very sel- 
 dom committed. 
 
 But an illicit process or improper treatment of the 
 major term is more common because it is not so trans- 
 parently false. If we argued indeed that ''because all 
 Anglo-Saxons love liberty, and Frenchmen are not 
 Anglo-Saxons, therefore they do not love liberty," the 
 fallacy would be pretty apparent ; but without a knowl- 
 edge of logic it would not be easy to give a clear ex- 
 planation of the fallacy. It is apparent that the major 
 term loving liberty, is undistributed in the major prem- 
 ise, so that Anglo-Saxons must be assumed to be only a 
 part of those who love liberty. Hence the exclusion 
 of Frenchmen from the class Anglo-Saxons does not 
 necessarily exclude them from the class who love liberty 
 (see Fig. 8). The conclusion of the false argument 
 
 Pio. 8. 
 
 Loving Liberty 
 Saxona j \__^/ 
 
 being negative distributes its predicate, the major term, 
 and as this is undistributed in the major premise we 
 have an illicit major, as we may briefly call this fal- 
 lacy.
 
 LAWS OF THOUGHT. 121 
 
 The following is an obscurer example of tlie same fallacy : 
 'Few students are capable of excelling in many branches o( 
 knowledge, and such as can so excel are deserving of high com- 
 mendation;" hence, "few students are deserving of high com- 
 mendation." The little word " few " has here the double mean< 
 ing before explained (p. 71), and means that " a few are, etc., and 
 the rest are not." The conclusion is thus really a negative prop- 
 osition, and distributes the major term "deserving of high com- 
 mendation." But this major term is clearly undistributed in the 
 major premise, which merely asserts tliat those who can excel in 
 many branches of knowledge are deserving, but says or implies 
 nothing about other students. 
 
 (5) The fifth rule is evidently founded on the prin- 
 ciple noticed in the last lesson, that inference can only 
 proceed where there is agreement, and that two differ- 
 ences or disagreements allow of no reasoning. Two 
 terms, as the third Canon states, may both differ from 
 a common term and yet may or may not differ from 
 each other. Thus if we were to argue that Americans 
 
 Pig. 9. 
 
 are not Europeans, and Virginians are not Europeans, 
 we see that both terms disagree with the middle term 
 6
 
 123 SYLLOGISMS. 
 
 Europeans, and yet they agree between themselves. In 
 other cases the two negative premises may be plainly 
 true while it will be quite uncertain whether the major 
 and minor terms agree or not. Thus it is true, for 
 instance, that " Colonists are not Europeans and Amer- 
 icans are not Europeans," but this gives us no right to 
 infer that Colonists are or are not Americans. The 
 two negative premises are represented in Fig. 9, by ex- 
 cluding the circles of Colonists and Americans from 
 that of Europeans ; but this exclusion may still be 
 effected whether Colonists and Americans coincide par- 
 tially, or wholly, or not at all. A breach of this rule 
 of the syllogism may be conveniently called the fallacy 
 of negative premises. It must not, however, be sup- 
 posed that the mere occurrence of a negative particle (not 
 or no) in a proposition renders it negative in the man- 
 ner contemplated by this rule. Thus the argument 
 
 " What is not compound is an element. 
 
 Gold is not compound ; 
 
 Therefore Gold is an element," 
 contains negatives in both premises, but is nevertheless 
 valid, because the negative in both cases affects the 
 middle term, which is really the negative term not-com- 
 pound. 
 
 (6) The sixth rule. The truth of the sixth rule 
 depends upon that of the axiom, that if two terms 
 agree with a common third term they agree with each 
 other, whence, remembering that a negative proposi- 
 tion asserts disagreement, it is evident that a negative 
 conchision could not be drawn from really affirmative 
 premises. The corresponding negative axiom prevents 
 our drawing an affirmative conclusion if either premise
 
 LAWS OF THOUGHT. 123 
 
 should be really negative. Only practice, however, will 
 enable the student to apply this and the preceding 
 rules of the syllogism with certainty, since fallacy may 
 be hidden and disguised by various forms of expression. 
 Numerous examples are given at the end of the book by 
 which the student may acquire facility in the analysis 
 of arguments. 
 
 The remaining rules of the syllogism, the 7th and 8th, 
 are by no means of a self-evident character and are in 
 fact corollaries of the first six rules, that is consequences 
 which follow from them. We shall therefore have to 
 show farther on that they are true consequences. We 
 may call a breach of the 7th rule & fallacy of particular 
 premises, and that of the 8th rule the fallacy of a uni- 
 versal conclusion from a particular premise, but these 
 fallacies may really be resolved into those of Illicit Pro- 
 cess, or Undistributed Middle. 
 
 For many details concerning the Aristotelian and 
 Scholastic Views of the Syllogism, and of Formal 
 Logic generally, see the copious critical notes to 
 Hansel's edition of Aldrich's Artis LogiccB Rudi- 
 menta. Second Edition. Oxford. 1852. 
 
 In this section, on "The Rules of the Syllo- 
 sfism,*' we have considered : 
 
 1. The Definition of * Syllogism.'^ 
 
 2. TJie Meaning of " Middle Term,'* 
 
 3. TJie Use of Middle Term in Sijllogism. 
 
 4. The Statement of the Bnles of the Syllogism. 
 
 5. Tlie Explanation of the Rules of the Syllo- 
 gism..
 
 124 SYLLOGISMS. 
 
 SECTION in. 
 
 THE MOODS AND FIGURES OF THE SYLLO- 
 GISM. 
 
 1. Explanation of "Moods." 
 
 We are now in full possession of those principles oi 
 reasoning, and the rules founded upon them, by which 
 a true syllogism may be known from one which only 
 seems to be a true one, and our task in the present sec- 
 tion is to ascertain the various shapes or fashions in 
 which a process of mediate inference or syllogism maj 
 be met with. We know that every syllogistic argument 
 must contain three propositions and three distinct terms 
 each occurring twice in those propositions. Each prop- 
 osition of the syllogism may, so far as we yet know, be 
 either affirmative or negative, universal or particular, 
 so that it is not difficult to calculate the utmost possible 
 number of modes in which a syllogism might conceiv- 
 ably be constructed. Any one of the four propositions 
 A, E, I, or O may in short be taken as a major premise, 
 and joined with any one of the same form as a minor 
 premise, and any one of the four again may be added 
 as conclusion. We should thus obtain a series of the 
 combinations or modes of joining the letters A, E, I, O, 
 a few of which are here written out : 
 
 AAA 
 
 AEA 
 
 AIA 
 
 AOA 
 
 EAA 
 
 EEA 
 
 AAE 
 
 AEE 
 
 AIE 
 
 AOE 
 
 EAE 
 
 EEE 
 
 AAI 
 
 AEI 
 
 All 
 
 AOI 
 
 EAI 
 
 EEI 
 
 AAO 
 
 AEO 
 
 AIO 
 
 AOO 
 
 EAO 
 
 Ac. 
 
 [t is obvious that there will be altogether 4 x 4 X 4 or 64
 
 MOODS AND FIGUBB8. 125 
 
 sticli combinations, of which "Z'i only are given above. 
 The student can easily write out the remainder by 
 carrying on the same systematic changes of the letters. 
 Thus beginning with AAA we change the right-hand 
 letter successively into E, I, and 0, and then do the 
 same, beginning with AEA instead ; after the middle 
 letter has been carried through all its changes we begin 
 to change the left-hand letter. With each change of 
 this we have to repeat all the sixteen changes of the 
 other letters, so that there will obviously be altogether 
 64 diflferent conceivable modes of arranging propositions 
 into syllogisms. We call each of these triplets of prop- 
 ositions a mood or form of the syllogism (Latin moaus, 
 shape). 
 
 2. The Number of Valid Moods. 
 
 We have to consider how many of such forms caR 
 really be used in valid arguments, as distinguished from 
 those which break one or more of the rules of the syllo- 
 gism. Thus the mood AEA would break the 6th rule, 
 that if one premise be negative the conclusion must be 
 so too; AIE breaks the converse part of the same rule, 
 that a negative conclusion can only be proved by a 
 negative premise ; while EEA, EEE, etc., break the 5th 
 rule, which prohibits our reasoning at all from two 
 negative premises. Examples of any of these moods 
 can easily be invented, and their falsity would be very 
 apparent; thus for AEA we might take 
 
 All Austrians are Europeans, 
 No Australians are Europeans ; 
 Therefore, all Australians are Austrians.
 
 126 SYLLOGISMS. 
 
 Many of the 64 conceivable moods are excluded by the 
 7th and 8th rules of the syllogism. Thus AIA and EIE 
 break the rule, that if one premise be particular the 
 conclusion must be so also, while IIA, 100, 010 and 
 many others, break the rule against two particular 
 premises. Some combinations of propositions may break 
 more than one rule ; thus 000 has both negative 
 premises and particular premises, and OOA also violates 
 as well the Gth rule. It is an admirable exercise in the 
 use of the syllogistic rules to write out all the 64 com- 
 binations and then strike out such as break any rule ; 
 the task, if pursued systematically, will not be so long 
 or tedious as might seem likely. It will be found that 
 there are only twelve moods which escape exclusion, 
 and may so far be considered good forms of reasoning, 
 and these are 
 
 AAA EAE lAI OAO 
 
 AAI EAO (lEO) 
 
 AEE EIO 
 
 AEO 
 
 All 
 
 AOO 
 
 Of these, however, lEO will have shortly to be rejectea, 
 because it will be found really to break the 4th rule, 
 and involves illicit process of the major term. There 
 are, then, only eleven moods of the syllogism which are 
 really valid ; and we may thus account for the whole of 
 the sixty-four moods. 
 
 No. of 
 Excluded by Moods 
 
 Negative premises, Rule 5 16 
 
 Particalar premises, " 7 12 
 
 One negative premise, " 6 13 
 
 One premise particular, " 8 8
 
 MOODS AND FIGURES. 127 
 
 No. af 
 Excluded by Mooda. 
 
 Negative conclusion. Rule 6 4 
 
 Illicit major ** 4 1 
 
 Total excluded 53 
 
 Valid moods 11 
 
 Total 64 
 
 3. Explanation of ** Figures.*' 
 
 We have by no means exhausted as yet all the pos- 
 sible varieties of the syllogism, for we have only deter- 
 mined the character, aflBrmative or negative, general or 
 particular of the propositions, but have not decided the 
 ways in which the terms may be disposed in them. 
 The major term must be the predicate of the conclusion, 
 but it may either be subject or predicate of the major 
 premise, and similarly the minor term or subject of the 
 conclusion, may be either the subject or predicate of 
 the minor premise. There thus arise four different 
 ways, or as they are called Figures, in which the terms 
 can be disposed. These four figures of the syllogism 
 are shown in the following scheme, taking 
 
 X to denote the major term 
 
 Y middle 
 
 Z minor " 
 
 Fig. 1. Fig. 2, Pig. 3. Pig. 4. 
 
 Major Premise YX XY YX XY 
 
 Minor " Z Y Z Y Y Z Y Z 
 
 Conclusion Z X Z X Z X Z X 
 
 These figures must be carefully committed to memory, 
 which will best be done by noting the position of tha
 
 128 SYLLOGISMS. 
 
 middle term, This term stands first as subject of the 
 major premise in the 1st Figure, second as predicate in 
 both premises of the 2d Figure, first again as subiecl 
 of both premises in the 3d Figure, and in an inter- 
 mediate position in the 4th Figure. In the conclusion, 
 of course, the major and minor terms have one fixed 
 position, and when the middle term is once correctly 
 placed in any figure we easily complete the syllogism. 
 
 The reader will hardly be pleased to hear that each of the 
 eleven valid moods will have to be examined in each of the four 
 figures separately, so that there are 44 cases still possible, from 
 which the valid syllogisms have to be selected. Thiis the mood 
 AEE in the first figure would be as follows : 
 
 All F's are X\ 
 No Z's are F's; 
 Therefore No Z'b are X's. 
 
 This would break the 4th rule and be an Illicit Major, because 
 Xis distributed in the conclusion, which is a negative proposi- 
 tion, and not in the major premise. In the second figure it would 
 be valid; 
 
 All X's are F's, 
 
 No Z'a are T s ; 
 Therefore No ^'s are Z 'a 
 
 In the third figure it becomes 
 
 All F's are X's, 
 
 No F's are Z's, 
 
 No Z'b are X's, 
 and again breaks the 4th rule, as reganls the major term. Lastly 
 in the 4th figure it is valid, as the reader may easily satisfy him- 
 self. 
 
 4. The Valid Moods in the Different Figrures. 
 
 When all the valid moods are selected out of tb 44
 
 MOODS AND FIGUKES. 
 
 IS$ 
 
 possible ones, there 
 
 are found to be altogether 24, whicb 
 
 are as follows: 
 
 
 
 Valid Moods of the Syllogism. 
 
 FWtt 
 Figure. 
 
 AAA 
 
 Second 
 Figure. 
 
 EAE 
 
 Third Fourth 
 Figure. figure. 
 
 AAI AAI 
 
 EAE 
 
 AEE 
 
 lAI AEE 
 
 All 
 
 EIO 
 
 All lAI 
 
 EIO 
 
 AOO 
 
 EAO EAO 
 OAO EIO 
 
 [AAI] 
 [EAO] 
 
 [EAO] 
 [AEO] 
 
 EIO 
 
 [AEO] 
 
 Five of the above moods are set apart and enclosed in bracketfl) 
 bcauBe though valid they are of little or no use. They are said 
 to have a weakened conclusion, because the conclusion is par- 
 ticular when a general one might have been drawn. Thus AAI, 
 in the first figure is represented by the example : 
 All material substances gravitate. 
 All metals are material substances , 
 Therefore some metals gravitate. 
 It is apparent that the conclusion only states a part ol the truth, 
 and that in reality aU metals grnvitate. It is not actually ax 
 erroneous conclusion, because it must be carefully remembered 
 (p. 84) that the affirminor of a subaltern or particular proposition 
 does not deny the corresponding general projxisitlon. It is quite 
 true that some metals gravitate, and it must be true because all 
 of them do so. But when we can as readily prove that all do 
 gravitate it is desirable to adopt this conclusion. 
 
 If we agree with most logicians to overlook the existence of 
 the five syllogisms with weakened conclusions, there will remain 
 nineteen which are at once valid and useful. In the nest section 
 certain ancient mnemonic lines will be furnished by which alone 
 it would be possible for most persons to carry in the memory 
 these 19 combinations ; but the reader will in the meantime be 
 able to gather from the statement of the moods above the truth 
 of the following remarks concerning the peculiar character of 
 each figure of the syllogism.
 
 ISO STLLOOISMS. 
 
 5. Conclusions Proved in the Different Pigrures. 
 
 (1) The first figure is the only one which proves the 
 proposition A, or has A for its conclusion. It is the 
 only figure, too, which can prove any one of the four 
 propositions A, E, I, 0. As regards the premises, it ia 
 especially important to note that the major premise is 
 always universal (A or E), and the minor premise aflBr- 
 mative (A or I) : this peculiarity will be further con- 
 sidered in the next lesson. 
 
 (2) The second figure proves only negative conclu- 
 sions (E or 0), and the reason is easily apparent. As 
 the middle term in this figure is the predicate of both 
 premises it would necessarily be undistributed in both 
 premises if these were affirmatives. It follows that one 
 premise must be negative and of course one only, so 
 that of the major and minor terms one must be in- 
 cluded or excluded wholly from the middle, and the 
 other at the same time excluded or included at least 
 partially. 
 
 To illustrate this we may take X, Y and Z to represent, as 
 before, the major, middle and minor terms of a syllogiRm, and 
 the four moods of this figure are then 
 
 EAE AEE 
 
 No X's are T% All X's are T's, 
 
 All Z'b are F's ; No Z 's are F's ; 
 
 .. No Z's are X'a. .'. No 27 are X'a. 
 
 ElO AOO 
 
 No X's are T% All X's are 7*8, 
 
 Some Z'b are F's ; Some Z'b are not F'sj 
 
 8om/> Zb are not X's. *. Some Z' are not X'b.
 
 MOODS AND FIQUBES. 
 
 131 
 
 The nature of the moods of the second figure Is clearlj 
 MhowD In the following figures : 
 
 Pig. 10. 
 (Cesare.) 
 
 
 Fig. 11. 
 (Camestres.) 
 
 Pig. 12. 
 (Testmo.} 
 
 It win also be observed that In the second figure the mlnoi 
 premise may be any of the four A, E, I, 0. 
 
 (3) The third figure only proves particulars (I or 0), 
 and it always has an affirmative minor premise (A or I). 
 It also contains the greatest number of moods, since in 
 no case is the conclusion a weakened one. 
 
 (4) The fourth figure is usually considered nnnatura' 
 and comparatively useless, because the same arguments 
 can be more clearly arranged in the form of the first 
 figure, which in some respects it resembles. Thus it 
 proves all the propositions except A, namely, E, I, O, 
 and its first mood AAI, is in reality a weakened form oi
 
 182 8YLL00ISMS. 
 
 AAA in the first figure. Many logicians, including in 
 recent times Sir W. Hamilton, have rejected the use ol 
 this figure altogether. 
 
 It is evident that tbe several figures of the syllogism possess 
 different characters, and logicians have thought that each figure 
 was best suited for certain special purposes. A Qerman logi 
 cian, Lambert, stated these purposes concisely, as follows : 
 " The first figure is suited to the discovery or proof of the prop- 
 erties of a thing; the second to the discovery or proof of the 
 distinctions between things ; the third to the discovery or proof 
 of instances and exceptions; the fourth to the discovery, or 
 exclusion, of the different species of genus." 
 
 It may be added that the moods Cesare and Camestres are often 
 used in disproving a statement, because they give a universal 
 negative conclusion, founded upon the exclusion of one class 
 from another. Thus if any one were still to assert that light con- 
 sists of material particles, it might be met by the following syUo- 
 gism; 
 
 "Material particles communicate impetus to 
 whatever they strike, 
 light does not communicate impetus to 
 whatever it strikes ; 
 Therefore light is not material particles." 
 
 The moods Baroko and Festino are less used, but allow of 
 particular conclusion being established. 
 
 When we wish, however, to establish objections or exceptions 
 to a general statement, which is indefed the natural way of meet- 
 ing it, we employ the third figure. The statement that "all 
 metals are solids " would at once be disproved by the exception 
 mereurp, as follows: 
 
 Mercury is not solid. 
 
 Mercury is a metal ; 
 
 Therefore some metal is not solid. 
 
 Were any one to assert that what is incomprehensible cannot 
 
 exist, we meet it at once with the argument that Infinity is in 
 
 comprehensible, but that infinity certainly exists, because w
 
 REDUCTION OF SYLLOGISMS. 133 
 
 cannot otherwise explain the nature of a curve line, or of a quan- 
 tity varying continuously ; therefore something that is incompre 
 hensible exists. In this case even one exception \a sufficient 
 entirely to negative the proposition, which really means that 
 because a thing is incomprehensible it cannot exist. But if one 
 incomprehensible thing does exist, others may also ; and all 
 authority is taken from the statement. 
 
 According to the Aristotelian system the third figure must also 
 be employed whenever the middle term is a singular term, be- 
 cause in Aristotle's view of the subject a singular term could not 
 stand as the predicate of a proposition. 
 
 In this section, on **The Moods and Figures 
 of the Syllogism," we have considered : 
 
 1. T7ie Explanation of Moods, 
 
 2. The Number of Valid Moods, 
 
 3. IVte Explanation of Fif/ures. 
 
 4. The Valid Moods in the Different Fif/ures. 
 
 5. Conclusions Proved in the Different Figures 
 
 8BGTI0IT lY. 
 
 THE REDUCTION OF SYLLOGISMS. 
 
 1. The Mnemonic Verses. 
 
 In order to facilitate the recollection of the nineteen 
 valid and useful moods of the syllogism, logicians in- 
 vented, at least six centuries ago, a most curious system 
 of artificial words, combined into mnemonic verses, 
 which may be readily committed to memory. This 
 device, however ingenious, is of a barbarous and wholly 
 unscientific character ; but a knowledge of its construc- 
 tion and use is still expected from the student of logic,
 
 184 SYLLOGISMS. 
 
 and the verses are therefore given and explained be. 
 law 
 
 Fiffure 1 i ^^^^^^> cElArEnt, dArll, fErlOque pri- 
 o^ * ( oris; 
 
 cs^^ 9 i cEsArE, cAmEstrEs, fEstluO, bArOkO 
 Uigure xj. -j ^^j. fAkOrO), secuudse ; 
 
 ( tertia, dArAptI, dIsAmIs, dAtlsI, f ElApt- 
 Figure 3. ] On, bOkArdO (or dOkAmO), fErlsOn, 
 
 ( habet ; quarta, insuper addit, 
 pj A j brAmAntIp, cAmEnEs, dImArls, fEsApO, 
 
 ^ ( frEsIsOn. 
 
 The words printed in ordinary type are real Latin words, signi- 
 fying that four moods whose artificial names are Barbara, Celarent. 
 Darii and Perio, belong to the first figure ; that four otheie be- 
 long to the second ; six more to the tliird ; while the fourth 
 figure moreover contains five moods. Each artificial name con- 
 tains three vowels, which indicate the propositions forming a 
 valid mood ; thus, GElAVKnt signifies the mood of the first figure, 
 which has E for a major premise, A for the minor, and E for the 
 conclusion. The artificial words altogether contain exactly the 
 series of combinations of vowels shown in the scheme for the 
 valid moods of the syllogism, excepting those in brackets. 
 
 2. Explanation of the Mnemonic Verses. 
 
 These mnemonic lines also contain indications of the 
 mode in which each mood of the second, third and 
 fourth figures can be proved by reduction to a corre- 
 sponding mood of the first figure. Aristotle looked 
 upon the first figure as a peculiarly evident and cogent 
 form of argument, the Dictum de omni et nullo being 
 directly applicable to it, and he therefore called it the 
 Perfect Figure. The fourth figure was never recog- 
 nized by him, and it is often called the Galenian figure,
 
 REDUCTION OF SYLLOGISMS. ISA 
 
 because the celebrated Galen is supposed to have dis- 
 covered it. The second and third figures were known 
 to Aristotle as the Imperfect Figures, which it was 
 necessary to reduce to the first figure by certain conver- 
 sions and transpositions of the premises, for which 
 directions are to be found in the artificial words. These 
 directions are as follows: 
 
 3 indicates that the proposition denoted by the pre- 
 ceding vowel is to be converted simply. 
 
 p indicates that the proposition is to be converted per 
 accide7is, or by limitation. 
 
 m indicates that the premises of the syllogism are to 
 be transposed, the major being made the minor of a 
 new syllogism, and the old minor the new major. The 
 m is derived from the Latin mutare, to change. 
 
 B, C, D, F, the initial consonants of the names, in- 
 dicate the moods of the first figure, which are produced 
 by reduction ; thus Cesare, Camestres and Camenes 
 are reducible to Celarent, Darapti, etc., to Darii, Fresi- 
 son to Ferio and so on. 
 
 k denotes that the mood must be reduced or proved 
 by a distinct process called Indirect reduction, or re- 
 ductio ad impossihile, which will shortly be considered. 
 
 Examples of Reduction. 
 
 (1) Direct Reduction. Let us now take some syllogism, say 
 In Camestres, and follow the directions for reduction. Let the 
 example be 
 
 All stars are self-luminous (1) 
 
 All planets are not self-luminous (3) 
 
 Therefore no planets are stars (3) 
 
 The first s in Camestres shows that we are to convert simplj 
 the minor premise. The m instructs us to change the order d
 
 1S6 SYLLOGISMS. 
 
 the premises, and the final to convert the conclusion simply 
 When all these changes are made we obtain 
 
 No self-luminous bodies are planets Converse of (3) 
 
 All stars are self-luminous (1) 
 
 Therefore no stars are planets Converse of (8) 
 
 This, it will be found, is a syllogism in Celarent, as might be 
 itnown from the initial G in Camestres. 
 As another example let us take Fesapo, for instance : 
 
 No fixed stars are planets. 
 All planets are round bodies: 
 Therefore some round bodies are not fixed stars. 
 
 According to the directions in the name, we are to convert 
 dmply the major premise, and by limitation the minor premisa 
 We liave then the following syllogism in Ferio : 
 
 No planets are fixed stars. 
 Some round bodies are planets ; 
 Therefore some round bodies are not fixed stars. 
 
 The reader will easily apply the same process of conversion or 
 transposition to the other moods, according to the directions 
 contained in their names, and the only moods it will be necessary 
 to examine especially are Bramantip, Baroko and Bokardo. Ab 
 %Q example of Bramantip we may take : 
 
 All metals are material substances. 
 All material substances are gravitating bodies ; 
 Therefore some gravitating bodies are metals. 
 The name contains the letter m, which instructs us to trans- 
 pose the premises, and the letter p, which denotes conversion by 
 imitation ; effectinj? these changes we have: 
 
 All material substances are gravitating bodies 
 All metals are material substances ; 
 Therefore some metals are gravitating bodies. 
 This is not a syllogism in Barbara, as we might have expected, 
 bat is the weakened mood AAI of the first figure. It is evident 
 tliat the premises yield the conclusion " all metals are gravitating 
 bodies," and we most take the letter p to indicate in this mood
 
 EEDUCTION OF SYLLOGISMS. 137 
 
 that the conclusion is weaker than it might be. In truth the 
 fourth figure is so imperfect and unnatural in form, containing 
 nothing but ill arranged syllogisms, which would have been 
 better stated in the first figure, that Aristotle, the founder of 
 logical science, never allowed the existence of the figure at alL 
 It is to be regretted that so needless an addition was made to the 
 somewhat complicated forms of tue syllogism. 
 
 (2) Indirect Reduction. The moods Baroko and Bokardo give 
 i. good deal of trouble because they cannot be reduced directly to 
 the first figure. To show the mode of treating these mooda we 
 will take X, Y, Z, to represent the major, middle and minor 
 terms of the syllogism, and Baroko may then be stated as fol 
 lows ; 
 
 All X's are Y'a, 
 Some Z's are not T's ; 
 Therefore Some Z'a are not X's. 
 
 Now if we convert the major premise by Contraposition (p. 89) 
 We have "all n()t-P''s are not-X's," and, making this the major 
 premise of the syllogism, we have 
 
 All not- T's are not X's, 
 Some Z's are not J^'s ; 
 Therefore Some Z's are not X's. 
 
 "Although both the above premises appear to be negative, this 
 '\B really a valid syllogism in Ferio, because two of the negative 
 particles merely affect the middle term (see p. 184), and we have 
 therefore effected the reduction of the syllogism. 
 
 Bokardo. when similarly stated, is as follows 
 Some Y's are not X's, 
 All Y'a are Z'a ; 
 Therefore Some Z's are not X's. 
 
 To reduce this, convert the major premise by negation, anfl 
 ihen transpose the premises. We have : 
 
 All F's are Z's, 
 Some not-X's are F's , 
 Thereiore Gome not-X's are Z's. 
 
 This conclusion \a the converse by negation of the former con
 
 138 SYLLOGISMS. 
 
 closion the truth of which is thus proved by redaction to a syllo 
 gism in Darii. 
 
 Both these moods, Baroko and Bokardo, may, however, b* 
 proved by a peculiar process of indirect reduction, closely anat 
 ogous to the indirect proofs often employed by Euclid in Geom- 
 etry. This process consists in supposing the conclusion of the 
 syllogism to be false, and its contradictory therefore true, when 
 a new syllogism can easily be constructed which leads to a con- 
 clusion contradictory of one of the original premises. Now it is 
 absurd in logic to call in question the truth of our own premises, 
 for the very purpose of argument or syllogism is to deduce a con- 
 clusion which will be true when the premises are true, 'i'he syl- 
 logism enables us to restate in a new form the information which 
 is contained in the premises, just as a machine may deliver to us 
 in a new form the material which is put into it. The machine, or 
 rather the maker of tiie machine, is not responsible for the quality 
 of the materials fximished to it, and similarly the logician is not 
 responsible in the least for the truth of his premises, but only 
 for their correct treatment. He must treat them, if he treat them 
 at all, as true ; and therefore a conclusion which requires the 
 falsity of one of our premises is altogether absurd. 
 
 To apply this method We may take Baroko, as before: 
 
 All X'b are F's (I) 
 
 Some Z'a are not F's (3) 
 
 Therefore Some Z'a are not X's (8) 
 
 If this conclusion be not true then its contradictory, "all Z*3 
 are X's," must of necessity be regarded as true (page 84). 
 Making this the minor premise of a new syllogism with the 
 original major premise we have : 
 
 All X's are F'b (1) 
 
 All Z's are X's contradictory of (3) 
 
 Hence All Z's are F's. 
 
 Now this conclusion in A, is the contradictory of our old minor 
 premise in 0, and we must either admit one of our own premises 
 to be false or allow that our original conclusion is true. The 
 latter is of course the alternative we choose.
 
 REDUCTION OF SYLLOGISMS. 189 
 
 We treat Bokardo in a very similar manner : 
 
 Some Y's are not X's (1) 
 
 All r's area's (2) 
 
 Therefore Some Z'a are not X's (8) 
 
 If this conclusion be not true, then "all Z'b are X'b" must b 
 true. Now we can make the syllogism : 
 
 All Z's are X's Contradictory of (3) 
 
 All T's are Z's (3) 
 
 Hence All F'a are X's. 
 
 Tliis conclusion is the contradictory of (1), the original major 
 premise, and as this cannot be allowed, we must either suppose 
 (2) the original minor premise to be false, which is equally im- 
 possible, or allow that our original conclusion is true. 
 
 It will be observed that in both these cases of Indirect Reduc- 
 tion or Proof we use a syllogism in Barbara, which fact is indi- 
 cated by the initial letters of Baroko and Bokardo. The same 
 process of Indirect proof may be applied to any of the other 
 moods, but it is not usual to do so. as the simpler ])rocess of 
 direct or as it is often called ostensive reduction is sufficient. 
 
 3. Conclusions from Particular Premises. 
 
 It will be remembered that when in Section 2 we 
 considered the rules of the syllogism, there were two 
 supplementary rules, the 7th and 8th, concerning par- 
 ticular premises, which were by no means of a self- 
 evident character, and which require to be proved by 
 the six more fundamental rules. We have now suffi- 
 ciently advanced to consider this proof with advantage. 
 The 7th rule forbids us to draw any conclusion from 
 two particular premises; now such premises must be 
 either II, 10, 01, or 00. Of these II contain no dis- 
 tributed term at all, so that the 3d rule, which requires 
 the middle term to be dtstributed, must be broken. 
 The premises 00 evidently break the 5th rule, against
 
 140 SYLLOGISMS. 
 
 negative premises. The conclusion of the pair 10 must 
 be negative by the 6th rule, because one premise is 
 negative; the major term therefore will be distributed, 
 but as the major premise is a particular affirmative it 
 cannot be distributed without committing the fallacy 
 of illicit process of the major, against rule 4. Lastly, 
 the premises 01 contain only one distributed term, the 
 predicate of the major premise. But as the conclusion 
 must be negative by rule 6th, the major term must be 
 distributed : we ought to have then in the premises two 
 distributed terms, one for the middle term, the other 
 for the major term ; but as the premises contain only a 
 single distributed term, we must commit the fallacy 
 either of undistributed middle or of illicit process of 
 the major term, if we attempt to draw any conclusion 
 at all. We thus see that in no possible case can a pair 
 of particular premises give a valid conclusion. 
 
 The 8th rule of the syllogism instructs us that if 
 one premise of a syllogism be particular the conclusion 
 must also be particular. It can only be sliown to be 
 true by going over all the possible cases and observing 
 that the six principal rules of the syllogism always re- 
 quire the conclusion to be particular. Suppose, for in- 
 stance, the premises are A and I ; then they contain 
 only one distributed term, the subject of A, and this is 
 required for the middle term by rule 3. Hence the 
 minor term cannot be distributed without breaking 
 rule 4, so that the conclusion must be the proposition I. 
 The premises AO would contain two distributed terms, 
 the subject oi A and the predicate of O ; but if wo were 
 to draw from them the conclusion E, the major and 
 minor terms would require to be distributed, so thai
 
 IBBEOULAB AND COMPOUND SYLLOGISMS. 141 
 
 the middle term would remain undistributed against 
 rule 3. The learner can easily prove the other cases 
 such as El by calculating the number of distributed 
 terms in a similar manner: it will always be found that 
 there are insufficient terms distributed in the premises 
 to allow of a universal conclusion. 
 
 In this section, on "The Reduction of Syllo- 
 gisms,'* we have considered : 
 
 1. The Mnetnonic Verses. 
 
 2. The Explanation of the Mnenotnic Verset, 
 
 3. Conclusions from Particular Premises, 
 
 SECTION Y. 
 
 IRREGULAR AND COMPOUND SYLLOGISMS. 
 
 1. Tlie Irregular Mode of Expressing Inferences. 
 
 It may seem surprising that arguments which are 
 met with in books or conversation are seldom thrown 
 into the form of regular syllogisms. Even if a com- 
 plete syllogism be sometimes met with, it is generally 
 employed in mere affectation of logical precision. In 
 former centuries it was, indeed, the practice for all 
 students at the universities to take part in public dis- 
 putations, during which elaborate syllogistic arguments 
 were put forward by one side and confuted by precise 
 syllogisms on the other side. This practice has not 
 been very long discontinued at the University of Ox- 
 ford, and is said to be still maintained in some conti
 
 142 SYLLOGISMS. 
 
 nental universities ; "but except in such school disputa- 
 tions it must be allowed that perfectly formal syllo- 
 gisms are seldom employed. 
 
 In truth, however, it Is not syllogistic arguments which 
 are wanting; wherever any one of the conjunctions, there- 
 fore, because, for, since, inasmuch as, consequently occurs, it is 
 certain that an inference is being drawn, and this will very prob- 
 ably be done by a true syllogism. It is merely the romplete 
 statement of the premises and conclusion, which is usually 
 neglected because the reader is generally aware of one or other 
 of the premises, or he can readily divine wliat is assuuied ; and 
 it is tedious and even oflfensive to state at full length what the 
 reader is already aware of. Thus, if I say "atmospheric air 
 must have weight because it is a material substance," I certainly 
 employ a syllogism ; but I think it quite needless to state the 
 premise, of which I clearly assume the truth, that "whatever 
 is a material substance has weight." The conclusion of the 
 syllogism is the first proposition, viz., "atmospheric air has 
 weight." The middle terra is "material substance," which doea 
 not occur in the conclusion ; the minor is "atmospheric air," and 
 the major, "having weight." The complete syllogism is evi- 
 dently : 
 
 All material substances have weight, 
 Atmospheric air is a material substance ; 
 Therefore atmospheric air has weight. 
 
 This is in the very common and useful mood Barbara. 
 
 2. Explanation of ** Entliynieme." 
 
 A syllogism when incompletely stated is usually called 
 an enthymeme, and this name is often supposed to be 
 derived from two Greek words (t'r, in, and Oviiog, mind), 
 80 as to signify that some knowledge is held by the 
 mind and is supplied in the form of a tacit, that is a 
 silent or understood premise. Most commonly this
 
 IKEEGULAR AND COMPOUND SYLLOGISMS. 143 
 
 will be the major premise, and then the enthjmeme 
 may be said to be of the First Order. Less commonly 
 the minor premise is unexpressed, and the enthymeme 
 is of the Second Order. Of this nature is the follow- 
 ing argument: "Comets must be subject to the law of 
 gravitation ; for this is true of all bodies wliich move in 
 elliptic orbits." It is so clearly implied that comets 
 move in elliptic orbits, that it would be tedious to state 
 this as the minor premise in a complete syllogism of 
 the mood Barbara, thus : 
 
 All bodies moving in elliptic orbits are subject to the 
 law of gravitation ; 
 
 Comets move in elliptic orbits ; 
 
 Therefore comets are subject to the law of gravita- 
 tion. 
 
 It may happen occasionally that the conclusion of a 
 syllogism is left unexpressed, and the enthymeme may 
 then be said to belong to the Third Order. This occurs 
 in the case of epigrams or other witty sayings, of which 
 the very wit often consists in making an unexpressed 
 truth apparent. Sir W. Hamilton gives as an instance 
 of this kind of enthymeme the celebrated epigram 
 written by Person the English scholar upon a contem- 
 porary German scholar : 
 
 '' The Germans in Greek 
 Are sadly to seek ; 
 Not five in five score. 
 But ninety-five more ; 
 All, save only Hermann, 
 And Hermann's a German." 
 
 It is evident that while pretending to make an excep-
 
 144 SYLLOGISMS. 
 
 tion of Hermann, the writer ingeniously insinuates 
 that since he is a German he has not a correct knowl- 
 edge of Greek. The wonderful speech of Antony over 
 the body of Caesar, in Shakspeare's greatest liistoricai 
 play, contains a series of syllogistic arguments of which 
 the conclusions are suggested only. 
 
 Even a single proposition may have a syllogistic 
 force if it clearly suggest to the mind a second premise 
 which thus enables a conclusion to be drawn. The ex- 
 pression of Home Tooke, " Men who have no rights 
 cannot justly complain of any wrongs," seems to be a 
 case in point ; for there are few people who have not 
 felt wronged at some time or other, and they would 
 therefore be likely to aigue, whether upon true or false 
 premises, as follows : 
 
 Men who have no rights cannot justly complain of 
 
 any wrongs ; 
 We can justly complain ; 
 Therefore we are not men who have no rights. 
 
 In other words, we have rights. 
 
 3. Prosyllogisins and Episylloj^i^isnis. 
 
 Syllogisms may be variously joined and combined 
 together, and it is convenient to have special names for 
 the several parts of a complex argument. Thus a syl- 
 logism which proves or furnishes a reason for one of 
 the premises of another syllogism is called a Prosyllo- 
 gism ; and a syllogism which contains as a promise tho 
 conclusion of another syllogism is called an Episyiio* 
 gism.
 
 IRREGULAR AND COMPOUND SYLLOGISM?, 14fi 
 
 Take the example : 
 
 All ^'s are A% 
 All (7 's area's; 
 Therefore all C's are A\ 
 But all D's are 6^'s ; 
 Therefore All D'a are ^'s. 
 
 This evidently contains two syllogisms in the mood 
 Barbara, the first of which is a Prosyllogism with 
 respect to the second, while the second is an Episyllo- 
 gism with respect to the first. 
 
 The peculiar name Epicheirema is given to a syllo- 
 gism when either premise is proved or supported by a 
 reason implying the existence of an imperfectly en- 
 pressed prosyllogism ; thus the form, 
 
 All B's are ^'s, for they are P's, 
 And all C"s are B% for they are Q's; 
 Therefore all C's are ^'s, 
 is a double Epicheirema, containing reasons for both 
 premises. The reader will readily decompose it into 
 three complete syllogisms of the mood Barbara. 
 
 4. Sorites. 
 
 A more interesting form of reasoning is found in the 
 chain of syllogisms commonly called the Sorites, from 
 the Greek word ocopog, meaning heap. It is usually 
 stated in this way : 
 
 All ^'s are ^'s, 
 All B's are C\ 
 All C's are D% 
 All D's are E's ; 
 Therefore all A'a are U'b.
 
 148 SYLLOGISMS. 
 
 The chain can be carried on to any length provided it 
 is perfectly consecutive, so that each term except the 
 first and last occurs twice, once as subject and once as 
 predicate. It hardly needs to be pointed out that the 
 sorites really contains a series of syllogisms imperfectly 
 ecpressed; thus 
 
 First Syllogism. Second Syllogism. Last Syllogism. 
 
 B'8 are C% C's are D's ; i>'s are B's. 
 
 A's are B'a ; A's are O's; J's are Z>'s; 
 
 .-. J's are C's. .*. A'b are Z>'s .'. A'b are JS'b. 
 
 Bach syllogism furnishes a premise to the succeeding 
 one, of which it is therefore the prosyllogism, and any 
 syllogism may equally be considered the episyllogism of 
 that which precedes. 
 
 In the above sorites all the premises were universal 
 and affirmative, but a sorites may contain one particu- 
 lar premise provided it be the first, and one negative 
 premise provided it be the last. The learner may 
 easily assnre himself by trial, that if any premise except 
 the first were particular the fallacy of undistributed 
 middle would be committed, because one of the middle 
 terms would be the predicate of one affirmative premise 
 and the subject of another particular premise. If any 
 premise but the last were negative there would be a 
 fallacy of illicit process of the major term. 
 
 It is not to be supposed that the forms of the syllogism 
 hitherto described are all the kinds of reasoning actually 
 employed in science or common life In addition to the hjpo- 
 thetical and disjunctive syllogisms and some other forms to be 
 described in succeeding sections, there are really mauy modes ot 
 reasoning of which logicians have not taken much notice as 
 ^et. This vna clearly pointed oat more than two htindred years
 
 lEREGULAB AND COMPOUND SYLLOGISMS. 147 
 
 ago by the writers of the Port Royal Logic, a work first printed 
 in the year 1662, but which has since been reprinted very often, 
 and translated into a great many languages. The book is named 
 from a place near Paris where a small religious community lived, 
 of which the authors of the book, namely Arnauld and Nicole, 
 and a contributor to it the great philosopher and mathematician 
 Pascal, were the most celebrated members. The Port Royal 
 Logic was to a considerable extent the basis of the well-known 
 Watts' Logic, but the reader can now be referred to an admirable 
 translation of the original work made by Professor Spencer 
 Baynes of St. Andrew's. 
 
 Many improvements of Logic may be found in this work, such 
 as the doctrine of Extension and Intension, already explained. 
 In the Ninth Chapter of the Third Part, moreover, it is wisely 
 pointed out that " little pains are taken in applying the rules oi'. 
 the syllogism to reasonings of which the propositions are com 
 plex, though this is often very difficult, and there are many 
 arguments of this nature which appear bad, but wliich are never, 
 theless very good ; and besides, the use of such reasonings is 
 much more frequent than that of syllogisms which are quite 
 simple." Some examples are given of the complex syllogisms 
 here referred to ; thus : 
 
 The sun is a thing insensible. 
 The Persians worship the sun ; 
 
 Therefore the Persians worship a thing insensible. 
 
 This is an argument which cannot be proved by the rules of 
 the syllogism, and yet it is not only evidently true, but is an ex- 
 ceedingly common kind of argument. Another example is as 
 follows : 
 
 The Divine Law commands us to honor kings ; 
 
 Louis XIV is a king ; 
 
 Therefore the Divine Law commands us to honor Ijouis XIV. 
 
 The reader will also find that arguments which are really quite 
 valid and syllogistic are expressed in language so that they 
 appear to have four distinct terms, and thus to break one of the 
 rules of the syllogism. Thus, if I say "Diamonds are combus- 
 tible, for they are composed of carbon and carbon is combustible,'
 
 148 SYLLOGISMS. 
 
 there are four terms employed, namely, diamonds, combustible\ 
 composed of carbon, and carbon. But it is easy to alter the con- 
 struction of the propositions so as to get a simple syllogism with- 
 jut really altering the sense, and we tlien have : 
 
 What is composed of carbon is combustible ; 
 
 Diamonds are composed of carbon ; 
 
 Therefore diamonds are combustible. 
 
 Elxamples are given at the end of the lxx)k of concise argu- 
 lOents, taken from Bacon's Essays and other writings, which the 
 (indent can reduce to the syllogistic form by easy alterations ; 
 ut it should be clearly understood that these changes are of an 
 cxtm-logical character, and belong more properly to the science 
 of language. . 
 
 6w Syllogisms in Extension and in Intension. 
 
 It may here be explained that the syllogism and the 
 sorites can be expressed either in the order of exten- 
 sion or that of intension. In regard to the number of 
 individual tilings the noble metals are part of the 
 metals, and the metals are part of the elements ; but in 
 regard to intension, that is to say the qualities implied 
 in the names, element is part of metal, and metal is 
 part of noble metal. So again in extension the genus 
 of plants Anemone is part of the order Ranunculacea?, 
 and this is part of the great class Exogens; but in in- 
 tension the character of Exogen is part of the character 
 of Ranunculaceae, and this is part of the character of 
 Anemone. Syllogistic reasoning is equally valid and 
 evident in either case, and we might represent the two 
 modes in ordinary language as follows : 
 
 Extensive Syllogism. 
 All Ranunculaceae are Exogens ; 
 The Anemone is ono of the Rannnculaces ; 
 Therefore the Anemone is an Exogen.
 
 OONWTIONAL SYLLOGISMS. 149 
 
 Intensive Syllogism. 
 
 All the qualities of Ranunculacese are qualities of Anemone , 
 All the qualities of Exogen are qualities of Ranunculaceae ; 
 Therefore all the qualities of Exogen are qualities of Anemone 
 
 Any sorites can be similarly represented either in extension or 
 intension. 
 
 Concerning the Aristotelian doctrine of the Enthymeme, see 
 Mansel's Aldrich, App., Note F, and Hamilton's Lectures on 
 Logic, Lecture XX. Port Royal Logic, translated by T. 
 Spencer Baynes, 5th ed. Edinburgh, 1861. 
 
 In this section, on "Irregular and Compound 
 Syllogisms,*' we have considered: 
 
 1. The Irregular Mode of Expressing Infer- 
 ences. 
 
 2. The Explanation of Enthymeme. 
 
 3. Prosyllogistns and Episyllogistns. 
 
 4. Sorites. 
 
 6. Syllogisms in Extension and Intension, 
 
 SECTION YI* 
 
 CONDITIONAL SYLLOGISMS. 
 
 1. Classification of Propositions. 
 
 It will be remembered that when treating of propo- 
 sitions we divided them into two distinct kinds, Cate- 
 gorical Propositions, and Conditional Propositions. 
 The former kind alone has hitherto been considered, 
 and we must now proceed to describe Conditional 
 propositions and the arguments which may be com- 
 posed of them.
 
 150 SYLLOGISMS. 
 
 Logicians have commonly described Conditional prop- 
 ositions 08 composed of two or more Categorical propo- 
 sitions united by a conjunction. This union may 
 happen in two ways, giving rise to two very different 
 species of conditionals, which we shall call Hypothetical 
 Propositions and Disjunctive Propositions. The way 
 in which the several kinds of propositions are related 
 will be seen in the following diagram : 
 
 C Categorical, 
 
 2. Antecedent and Consequent. 
 
 A conditional proposition may be further described 
 as one which makes a statement under a certain con- 
 dition or qualification restricting its application. In 
 the hypothetical form this condition is introduced by 
 the conjunction if, or some other word equivalent to 
 it. Thus 
 
 " If iron is impure, it is brittle " 
 
 is a hypothetical proposition consisting of two distinct 
 categorical propositions, the first of which, "Iron is 
 impure," is called the Antecedent; the second, "It is 
 brittle," the Consequent. In this case " impurity " is 
 the condition or qualification which limits the applica- 
 tion of the predicate brittle to iron. 
 
 It was asserted by Home Tooke in his celebrated work, TTie 
 Diversions of Purley, that all conjunctions are the remains or 
 corrupted forms of verbs. This is certainly true in the case of 
 the hypothetical conjunction ; for the word if in old English is 
 written gif or gyf, and is undoubtedly derived from the verb tt
 
 CONDITIONAL SYLLOGISMS. 151 
 
 give. We may actually substitute at present any verb of similar 
 
 meaning, as for instance grant, allow, suppose. Thus, we may 
 
 say 
 
 " Grant that iron is impure, and it is brittle." 
 
 " Suppobing that iron is impure, it is brittle." 
 
 3. Kinds of Hypothetical Syllogrisms. 
 
 The hypothetical proposition might be employed in 
 arguments of various form, but only two of these are 
 of sufficient importance to receive special names. The 
 hypothetical syllogism consists of two premises, called 
 the major and minor, as in the case of the ordinary 
 syllogism. The major premise is hypothetical in form ; 
 the minor premise is categorical, and according as it is 
 affirmative or negative the argument is said to be a 
 Constructive or a Destructive hypothetical syllogism. 
 Thus the form, 
 
 If A isB, CiaD; 
 
 But AisB; 
 
 Therefore C is Z), 
 is a constructive hypothetical syllogism. 
 
 It must be carefully observed that the minor premise 
 affirms the antecedent of the major premise, whence 
 the argument is said to be of the modus ponens, or 
 mood which posits or affirms. It is probably one of 
 the most familiar and common kinds of argument. 
 
 The form, 
 
 If ^ is 5, CisD', 
 
 But C is not D ; 
 Therefore A is not B, 
 
 represents the corresponding Destructive hypothetical 
 syllogism, also called the modus tollens, or the mood 
 which removes the consequent. It must be carefully
 
 162 SYLLOGISMS. 
 
 observed again that it is the consequent, not the ante- 
 cedent, wliich is denied. 
 
 4. The Rule for Hypothetical Syllogrisms. 
 
 The only rule which is requisite for testing the 
 validity of such syllogisms embodies what we have 
 observed above, viz., that either the antecedent must 
 be affirmed, or the consequent denied. If either part 
 of this rule be broken, a serious fallacy will be com- 
 mitted. Thus the apparent argument, 
 
 If ^ is 5, CisD'y 
 But <7 is Z) ; 
 Therefore A is B, 
 
 is really a fallacy which we may call the fallacy of affirm- 
 ing the consequent, and its fallacious nature is readily 
 understood by reflecting that " A being 5" is not stated 
 to be the only condition on which C is D. It may 
 happen that when E is F, or is iT, or under a hun- 
 dred other circumstances, G is D, so that the mere fact 
 of G being D is no sufficient proof that A is B. Thus, 
 if a man's character be avaricious he will refuse to give 
 money for useful purposes ; but it does not follow that 
 every person who refuses to give money for such pur- 
 poses is avaricious. There may be many proper reasons 
 or motives leading him to refuse ; he may have no 
 money, or he may consider the purpose not a useful 
 one, or he may have more useful purposes in view. 
 
 A corresponding fallacy arises from denying the ante- 
 cedent, as in the form 
 
 U A is B, G 18 D ; 
 But A is not B ; 
 Therefore G is not D.
 
 CONDITIONAL SYLLOGISMS. 163 
 
 The error may be explained in the same way; for aa 
 "A being li " is not stated to be the only condition of 
 C being D, we may deny this one condition to be true, 
 but it is possible that the consequent may happen to be 
 true for other reasons, of which we know nothing. 
 Thus if a man is not avaricious we cannot conclude 
 that he will be sure to give money whenever asked. 
 Or take the following example : 
 
 "If the study of Logic furnished the mind with a 
 multitude of useful facts like the study of other sciences, 
 it would deserve cultivation ; but it does not furnish 
 the mind with a multitude of useful facts ; therefore it 
 does not deserve cultivation." 
 
 This is evidently a fallacious argument, because the 
 acquiring of a multitude of useful facts is not the only 
 ground on which the study of a science can be recom- 
 mended. To correct and exercise the powers of judg- 
 ment and reasoning is the object for which Logic 
 deserves to be cultivated, and the existence of such 
 other purpose is ignored in the above fallacious argu- 
 ment, which evidently involves tfie denial of the ante- 
 cedent. 
 
 6. The Beduction of Hypothetical to Categorical 
 Syllogisms. 
 
 Although it is usual in logical works to describe the 
 hypothetical proposition and syllogism as if they were 
 different in nature from the categorical proposition and 
 syllogism, yet it has long been known that the hypo- 
 theticals can be reduced to the categorical form, and 
 brought under the ordinary rules of the syllogism. Aa
 
 154 SYLLOQISMS. 
 
 t 
 
 a general rule the hypothetical proposition can hi 
 readily converted into a universal affirmative proposi- 
 tion (A) of exactly the same meaning. Thus oui 
 instance, "If iron is impure, it is brittle," becomea 
 simply, "Impure Iron is brittle." In making thia 
 alteration in a hypothetical syllogism it will be found 
 necessary to supply a new minor term ; thus in the 
 case. 
 
 If iron is impure it is brittle ; 
 
 But it is impure ; 
 
 Therefore it is brittle, 
 
 we have to substitute for the indefinite pronoun i(, the 
 iron in question, and we obtain a correct categorical 
 syllogism in the mood Barbara : 
 
 Impure iron is brittle ; 
 
 The iron in question is impure iron ; 
 
 Therefore the iron in question is brittle. 
 
 Sometimes the reduction requires a more extensive change 
 f language. For instance, 
 
 If the barometer is falling, bad weather is coming , 
 But the barometor is falling ; 
 Therefore bad weather is coming, 
 
 may be represented in the following form : 
 
 The circumstances of the barometer falling are the circumstances 
 
 of bad weather coming ; 
 But these are the circumstances of the barometer falling ; 
 Therefore these are the circumstances of bad weatlier coming. 
 
 As an instance of the Destructive Hypothetical syllogism wc 
 nay take : 
 
 If Aristotle Is right, slavery is a proper form of Bociety ; 
 But slaven,' is not a proper form of societj' ; 
 Therefore Aristotie is not right
 
 CONDITIONAL SYLLOGISMS. 165 
 
 Thin becomes as a categorical - 
 
 The case of Aristotle being right is the case of slavery being a 
 
 proper form of society; 
 But this is not the case ; 
 Therefore this is not the case of Aristotle being right. 
 
 If not reducible by any other form of expression, hypothetical^ 
 can always be reduced by the use of the words case of. 
 
 6. Fallacies in Hypothetical Syllo^sms. 
 
 It will now be easily made apparent that the fallacy 
 of afl&rming the consequent is really a breach of the 
 third rule of the syllogism, leading to an undistributed 
 middle term. Our example may be as before : 
 
 If a man is avaricious he will refuse money ; 
 But he does refuse money ; 
 Therefore he is avaricious. 
 
 This becomes as a categorical syllogism. 
 
 All avaricious men refuse money ; . 
 But this man refuses money ; 
 Therefore this man is avaricious. 
 
 This is the mood AAA in the second figure ; and the 
 middle term, refusing money, is undistributed in both 
 premises, so that the argument is entirely fallacious. 
 
 Again, the fallacy of denying the antecedent is equiv- 
 alent to the illicit process of the major. Our former 
 example (p. 153) may thus be represented : 
 
 " A science which furnishes the mind with a multi- 
 tude of useful facts deserves cultivation ; but Logic is 
 not such a science; therefore Logic does not deserve 
 cultivation."
 
 156 SYLLOGISMS, 
 
 This apparent syllogism is of the mood AEE in the 
 first figui'e, whicli breaks the fourth rule of the syllo- 
 gism, because the major term, deserving culhvation, is 
 distributed in the negative conclusion, but not in the 
 aBBrmative major premise. 
 
 7. Di^unctive Syllogrisms. 
 
 We now pass to the consideration of the disjunctive 
 proposition, which instead of a single predicate has 
 several alternatives united by the disjunctive conjunc- 
 tion or, any one of which may be affirmed of the subject. 
 **A member of the House of Commons is either a repre- 
 sentative of a county, or of a borough, or of a Univer- 
 sity," is an instance of such a proposition, containing 
 three alternatives; but there may be any number of 
 alternatives from two upwards. 
 
 The disjunctive syllogism consists of a disjunctive 
 major premise with a categorical proposition, either 
 afRrmative or negative, forming the minor premise. 
 Thus arise two moods : 
 
 (1) The affirmative mood is called by the Latin words 
 modus ponendo tollens (the mood which by affirming 
 denies), and may be thus stated : 
 
 A is either B or C, 
 But ^ is ^ ; 
 Therefore A is not C. 
 
 This form of argumenC proceeds on the supposition 
 that if one alternative of a disjunctive proposition be 
 held true, the others cannot also be true. Thus " the 
 time of year must bo cither spring, summer, autumn or 
 winter," and if it be spring it cannot be summei;
 
 CONDITIONAL SYLLOGISMS. 157 
 
 autnmn or winter; and so on. But it has been ob- 
 jected by Whately, Mansel, Mill, as well as many 
 earlier logicians, that this does not always hold true. 
 Thus if we say that "a good book is valued either foi 
 the usefulness of its contents or the excellence of its 
 style," it does not by any means follow because the con- 
 tents of a book are useful that its style is not excel- 
 lent. We generally choose alternatives which are in- 
 consistent with each other ; but this is not logically 
 necessary. 
 
 (2) The other form of disjunctive syllogism, called 
 the modus tollendo ponens (the mood which by deny- 
 ing affirms), is always of necessity cogent, and is as 
 follows: 
 
 A is either B or C, 
 
 But A is not B', 
 
 Therefore A is C. 
 
 Thus if we suppose a book to be valued only for the 
 usefulness of its contents or the excellence of its style, 
 it follows that if a book be valued, but not for the 
 former reason, it must be for the latter ; and vice versa. 
 K the time of year be not spring, it must be summer, 
 autumn or winter ; if it be not autumn nor winter, it 
 must be either spring or summer ; and so on. In short 
 if any alternatives be denied, the rest remain to be 
 affirmed as before. It will be noticed that the disjunc- 
 tive syllogism is governed by totally different rules 
 from the ordinary categorical syllogism, since a nega- 
 tive premise gives an affirmative conclusion in the 
 former, and a negative conclusion in the latter.
 
 158 SYLLOGISMS. 
 
 8. The Dilemma. 
 
 There yet remains a form of argument called the 
 Dilemma, because it consists in assuming two alterna- 
 tives, usually called the horns of the dilemma, and yet 
 proves something in either case (Greek, dt- two ; ^fjinfia, 
 assumption). Mr. Mansel defines this argument as "a 
 syllogism, having a conditional major premise with more 
 than one antecedent, and a disjunctive minor." There 
 are at least three forms in which it may be stated. 
 
 (1) The first form is called the Simple Constructive 
 Dilemma : 
 
 If ^ is 5, GiaD; and if ^ is i^, GisD: 
 But either A is B, or B ib F; 
 Therefore C is D. 
 
 Thus **if a science furnishes useful facts, it is worthy 
 of being cultivated ; and if the study of it exercises the 
 reasoning powers, it is worthy of being cultivated ; but 
 either a science furnishes useful facts, or its study exer- 
 cises the reasoning powers; therefore it is worthy of 
 being cultivated." 
 
 (2) The second form of dilemma is the Complex Con- 
 structive Dilemma, which is as follows: 
 
 IfAisB,C\BD; and if E\bF, G is H', 
 But either A is B, or E is F', 
 Therefore either G is D, or G is H. 
 
 It is called complex because the conclusion is in the 
 disjunctive form. As an instance we may take the 
 argument, '' If a statesman who sees his former opinions 
 to be wrong doe^i not alter his course, he is guilty of 
 deceit; and if he does alter his course, he is open to a
 
 CONDITIONAL SYLLOGISMS. 169 
 
 
 
 charge of inconsistency ; but either he does not alter 
 his course, or he does ; therefore he is either guilty of 
 deceit, or he is open to a charge of inconsistency." In 
 this case, as in the greater number of dilemmas, the 
 terms A, B, G, D, etc., are not all different. 
 
 (3) The Destructive Dilemma is always complex, be-i 
 cause it could otherwise be resolved into two uncon- 
 nected destructive hypothetical syllogisms. It is in the 
 following form : 
 
 If ^ is 5, OiaD; and if ^ is i^, OisH; 
 But either is not D, or G is no*", ff ; 
 Therefore either A is not B, or E is not F. 
 
 For instance, " If this man were wise, he would not 
 speak irreverently of Scripture in jest ; and if he were 
 good, he would not do so in earnest ; but he does it 
 either in jest or earnest ; therefore he is either not wise, 
 or not good," * 
 
 Dilemmatic arguments are, however, more often fallacious 
 than not, because it is seldom possible to find instances where 
 two alternatives exhaust all the possible cases, unless indeed one 
 of them 1)6 the simple negative of the other m accordance with 
 the law of excluded middle. Thus if we were to argue that " if 
 ft pupil is fond of learning he needs no stimulus, and that if he 
 dislikes learning no stimulus will be of any avail, but as he is 
 either fond of learning or dislikes it, a stimulus is either needless 
 or of no avail," we evidently assume improperly the disjunctive 
 minor premise. Fondness and dislike are not the only two pos- 
 sible alternatives, for there may be some who are neither fond of 
 learning nor dislike it, and to these a stimulus in the shape of 
 rewards may be desirable. Almost anything can be proved if wa
 
 160 SYLLOGISMS. 
 
 are allowed thus to pick out two ot the possible aitemativev 
 whicli are ia our favor, aud argue from these alone. 
 
 A dilemma can often be retorted by prod ucing as cogent a 
 dilemma to the contrary effect. Thus an Athenian mother, ac- 
 cording to Aristotle, addressed her son in the following words: 
 "Do not enter into public business; for if you say what is just. 
 men will hate you ; and if you stiy what is unjust the gods will 
 hate you." To which Aristotle suggests the following retort "J 
 ought to enter into public affaire ; for if I say what is just, th 
 gods will love me ; and if I say what is unjust, men will lov* 
 me." 
 
 Mansel's Aldrich, App. Note 1, on the Hypothetical Syllogism 
 
 In this section, on "Conditional Syllogisms, '^ 
 we have considered: 
 
 1. The Classijiration of Propositions, 
 
 2. Antecedent and Consequent. 
 
 3. The Kinds of Hi/itothetictil Sylloffistns. 
 
 4. The Hale for Hf/pothetical Syllogistns, 
 
 6. The Rednetion of Hypothetical Syllogisms #l 
 Categorical Syllogistns. 
 
 6. Fallacies in Hypothetical Syllogisnui, 
 
 7. Disjunctive Syllogisms, 
 8> The J>Uetnmi,
 
 CHAPTER IV. 
 
 FALLACIES. 
 
 In order to acquire a satisfactory knowledge of the 
 rules of correct thinking, it is essential that we should 
 become acquainted with the most common kinds of 
 fallacy; that is to say, the modes in which, by neglect- 
 ing the rules of logic, we often fall into erroneous 
 reasoning. In previous lessons we have considered, as 
 it were, how to find the right road ; it is our task here 
 to ascertain the turnings at which we are most liable to 
 take the wrong road. 
 
 In describing the fallacies, I shall follow the order 
 and adopt the mode of classificatiou which has been 
 usual for the last 2000 years and more, since in fact 
 the great teacher Aristotle first explained the fallacies. 
 According to this mode of arrangement fallacies are 
 divided into two principal groups, containing the logi- 
 cal and the material fallacies. 
 
 1. The logical fallacies are those which occur in the 
 mere form of the statement ; or, as it is said in the old 
 Latin expressions, in dictione, or in voce. It is supposed 
 accordingly that fallacies of this kind can be discovered 
 without a knowledge of the subject-matter with which 
 the argument is concerned. 
 
 2. The material fallacies, on the contrary, arise out- 
 side of the mere verbal statement, or, as it is said, eoctra 
 diciionemj they are concerned consequently, with the
 
 162 FALLACIES. 
 
 subject of the argument, or in re (in the matter), and 
 cannot be detected and set right but by those acquainted 
 with the subject. 
 
 These two classes of fallacies will now be considered 
 in the following sections; (1) Logical Fallacies^ 
 (2) Material Fallacies, 
 
 8BGTI0IT ! 
 LOGICAL FALUCIEa 
 
 1, Classiflcation of Logical Fallacies. 
 
 The 1 jgical fallacies may be divided into the purely 
 fogical and semi-logical, and we may include in the 
 former class the distinct breaches of the syllogistic 
 rules which have already been described. 
 
 (1) We may enumerate as Purely Logical Fallacies : 
 
 1. Fallacy of four terras {Quaternio Terminorum) 
 Breach of Rule 1 ; 
 
 2. Fallacy of undistributed middle Breach of Rule 3 ; 
 
 3. Fallacy of illicit process, of the major or minor 
 term Breach of Rule 4; 
 
 4. Fallacy of negative premises Breach of Rule 5 ; 
 as well as breaches of the 6th rule, to which no distinct 
 name has been given. Breaches of the Tth and 8th 
 mles may be resolved into the preceding (p. 140), but 
 they may also bo described as in p. 123. 
 
 (2) The other part of the chissof logical fallacies con- 
 tains Semi-logical fallacies, which are six in number 
 as follows :
 
 LOaiCAL FALLACIES. 168 
 
 L Fallacy of Equivocation. 
 
 2. Fallacy ot* Amphibology. 
 
 8. Fallacy of Composition. 
 
 4. Fallacy of Division. 
 
 d. Fallacy of Accent. 
 
 6. Fallacy of Figure of Speech. 
 
 
 
 These I shall describe and illustrate in successioiL 
 
 2. The Fallacy of Equivocation. 
 
 Equivocation consists in the same term being used in 
 two distinct senses ; any of the three terms of the syllo- 
 gism may be subject to this fallacy, but it is usually the 
 middle term which is used in one sense in one premise 
 and in another sense in the other. In this case it ii 
 often called the fallacy of ambiguous middle, and when 
 we distinguish the two meanings by using other suitable 
 modes of expression it becomes apparent that the sup- 
 posed syllogism contains four terms. The fallacy of 
 equivocation may accordingly be considered a disguised 
 fallacy of four terms. Thus if a person were to arguf 
 that "all criminal actions ought to be punished by law* 
 prosecutions for theft are criminal actions ; therefore 
 prosecutions for theft ought to be punished by law," 
 it is quite apparent that the term "criminal action*' 
 means totally different things in the two premises, and 
 that there is no true middle term at all. Often, how- 
 ever, the ambiguity is of a subtle and difficult character, 
 80 that different opinions may be held concerning it 
 Thus we might argue : 
 
 "He who harms another should be punished. H* 
 who communicates an infectious disease to another per-
 
 164 FALLAOIBS. 
 
 Bon harms him. Therefore he who communicates an 
 infectious disease to another person should be pun* 
 ished.'* 
 
 This may or .may not be held to be a correct argu- 
 ment according to the kinds of actions we should con- 
 sider to come under the term harm, according as we 
 regard neghgence or malice requisite to constitute harm. 
 Many difficult legal questions are of this nature, as, for 
 Instance : 
 
 Nuisances are punishable by law ; 
 
 To keep a noisy dog is a nuisance; 
 
 To keep a noisy dog is punishable by law. 
 
 The question here would turn upon the degree of 
 nuisance which the law would interfere to prevent. Or 
 again: 
 
 Interference with another man's business is illegal ; 
 
 Underselling interferes with anotlier man's business ; 
 Therefore underselling is illegal. 
 
 Here the question turns upon thekind of interference^ 
 and it is obvious that underselling is not the kind of 
 interference referred to in the major premise. 
 
 3. The Fallacy of Amphibologry. 
 
 The Fallacy of Amphibology consists in an ambiguous 
 grammatical structure of a sentence, which produces 
 misconception. A celebrated instance occurs in the 
 prophecy of the spirit in Shakspeare's Henry VI. : 
 ** The Duke yet lives that Henry shall depose," which 
 leaves it wholly doubtful whether the Duke shall depose 
 Henry, or Henry the Duke. This prophecy is doubt- 
 less an imitation of those which the ancient oracle of
 
 LOGICAL FALLACIES. 16fi 
 
 Delphi is reported to have uttered ; and it seems that 
 this fallacy was a great resource to the oracles wlio were 
 not confident in their own powers of foresight. The 
 Latm language gives great scope to misconstructions, 
 because it does not require any fixed order for the words 
 of a sentence, and when there are two accusative cases 
 with an infinitive verb, it may be difficult to tell except 
 from the context which comes in regard to sense before 
 the verb. The double mejiuiug which may be given to 
 " twice two and three " arises from amphibology ; it 
 may be 7 or 10, according as we add the 3 after or be- 
 fore multiplying. In the careless construction of sen- 
 tences it is often impossible to tell to what part any 
 adverb or quahfying clause refers. Thus, if a person 
 says "I accomplished my business and returned the 
 day after," it may be that the business was accomplished 
 on the day after as well as the return; but it may 
 equally have been finishsd on the previous day. Any 
 ambiguity of this kind may generally be avoided by a 
 simple change in the order of the words ; as for 
 instance, "I accomplished my business, and, on the day 
 after, returned." Amphibology may sometimes arise 
 from confusing the subjects and predicates in a com- 
 pound sentence, as if in "platinum and iron are very 
 rare and useful metals," I were to apply the predicate 
 useful to platinum and rare to iron, which is not 
 intended. The word "respectively" is often used to 
 show that the reader is not at liberty to apply each 
 predicate to each subject. 
 
 4. The Fallacy of Composition. 
 
 The Fallacy of Composition is a special case ot equivo- 
 cation, arising from the confusion of an universal and a
 
 166 FALLACIES. 
 
 collective term. In the premises of a syllogism we 
 may affirm something of a class of things distributively^ 
 that is, of each and any separately, and then we may m 
 the conclusion infer the same of the whole put together. 
 Thus we may say that "all the angles of a triangle are 
 less than two right angles," meaning that any of the 
 angles is less than two right angles ; but we must not 
 infer that all the angles put together are less than two 
 right angles. We must not argue that because every 
 member of a jury is very likely to judge erroneously, 
 the jury as a whole are also very likely to judge errone- 
 ously ; nor that because each of the witnesses in a law 
 case is liable to give false or mistaken evidence, no con- 
 fidence can be reposed in the concur'-ent testimony of a 
 number of witnesses. 
 
 6. The Falla^jy of Division. 
 
 The Fallacy of Division is the converse of the pre- 
 ceding, and consists in using the middle term collec- 
 tively in the major premise, but distributively in the 
 minor, so that the whole is divided into its parts. Thus 
 it might be argued, " All the angles of a triangle are 
 (together) equal to two right angles ; -4 5 6' is an angle 
 of a triangle; therefore ABC is equal to two nght 
 angles." Or again, "The inhabitants of the town con- 
 sist of men, women and children of all ages ; those 
 who met in the Guildhall were inhabitants of the town; 
 therefore they consisted of men, women and children 
 of all ages;" or, "The judges of the court of appeal 
 cannot misinterpret the law ; Lord A. B. is a judge of 
 the court of appeal ; therefore he cannot misinterpret 
 the law."
 
 LOGICAL FALLACIES. 167 
 
 6. The Fallacy of Accent. 
 
 The Fallacy of Accent consists in any ambiguity 
 arising from a misplaced accent or emphasis thrown 
 upon some word of a sentence. A ludicrous instance is 
 liable to occur in reading Chapter XIII of the First 
 Book of Kings, verse 27, where it is said of the prophet 
 *'And he spake to his sons, saying, Saddle me the ass. 
 And they saddled /tm." The italics indicate that the 
 word him was supplied by the translators of the author- 
 ized version, but it may suggest a very different mean- 
 ing. The Commandment " Thou shalt not bear false 
 witness against thy neighbor" may be made by a 
 slight emphasis of the voice on the last word to imply 
 that we are at liberty to bear false witness against other 
 persons. Mr. De Morgan, who remarks this, also points 
 out that the erroneous quoting of an author, by unfairly 
 separating a word from its context or italicising words 
 which were not intended to be italicised, gives rise to 
 cases of this fallacy. 
 
 It is curious to observe how many and various may be the 
 meanings attributable to the same sentence according as 
 emphasis is thrown upon one word or another. Tims tlie sen- 
 tence " The study of Logic is not supposed to communicate a 
 knowledge of many useful facts," may be made to imply that the 
 study of Logic does communicate such a knowledge, although it 
 is not supposed to ; or that it communicates a knowledge of &few 
 useful facts ; or that it communicates a knowledge of many vse- 
 less facts. Tliis ambiguity may be explained by considering that 
 if you deny a thing to have the group of qualities A, B, C, D, 
 the truth of your statement will be satisfied by any one quality 
 being absent, and an accented pronunciation will often be used 
 to indicate that which the speaker believes to be absent. If you 
 deny that a particular fruit is ripe and sweet and well-flavored.
 
 168 I-ALLACIES. 
 
 it may be unripe and sweet and well-flavored ; or ripe and soui 
 and well-flavored ; or ripe and sweet and ill flavored ; or iiuy two 
 or even all three qualities may be absent. But if you deny it to 
 be ripe and sweet and well-flavored, the denial would be under 
 stood to refer to the last quality. Jeremy Bentham was so much 
 afraid of being misled by this fallacy of accent that he employed 
 a person to read to him, as I have heard, who had a peculiarly 
 monotonous manner of reading. 
 
 7. The Fallacy of the Figure of Speech. 
 
 The Fallacy of the Figure of Speech is the sixth and 
 last of the semi-logical fallacies, and is of a very trifling 
 character. It appears to consist in any grammatical 
 mistake or confusion between one part of speech and^ 
 another. Aristotle gravely gives the following instance: 
 " Whatever a man walks he tramples on ; a man walks 
 the whole day ; therefore he tramples on the day." 
 Here an adverbial phrase is converted into a noun 
 object. 
 
 In this Section, on " Logical Fallacies,*' we hav 
 considered : 
 
 1 . The Classification of Logical Fallacies, 
 
 2. The FalUKty of Equivocation. 
 
 3. The Fat lacy of Amphibology, 
 
 4. The Fallacy of Composition. 
 
 5. The Fitllacy of Division. 
 
 6. The Fallacy of Accent, 
 
 7. The Fallacy of the Figure of Speech*
 
 XATEBIAL FALLACIES. 169 
 
 SECTION II* 
 
 MATERIAL FALLACIES. 
 
 1. The Classification of Material Fallacies. 
 
 The Material fallacies are next to be considered ; and 
 their importance is very great, although it is not easy 
 to illustrate them by brief examples. There are alto- 
 gether seven kinds of such fallacies enumerated b> 
 Aristotle and adopted by subsequent logicians, as foJ 
 lows : 
 
 1. The Fallacy of Accident. 
 
 2. The Converse Fallacy of Accident. 
 
 3. The Irrelevant Conclusion. 
 
 4. The Petitio Principii. 
 
 5. The Fallacy of the Consequent or Non sequitur 
 
 6. The False Cause. 
 
 7. The Fallacy of Many Questions. 
 
 2. The Fallacy of Accident and its Converse. 
 
 Of these the first two are conveniently described to- 
 gether. The fallacy of accident consists in arguing 
 erroneously from a general rule to a special case, where 
 a certain accidental circumstance renders the rule inap- 
 plicable. The converse fallacy consists in arguing from 
 a special case to a general one. This latter fallacy is 
 usually described by the Latin phrase a dicto secnndiiftt 
 quid ad dictum simpliciter, meaning "from a state- 
 ment under a condition to a statement simply or with- 
 9
 
 170 FALLACIES. 
 
 out that condition." Mr. De Morgan has remarked 
 in his very interesting chapter on Fallacies* that 
 we ought to add a third fallacy, which would con- 
 sist in arguing from one special case to another specicu. 
 case. 
 
 A few examples will illustrate these kinds of fallacy, 
 but much difficulty is often encountered in saying to 
 which of the three any particular example is best 
 referred. A most ancient example repeated in almost 
 every logical hand-book is as follows: "What you 
 bought yesterday you eat to-day; you bought raw meat 
 yesterday; therefore you eat raw meat to-day." The 
 assertion in the conclusion is made of meat with the 
 accidental quality of rawness added, where the first 
 premise evidently speaks of the substance of the meat 
 without regard to its accidental condition. This then 
 is a case of the direct fallacy. If it is argued again 
 that because wine acts as a poison when used in ex- 
 cess it is always a poison, we fall into the converse 
 fallacy. 
 
 It would be a case of the direct fallacy of accident 
 to infer that a magistrate is justified in using his power 
 to forward his own religious views, because every man 
 has a right to inculcate his own opinions. Evidently a 
 magistrate as a man has the rights of other men, but in 
 his capacity of a magistrate he is distinguished from 
 other men, and he must not infer of his special powers 
 in this respect what is only true of his rights as a 
 man. For another instance take the following: "He 
 who thrusts a knife into another person should be 
 
 Formal Logic, Chap. Xm.
 
 MATEBIAL FALLACIES. 171 
 
 punished; a surgeon in operating does so ; therefore he 
 should be punished." Though the fallacy of this is 
 absurdly manifest, it is not so manifest how we are to 
 classify the error. We may for instance say that as a 
 general rule whoever stabs or cuts another is to be 
 punished unless it can be shown to have been done 
 under exceptional circumstances, as by a duly qualified 
 surgeon acting for the good of the person. In this case 
 the example belongs to the direct fallacy of accident. 
 In another view we might interpret the first premise to 
 mean the special case of thrusting a knife maliciously ; 
 to argue from that to the case of a surgeon would 
 be to infer from one special case to another special 
 case. 
 
 It is undoubtedly true that to give to beggars pro- 
 motes mendicancy and causes evil ; but if we interpret 
 this to mean that assistance is never to be given to 
 those who solicit it, we fall into the converse fallacy of 
 accident, inferring of all who solicit alms what is 
 only true of those who solicit alms as a profession. 
 Similarly it is a very good rule to avoid lawsuits 
 and quarrels, but only as a general rule, since there 
 frequently arise circumstances in which resort to the 
 law is a plain duty. Almost all the difficulties which 
 we meet in matters of law and moral duty arise from 
 the impossibility of always ascertaining exactly to what 
 cases a legal or moral rule does or does not extend ; 
 hence the interminable differences of opinion, even 
 among the judges of the land. 
 
 3. The Fallacy of Irrelevant Conclusion. 
 
 The Third Material Fallacy is that of the Irrelevant
 
 173 FALLACIES. 
 
 Conclusion, technically called the Ignoratio Elenohi, or 
 literally Ignorance of the Refutation. It consists in 
 arguing to the wrong point, or proving one thing in 
 such a manner that it is supposed to be something else 
 that is proved. Here again it would be difficult to 
 adduce concise examples, because the fallacy usually 
 occurs in the course of long harangues, where the 
 multitude of words and figures leaves room for con- 
 fusion of thought and forgetful ness. This fallacy is in 
 fact the great resource of those who have to support a 
 weak case. It is not unknown in the legal profes- 
 sion, and an attorney for the defendant in a lawsuit 
 is said to have handed to the barrister his brief 
 marked, "No case; abuse the plaintiff's attorney." 
 Whoever thus uses what is known as argumentum 
 ad hominem, that is an argument which rests, not 
 upon the merit of the case, but the character or 
 position of those engaged in it, commits this fallacy. 
 If a man is accused of a crime it is no answer to 
 say that the prosecutor is as bad. If a great change 
 in the law is proposed in Parliament, it is an Irrele- 
 vant Conclusion to argue that the proposer is not 
 the right man to bring it forward. Every one who 
 gives advice lays himself open to the retort that he 
 who preaches ought to practise, or that those who live 
 in glass houses ought not to throw stones. Never- 
 theless there is no necessary connection between the 
 character of the person giving advice and the goodness 
 of the advice. . 
 
 The argumentum ad populum is another form of 
 Irrelevant Conclusion, and consists in addressing argu- 
 ments to a body of people calculated to excite their
 
 MATERIAL FALLACIES. 173 
 
 feeling and prevent them from forming a dispassionate 
 judgment upon the matter in hand. It is the great 
 weapon of rhetoricians and demagogues. 
 
 4. The Fallacy of Petitio Priiicipil. 
 
 Petitio Principii is a familiar name, and the nature of 
 the fallacy it denotes is precisely expressed in the phrase 
 begging the questioji. Another apt name for the fallacy 
 is circulus in yrohando, or "a circle in the proof." It 
 consists in taking the conclusion itself as one of the 
 premises of an argument. Of course the conclusion 
 of a syllogism must always be contained or implied in 
 the premiseSj but only when those premises are com- 
 bined, and are distinctly different assertions from the 
 conclusion. Thus in the syllogism, 
 
 B'v& C, 
 
 A is 5, 
 
 therefore A is G, 
 
 the conclusion is proved by being deduced from two 
 propositions, neither of which is identical with it ; but 
 if the truth of one of these premises itself depends 
 upon the following syllogism, 
 
 CisJ?, 
 
 ^is G, 
 
 therefore A is 5, 
 
 it is plain that we attempt to prove a proposition by 
 itself, which is as reasonable as attempting to support a 
 body upon itself. It is not easy to illustrate this kind 
 of fallacy by examples, because it usually occurs in
 
 174 FALLACIES. 
 
 long aigametits, and especially in wordy metaphysicdl 
 writings. We are very likely to fall into it, however, 
 when we employ a mixture of Saxon and Latin or 
 Greek words, so as to appear to prove one proposition 
 by another which is really the same expressed in differ 
 ent terms, as in the following: "Consciousness must 
 be immediate cognition of an object ; for I cannot be 
 said really to know a thing unless my mind has been 
 affected by the thing itself." 
 
 In the use of the disjunctive syllogism this fallacy Is likely to 
 happen ; for by enumerating only those alternatives which favor 
 one view and forgetting the others it is easy to prove anything. 
 An instance of this occurs in the celebrated sophism by which 
 some of the ancient Greek Philosophers proved that motion was 
 impossible. For, said they, a moving body must move either in 
 the place where it is or the place where it is not ; now it is absurd 
 that a body can be where it is not, and if it moves it cannot be in 
 the place where it is; therefore it cannot move at all. The 
 error arises in the assumption of a premise which begs the ques- 
 tion ; the fact of course is that the body moves between the place 
 where it is at one moment and the place where it is at tlie next 
 moment. 
 
 Jeremy Bentham, however, pointed out that the use even of a 
 single name may imply a Petitio Principii. Thus in a Clmrch 
 assembly or synod, where a discussion is taking place as to 
 whether a certain doctrine should be condemned, it would be a 
 Petitio Principii to arg^e that the doctrine is heresy, and there- 
 fore it ought to be condemned. To assert that it is heresy is to 
 beg the question, because every one understands by heresy a 
 doctrine which is to be condemned. Similarly in Parliament a 
 oill is often opposed on the ground that it is unconstitutional and 
 therefore ought to be rejected ; but as no precise definition can be 
 given of what is or is not constitutional, it means little more than 
 that the measure in distasteful to the opponent. Names whicL 
 are used in this follacious manner were aptly called by Benthani
 
 MATERIAL FALLACIES. 176 
 
 Question-begging Epithets. In like manner we beg the ques- 
 ion when we oppose any change by saying that it is un-English. 
 
 5. The Fallacy of the Gousequent. 
 
 The Fallacy of the Consequent is better understood by 
 ihe familiar phrase noti sequitur. We may apply this 
 Jiame to any argument which is of so loose and incon- 
 sequent a cliaracter that no one can discover any 
 cogency in it. It thus amounts to little more than 
 the assertion of a conclusion which has no connection 
 with the premises. Professor De Morgan gives as an 
 example the following: "Episcopacy is of Scripture 
 origin ; the Church of England is the only Episcopal 
 Church in England; ergo, the Church established is 
 the Church that should be supported." 
 
 O. The Fallacy of False Cause. 
 
 By the Fallacy of the False Cause I denote that 
 which has generally been referred to by the Latin 
 phrase non causa pro causd. In this fallacy we assume 
 that one thing is the cause of another without any 
 sufficient grounds. A change in the weather is even 
 yet attributed to the new moon or full moon which had 
 occurred shortly before, although it has been demon- 
 strated over and over again that the moon can have 
 no such effect. In former centuries any plague or other 
 public calamity which followed the appearance of a 
 comet or an eclipse was considered to be the result 
 of it. The Latin phrase post hoc ergo propter hoc 
 (after this and therefore in consequence of this) exactly 
 describes the character of these fallacious conclusions.
 
 176 lALLAGIM* 
 
 Though we no longer dread signs and omens, yet wt 
 often enough commit the fallacy ; as when ^e assume 
 that all the prosperity of England is the result of the 
 national character, forgetting that the plentiful coal in 
 the country and its maritime position have contributed 
 to the material wealth. It is no doubt equally falla- 
 cious to attribute no importance to national character, 
 and to argue that because England has in past centuries 
 misgoverned Ireland all the present evils of Ireland are 
 due to that misgovemment. 
 
 7. The Fallacy of Many Questions. 
 
 Lastly, there is the somewhat trivial Fallacy of Many 
 Questions, which is committed by those who so combine 
 two or three questions into one that no true answer can 
 be given to them. I cannot think of a better example 
 than the vulgar pleasantry of asking, " Have you left 
 off beating your mother ?" Questions equally as unfair 
 are constantly asked by barristers examining witnesses 
 in a court of justice, and no one can properly be re- 
 quired to answer Yes or No to every question which 
 may be addressed to him. As Aristotle says, *' Several 
 questions put as one should be at once decomposed into 
 their several parts. Only a single question admits of a 
 single answer: so that neither several predicates of one 
 subject, nor one predicate of several subjects, but only 
 one predicate of one subject, ought to be affirmed or 
 ienied in a single answer." 
 
 Read Professor De Morgan's exce11<'nt and amusing Cliaptei 
 
 on Fallacies, Formal Logir, C\y.\.\). XIII. 
 Whately's Remarks on Fallacies, Elementt of Logic, Book III 
 
 are oftea very original and acut.
 
 MATERIAL FALLACIES. 177 
 
 In this Section, on "Material Fallacies," W 
 have considered : 
 
 1. The Classifivation of Material F'aUacies, 
 
 2. The Fallacy of Accidetit and its Citnrerse* 
 
 3. The Fallacy of Irrelevant Conclusion* 
 
 4. The Fallacy of Petitio Principii, 
 6. The Fallacy of the Consequent. 
 
 6. The Fallacy of the False Cause, 
 
 7. Th*.Falliicy of Many Questions,
 
 SHAPTHB V. 
 
 INDUCTION. 
 
 The subject of Induction, as si process of inference, 
 may be considered under the following divisions : (1) 
 T/ie Inductive Syllogism ; (2) The Forms 
 of Induction, 
 
 SEGTION ! 
 
 THE INDUCTIVE SYLLOGISM. 
 
 1. Induction and Deduction Contra.sted. 
 
 We have in previous chapters considered deductive 
 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 individual 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 "aluminium is a metal," I 
 am enabled by a syllogism in the mood Barbara to infer 
 that "aluminium is a good conductor of heat." As 
 this is a proposition concerning one metal only, it is 
 evidently less general than the premise, which referred 
 to all metals whatsoever. In induction, on the con-
 
 INDUCTION. 179 
 
 trary, we proceed from less general, oi even from indi- 
 vidual 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, etc., 
 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 process of 
 reasoning. 
 
 2, Explanation of Traduction. 
 
 It is true that we may reason without rendering 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 indi- 
 cated by a spectrum of one bright red line. 
 
 In these examples all the propositions are singular 
 propositions, and merely assert the identity of singular 
 terms, so that there is no alteration 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.
 
 180 INDUCTION. 
 
 3. Importance of Induction. 
 
 Induction is a much more difficult and more impor- 
 tant kind of reasoning process than Traduction 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, and some philosophers think the whole, of our 
 knowledge, is ultimately due to inductive reasoning. 
 The mind, it is plausibly 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 world within 
 the human mind. Even when we argue synthetically 
 and deductively from simple ideas and truths which 
 seem to be read}' 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 observation 
 or induction of an almost unconscious kind. This is s 
 debated point upon which I will not here speak posi- 
 tively ; but if the truth be as stated. Induction will b(- 
 the mode by which all the materials of knowledge are 
 brought to the mind and analyzed. Deduction will 
 then be the almost equally importfint process by which 
 the knowledge thus acquired is utilized, and by which 
 new inductions of a more complicated character, as we 
 shall see, are rendered possible.
 
 INDUCTIVE SYLLOGISMS. 181 
 
 4. Perfect and Imperfect Induction. 
 
 An Induction, that is an act of Inductive reasoning, 
 is called Perfect wheu 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 impossible 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-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 Imperfect 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. 
 
 'J. The Dift'erence between Perfect and Inipei> 
 feet Induction. 
 
 It is obvious that there is a great difference between 
 Perfect and Imperfect Induction. The latter includes 
 some process by which we are enabled to make asser- 
 tions concerning things that we have never seen or 
 examined or even known to exist. But it must be care- 
 fully remembered also that no Imperfect Induction can 
 give a certain conclusion. It may be highly probable 
 or nearly certain that the cases unexamined will re*
 
 183 INDUCTION. 
 
 semble those which have been examined, but it can 
 never be certain. It is quite possible, for instance, 
 that a new planet might go rouad the sue in an opposite 
 direction to the other planets. In the case of the satel- 
 lites belonging to the planets more than one exception 
 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 proba- 
 bility or likelihood that all instances will agree with 
 those examined. Perfect Induction, on the other hand, 
 gives a necessary and certain conclusion, but it asserts 
 nothing beyond what was asserted in the premises. 
 
 Mp. Mill, indeed, differs from almost all other logicians in hold- 
 ing that Perfect Induction is improperly called Induction, because 
 it does not lead to any new knowledge. He defines Induction as 
 inference from the known to the unknown, and considers the unex- 
 amined 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 scientific value whatever, be- 
 cause the conclusion is a mere reassertion in a briefer form, a 
 mere summing up of tne premises I may point out, however, 
 that if Perfect Induction were no more than a process of abbre 
 iation it is yet of great importance, and requires to be continu- 
 ally used in. science and common life. Without it we could never 
 make a comprehensive btateraent, but should ha obliged to enu- 
 merate every particular. 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 bo required to go 
 over tlie list of books every time we desired to mnke any one 
 acquainted with the contents of the library. The fact is, that 
 the power of expressing 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 consiste in nothing but a series of
 
 INDUCTIVE SYLLOGISM. 183 
 
 processes for abbreviatiag addition and subtraction, and enabling 
 us to deal with a great number of units in a very short time, so 
 Perfect Induction is absolutely necessary to enable us to deal 
 with a great number of particular facts in a very brief space. 
 
 6. The Perfect Inductive SyHog:ism. 
 
 It is usual to represent Perfect Induction in the 
 form of an Inductive Syllogism, as in the following 
 instance . 
 
 Mercury, Venus, the Earth, etc., all move round the 
 
 sun from West to East; 
 Mercury, Venus, the Earth, etc., are all the known 
 
 Planets ; 
 Therefore all the known planets move round the sun 
 
 from West to East. 
 
 This argument is a true Perfect Induction because 
 the conclusion only makes an assertion of all known 
 planets, which excludes all reference to possible future 
 discoveries ; and we may suppose that all the known 
 planets have been enumerated in the premises. The 
 form of the argimient appears to be tiiat of a syllogism 
 in the third figure, namely Darapti, the middle term 
 consisting in the group of the known planets. In 
 reality, however, it is not an ordinary syllogism. The 
 minor premise states not that Mercury, Venus, the 
 Earth, Neptune, etc., are contained among the known 
 planets, but that they are those planets, or are identi- 
 cal with them. This premise is then a doubly uni- 
 versal proposition of a kind not recognized in the Aris- 
 totelian Syllogism. Accordingly we may observe thai 
 the conclusion is a universal proposition, which is not 
 allowable in the third figure of the syllogism.
 
 184 INDUCTION. 
 
 As another example of a Perfect Induction we maj 
 take 
 January, February December, each contain 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. 
 
 7. The Perfect Inductive Syllogism Di^iinctlve, 
 
 Although Sir W. Hamilton has entirely rejected the 
 Qotion, it seems worthy of inquiry whether the Induc- 
 tive Syllogism be not really of the Disjunctive form of 
 i^yllogism. Thus I 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 
 80 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 affirmed. The fact is that the 
 major premise of the syllogism given above is a com- 
 pound sentence with twelve subjects, and is there- 
 fore equivalent to twelve distinct logical propositions. 
 The minor premise is either a disjunctive proposition, 
 as I have represented it, or sometliing quite different 
 from anything we have elsewhere had. 
 
 8. The Imperfect Inductive Syllogism. 
 
 From Perfect Induction we shall have to pass to 
 Imperfect Induction ; but the opinions of Logicians are
 
 INDUCTIVE SYLLOGISM. 185 
 
 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, 
 
 ve evidently employ a false minor premise, because this, 
 that, and the other magnet which we have examined, 
 cannot possibly be all existing magnets. In whatever 
 form we put it there 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 considers that this 
 assumption should be expressed in one of the premises, 
 and he represents Induction as a Syllogism in Barbara 
 \s 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. 
 
 9. The Fundamental Assumption of Induction. 
 
 But though the above is doubtless a correct expres- 
 sion 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 assumption, and 
 under what circumstances such an assumption would 
 be likeiy to prove true. Some writers have asserted 
 that there is a Principle, called the Uniformity of Nature,
 
 188 INDUCTION. 
 
 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. 
 
 In his original work, and also in Ms " Principles of Science,* 
 Professor Jevons expresses his dissent from tlie doctrine of tho 
 Uniformity of Nature. This has led him into a controversy which 
 it would be only perplexing to review in tliis connection, and the 
 student is therefore referred below to the authorities who have 
 most ably treated the subject. It is perhaps sufficient for the 
 young learner to know that the truth of the doctrine of the 
 Uniformity of Nature is essential to the validity of an Imperfect 
 Induction. 
 
 The advanced student may consult the following with advan- 
 tage: 
 Mansel's Aldrich, Appendix, Notes G and H. 
 Hamilton's Lectures on Logic, Lecture XVII, and Appendix 
 
 VII, On Induction and Extimple. 
 J. S. Mill's System of Logic, Book III, Chap. 2, Of Inductions 
 
 improperly Ko-called. Also, Jevons' Principles of Science, 
 
 pp. 218, 229 ; and Fowler's Inductive. Logic, Third Edition, 
 
 pp. xi, xxiii. 
 
 In this section, on " The Inductive Syllogrism,*' 
 we have considered : 
 
 1. Induction and Deduction Contrasted. 
 
 2. The Explanation of Traduction. 
 
 3. The Importance of Induction. 
 
 4. Perfect and Imperfect Induction. 
 
 5. The Difference between Perfect and Imperfect 
 Induction. 
 
 6. Tlie Perfect Inductii^e Sj/llof/ism. 
 
 7. The Perfect Inductive St/lfor/isiu Disjunctive. 
 
 8. The Imperfect Inductive Si/llogism. 
 
 9. The Fundamental Asnumption of Induction.
 
 FOBMS OF INDUCTION. 187 
 
 8BCTIGH IL 
 
 THE FORMS OF INDUCTION. 
 1. The Character of the Data. 
 
 It is now indispensable that we should consider with 
 great care upon what grounds Imperfect Induction is 
 founded. No difficulty is encountered in Perfect In- 
 duction because all possible cases which can come 
 under the general conclusion 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 reasoning, 
 which require that the information contained in the 
 conclusion should be shown only from the data, and 
 that we should merely unfold, or transform into an 
 explicit statement what is contained in the premises 
 implicitly. 
 
 In Imperfect Induction the process seems to be of a 
 vvhoUy different character, since the instances concern- 
 ing which we acquire knowledge may be infinitely more 
 numerous than those from which we acquire the knowl- 
 edge. 
 
 (1) Geometrical Reasoning has a close resemblance 
 to inductive reasoning. When in the fifth proposition 
 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 particular triangle as an ex- 
 ample. A figure is given which the reader is requested
 
 188 INDUCTION. 
 
 to regard as having two equal sides, and it is conclu. 
 sively 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 triangles ; 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 evidently be an infinite number of isosceles tri- 
 angles as regards the length of the equal sides, and each 
 of these may be infinitely varied by increasing or 
 diminishing the contained angle, so that the number of 
 possible isosceles triangles is infinite ; and yet we are 
 asked to believe of this incomprehensible number of 
 objects what we have proved only of one single speci- 
 men. This might seem to be the most extremely Im- 
 perfect Induction possible, and yet every one allows 
 that it gives us really certain knowledge. We do know 
 with as much certainty as knowledge can possess, that 
 if lines be conceived as drawn from the earth to two 
 stars equally distant, 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 Jcnow that 
 all isosceles triangles exactly resemble 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
 
 FOBMS OF INDUCTION. 189 
 
 the proof depended they were purely accidenbil cir- 
 cumstances; 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 knowl- 
 edge contained in the mathematical sciences not only all the 
 geometrical truths, but all general algebraical truths. It was 
 shown, for instance, in page 61, that if a and b be two quantities, 
 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 b7, the product of the 
 sum and difference is 17x3=51; the squares of the quantities 
 are 10 x 10 or 100 and 7 x 7 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 proved algebiaically there was no 
 condition which restricted the result to any particular numbers, 
 and a and b might consequently be any numbers whatever. This 
 generality of algebraical reasoning by which a property is proved 
 of infinite varieties of numbers at once, is one of the chief ad- 
 vantages of algebra over arithmetic. 
 
 (2) Mathematical Induction, or Demonstrative Induc- 
 tion, is a process which shows the powers of retisoiiing 
 in a very conspicuous way. A good example is found in 
 the following problem: If we take the first two con- 
 secutive odd numbers, 1 and 3, and add them together, 
 the sum is 4, or exactly twice tioo ; if we take three 
 such numbers 1-1-3 + 5, the sum is 9, or exactly three 
 times three; if we take /o'/r, namely l+3-r5-f 7, the 
 sum is 16, or exactly /o2/r 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 multiplied 
 by itself. Any one who knows a very little algebra can 
 prove that this remarkable law is universally true, os
 
 190 INDUCTION. 
 
 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+ ...+(2w-l) = . 
 
 Now add 2n + 1 to each side of the equation. It fol 
 lows that 
 
 1 + 3 4-5 + 7+ +{2nl) + {2n + l) = 7i^ + 2n + l. 
 
 But the last quantity n^ + 271 + 1 is just equal to 
 (n + 1)^; so that if the law is true for n terms it is true 
 also for w + 1 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 
 Jabor could a person ascertain by trial what is the sum 
 of the first bilHon odd numbers, and yet symbolically 
 or by general reasoning we know with certainty that 
 they would amount to a billion billion, and neither 
 more nor less even by a unit. This process of Mathe- 
 matical Induction is not exactly the same as Geo- 
 metrical Induction, because each case depends upon the 
 last, but the proof rests upon an equally narrow basis 
 of experience, and creates knowledge of equal certainty 
 and generality. Such mathematical truths depend 
 upon observation 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 undoubtingly believe 
 what is true of one case to bo true of another. 
 
 (3) Uncertain Data. It is very instructive to contrast 
 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 multiplied by itself, added to itself and then added
 
 FORMS OF INDUCTION. 191 
 
 to 41, the result would be a prime number, that is a 
 number which could not be divided by any other in- 
 tegral number except unity ; in symbols, 
 
 a;* + a; + 41= prime number. 
 
 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 successively made equal 
 to the numbers in the first line below, the expression 
 ir2+a:4-41 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 is found that the 
 rule does not always hold true, but fails when a;=40. 
 Then we have 40 x 40 + 40 + 41 = 1681, but this is clearly 
 equal to 41x40 + 41 or 41x41, and is not a prime 
 number. 
 
 In that branch of mathematics which treats of the peculiar 
 properties and kinds of numbers, other propositions depending 
 solely upon observation have been asserted to be ahvays true. 
 Thus Fermat believed that 2^ + 1 always represents 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 instance 
 proves a general and certain pule, while in others a very 
 great number of instances are insufficient to give any 
 certainty at all; all depends upon the perception we
 
 192 INDUOTION. 
 
 have of similarity or identity between one casb and an- 
 other. We can perceive no similarity between all prime 
 numbers which assures us that because one is repre- 
 ueuted by a certain formula, also another is ; but we 
 do find such similarity between the sums of odd num- 
 bers, or between isosceles triangles. 
 
 (4) Inductions in Physical Science Involve Exactly 
 Similar Differences. When a chemist analyzes a few 
 grains of water and finds that they contain exactly 8 
 parts of oxygen and 1 of hydrogen for 9 parts of water, 
 he feels warranted in asserting that the same is true ot 
 all pure water wliatever be its origin, and whatever be 
 the part of the world from which it comes. But if he 
 analyze 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 searwater 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. Ex- 
 tended experience shows that granite is very variable in 
 composition, but that sea-water is rendered pretty uni- 
 form by constant mixture of currents. Nothing but 
 experience in these cases could inform us how far we 
 may assert safely of one sample what we have ascertained 
 of another. But we have resison to believe that chemi- 
 cal compounds are naturally fixed and invariable in 
 composition, according to Dalton's laws of combining 
 proportions. No d priori reasoning from the principles 
 of thonght could have told us this, and we only leam 
 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 w
 
 FORMS OV INUUCTION. 198 
 
 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 analysis 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 In- 
 ductions in physical science are only probable, or that 
 if certain, it is only liypotheticul certainty they possess. 
 Can I be absolutely oertain that all water contains one 
 part of hydrogen in nine ? " I am certain only on two 
 conditions: 
 
 1. That this was certainly the composition of the 
 sample tried. 
 
 2. That any other substance I call water exactly 
 
 resembles that sample. 
 But even if the first condition be undoubtedly true, I 
 tan not be certain of the second. For how do I know 
 what is water except by the fact of its being a trans- 
 parent liquid, freezing into a solid and evaporating into 
 steam, possessing a high specific heat, and a number of 
 other distinct properties? But can I be absolutely cer- 
 tain that every liquid possessing all these properties is 
 water? Practically I can be certain, but theoretically 
 I cannot. Two substances may have been created so 
 like each other that we should never yet liave discovered 
 the difference ; we might then be constantly misled by 
 assuming of the one what is only true of the other. 
 That this should ever happen with substances possess- 
 ing the very distinct qualities of water is excessively 
 improbable, but so far is it from being impossible oi 
 improbable in other cases, that it has often happened. 
 9
 
 194 INDUCTION. 
 
 Most of the new elements discovered in late years have, with 
 out doubt, l)eeu mistaken previously for other elements. Csesium 
 and Rubidium had been long mistaken for each other, and for 
 Potassium, before they were distinguished by Bunsen and Kirch- 
 hoff by means of the spectroscope. As they are now known to 
 be widely distributed, although in small quantities, it is certain 
 that what was supposed to be Potassium in many thousands of 
 analyses was partly composed of difl'erent substances. Selenium 
 had probably been confused with Sulphur, and there are certain 
 metals for instance, Rhodium, Ruthenium, Iridium, Osmium, 
 and Beryllium Yttrium, Erbium, Cerium, Lanthanum, and 
 Didymium Cadmium and Indium which have only recently 
 been distinguished. The progress of science will doubtless show 
 that we are mistaken in many of our identifications, and various 
 difficulties thus arising will ultimately be explained. 
 
 (5) Future Phenomena. Take again a very ditlerent 
 case of induction. Are we certain that the sun will rise 
 again to-morrow morning as it has risen for many 
 thousand years, and probably for some hundred million 
 years? We are certain only on this condition or hypo- 
 thesis, that the planetary system proceeds to-morrow as 
 it has proceeded for so long. Many causes miy exist 
 which might at any moment defeat all our calculations ; 
 our sun is believed to be a variable star, and foi what 
 we know it might at any moment suddenly explode or 
 flure up, as certain other stars have been observec' to 
 do, and we should then be all turned into thin lumi- 
 nous vapor in a moment of time. It is not at ail impos- 
 sible that ji collision did once occur in the planetary 
 system, and that the minute planets or asteroids are the 
 result. Even if there is no large meteor, comet or 
 other body capable of breaking up the earth h\ colli- 
 gion, yet it is probable that the sun moves throug-i* space 
 t the rate of nearly 300 miles per minute, and i* *ime
 
 FORMS OF INDUCTION. 19ft 
 
 other star should meet us at a similar rate the 
 consequences would be inconceivably terrible. It 
 is highly improbable, however, that such an event 
 should come to pass even in the course of a million 
 years. 
 
 (G) General Law from the Inspection of Data. No 
 mere Imperfect Induction can give certain knowledge ; 
 all inference proceeds upon the assumption that new 
 instances will exactly resemble old ones in all material 
 circumstances; but in natural phenomena this is purely 
 hypothetical, and we may constantly find ourselves in 
 error. In Mathematical Induction certainty arose from 
 the cases being hypothetical in their own nature, or 
 being made so as exactly to correspond with the condi- 
 tions. We cannot assert that any triangle existing in 
 nature has two equal sides or two equal angles, and it 
 is even impossible in practice that any two lines or 
 angles can be absolutely equal. But it is nevertheless 
 true that if the sides are equal the angles are equal. 
 All certainty of inference is thus relative and hypothe- 
 tical. Even in the syllogism the certainty of the con- 
 clusion only rests on the hypothesis of certainty in 
 the premises. It is probable, in fact, that all reason- 
 ing reduces itself to a single type that what is true of 
 one thing will be true of another thing, on condition of 
 there being an exact resemblance between them in all 
 material circumstances. 
 
 2. Special Kinds of Iiiductioii. 
 
 There are two special varieties of Induction that 
 deserve to be more particularly noticed : 
 
 (1) Reasoning by Analogy. In strictness an analogy
 
 196 INDUCTION. 
 
 is not an identity of one thing with another, but an 
 identity of relations. In the case of numbers 7 is not 
 identical with 10 nor 14 with 20, but the ratio of 7 to 
 10 is identical with the ratio of 14 to 20, so that there is 
 an analogy between these numbers. To multiply two 
 by two is not the same thing as to construct a square 
 upon a line two units long ; but there is this analogy 
 that there will be just as many units of area in the 
 square as there are units in the product of two by two. 
 This analogy is so evident that we fearlessly assert a 
 square mile to consist of 1760 x 1760 square yards with- 
 out any trial of the truth. In ordinary language, how- 
 ever, analogy has come to mean any resemblance be- 
 tween things which enables us to believe of one what 
 we know of the other. 
 
 Thus the planet Mars possesses an atmosphere, with 
 clouds and mist closely resembling our own ; it has seas 
 distinguished from the land hy a greenish color, and 
 polar regions covered with snow. The red color of the 
 planet seems to be due to the atmosphere, like the red 
 color of our sunrises and sunsets. So much is simihir 
 in the surface of Mars and the surface of the Earth that 
 we readily argue that there must be inhabitants there 
 as here. All that we can cert-ainly say, however, is, 
 that if the circumstances be really similar, and similar 
 germs of life have been created there as here, there 
 must be inhabitants. The fact that many circum- 
 ptiinces are similar increases the probability. But be- 
 tween the Earth and the Sun the analogy is of a much 
 fainter character; we speak indeed of the sun's atmos- 
 phere being subject to storms and filled with clouds, 
 but these clouds are heated probably beyond the tem*
 
 FORMS OF INDUCTION". 197 
 
 perature of our hottest furnaces ; if they produce rain 
 it must resemble a shower of melted iron ; and the sun- 
 spots are perturbations of so tremendous a size and 
 character, that the earth together with half-a-dozen of 
 the other planets could readily be swallowed up in one 
 of them. It is plain then that there is little or no 
 analogy between the Sun and the Earth, and we can 
 therefore with difficulty form a conception of anything 
 going on in a sun or star. 
 
 Argument from analogy may be defined as direct inductive 
 inference from one instance to any similar instance. It may, as 
 Mr. Mill says, be reduced to the following formula : 
 
 "Two things resemble each other in one or more respects ; a 
 certain proposition is true of the one ; therefore it ia true of the 
 other." This is no doubt the type of all reasoning, and the cer- 
 tainty of the process depends entirely upon the degree of resem- 
 blance or identity between the cases. In geometry the cases are 
 absolutely identical in all material points by hypothesis, and no 
 doubt attaches to the inference ; in physical science the identity 
 is a question of probability, and the conclusion is in a like degree 
 probable. It should be added that Mr. Mill considers Geometri- 
 cal and Mathematical Induction not to be properly called Induc- 
 tion, for reasons of which the force altogether escapes my appre- 
 hension ; but the reader will find his opinions in the 2d chapter 
 of the third book of his System of Logic. 
 
 (2) Reasoning by Examples is a form of inductive 
 inference consisting in the constant use of examples 
 and instances. The best way to describe the nature of 
 a class of things is to present one of the things itself, 
 and point out the properties which belong to the class 
 as distinguished from those peculiar to the thing. 
 Throughout these lessons, as throughout every work 
 on logic, instances of propositions, of compound oi
 
 198 INDUCTION. , 
 
 complex sentences, of syllogisms, etc., are continually 
 used, and the reader is asked to apply to all similar 
 cases what he observes in the examples given. It is 
 assumed that the writer selects such examples as truly 
 exhibit the properties in question. 
 
 While all inductive and analogical inferences rest upon the 
 same principles there are wide differences between the sources of 
 probability. In analogy we have two cases wliicli resemble each 
 other in a great many properties, and we infer that some addi- 
 tional property in one is probably to be found in the other. The 
 very narrow basis of experience is compensated by the high de- 
 gree of similarity. In the processes more commonly treated under 
 the name Induction, the things usually resemble each other only 
 in two or three properties, and we require to have more instances 
 to assure us that what is true of these is probably true of all 
 similar msiances. The less, in short, the intension of the resetn 
 blance the greater must be the extension of our inquiries. 
 
 Mr. Mill's System of Logic, Book III, Chap. XX. Of Analogy. 
 Mansel's Aldruih, App. Note H, On Example and Analogy. 
 
 In thi.s section, on " Tlie Forms of Induction,*' 
 we have considered : 
 
 1, The Character of the Data. 
 
 2. Special Kinds of Induction.
 
 CHAPTER yi. 
 METHOD. 
 
 In the investigation and communication of truth, we 
 may employ various modes of procedure, some of which 
 must be better than others. Whatever mode we em- 
 ploy is called our Method. This part of our subject is 
 strictly Applied Logic, being little more than the appli- 
 cation of the principles already discussed to the practi- 
 cal cases of discovery and exposition. We shall con- 
 sider Method in the following sections under these 
 three topics: (1) Inductive Method; (2) De- 
 ductive Method; (3) Complete Method. 
 
 The InductivP" Method is sometimes called the Method of Dis- 
 covery, and sometimes the Analytical Method. It begins with 
 facts apparent to the powers of observation, and has tlie difficult 
 task of detecting those universal laws or general principles wliich 
 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 which are more 
 simple or better known in nature {notiora naturee). The Deduc- 
 tive Method, Method of Instruction, or Synthetic Method, pro- 
 ceeds in the opposite direction, beginning witli the things notiora 
 naturw, and proceeding to show or explain the things nobig 
 notiora. The difference is almost like that between 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 except 
 such as he may meet in his own diligent and sagacious search. 
 
 It is very important indeed that the reader should clearly 
 apprehend the meanings of Analysis and Synthesis. Analysis \a
 
 200 METHOD. 
 
 the process of separating a whole into its parts, and Synthesis 
 the combinaiiou of parts into a whole. The analytical chemist, 
 who receives a piece of mineral for examination, may be able to 
 separate completely tlie 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 to- 
 gether carefully weighed quantities of certain simple substances 
 and combines them into a new compound substance ; this is 
 chemical synthesis. Logical analysis and synthesis 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 example in the elements of geometry. In Euclid we 
 begin with certain simple notions of points, straight lines, 
 angles, right angles, circles, etc. 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 triangle. Joining 
 four other equal lines at right 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 shown in the 47th Proposition of Euclid's first l)ook. This is 
 a perfect instance of combining simple ideas into more complex 
 ones. 
 
 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 nroperties 
 which it possesses, to resolve it into its se^parate parts, and to 
 amsider the properties of those parts each distinct from the 
 oUhera 
 
 To express the difference between knowledge derived deduc- 
 tively and that obtained inductively, the T^atin phrases d priori 
 and fi posteriori are often used. By A priori reasoning we mean 
 argument based on truths previously known ; A posteriori rea 
 toning, on the contrary, proceeds to infer from the consequences
 
 INDUCTIVE METHOD. 201 
 
 of a general truth what that general truth is. Many philosophers 
 consider that the mind is naturally in possession of certain lawa 
 or truths which it must recognize in every act of thought ; all 
 Buch, if they exist, would be d priori truths. It cannot be 
 doubted, for instance, that we must always recognize in tliought 
 the three Primary Laws of Thought. We have there an a piiori 
 knowledge that " matter cannot both have weight and be without 
 weight," or that "every thing must be either self-luminous or 
 not self-luminous." 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 acquainted with all the secrets of creation, we have 
 to learn them by observation, or by the a posteriori method. 
 
 SBGTIOIT I, 
 
 INDUCTIVE METHOD. 
 
 1. The Search for Facts. 
 
 All knowledge, it may be safely said, must be ulti- 
 mately founded upon experience, which is but a general 
 name for the various feelings impressed upon the mind 
 at any period of its existence. The mind never creates 
 entirely new knowledge independent of experience, and 
 all that the reasoning powers can do is to arrive at the 
 full meaning of the facts which are in our possession. 
 In previous centuries men of the highest ability have 
 held that the mind of its own power alone could, by 
 sufficient cogitation, discover what things outside us
 
 *402 MBTHOD. 
 
 should be, and would be found to be on examination. 
 They thought that we were able to anticipate Natun 
 by evolving from the human mind an idea of what 
 things would be made by the Creator. The celebrated 
 philosopher Descartes thus held that whatever the 
 mind can clearly conceive may be considered true ; but 
 we can conceive the existence of mountains of gold or 
 oceans of fresh water, which do not as a fact exist. 
 Anything that we can clearly conceive must be con- 
 formable to the laws of thought, and its existence is 
 then not impossible, so far as our intellect is concerned ; 
 but the forms and sizes and manners in which it has 
 pleased the Creator to make things in this or any other 
 part of the universe, cannot possibly be anticipated by 
 the exceedingly limited wisdom of the human mind, 
 and can only be learnt by actual examination of exist- 
 ing things. 
 
 In the latter part of the 13th century the great Roger Bacon 
 clearly taught in England the supreme importance of ex{x;rienc6 
 as the basis of knowledge; but the same doctrine was also, by a 
 curious coincidence, again uplield in the 17th century by the 
 great Chancellor Francis Bacon, after whom it has been called 
 the Baconian Philosophy. I believe tliat Roger Bacon was even 
 a greater man than Francis, whose fame is best known ; but the 
 words in which Francis Bacon procleimed the imjwrtance of 
 experience and experiment must lie ever memorable. In the 
 beginning of his great worK, the Novum Organum, or New In- 
 atrument, he thus points out our proper position as learners in 
 the world of nature. 
 
 " Man, the Servant and Interpreter of Nature, Ciin do and 
 understand as much as he has observed concerning the order of 
 nature in outward things or in tiie mind ; more, he can neither 
 know nor do." 
 
 The above is the first of tlie aphorisms or paragraphs with
 
 INDUCTIVE METHOD. 203 
 
 which the Ifovum Organum commences. In the second aphorism 
 lie asserts that the unaided mind can effect little and is liable tc 
 err ; assistance in the form of a definite logical method is requi- 
 site, and this it was the purpose of his New Instrument to fur- 
 nish. The 8d and 4th aphorisms must be given entire; they 
 are; 
 
 " Human science and human power coincide, because ignorance 
 of a cause deprives us of the effect. For nature is not conquered 
 except by obedience ; and what we discover as a cause by con- 
 templation becomes a rule in operation." 
 
 "Man can himself do nothing else than move natural bodies 
 to or from each other ; nature working within accomplishes the 
 rest. " 
 
 Thus we see that the first essential in the inductive 
 method is a knowledge of facts. This is obtained in 
 two ways: 
 
 (1) By Observation. -To observe is merely to notice 
 events and changes which are produced in the ordinary 
 course of nature, without being able, or at least attempt- 
 ing, to control or vary those changes. Thus the early 
 astronomers observed the motions of the sun, moon 
 and planets among the fixed stars, and gradually de- 
 tected many of the laws or periodical returns of those 
 bodies. Thus it is that the meteorologist observes the 
 ever-changing weather, and notes the height of the 
 barometer, the temperature and moistness of the air, 
 the direction and force of the wind, the height and 
 character of the clouds, without being in the least able 
 to govern any of these facts. The geologist again is 
 generally a simple observer when he investigates the 
 nature and position of rocks. The zoologist, the bota- 
 nist, and the mineralogist usually employ mere observa- 
 tion when they examine the animals, plants, and
 
 204 METHOD. 
 
 minerals, as they are met with in their natural cond\ 
 tion. 
 
 (2) By Experiment. In experiment, on the contrary, 
 we vary at our will the combinations of things and cir- 
 cumstances, and then observe the result. It is thus 
 that the chemist discovers the composition of water by 
 using an electric current to separate its two constituents, 
 oxygen and hydrogen. The mineralogist may employ 
 experiment when he melts two or three substances 
 together to ascertain how a particular mineral may 
 have been produced. Even the botanist and zoologist 
 are not confined to passive observation ; for by remov- 
 ing animals or plants to different climates and different 
 Boils, and by what is called domestication, they may 
 try how far the natural forms and species are capable 
 of alteration. 
 
 It is obvious that experiment is the most potent and 
 direct mode of obtaining facts where it can be applied. 
 We might have to wait years or centuries to meet 
 bccidentally with facts which we can readily produce at 
 any moment in a laboratory ; and it is probable that 
 most of the chemical substances now known, and many 
 excessively useful products, would never have been dis- 
 covered at all by waiting till nature presented them 
 spontaneously to our observation. Many forces and 
 changes too may go on in nature constantly, but in so 
 slight a degree as to escape our senses, and render some 
 experimental means necessary for their detection. Elec- 
 tricity doubtless operates in every particle of matter, 
 |x?rhap3 at every moment of time; and even the ancienta 
 could not but notice its action in the loadstone, in 
 lightning, in the Aurora Borealis, or in a piece ol
 
 INDUCTIVE METHOD, 206 
 
 rabbed amber (electrum). But in lightning electricity 
 was too intense and dangerous; in the other Ciises it 
 was too feeble to be properly understood. The science 
 of electricity and magnetism could only advance by 
 getting regular supplies of electricity from the common 
 electric machine or the galvanic battery, and by making 
 powerful electro-magnets. Most if not all the effects 
 which electricity produces must go on in nature, but 
 altogether too obscurely for observation. 
 
 Experiment, again, is rendered indispensable by tho 
 fact that on the surface of the earth we usually meet 
 substances under certain uniform conditions, so that 
 we could never learn by observation what would be the 
 nature of such substances under other conditions. Thus 
 carbonic acid is only met in the form of a gas, proceed- 
 ing from the combustion of carbon ; but when exposed 
 to extreme pressure and cold, it is condensed into a 
 liquid, and may even be converted into a snow-like 
 solid substance. Many other gases have in like manner 
 been liquefied or solidified ; and there is reason to be- 
 lieve that every substance is capable of taking all the 
 three forms of solid, liquid and gas, if only the condi- 
 tions of temperature and pressure can be sufficiently 
 varied. Mere observation of nature would have led us, 
 on tho contrary, to suppose that nearly all substances 
 were fixed in one condition only, and could not be con- 
 verted from solid into liquid and from liquid into gas. 
 
 It must not be supposed, however, that we can draw any pre- 
 cise line between observation and experiment, and say where 
 the one ends and the other begins. The difference is rather one 
 of degree than of kind ; and all we cfin say is that the more we 
 vary the conditions artificially the more we employ experiment
 
 206 METHOD. 
 
 I have said that meteorology is a science of nearly pare observa- 
 tion, but if we purposely ascend mountains to observe the rare- 
 faction aud cooling of the atmosphere by elevation, or if we make 
 balloon ascents for the same purpose, like Qay Lussac and 
 Glaisher, we so vary the mode of observation as almost to rendei 
 it experimental. Astronomers again may almost be said to ex- 
 periment instead of merely observing when they simultaneously 
 employ instruments as far to the north, and as far to the south, 
 upon the earth's surface as \ ossible, in order to observe the ap- 
 parent difference of place of Venus when crossing the sun in a 
 transit so as thus to compare the distances of Venus and the sun 
 with the dimensions of the earth. 
 
 2. The Rule for Observation. 
 
 Logic can give little or no aid in making an acute or 
 accurate observer. There are no definite rules which 
 can be laid down upon the subject. To observe well is 
 an art which can only be acquired by practice and 
 training ; and it is one of the greatest advantages of the 
 pursuit of the Natural Sciences that the faculty of clear 
 and steady observation is thereby cultivated. Logic 
 can, however, give us this caution, which has been well 
 pointed out by Mr. Mill to discriminate accurately 
 between what we really do observe and what we only 
 infer from the facts observed. So long as we only 
 record and describe what our senses have actually 
 witnessed, we cannot commit an error ; but the moment 
 we presume or infer anything we arc liable to mistake. 
 For instance, we examine the sun's surface with a tele- 
 scope and observe that it is intensely bright except 
 where there are small breaks or circular openings in 
 the surface with a dark interior. We are in-esistibly 
 led to the conclusion that the inside of the sun is colder 
 ind darker than the outside, and record as a fact tliat
 
 INDUCTIVE METHOl,. 207 
 
 we saw the dark interior of the sun through certain 
 openings in its luminous atmosphere. Such a record, 
 however, would involve mistaken inference, for we saw 
 nothing but dark spots, and we should not have done 
 more in observation than record the shape, size, appear- 
 ance and change of such spots. Whether they are dark 
 clouds above the luminous surface, glimpses of the dark 
 interior, or, as is now almost certainly inferred, something 
 entirely different from either, can only be proved by a 
 comparison of many unprejudiced observations. 
 
 The reader cannot too often bear in min^ the caution 
 against confusing facts observed with infere.ices from 
 those facts. It is not too much to say that nin*^-tenths 
 of what we seem to see and hear is inferred, not nally 
 felt. Every sense possesses what are called acquired 
 perceptions, that is, the power of judging unconsciously, 
 by lon^ experience, of many things which cannot be 
 the objects of direct perception. The eye cannot see 
 distance, yet we constantly imagine and say that we 
 see things at such and such distances, unconscious that 
 it is the result of judgment. As Mr. Mill remarks, it is 
 too much to say *'I saw my brother." All I j^ositivel^ 
 know is that I saw some one who closely resembled my 
 brother as far as could be observed. It is by judg- 
 ment only I can assert he was my brother, and that 
 judgment may possibly be wrong. 
 
 Nothing is more important in observation and experi- 
 ment than to be uninfluenced by any prejudice or theory 
 in correctly recording tlie facts observed and allowing 
 to them their proper weight. He who does not do so 
 will almost always be able to obtain facts in support of 
 an opinion however erroneous.
 
 208 METHOD. 
 
 8* The Uses of Hypothesis and Theory. 
 
 In order to carry on observation and experiment sue 
 cessfuUy, it is frequently necessary to form some hypo* 
 thesis, or theory, to direct the course of inquiry. We 
 ^vill therefore notice these forms of supposition more 
 particularly. 
 
 (1) Hypothesis is derived from the Greek words v-rrd, 
 under, and Oioig, placmr/, and is therefore exactly 
 synonymous with the Latin word supposition a placing 
 under, whence our common word supposition. It ap- 
 peal's to mean in science the imagining of some thing, 
 force or cause, which underlies the phenomena we are 
 examining, and is the agent in their production with- 
 out being capable of direct observation. In mailing 
 a hypothesis we assert the existence of a cause on the 
 ground of the effects observed, and the probability 
 of its existence depends upon the number of diverse 
 facts or partial laws that we are thus enabled to ex- 
 nlain or reduce to harmony. To be of any value at all 
 a hypothesis must harmonize at least two different 
 facts. If we account for the effects of opium by sa}ing 
 leith Moliere that it possesses a dormitive power, or say 
 that the magnet atti^acts because it has a magnetic 
 power, every one can see that we gain nothing. We 
 know neither more nor less about the dormitive or 
 magnetic power than we do about opium or the mag- 
 net. But if we suppose the magnet to attract because 
 it is occupied by circulating currents of electricity the 
 hypothesis may seem a very improbable one. but ia 
 valid, because we thus draw a certain analogy between 
 a magnet and a coil of wire conveying electricity. Such
 
 INDUCTIVE METHOD. 209 
 
 a coil of wire attracts other coils exactfy in the way that 
 one magnet attracts another ; so that this hypothesis 
 enables us to harmonize several diflPerent facts. The ex- 
 istence of intense heat in the interior of the earth is hypo- 
 thetical in so far as regards the impossibility of actually 
 seeing and measuring the heat directly, but it harmo 
 nizes so many facts derived from different sources that 
 we can hardly doubt its existence. Thus the occurrence 
 of hot springs and volcanoes are some facts in its favor, 
 though they might be explained on other grounds ; the 
 empirical law that the heat increases as we sink mines 
 in any part of the earth's surface is stronger evidence. 
 The intensely heated condition of bhe sun and other 
 stars is strongly confirmatory as showing that other 
 bodies do exist in the supposed condition of the earth's 
 interior. The cool state of the earth's surface is per- 
 fectly consistent with its comparatively small size and 
 the known facts and laws concerning the conduction 
 and radiation of heat. And the more we learn con- 
 cerning the way in which the sun's heat is supplied by 
 the fall of meteoric matter, the more it is probable that 
 the earth may have been intensely heated like the sun 
 at some former time, altiiough for an immense period 
 ic has been slowly growing colder. A supposition 
 coinciding with so many facts, laws, and other probable 
 hypotheses, almost ceases to be hypothetical, and its 
 high probability causes it to be regarded as a known 
 fact. 
 
 Provided it is consistent with tLe laws of thought there is 
 nothing that we may not have to accept as a probable hypothesis, 
 however difScolt it may be to conceive and understand. The 
 force of gravity is hypothetical in so far that we know it only bi
 
 210 METHOD. 
 
 its effects upon the motions of bodies. Its decrease at a distanoa 
 harmonizes exactly indeed with the way in which light, sound, 
 electric or magnetic attractions, and in fact all influences wliich 
 emanate from a point and spread through space, decrease ; hence 
 it is probable that the law of the inverse square is absolutely 
 true. But in other respects gravity is strongly opposed to all our 
 ideas. If sound could travel to the sun as rapidly as in the 
 earth's atmosphere it would require nearly fourteen years to 
 reach its destination; were the sun and earth united by a solid 
 continuous bar of iron, a strong pull at one end would not be felt 
 at the other until nearly three years had passed. Light indeed 
 comes from the sun in rather more than eight minutes ; but what 
 are we to think of the force of gravity, which appears to reach 
 the sun in an instant so short that no calculations have yet been 
 able to detect any interval at all? In fact there seems some 
 reason to suppose that gravity is felt instantaneously throughout 
 the immeasurable regions of space. 
 
 {%) The word Theory has constantly been used in the 
 l&st few lessons, and deserves some examination. It 
 comes from the Greek dewpia, meaning contemplation, 
 reflection or speculation ; but this gives us little clue to 
 its modern use. In reality the word is highly am- 
 biguous, being sometimes used as equivalent to hypo- 
 thesis, at other times us equivalent to general law or 
 truth. When people form theories concerning comets, 
 the sun, the cause of earthquakes, etc., they imagine a 
 great many things which may or may not exist ; such 
 theories are really complicated hypotheses, and should 
 be so called. In this sen.se there are two theories of 
 electricity, one of which supposes the existence of a 
 single fluid which accumulates in some places and has 
 then a tendency to discharge itself towards places where 
 there is a deficiency, just as water always t^nds to find 
 its level ; the other supposes the existence of two fluids
 
 IKDUCTIVE METHOD. 211 
 
 rhich are commonly united, but when separated tend 
 to rush back into union again. These so-called theories 
 are really hypotheses, because we have no independent 
 evidence of the existence of any fluid, and it is now 
 almost certain that there is no such thing. The atomic 
 theory, again, is really a hypothesis suggested by Dal- 
 ton to explain the remarkable laws which he detected 
 in the proportions of chemical elements which com- 
 bine together. It is a valid hypothesis in so far 
 as it does really explain the fixedness of the quantities 
 which combine; but it is purely hypothetical as regards 
 the shapes, properties or absolute magnitudes of the 
 atoms, because we have no facts which it can harmonize 
 in these respects, and no apparent means of gaining 
 them. 
 
 In another and more proper sense theory is opposed 
 to practice, just as the general is opposed to the par- 
 ticular. The theory of gravitation means all the more 
 general laws of motion and attraction on which New- 
 ton founded his system of the Universe. We may 
 know what those laws are without being able to 
 determine the place of a planet or make any prac- 
 tical use of them ; the particular results must be 
 calculated out by skilful astronomers before navi- 
 gators, travellers or others can make practical use of 
 them in the determination of the latitude or longi- 
 tude. When we speak of the mathematical theory 
 of sound, the lunar theory, the theory of the tides, 
 the word is employed without any special reference 
 to hypothesis, and is merely equivalent to general 
 knowledge or science, implying tlie possession of a 
 complete series of general and accurate laws, but in no
 
 tl2 METHOD. 
 
 way distinguishing them from accurate knowledge in 
 general. When a word is really used in an equivocal 
 manner like theory, it is not desirable to attempt to 
 give it an accurate definition which would be imagi- 
 nary and artificial. 
 
 4. Definitions of Terms Employed in 
 Investigation. 
 
 It is important that the learner should have precise 
 ideas of the meaning of the following words employed 
 in the investigation of truth, and accordingly these 
 definitions are introduced at this point. 
 
 (1) The word Fact is used very often in this as in 
 most books, and demands a few remarks. It is derived 
 from factum^ the past participle of facere, to do, and 
 would thus mean something which is done, an act, or 
 deed ; but the meaning is evidently greatly extended by 
 analogy. We usually oppose to each other fact and 
 theory, but just as theory seems to have two ambiguous 
 meanings, so I believe that fact is ambiguous. Some- 
 times it means what is certain and known by the evi- 
 dence of the senses, as opposed to what is known only 
 probably by hypothesis and inference ; at other times it 
 J8 contrasted to a general law, and is equivalent to a 
 particular instance or case. A law of great generality 
 may often be as certain and true, especially in mathe- 
 matics, as the particular facts coming under it, so that 
 the contrast must in this case be that between the 
 general and particular. We often use the word too in 
 common life, as merely equivalent to fruih ; thus we 
 might say, " It is a fact that the primary laws of 
 thought are the foundation of -reasoning." In short, as
 
 INDUCTIVE METHOD. 213 
 
 theory means ambiguously what is hypothetical, general, 
 abstract, or uncertain, so fact is equally ambiguous, 
 and means confusedly what is intuitively knowu, par 
 ticular, concrete or certain. 
 
 (2) The word Phenomenon will also be often used. 
 It means simply anything which appears, and is there- 
 fore observed by the senses ; the derivation of the 
 word from the Greek word ^aiv6fj,evov, thai which op- 
 pears, exactly corresponds to its logical use. 
 
 (3) By the Cause of an event we mean the circum. 
 stances which must have preceded in order that the 
 event should happen. Nor is it generally possible to 
 say that an event has one single cause and no more. 
 There are usually many different things, conditions or 
 circumstances necessary to the production of an effect, 
 and all of them must be considered causes or necessary 
 parts of the cause. Thus the cause of the loud explo- 
 sion in a gun is not simply the pulling of the trigger, 
 which is only the last apparent cause or occasion of the 
 explosion ; the qualities of the powder, the proper form 
 of the barrel, the existence of some resisting charge, 
 the proper arrangement of the percussion cap and 
 powder, the existence of a surrounding atmosphercj 
 are among the circumstances necessary to the loud re- 
 port of a gun ; any of them being absent it would noJ 
 have occurred. 
 
 (4) The learner will perhaps have noticed the fre- 
 quent use of the word Tendency, and I have repeatedly 
 spoken of a cause as tending to produce its effect. If 
 the joint and homogeneous action of causes has been 
 clearly explained, it will now be clear that a tendency 
 means a cause which will produce an effect unless there
 
 314 METHOD 
 
 be opposite causes, which, in combinatior, with i^ 
 counteract and disguise that effect. Tlius when we 
 throw a stone into the air the attractive power of the 
 earth tends to make it fall, but the upward motion we 
 have impressed upon it disguises the result for a certain 
 time. The interminable revolving motion of the moon 
 round the earth is the result of two balanced tendencies, 
 that towards the earth, and that to proceed onward in 
 a straight line. The laws of motion and gravity are 
 such that this balance must always be preserved ; if the 
 moon by any cause were brought nearer to the earth its 
 tendency to fly off would be increased, and would ex- 
 ceed the effect of gravity until it had regained its proper 
 distance. A tendency then is a cause which may or 
 may not he counteracted. 
 
 (5) By an Antecedent we mean any thing, condition, 
 or circumstance which exists before or, it may De, at 
 the same time with an event or phenomenon. J3y a 
 Consequent we mean any thing, or circumstance, event, 
 or phenomenon, which is different from any of the 
 antecedents and follows after their conjunction or put- 
 ting together. It does not follow that an antecedent is 
 a cause, because the effect might have happened with- 
 out it. Thus the sun's light may be an antecedent to 
 the burning of a house, but not the cause, because the 
 house would bum equally well in the night. A neces- 
 sary or indispensable antecedent is, however, identical 
 with a cause, being that without which the effect would 
 not take place. 
 
 (C) A Law is a uniform mode of sequence, or rule of 
 action. The laws of nature are universal modes of 
 sequence, or general expressions for the order of phe-
 
 INDUCTIVE METHOD. 215 
 
 nomena. They are not causes, but the rules according 
 to which causes act. 
 
 5. Canons of Induction. 
 
 Mr. Mill has laid down several rules, or canons, for 
 the inductive determination of the laws of nature. 
 These rules express certain methods of induction. 
 
 (1) The first method of induction is tliat which Mr. 
 Mill has aptly called the Method of agreement. It de- 
 pends upon the rule that ''If two or more instances of 
 the phenomenon under investigation have only one cir- 
 cumstance in common, the circumstance in which alone 
 all the instances agree, is the cause (or effect) of the 
 given phenomenon." The meaning of this First Canon 
 of inductive inquiry might, I think, be more briefly 
 expressed by saying that the sole itivariable antecedent 
 %f a phenomenon is probably its cause. 
 
 To apply this method we must collect as many in- 
 stances of the phenomenon as possible, and compare 
 together their antecedents. Among these the causes 
 will lie, but if we notice that certain antecedents are 
 present or absent without appearing to affect the result, 
 we conclude that they cannot be necessary antecedents. 
 Hence it is the one antecedent or group of antecedents 
 always present, when the effect follows, that we con- 
 sider the cause. For example, bright prismatic colors 
 are seen on bubbles, on films of tar floating upon water^ 
 on thin plates of mica, as also on cracks in glass, or 
 between two pieces of glass pressed together. On ex- 
 amining all such cases they seem to agree in nothing 
 but the presence of a very thin layer or plate, and it 
 ippears to make no appreciable difference of what kind
 
 il6 METHOD. 
 
 of matter, solid, liquid, or gaseous, the plate is made. 
 Hence, we conclude that such colors are caused merely 
 by the thinness of the plates, and this conclusion ig 
 proved true by the theory of the interference of light. 
 Sir David Brewster beautifully proved in a similar way 
 that the colors seen upon mother-of-pearl are not caused 
 by the nature of the substance, but by the form of the 
 surface. He took impressions of the mother-of-pearl 
 in wax, and found that although the substance wa? 
 entirely different the colors were exactly the same. 
 And it was afterwards found that if a plate of metal 
 had a surface marked by very fine close grooves, it 
 would have iridescent colors like those of mother-of- 
 pearl. Hence it is evident that the form of the sur- 
 face, which is the only invariable antecedent or condi- 
 tion requisite for the production of the colors, must be 
 their cause. 
 
 The method of agreement is subject to a serious difficulty, 
 called by Mr. Mill the Plurality of Causes, consisting in the fact 
 that the same effect may in different instances be owing to differ- 
 ent causes. Thus if we inquire accurately into the cause of beat 
 we find that it is produced by friction, by burning or combustion, 
 by electricity, by pressure, etc.; so that it does not follow that if 
 there happened to be one and the same thing present in all the 
 cases we examined this would be the cause. 
 
 (2) The second method of induction which we will 
 now consider is free from this difficulty, and is known 
 as the Method of Difference. It is stated in Mr. Mill's 
 Second Canon as follows: 
 
 " If an instance in which the phenomenon under in- 
 vestigation occurs, and an instance in which it does not 
 occur, have every circumstance in common save one,
 
 INDUCTIVE METHOD. 217 
 
 that one occurring only in the former, the circum- 
 Btance in which alone the two instances dilBFer, is the 
 effect, or the cause, or an indispensable part of the 
 cause, of the phenomenon." 
 
 In other words, we may say that the antecedent which 
 is invariably present when the phenomenon follows, 
 and invariably absent when it is absent, other circum- 
 stances remaining the same, is the cause of the phe- 
 nomenon in those circumstances. 
 
 Thus we can clearly prove that friction is otie cause 
 of heat, because when two sticks are rubbed together 
 they become heated ; when not rubbed they do not be- 
 come heated. Sir Humphrey Davy showed that even 
 two pieces of ice when rubbed together in a vacuum 
 produce heat, as shown by their melting, and. thus com- 
 pletely demonstrated that the friction is the source and 
 cause of the heat. We prove that air is the cause of 
 sound being communicated to our ears by striking a 
 Oell in the receiver of an air-pump, as Hawksbee first 
 did in 1705, and then observing that when the receiver 
 is full of air we hear the bell ; when it contains little or 
 no air we do not hear the bell. We learn that sodium 
 or any of its compounds produces a spectrum having 
 a bright yellow double line by noticing that there is no 
 such line in the spectrum of light when sodium is not 
 present, but that if the smallest quantity of sodium be 
 thrown into the flame or other source of light, the 
 bright yellow line instantly appears Oxygen is the 
 cause of respiration and life, because if an animal be 
 put into a jar full of atmospheric air, from which the 
 oxygen has been withdrawn, it soon becomes suffocated. 
 
 This is essentially the great method of experiment, and its 
 10
 
 218 METHOD. 
 
 utility mainly depends upon the precaution of only varying one 
 eireurmtaiice at a time, all other circumdances being maintained 
 just a they were. This is expressed in one of the rules for con- 
 ducting experiments given by Thomson and Tait in their great 
 treatise on Natural Philosophy, Vol. I, p. 307, as follows :-^ 
 
 " In all cases when a particular agent or cause is to be studied, 
 experiments should be arranged in such a way as to lead if pos- 
 sible to results depending on it alone ; or, if this cannot be done, 
 they should be arranged so as to increase the effects due to the 
 cause to be studied till these so far exceed the unavoidable con- 
 comitants, that the latter may bo considered as only disturbing, 
 not essentially modifying, the effects of the principal agent." 
 
 It would be an imperfect and unsatisfactory experiment to 
 take air of which the oxygen has been converted into carbonic 
 acid by the burning of carbon, and argue that, because an animal 
 dies in such air, oxygen is the cause of respiration. Instead of 
 merely withdrawing the oxygen we have a new substance, car- 
 bonic acid, present, which is quite capable of killing the animal 
 by its own poisonous properties. Tlie animal, in fact, would be 
 suffocated even when a considerable proportion of oxygen re- 
 mained, so that the presence of the carbonic acid is a disturbing; 
 circumstance which confuses and vitiates the experiment. 
 
 It is ix)S8ible to prove the existence, and even to measure the 
 amount of the force of gravity, by delicately suspending a small 
 ball about the size of a marble and then suddenly bringing a very 
 heavy leaden ball weighing; a ton or more close to it. The small 
 ball will be attracted and set in motion ; but the experiment 
 would not be of the least value unless performed with the utmost 
 precaution. It is obvious that the sudden motion of the large 
 leaden ball would disturb the air, shake the room, cause currents 
 in the air by its coldness or warmth, and even occasion electric 
 attractions or repulsions ; and these would probably disturb the 
 small ball far more than the force of gravitation. 
 
 Beautiful instances of experiment according to this method are 
 to be found, as Sir John Ilerschel has pointed out, in the re- 
 searches by which Dr. Wells discovered the cause of dew. If on 
 a clear calm night a sheet or other covering be stretched a foot 
 or two above the earth , so as to screen the ground below from the
 
 INDUCTIVE METHOD. 219 
 
 open sky dew will be found on the grass around tlie screen ba 
 not beneath it. As the temperature aud moistuess of the air, ana 
 other circumstances, are exactly the same, the open sky must be 
 an indispensable antecedent to dew. Tlie same experiment is, 
 indeed, tried for us by nature, for if we make observations of dew 
 during two niglits which differ in nothing but the absence of 
 clouds in one and their presence in the other, we shall find that 
 the clear open sky is requisite to the formation of dew. 
 
 It may often happen that we cannot apply the method of differ- 
 ence perfectly by varying only one circumstance at a time. Thus 
 we cannot, generally speaking, try the qualities of the same sub- 
 stance in the solid and liquid condition without any other change 
 of circumstances, because it is necessary to alter the temperature 
 of the substance in order to liquefy or solidify it. The tempera- 
 ture might thus be the cause of what we attribute to the liquid 
 or solid condition. Under such circumstances we have to resort 
 to what Mr. Mill calls the joint method of agreement and differ- 
 ence, which consists in a double application of the method of 
 agreement, first to a number of instances where an effect is pro- 
 duced, and secondly, to a number of quite different instances where 
 tne effeci it xiot produced. It is clearly to be understood, however, 
 that the negative instances differ in several circumstances from the 
 positive ones ; for if they differed only in one circumstance we 
 might apply the simple method of difference. Iceland spar, for 
 instance, has a curious power of rendering things seen through 
 it apparently double. This phenomenon called double refraction, 
 also belongs to many other crystals ; and we might at once prove 
 it to be due to crystalline structure could we obtain any trans- 
 parent substance crystallized and uncrystallized, but subject to no 
 other alteration. We have, however, a pretty satisfactory proof 
 by observJDg that uniform transparent uncrystallized substances 
 agree in not possessing double refraction, and that crystalline 
 substances, on the other hand, with certain exceptions which are 
 easily explained, agree in possessing the power in question. 
 
 (3) The principle of tlie Joint Method may be stated 
 
 in the following rnle, which is Mr. Mill's Third Canon ; 
 
 " If two or more instances in which the pheuoraenoc
 
 220 METHOD. 
 
 occurs have only one circumstance in common, while 
 two or more instances in which it does not occur have 
 nothing in common save the absence of that circum- 
 stance; the circumstance in which alone the two sets 
 of instances (always or invariably) differ, is the efifect, 
 or the cause, or an indispensable part of the cause, of 
 the phenomenon." 
 
 1 have inserted the words in parentheses, as without them the 
 canon seems to me to express exactly tlie opposite of what Mr. 
 Mill intends. 
 
 It may facilitate the exact comprehension of these inductive 
 methods if I g^vethe following symbolic representation of them 
 in the manner adopted by Mr. Mill. Let A, B, G, D, E, etc, 
 be antecedents which may be variously combined, and let a, b, e, 
 d, e, etc., be effects following from them. If tlien we can collect 
 the following sets of antecedents and effects 
 
 Antecedents. Consequent* 
 ABC abe 
 
 ADE ode 
 
 AFO afg 
 
 AHK ahk 
 
 we may apply the method of agreement, and little doubt will 
 remdn that A, the sole invariable antecedent, is the cause of a. 
 
 The method of difference is sufficiently represented by- 
 Antecedents. Consequents 
 ABO dbc 
 BO ft 
 
 Here while B and O remain perfectly unaltered we find that the 
 presence or absence of A occasions the presence or absence of a. 
 of which it is tliereforo the cause, in the presence of B and 0. 
 But the readier may be cautioned against thinking tliat this provoi 
 il to be the cause of a under all circumBtances whatever.
 
 INDUCTIVE METHOD. 221 
 
 The joint method of agreement and difference is similarly 
 
 represented hy 
 
 
 Antecedents. 
 
 Consequeuta. 
 
 ABG 
 
 abe 
 
 ADB 
 
 ode 
 
 AFQ 
 
 <tfg 
 
 AHK 
 
 ahk 
 
 PQ 
 
 K 
 
 B8 
 
 n 
 
 TV 
 
 f 
 
 XT 
 
 m 
 
 Here the presence of A is followed as in the simple method of 
 agreement by a ; and the absence of ^4, in circumstances differ 
 ing from the previous ones, is followed by the absence of a. 
 Hence there is a very high probability that A is the cause of a. 
 But it will easily be seen that A is not the only circumstance in 
 which the two stits of instances differ, otherwise to any pair we 
 might apply the simple method of difference. But the presence 
 of ^ is a circumstance in which one set invariably, or uniformly, 
 or always, differs, from the other set. This joint method is thug 
 a substitute for the simpler method of difference in cases where 
 that cannot be properly brought into action. 
 
 (4) As soon as phenomena can be measured we can 
 apply a further method of induction of a very important 
 character. It is the method of difference indeed applied 
 under far more favorable circumstances, where every 
 degree and quantity of a phenomenon gives us a new 
 experiment and proof of connection between cause and 
 effect. It may be called the Method of Concomitant 
 Variations, and is thus stated by Mr. Mill, in what he 
 entitles the Fifth Canon of Induction : 
 
 *' Whatever phenomenon varies in any manner vi^hen*
 
 222 METHOD. 
 
 ever another phenomenon varies in some particulai 
 manner, is either a cause or an effect of that phe- 
 nomenon, or is connected with it through some fact 
 of causation." 
 
 Sir John Herschel's statement of the same method is 
 as follows : " Increase or diminution of the effect, with 
 the increased or diminished intensity of the cause, in 
 cases which admit of increase and diminution," to 
 which he adds, ''Reversal of the effect with that of 
 the cause." 
 
 The illustrations of this method are infinitely numer- 
 ous. Thus Mr. Joule, of Manchester, conclusively 
 proved that friction is a cause of heat by expending 
 exact quantities of force in rubbing one substance 
 against another, and showed that the heat produced 
 was exactly greater or less in proportion as the force 
 was greater or less. We can apply the method to many 
 cases which had previously been treated by the simple 
 method of difference; thus instead of striking a bell in 
 a complete vacuum we can strike it with a very little 
 air in the receiver of the air-pump, and we then hear a 
 very faint sound, which increases or decreases every 
 time we increase or decrease the density of the air. 
 This experiment conclusively satisfies any person that 
 air is the cause of the transmission of sound. 
 
 It is this method which often enables us to detect the 
 material connection which exists between two bodies. 
 For a long time it had been doubtful whether the red 
 flames seen in total eclipses of the sun belonged to the 
 sun or the moon ; but during the last eclipse of the 
 sun it was noticed that the flames moved v)ith the sun, 
 and were gradually covered and uncovered by the moon
 
 nTDUCnVE METHOD. 223 
 
 at successive instants of the eclipse. No one could 
 doubt thenceforth that tliey belonged to the sun. 
 
 Whenever, again, phenomena go through Periodic Changes, 
 alternately increasing and decreasing, we should seek for other 
 phenomena which go through changes in exactly the same 
 periods, and there will probably be a connection of cause and 
 effect. It is thus that the tides are proved to be due to the at- 
 traction of the moon and sun, because the periods of high and 
 low, spring and neap tides, succeed each other in intervals cor- 
 responding to the apparent revolutions of those bodies round the 
 earth. The fact that the moon revolves upon its own axis in 
 exactly the same period that it revolves round the earth, so that 
 for unknown ages past the same side of the moon has always 
 been turned towards the earth, is a most perfect case of concoini- 
 tant variations, conclusively proving that the earth's attraction 
 governs the motions of the moon on its own axis. 
 
 The most extraordinary case of variations, however, consists in 
 the connection which has of late years been shown to exist be- 
 tween the Aurora Borealis, magnetic storms, and the spots on the 
 Bun. It has only in the last 30 or 40 years become known that 
 the magnetic compass needle is subject at intervals to very slight 
 but curious movements ; and at the same time there are usually 
 natural currents of electricity produced in telegraph wires so as 
 to interfere with the transmission of messages. Tliese disturb- 
 ances are known as magnetic storms, and are often observed to 
 occur when a fine display of the Northern or Southern Lights is 
 taking place in some part of the earth. Observations during 
 many years have shown that these storms come to their worst at 
 the end of every eleven years, the maximum taking place about 
 the present year, 1870, and then diminish in intensity until the 
 next period of eleven years has passed. Close observations of 
 the sun during 30 or 40 years have shown that the size and num- 
 ber of the dark spots, which are gigantic storms going on upon 
 the sun's surface, increase and decrease exactly at the sam 
 periods of time as the magnetic storms upon the earth's surface. 
 No one can doubt, then, that these strange phenomena are con 
 Qected together, though the mode of the connection is quite uj
 
 224 METHOD. 
 
 known. It is now believed that the planets Jupiter, Saturn 
 Venus and Mars, are the real causes of the disturbances; for Bal- 
 four Stewart and Warren de la Rue have shown that an exact 
 correspondence exists between the motions of these planets and 
 the periods of tlie sun-spots. This is a most remarkable and 
 extensive case of concomitant variations. 
 
 (5) We have now to consider a method of induction 
 which must be employed when several causes act at 
 once and their effects are all blended together, pro- 
 ducing a joint effect of the same kind as the separate 
 effects. If in one experiment friction, combustion, 
 compression and electric action are all going on at once, 
 each of these causes will produce quantities of heat 
 which will be added together, and it will be difficult or 
 impossible to say how much is due to each cause 
 separately. We may call this a case of tiie homogeneous 
 intermixture of effects, the name indicating that the 
 joint effect is of the same kind as the separate eflFects. 
 Tt is distinguished by Mr. Mill from cases of the hetero- 
 geneous, or, as he says, the heteropathic intermixture 
 of effects, where the joint effect is totally different in 
 kind from the separate effects. Thus if we bend a bow 
 too much it breaks instead of bending further ; if we 
 larm ice it soon ceases to rise in temperature and 
 melts ; if we warm water it rises in temj)erature homo- 
 geneously for a time but then suddenly ceases, and an 
 effect of a totally different kind, the production of 
 vapor, or possibly an exj)losion, follows. 
 
 Now when the joint effect is of a heterogeneous kind 
 the method of difference is sufficient to ascertain the 
 cause of its occurrence. Whether a bow or a spring 
 irill break with a given weight may easily be tried, and
 
 IITDUCTIVE METHOD. 225 
 
 whether water will boil at a given temperature in ant 
 given state of the barometer may also be easily ascer- 
 tained. But in the homogeneous intermixture of eflfecta 
 we have a more complicated task. There are several 
 causes each producing a part of the effect, and we want 
 to know how much is due to each. In this case we 
 must employ a further inductive method, called by Mi. 
 Mill the Method of Residues, and thus stated in his 
 Fourth Canon : 
 
 *' Subduct from any phenomenon such part as is 
 known by previous inductions to be the effect of cer- 
 tain antecedents, and the residue of the phenomenon is 
 the effect of the remaining antecedents." 
 
 If we know that the joint effect a, h, c is due to the 
 causes A, B^ and C, and can prove that a is due to A 
 and h to B, it follows that c must be due to C. There 
 cannot be a simpler case of this than ascertaining the 
 exact weight of any commodity in a cart by weighing 
 the cart and load, and then subtracting the tare or 
 weight of the cart alone, which had been previously 
 ascertained. "We can thus too ascertain how much of 
 the spring tides is due to the attraction of the sun, pro- 
 vided we have previously determined the height of the 
 tide due to the moon, which will be about the average 
 height of the tides during the whole lunar month. 
 Then subtracting the moon's tide the remamder is the 
 sun's tide. 
 
 Newton employed this method in a beautiful experiment to 
 determine the elasticity of substances by allowing balls made of 
 the substances to swing against each other, and then observing 
 how far they rebounded compared with their oric^nal fall. But 
 the loss of motion is due partly to imperfect elasticity and partly
 
 226 METHOD. 
 
 to the reaistance of the air. He determined the amount of th 
 latter effect in the simplest manner by allowing the balls to 
 wing without striking each other, and observing how much each 
 ribratiou was less than the last. In this way he was enabled 
 easily to calculate the quantity that must be subtracted for the 
 Tesistance of the air. 
 
 It is this method that we employ in making allowance for th 
 errors or necessary corrections in observations. Few ther- 
 mometers are quite correct ; but if we put a thermometer into 
 melting snow, which has exactly the temperature of 0" Centi- 
 grade, or 32 Fahr., we can observe exactly how much below or 
 above the true point the mercury stands, and this will indicate 
 how much we ought to add or subtract from readings of the 
 thermometer to make them correct. The height of the barometer 
 is affected by several causes besides the variation of the pressure 
 of the air. It is decreased by the capillary repulsion between 
 the glass tube and the mercury ; it is increased by the expansion 
 of the mercury by heat, if the temperature be above 32 Fahr. ; 
 and it may be increased or decreased by any error in the length 
 of the mensnre employed to determine the height. In an accurate 
 observation ail these effects are calculated and allowed for in the 
 nal result. 
 
 In all sciences which allow of measurement of quantities this 
 method is employed, but more especially in astronomy, tlie most 
 exact of ail the sciences. Almost all the causes and effects in as- 
 tronomy have been found out as residual phenomena, that is, by 
 calculating the effects of all known attractions upon a planet or 
 satellite, and then observing how far it is from the place thus pie- 
 dicted. When this was very carefully done in the case of Uranus, 
 it was still found that the planet was sometimes before and some- 
 times behind its true place. This residual effect pointed to the 
 3xi8tence of some cause of attraction not then known, but which 
 was in consequence soon discovered in the shape of the planet 
 Neptune. The motions of several comets have in this way been 
 calculated, but it is observed that they return each time a little 
 Ater than they ought. This retardation points to the existence 
 of some oi)8tructive power in the space passed through, the 
 oatare of which is not yet understood.
 
 DEDUCTIVE METHOD. 22? 
 
 The student is strongly recommended to read Sir J. Herschera 
 Preliminary Discourse on the Study of Natural Philos'/phy 
 (Lardner's Cabinet CydopcBdia), especially Part II, CLiaps. 4 
 to 7, concerning Observation, Experiment, and the Inductive 
 Processes generally ; Mill's System of Logic, Book III, Chaps. 
 8, 10, 13 and 14. 
 
 In this section, on "Inductive Method," we 
 have considered: 
 
 1. The Search for Facts, 
 
 2. The Rule for Observation, 
 
 3. The Uses of Hyitotliesis and Theory 
 
 4. Dejinitions of Tertns Employed in Investi' 
 
 gation. 
 a. Canons of Induction, includiuf/ : 
 
 (1) The Method of Agreementf 
 
 (2) The Method of Difference, 
 
 (3) The Joint Method^ 
 
 (4) The Method of Concotnifant Variations, 
 
 (5) TJie Method of Residues, 
 
 SBCTIOIT n. 
 
 DEDUCTIVE METHOD. 
 1. The Predicables. 
 
 There are certain logical terms known as predicables 
 meaning the kinds of terras or attributes wliicli raaj? 
 always be predicated of any subject. Inasmuch as all 
 truth known to man may be stated in tbe form of a 
 proposition, it is important to know what these predi- 
 cables are. They are five in number: genus, species, 
 difference, property, and accident ; and when properlv
 
 238 METHOD. 
 
 employed are of exceeding use aud importance in logical 
 science. It would neither be possible nor desirable in 
 this work to attempt to give any idea of the various, 
 and subtle meanings which have been attributed to the 
 predicables by ancient writers, and the most simple and 
 useful view of the subject is what alone can be given 
 here. 
 
 (1) Any class of things may be called a genus (Greek 
 yevog, race or kind), if it be regarded as made up of 
 two or more species. "Element" is a genus when we 
 consider it as divided into the two species "metallic 
 and non-metallic.'* Triangle is a genus as regards the 
 species acute-angled, right-angled, and obtuse-angled. 
 
 (2) On the other hand, a species is any class which 
 is regarded as forming part of the next larger class, so 
 that the terms genus and species are relative to each 
 other, the genus being the larger class which is divided, 
 and the species the two or more smaller classes into 
 which the genus is divided. 
 
 (3) The difTerence may be defined as the quality or 
 sum of qualities which mark out one part of a genus 
 from the other part or parts. The difference (Latin 
 differentia, Greek dia(popd) cannot have any meaning 
 except in intension ; and when we use all the terms 
 wholly in intension we may say that the difference added 
 to the genus makes the species. Thus, if " building" be 
 the genus, and we add the difference " used for a dwell- 
 ing," we get the species " house." If we take " triangle " 
 as the genus, it means the sum of the qualities of 
 "three-sided rectilineal figure;" if we add the quality 
 of "having two sides equal," we obtain the species 
 "isosceles triangle."
 
 DEDUCTIVE METHOD. 229 
 
 It is indispensable, however, to regard these expressions in 
 the double meaning of extension and intension. From the ex- 
 planation of these different meanings in a previous chapter it 
 . will be apparent that the extent of a genus or species is simplj 
 the number of individuals included in it, and there will always 
 be fewer individuals in the species than in tlie genus. In extent 
 the genus buok includes all books of whatever size, language, or 
 contents ; if divided in respect to size the species of book are folio, 
 quarto, octavo, duodecimo, etc ; and, of course, each of these species 
 contains much fewer individual books than the whole genus. 
 
 In intension the genus means, not the individual things con- 
 tainec^ in it, but the sum of the qualities common to all those 
 things, and sufficient to mark them out clearly from other classes. 
 The species similarly means the sum of the qualities common to 
 all the individuals forming part of the genus, and sufficient to 
 mark them out from the rest of the genus, as well as from all other 
 things. It is evident, therefore, that there must be more qualities 
 implied in the meaning of the species than of the genus, for the 
 species must contain all the qualities of the genus, as well as a 
 certain additional quality or qualities by which the several 
 species are distinguished from each other. Now these additional 
 qualities form the difference. 
 
 It will easily be seen that the same class of things may be 
 both a genus and a species at the same time, according as we re- 
 gard it as divided into smaller classes or forming part of a larger 
 class. Thus triangle, which is a genus as regards isosceles 
 triangle, is a species as regards right-lined geometrical figures. 
 House is a species of building, but a genus with respect to man- 
 sion, cottage, villa, or other kinds of houses. We may, in fact, 
 have an almost interminable chain of genera and species, each class 
 being a species of the^ass next above it. and a genus as regards 
 that next below. Thus the genus British subject has the species 
 Born in the United Kingdom, Colonial-born, and Naturalized. 
 Each of these becomes a genus as regards the species male and 
 female ; each species again may be divided into adult and minor, 
 educated, uneducated, employed in some occupation or unem- 
 ployed, self-maintaining, maintained by friends, or pauper ; and 
 o on. The subdivision may thus proceed until we reach a class
 
 230 METHOD. 
 
 of so restricted extent, that it cannot be divided except into 
 individuals ; in this case the species is called the lowest species 
 or inflma species. All the intermediate genera and species of 
 the chain are called subaltern (Latin sub, under, and alter, the 
 other of two), because they stand one under the other. If there 
 is a genus wliich is not regarded as a species, that is, as part of 
 any higher genus, it is called the summum genus, the highest 
 genus, or genu^ generalissimum, the most general genus. It is 
 questionable whether we can thus set any limit to the chain of 
 classes. The class British subject is certainly not an absolute 
 summum genus, since it is but a species of 7nan, which is a 
 species of animal, living being, inhabitant of the earth, sub- 
 stance, and so on. If there were any real summum genus it 
 would probably be "Being," or " Thinjj," or "Object conceiv- 
 able ; " but we may usefully employ the terra to signify the 
 highest class of things comprehended in any science or classifica- 
 tion. Thus ' material substance " is the summum genus examined 
 JD the science of chemistry ; " inhabitant of the United King- 
 dom " is the summum genus enumerated and classified in the 
 British census. Logical terms are only a species of words or 
 phrases, but they are the summum genus as regards logic, which 
 has nothing to do with the various parts of speech and the rela- 
 tions of words, syllables, and letters, examined by grammarians. 
 
 Several very useful expressions have been derived from the 
 words genus and species. When a thing is so peculiar and un- 
 like other things that it cannot ensily be brought into one class 
 with them, it is said to be sui generis, or of its own genus; thus 
 the rings of Saturn are so diflTcrent from anything else among 
 the heavenly bodies that they may fairly be called sui generis. 
 In zoology, the Omithorhynchus, or Australian Duck-bill, the 
 AmphioxuB, and some other animals, are^fc peculiar that they 
 may be called sui generis. When a substance is the same in all 
 its parts, or w^hon a number of things are all alike;, we say that 
 they are liomttgeneous (Greek 6n<ir,, like, j'fvoc. kind), that is, of the 
 same nature ; otherwise they may be called heterogeneous (Greek 
 frepof, other). 
 
 It is necessnry to distinguish carefully the purely logical use of 
 the terms genua and species from their peculiar use in natural
 
 DEDUCTIVE METHOD. 231 
 
 history. A species is there a class of plants and animals sup 
 posed to have descended from coramon parents, and to be the 
 narrowest class jwssessing a fixed form ; the genus is the next 
 higher class. But if we accept Darwin's theory of the origin of 
 species, this definition of species becomes entirely illusory, since 
 diflFerent genera and species must have according to this theory 
 descended from common parents. The species then denotes a 
 merely arbitrary amount of resemblance which naturalists choose 
 to fix upon, and which it is not possible to define more exactly. 
 This use of the term, then, has no connection whatever with the 
 logical use, according to which any class of things whatever is a 
 species, provided it is regarded as part of a wider class or genus. 
 
 (4) The fourth of the Predicables is Property (Latin 
 proprium, Greek Idiov, own), which it is hardly possible 
 to define in a manner free from objection and difficulty, 
 but which may perhaps be best described as any quality 
 which is common to the whole of a class, but is not 
 necessary to mark out that class from other classes. 
 Thus it is a property of the genus " triangle" to have 
 the three internal angles equal to two right angles ; this 
 is a very remarkable circumstance, which is always 
 true of triangles, but it is not made a part of the genus, 
 or is not employed in defining a triangle, because the 
 possession of three straight sides is a sufficient mark. 
 The properties of geometncal figures are very numer- 
 ous ; the Second Book of Euclid is occupied in proving 
 a few properties of rectangles; the Third Book simi- 
 larly of circles. As we commonly use the term property 
 it may or may not belong to other objects as well as 
 those in question : some of the properties of the circle 
 may belong also* to the ellipse ; some of the properties 
 of man, as for instance the power of memory, or o/ 
 anger, may belong to other animals.
 
 232 METHOD. 
 
 Logicians have invented various subtle divisions of pro- 
 perties, but it will be suflBcient to say that a peculiar property is 
 one wliich belongs to the whole of a class, and to that class only, 
 as laitghter is supposed to belong only to mankind ; the property 
 of containing the greatest space in a line of given length is pecu- 
 liar to circles. When a property is not peculiar, it may belong to 
 other classes of objects as well as that of which it is called the 
 property. We may further distinguish the Generic Property, or 
 that which belongs to the whole of the genus, from the Specific 
 Property, which belongs to the whole of a lowest species. 
 
 (5) Lastly, an accident (Latin accidens, Greek avn3f' 
 (iTjKug) is any quality which may indifferently belong or 
 not belong to a class, as the case may be, without 
 affecting the other qualities of the class. The word 
 means that which falls or happens by chance, and has 
 no necessary connection with the nature of a thing. 
 Thus the absolute size of a triangle is a pure accident as 
 regards its geometrical properties; for whether the side 
 of a triangle be ^ of an inch or a million miles, what- 
 ever Euclid proves to be true of one is true of the other. 
 The birthplace of a roan is an accident concerning him, 
 as are also the clothes in which he is dressed, the posi- 
 tion in which he rests, and so on. Some writers dis- 
 tinguish separable and inseparable accidents. Tiius 
 the clothes in which a man is dressed is a separable 
 accident, because they can be changed, as can also his 
 position, and many other circumstances; but his birth- 
 place, his height, his Christian name, etc., are insepa- 
 rable accidents, because they can never he changed, 
 although they have no necessary or important relation 
 to his general character. 
 
 As an illustration of some part of the scheme of classification 
 described under the name of Prodicables, I may here give, as ii 
 usual in manuals of Logic, the Tree of Porphyry, a sort of ex-
 
 DEDUCTIVE METHOD. 
 
 233 
 
 ample of classification invented by one of the earliest Greek 
 logicians, named Porphyrias. I have simplified the common 
 form in which it is given by translating the Latin names and 
 omitting superfluous words. 
 
 In this Tree we observe a succession of genera and species 
 Substance, Body, Living Being, Animal and Man. Of these, 
 Substance is the summvm genua, because it is not regarded as a 
 species of any higher class ; Man is the infima species, because 
 It is a class not divided into any lower class, but only into 
 individuals, of whom it is usual to specify Socrates and Plato. 
 
 Substance, 
 
 Corporeal, 
 
 Incorporeal, 
 
 Body, 
 
 Animate, 
 
 Inanimate, 
 
 Living Being, 
 I Sensible, Insensible. 
 
 Animal, 
 
 Rational, 
 
 Irrational. 
 
 Man, 
 
 Socrates, Plato, and others. 
 
 Body, Living Being, and Animal are called subaltern genera
 
 234 METHOD. 
 
 and species, because each is a species as regards the next highei 
 g^nus, and a genus as regards the uext lower species. The 
 qualities implied in the adjectives Corporeal, Animate, Sensible 
 [i.e. capable of feeling) and Rational are the successive diflferencec 
 which occasion a division of eacli genus into species. It will 
 be evident that the negative parts of the genera, namely Incor- 
 poreal Substance, Inanimate Body, etc., are capable of sub- 
 division, which has not been carried out in order to avoid 
 confusing the figure. 
 
 2. Logical Division. 
 
 Logical division is the name of the process by which 
 we distinguish the species of which a genus is composed. 
 Thus we are said to divide tiie genus "book" when 
 we consider it as made up of the groups folio, quarto, 
 octavo, duodecimo books, etc., and the size of the books 
 is in this case the ground, basis, or principle of divi- 
 sion, commonly called the Fundamentum Divisionis. In 
 order that a quality or circumstance may be taken as 
 the basis of division, it must be present with some and 
 absent with others, or must vary with the different 
 species comprehended in the genus. A generic property 
 of course, being present in the whole of the genus, can- 
 not serve for the purpose of division. Three rules may 
 be laid down to which a sound and useful division must 
 conform : 
 
 1. The constituent species must exclude each other. 
 
 2. The constituent species must be equal when added 
 together to the genus. 
 
 3. The division must be founded upon one principle 
 or basis. 
 
 It would be obviously absurd to divide books into folio, quarto, 
 French, German and dictionari(>s, because these species overlap 
 each other, and there may be French or German dictionaries 
 which happen to be quarto or folio and belong to three different
 
 DEDUCTIVE METHOD. 235 
 
 species at ouce. A division of this kind is said to be a Cross 
 Division, because there is more than one principle of division, 
 and the several species in consequence cross each otlier and pro- 
 duce confusion. If I were to divide rectilineal figures into tri- 
 angles, parallelojrramB, rectangles and polygons of more than 
 four sides, I should commit all the possible faults in ono division. 
 The species parallelogram and rectangle do not exclude each 
 other, since all rectangles must be parallelograms ; the con- 
 stituent species are not altogether equal to the genus rectilineal 
 figure, since irregular four-sided figures which are not parallelo- 
 grams have been omitted ; and there are three principles of divi- 
 sion, namely the number of sides, the directions of those sidesi 
 and the angles contained. But when subdivision is employed, 
 and each of the species is ronsidered as a genus which may be 
 subjected to a further separation, a new principle of division may 
 and in fact must be employed each time. Thus I can divide 
 rectilineal figures according to the three principles mentioned 
 above: 
 
 Eectilineal Figure 
 
 8 sides 4 sides more than 4 sides 
 
 Triangle Quadrilateral Polygon 
 
 with parallel sides without parallel 
 
 Parallelogram sides 
 
 Trapezium. 
 
 Here the principles of division are the number of their sides, 
 and in the case of four-sided figures their parallelism. Triangles 
 do not admit of division in this second respect. We may make a 
 new division of parallelograms, adopting the equality of sides 
 and the size of the angles as the principles ; thus : 
 Parallelogram 
 
 adjoining sides adjoining sides 
 
 equal not equal 
 
 I I ' I. . 
 
 right- not right- right- not right 
 
 angled angled angled angled 
 
 Square Rhombus Oblong Rhomboid
 
 236 METHOD. 
 
 3. Dichotomy, or Exhaustive Division. 
 
 The most perfect divisions in a logical point of view 
 are })roduced by continually dividing each genus into 
 two species by a difference, of wiiich an example has 
 been given in the Tree of Porphyry. This process is 
 called Dichotomy (Greek (Ux"; in two; Te/tj'w, to cut) ; 
 it is also called Exhaustive Division because it always of 
 necessity obeys the second rule, and provides a place 
 for every possible existing thing. By a law of Thought 
 considered in a previous chapter, every thing must 
 either have a quality or not have it, so that it must fall 
 '.nto one or other division of the genus. This process 
 of exhaustive division has considerable importance, but 
 in practice it is not by any means always necessary or 
 convenient. It would, for instance, produce a need- 
 l*sly long classification if we divided rectilineal figures 
 t hus : 
 
 Rectilineal figure 
 
 I I 
 
 3-8ided not S-sided 
 
 Triangle 
 
 4-8ided not 4-8ided 
 
 Quadrilateral 
 
 5-8ided not 5-sided 
 
 Pentagon etc. 
 
 As we know beyond all doubt that every figure must 
 have 3, 4, 5, 6, or more sides, and no figure can belong 
 to more than one group, it is much better at once to 
 enumerate the parts as Triangle, Quadrilateral, Penta- 
 gon, Hexagon, etc. Again, it would be very awkward 
 if we divided the counties of England into Middlesex
 
 DEDUOTIVB METHOD. 237 
 
 and not-Middlesex ; the latter into Surrey and not- 
 Surrey ; the hitter, again, into Kent and not-Kent. Di- 
 chotomy is useless, and even seems absurd in these cases, 
 because we can observe the rules of division certainly in 
 a much briefer division. But in less certain branches of 
 knowledge our divisions can never be free from possible 
 oversight unless they proceed by dichotomy. Thus, 
 if we divide the population of the world into three 
 branches, Aryan, Semitic, and Turanian, some race 
 might ultimately be discovered which is distinct from 
 any of these, and for which no place has been provided ; 
 but had we proceeded thus 
 
 Man 
 
 ! 
 
 Aryan not- Aryan 
 
 Semitic not-Semitio 
 
 Turanian not Turanian, 
 
 it 18 evident that the new race would fall into the last 
 group, which is neither Aryan, Semitic, nor Turanian. 
 All the divisions of naturalists are liable to this incon- 
 venience. If we divide Vertebrate Animals into Mam- 
 malia, Birds, Reptiles, and Fish, it may any time 
 happen that a new form is discovered which belongs to 
 none of these, and therefore upsets the division. 
 
 A further precaution required in Division is not to proceed 
 from a high or wide genus at once to a low or narrow species, or, 
 as the phrase is, divisio nonfaciat sal turn (the division should not 
 make a leap) The species should always be those of the 
 proximate or next higher genus ; thus it would obviously be
 
 238 METHOD. 
 
 Inconvenient to begin by dividing geometrical figures into those 
 which have parallel sides and those which have not ; but tliis 
 principle oi division is very proper when applied to the proximate 
 genus. 
 
 Logical division must not be confused with physical division or 
 Partition, by which an individual object, as a tree, is regarded as 
 composed of its separate parts, root, trunk, branches, leaves, etc 
 There is even a third and distinct process, called Metaphysical 
 Division, which consists in regarding a thing as an aggregate of 
 qualities and separating these in thought; as when we discrimi- 
 nate the form, color, taste, and smell of an orange. 
 
 4. Deiluitiou. 
 
 Next to division the most important process of de- 
 ductive method is Logical Definition, by which we 
 determine the common qualities or marks of the objects 
 belonging to any given class of objects. We must give 
 in a definition the briefest possible statement of such 
 qualities as are sufficient to distinguish the class from 
 other classes, and determine its position in the general 
 classification of conceptions. Now this will be fulfilled 
 by regarding the class as a species, and giving the proxi- 
 mate genus and the difference. The word genus is here 
 used in its Intensive meaning, and denotes the qualities 
 belonging to all of the genus, and sufficient to mark 
 them out ; and as the difference marks out the part of 
 the genus in question, we get a perfect definition of tlie 
 species desired. But we should be careful to give in a 
 definition no superfluous marks; if these are accidents 
 and do not belong to the whole, the definition will be 
 improperly narrowed, as if we were to define Quadri- 
 lateral Figures as figures with four equal sides; if the 
 superfluous marks belong to all the things defined they 
 are Properties, and have no effect upon the definition
 
 DEDUCTIVE METHOD. 289 
 
 whatever. Thus if 1 define parallelograms as "four- 
 sided rectilineal figures, with the opposite sides equal 
 and parallel, and the opposite angles equal," I have 
 added two properties, the equality of the opposite sides 
 and angles which necessarily follow from the parallelism 
 of the sides, and only add to the complexity of the 
 definition without rendering it more precise. 
 
 There are certain rules usually given in logical 
 works which express the precautions necessai-y in de- 
 finition. 
 
 1. A definitiofi should state the essential attributes 
 of the species defined. So far as any exact meaning 
 can be given to the expression "essential attributes," 
 it means, as explained above, the proximate genus and 
 difference. 
 
 3. A definition must not contain the name defined. 
 For the purpose of the definition is to make the species 
 known, and as long as it is not known it cannot serve 
 to make itself known. When this rule is not observed, 
 there is said to be " circulus in definiendo," or " a circle 
 in defining," because the definition brings us round 
 again to the very word from which we started. This 
 fault will usually be committed by using a word in the 
 definition which is really a synonym of the name de- 
 fined, as if I were to define " Plant " as "an organized 
 being possessing vegetable life," or elements as simple 
 substances, vegetable being really equivalent to plant, 
 and simple to elementary. If I were to define metals 
 as "substances possessing metallic lustre," I should 
 either commit this fault, or use the term metallic lustre 
 in a sense which would admit other substances, and 
 thus break the following rule.
 
 240 METHOD. 
 
 3. A definition must be exactly equivalent to tht 
 species defined, that is to say, it must be an expression 
 the denotation of which is neither narrower nor wider 
 than the species, so as to include exactly the same ob- 
 jects. The definition, in short, must denote the species, 
 the whole species, and nothing but the species, and this 
 may really be considered a description of what a defini- 
 tion is. 
 
 4. A definition must not be expressed in obscure, 
 figurative, or ambiguous language. In other words, 
 the terms employed in the definition must be all exactly 
 known, otherwise the purpose of the definition, to make 
 us acquainted with the sufficient marks of the species, 
 is obviously defeated. There is no worse logical fault 
 than to define ignotum per igyiotius, the unknown by 
 the still more unknown. Aristotle's definition of the 
 Boul as " The Entelechy, or first form of an organized 
 body which has potential life," certainly seems subject 
 to this objection. 
 
 5. And lastly, A definition must not he negative where 
 it can be affirmative. This rule, however, is often not 
 applicable, and is by no means always binding. 
 
 5. Cla8sitication. 
 
 The joint use of division and definition is necessary 
 in the important work of classification, so prominent 
 in all scientific investigations. 
 
 Classification may perhaps be best defined as the 
 arrangement of things, or our notions of them, according 
 to their resemblances or identifies. Every class should 
 be so constituted as to contain objects exjictly resem- 
 bling each other in certain definite qualities, which are
 
 DEDUCTIVE METHOD. 24i 
 
 stated in the definition of the class. The more numer- 
 ous and extensive the resemblances whicli are thua 
 indicated by any system of classes, the more perfect and 
 useful must that system be considered. 
 
 A collection of objects may generally 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 their size, [2) according to 
 the language in which they are written, (3) according 
 to the alphabetic order of their author's 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 combined. 
 Each different arrangement presents some peculiar con- 
 venience, and that mode must be selected which best 
 meets the especial purpose of the library or catalogue. 
 The population of a kingdom, again, may be classified 
 in an almost endless number of ways with regard to 
 different purposes or sciences. The population of the 
 United Kingdom 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, Scandinavians, 
 etc. The statist arranges them according to age; to 
 condition, as married, unmarried, widowed, etc.; to 
 state of body, as able, incapacitated, blind, imbecile. 
 The political economist regards the innumerable trades 
 which are carried on, and classifies them in a complex 
 manner. The lawyer again treats every one as a minor, 
 11
 
 24?. METHOD. 
 
 an adult, a feme sole, a feme couverte, a guardian, 
 ward, trustee, felon, ancl so on. 
 
 The derivation of the word class is somewhat curious. In 
 ancient Rome it was tlie practice to summon the whole people 
 together at certain periods, and tliis ceremony was known as a 
 cldsis, from the Greek KTidaic, or k/J/oi^, derived from Kaleu, to 
 call together. Servius TuHius is said to have divided the people 
 into six orders, according to the amount of tribute they could pay, 
 and these orders were not unnaturally called the classes of tlie 
 people. Hence the name came by degrees to be applied to any 
 organized body of people, such as an army ; thence it was trans- 
 ferred to a fleet of vessels as marshalled in a fixed order, and was 
 finally extended by analogy to any collection of objects carefully 
 arranged. When, however, we now speak of the lower or higher 
 classes of the people it is curious that we are restoring the word 
 very nearly to its original meaning. 
 
 6. Requisites of a Good Classification. 
 
 A good classification has certain requisites, which 
 may be named as follows : 
 
 (1) The first requisite of a good classification is, that 
 it shall 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 prac- 
 tical use of the classification. All those things must be 
 arranged together which require to be treated alike, 
 and those things must be separated whicli require to be 
 treated separately. Thus a lawyer has no need to classify 
 persons according to the counties of England they were 
 bom in, because the law is the same independently of 
 counties ; but so far as a Scotchman, a Manx man, or 
 an alien, is under different laws from the English-bom 
 man, we shall require to classify them apart. A gar'
 
 DEDUCTIVE METHOD. 243 
 
 dener is quite right in classifying plants as annuals, 
 biennials, perennials; as herbs, shrubs, trees; as ever- 
 green and deciduous ; or according to the soil, tempera- 
 ture and other circumstances which affect them, because 
 these are points which must guide him in treating 
 some differently from others. 
 
 (2) Another and, in a scientific point of view, the 
 most important requisite of a good classification, is 
 that it shall enable the greatest possible 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 generally 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 convenient to many 
 purposes, but is artificial because it allows of few or no 
 general assertions. We cannot make any general asser- 
 tion whatever about persons because their names happen 
 to begin with an A or a B, a P or a TV. Even those 
 who agree in bearing the name Smith or Taylor or 
 Kobinson might be submitted to the inductive method 
 of agreement without the discovery of any common 
 circumstance which could be stated in a general propo- 
 sition or law. It is true that if we investigated the 
 antecedents of the Evanses and Joneses we sliould find 
 them nearly all to be Welsh, and the Campbells to be
 
 244 METHOD. 
 
 Scotch, and those who bear a very peculiar name would 
 often be found to descend from common ancestors. So 
 far even an alphabetic arrangement embodies some- 
 tuing that is natural in it, and enables general asser- 
 tions to be made. Hardly any arrangement can be 
 made, in fact, which will not indicate some vestiges of 
 important relations and resemblances ; but what we 
 want is a system which will reveal all the most impor- 
 tant general truths. 
 
 (3) For this purpose we must select as the ground of 
 union those characters which carry with them most other 
 characters. We have considered the proprium as a 
 quality which belongs to the whole of a class without 
 forming part of the definition of the class. Now we 
 ought to frame the definition of a class that it may con- 
 tain as few characters as possible, but that as many 
 other characters, properties, or propria, as possible, 
 shall be attributable to the things contained in the class. 
 Every one can see, for instance, that animals form one 
 great group of beings, which have many characters in 
 common, and that plants form another group. Animals 
 have sensation, voluntary motion, consume carbona- 
 ceous food, and evolve carbonic acid, possess a stomach, 
 and produce fat. Plants are devoid of sensation and 
 voluntary motion, produce carbonaceous tissue, absorb 
 carbonic acid, and evolve oxygen, possess no stomach, 
 and produce starch. At one time it might have been 
 thought that almost any of the charact<3rs named was a 
 sufficient mark of the group to which a being belonged. 
 Whatever had a stomach, was an animal; whatever 
 had not, was a plant; whatever produced starch or 
 evolved oxygen was called a plant ; whatever absorbed
 
 DEDUCTIVE METHOD. ^45 
 
 oxygen or produced fat was an animal. To the present 
 day these statements remain generally true, so that we 
 may make assertions in the form of the proposition U, 
 that "all animals are all beings that evolve carbonic 
 acid, and all plants are all beings that absorb carbonic 
 acid." But in reality the exceptions are many, and 
 increasing research makes it continually more apparent 
 that there is no definite line to be drawn between 
 animal and vegetable life. This, of course, is not a 
 failure of logical science, but a fact of great significance 
 concerning the things themselves. 
 
 7. Denomination. 
 
 In order to employ our results of classification, if not 
 in the formation of classes, we need to name the pro- 
 duct of our labors of division and definition. This 
 process is Denomination. 
 
 It is apparent that language serves three distinct and 
 almost independent purposes : 
 
 1. As a means of communication. 
 
 2. As a mechanical aid to thought. 
 
 3. As an instrument of record and reference. 
 
 In its first origin language was used chiefly if not 
 exclusively for the first purpose. Savage tribes exist in 
 great numbers at the present day who seem to accumu- 
 late no knowledge. We may even say that the lower 
 animals often possess some means of communication by 
 sounds or natural signs which constitute language in 
 the first sense, though they are incapable of reasoning 
 by general notions. 
 
 Some philosophers have held that it is impossible to 
 carry on reasoning without the use of language. The
 
 346 METHOD. 
 
 true nominalist went so far as to say that there are nd 
 such things as general notions, and that general names 
 therefore constitute all that is general in science and 
 reasoning. Though this is no doubt false, it must 
 nevertheless be allowed that unless general ideas were 
 fixed and represented by words, we could never attjiin 
 to sustained thought such as we at present enjoy. The 
 use of language in the second purpose is, doubtless, 
 indispensable in a practical point of view, and reason- 
 ing may almost be considered identical with the correct 
 use of words. When language is used solely to assist 
 reasoning there is no need that the meaning of each 
 word should be fixed; we might use names, as the let- 
 ters X, y, z, a, b, c, etc., are used in algebra to denote 
 any quantity that happeiis to occur in a problem. All 
 that is requisite is never to confuse the meaning attri- 
 buted to a word in one argument with the different 
 meaning attributed in another argument. Algebra 
 may, in fact, be said to consist of a language of a very 
 perfect kind adapted to the second purpose only, and 
 capable of leading a person to the solution of a problem 
 in a symbolical or mechanical manner. 
 
 Language, as it is furnished to us ready made by the 
 habitual growth of centuries, is capable of fulfilling all 
 three purposes, though by no means in a perfect man- 
 ner. As words possess a more or less fixed customary 
 meaning we can not only reason })y their aid, but com- 
 municate our thoughts or record them ; and it is in 
 this last respect we have now to treat the subject. 
 
 The multitude of facts required for the establish- 
 ment of a science could not be retained in the memory' 
 with sufiBcient accuracy. Hence an indispensable sub-
 
 DEDUCTIVE METHOD. 247 
 
 eidiary of reasoning is the means of describing and re- 
 cording our observations. Thus only can knowledge 
 be accumulated, so that each observer shall start with 
 the advantage of knowing what has been previously 
 recorded and proved. It will be necessary then to con- 
 sider the mode in which language serves for the regis- 
 tration of i"acts, and to investigate the requisite quali- 
 ties of a philosophical language suitable to the needs of 
 science. 
 
 As an instrument of record language must evidently 
 possess two principal requisites: 
 
 1. Precision or definiteness of meaning. 
 
 2. Completeness. 
 
 A name is Avorse than useless unless, when used to 
 record a fact, it enables us to ascertain what was the 
 nature of the fact recorded. Accuracy and precision is 
 then a more important quality of language than abun- 
 dance. The want of an appropriate word will seldom 
 give rise to actual error and fallacy; it will merely 
 oblige us to employ a circumlocutory phrase or else 
 leave the fact unrecorded. But it is a self-evident con- 
 venience that whenever a thing, notion, or quality has 
 often to be referred to there should be a name appro- 
 priate! to the purpose, and there ought to be one 
 name only. 
 
 It may not previously have struck the learner, but it is certainly 
 true, that description is impossible without the assertion of 
 resemblance between the fact described and some other fact. 
 We can describe a thing only by giving it a name ; but how can 
 we learn the meaning of that name ? If we describe the name 
 by other names we only have more names of which the meanings 
 are required. We must ultimately learn the meanings, not from 
 names, but from things which bear those names. If any one were
 
 248 METHOD. 
 
 ignorant of the meaning of blue ho could not be informed but by 
 reference to something that excited in him the sensation of blue- 
 ness, and had he been blind from birth he could not acquire any 
 notion of what blueness is. There are, indeed, a number of 
 words so familiar to us from childhood that we cannot tell when 
 or how we learned their meanings, though it must have been by 
 reference to things. But when we come to the more precise use 
 of names we soon have to make fresh reference to physical ob- 
 jects. Then we should describe tlie several kinds of blue color 
 as sky-blue, azure-blue, indigo-blue, cobalt-blue ; green color we 
 likewise distinguish as sea green, olive-green, emerald-green, 
 grass green, etc. The shapes of leaves are described in Botany 
 by such names as ovate, lanceolate, linear, pinnate, peltate, refer- 
 ring the mind respectively to an egg, a lance, a line, a feather, 
 and a shield. In recording dimensions it is equally impossible 
 to avoid comparison with the dimensions of other things, A 
 yard or a foot has no meaning unless there be a definite standard 
 yard or foot which fixes its meaning; and the learner is prob- 
 ably aware that when the physical standard of a length is once 
 completely lost it can never be recovered. The word is nothing 
 unless we somewhere have the thing to which it corresponds. 
 
 See Dr. VVhewell's "Aphorisms concerning the Language of 
 Science." at the end of his Philosophy of the Inductive 
 Sciences. 
 
 Thomson's Outline of the Laws of Thx>ught, contains most 
 interesting remarks on the general nature and use of Lan- 
 guage, Sections 17-31. 
 
 In this section, on "Deductive Method,** we 
 have considered : 
 
 1. The Predicables. 
 
 2. Lof/ical Division. 
 
 3. Dichotomy, or Exhaustive Division, 
 
 4. Definition. 
 
 5. Classification. 
 
 6. Requisites of a Ottod Classification. 
 
 7. Denomination.
 
 OOMPLBTE METHOD. ^9 
 
 SBGTIOXT in. 
 
 COMPLETE METHOD. 
 
 1. Empirical aud Rational Kuowledge. 
 
 When a law of nature is ascertained purely by in 
 duction from certain observations or experiments, and 
 has no other guarantee for its truth, it is said to be an 
 empirical law. As Mr. Mill says, " Scientific inquirers 
 give the uame of Empirical Laws to uniformities wiiif b 
 observation or experiment has shown to exist, but on 
 which they hesitate to rely in cases varying much from 
 those which have been actually observed, for want of 
 seeing any reason why such a law ghould exist." The 
 name is derived from the Greek word efmtupia, meaning 
 experience or trial. Instances of such laws are abun- 
 dant. We learn empirically that a certain strong yellow 
 color at sunset, or an unusual clearness in the air, por- 
 tends rain ; that a quick pulse indicates fever ; that 
 horned animals are always ruminants; that quinine 
 affects beneficially the nervous system and the health of 
 the body generally ; that strychnine has a terrible effect 
 of the opposite nature : all these are known to be true 
 by repeated observation, but we can give no other rea- 
 son for their being true, that is, we cannot bring them 
 into harmony with any other scientific facts; nor could 
 we at all have deduced them or anticipated them on the 
 ground of previous knowledge. The connection be- 
 tween the sun's spots, magnetic storms, auroras, and 
 the motions of the planets mentioned in the last lesson, 
 is perhaps the most remarkable known instance of an
 
 250 METHOD. 
 
 empirical induction ; for no hint has yet been given ol 
 the way in which these magnetic influences are exerted 
 throughout the vast dimensions of the planetary system. 
 The qualities of the several alloys of metals are also 
 good instances of empirical knowledge. No one can 
 tell before mixing two or three metals for the first time 
 in any given proportions what tlie qualities of the mix- 
 ture will be that brass should be both harder and more 
 ductile than either of its constituents, copper and zinc ; 
 that copper alloyed with the very soft metal tin should 
 make hard and sonorous bell-metal ; that a certain mix- 
 ture of lead, bismuth, tin and cadmium, should melt 
 with a temperature (65 cent.) far below that of boiling 
 water. 
 
 However useful may be empirical knowledge, it is yet 
 of slight importance compared with the well-connected 
 and perfectly explained body of knowledge which con- 
 stitutes an advanced and deductive science. It is in 
 fact in proportion as a science becomes deductive, and 
 enables us to grasp more and more apparently uncon- 
 nected facts under the same law, that it becomes per- 
 fect. He who knows exactly why a thing happens, will 
 also know exactly in what cases it will happen, and 
 what difference in the circumstances will prevent the 
 event from happening. Take for instance the simple 
 effect of hot water in cracking glass. This is usually 
 learnt empirically. Most people have a confused idea 
 that hot water has a natural and inevitable tendency to 
 break glass, and that thin glass, being more fragile than 
 other glass, will be more easily broken by hot water. 
 Physical science, however, gives a very clear reason for 
 the effect, by showing that it is only one case of the
 
 COMPLETE METHOD. 251 
 
 general tendency of heat to expand substances. The 
 (Stack is caused by the successful effort of the heated 
 glass to expand in spite of the colder glass with which 
 it is connected. But then we shall see at once that the 
 same will not be true of thin glass vessels ; the heat 
 will pass so quickly through that the glass will be nearly 
 equally heated ; and accordingly chemists habitually 
 use thin uniform glass vessels to hold or boil hot liquids 
 without fear of the fractures which would be sure to 
 take place in thick glass vessels or bottles. 
 
 We have hitherto treated of Deduction and Induction as if they 
 were entirely separate and independent methods. In reality they 
 are frequently blended or employed alternately in the pursuit of 
 truth ; and it may be said that all the more important and exten- 
 sive investigations of science rely upon one as much as upon the 
 other. It is probably the greatest merit in Mr. Mill's logical 
 writings that he points out the entire insuflSciency of what is 
 called the Baconian Method to detect the more obscure and 
 difficult laws of nature. Bacon advised that we should always 
 begin by collecting facts, classifying them according to their 
 agreement and difference, and gradually gathering from them 
 laws of greater and greater generality. He protested altogether 
 against "anticipating nature," that is, forming our own hypoth- 
 eses and theories as to what the laws of nature probably are, and 
 he seemed to think that systematic arrangement of facts would 
 take the place of all other methods. The learner will soon see 
 that the progress of Science has not confirmed his opinions. 
 
 2. The Elements of Complete Method. 
 
 Combined or Complete Method, consists in the alter- 
 nate use of induction and deduction. It may be said 
 to have three steps, as follows : 
 
 1. Direct Induction.
 
 252 METHOD. 
 
 2. Deduction, or, as Mr. Mill calls it, Ratiocination. 
 
 3. Verification. 
 
 The first process consists in such a rough and simple 
 appeal to experience as may give us a glimpse of the 
 laws which operate, without being sufficient to establish 
 their truth. Assuming them as provisionally true, we 
 then proceed to argue to their effects in other cases, and 
 a further appeal to experience either verifies or negatives 
 the truth of the laws assumed. There are, in short, 
 two appeals to experience connected by the intermediate 
 use of reasoning. Newton, foi instance, having passed a 
 ray of san-light through a glass prism found that it 
 was spread out into a series of colors resembling those 
 of the rainbow. He adopted the theory that white 
 light was actually composed of a mixture of different 
 colored lights, which become separated in passing 
 through the prism. He saw that if this were true, and 
 he were to pass an isolated ray of the spectrum, for 
 instance, the yellow ray, through a second prism, it 
 ought not to be again broken up into different colors, 
 but should remain yellow whatever was afterwards done 
 with it. On trial lie found this to be the case, and 
 afterwards devised a succession of similar confirmatory 
 experiments which verified his theory beyond all pos- 
 sible doubt. 
 
 The greatest result of the complete method is no less than the 
 theory of gravitation, which makes a perfect instance of its 
 procedure. In this case the preliminary induction consisted, we 
 may suppose, in the celebrated fail of the apple, which occurred 
 while Newton was sitting in an orchard during his retirement 
 from London, on account of tlie Great Plague. The fall of the 
 apple, we are told, led Newton to reflect that there must be a
 
 COMPLETE METHOD. 253 
 
 power tending to draw bodies towards tlie earth, and he asked 
 himself the question why the moon did not on tbat account tall 
 upon the earth. The Lancashire astronomer Horrocks suggested 
 to his mind another fact, namely, that when a stone is whirled 
 round attached to a string, it exerts a force upon tlie string, ofken 
 called centrifugal force. Horrocks remarked that the planets in 
 revolving round the sun must tend in a similar way to fly ofl 
 from the centre. Newton was acquainted with Horrocks' views, 
 and was thus possibly led to suppose that the earth's attractive 
 force might exactly neutralize the moon's centrifugal tendency, 
 so as to maintain that satellite in constant rotation. 
 
 But it happened that the world was in possession of certain 
 empirical laws concerning the motions of the planets, without 
 which Newton could scarcely have proceeded further. Kepler 
 had passed a lifetime in observing the heavenly bodies, and 
 forming hypotheses to explain their motions. In general his 
 ideas were wild and unfounded, but the labors of a lifetime were 
 rewarded in the establishment of the three laws which bear his 
 name, and describe the nature of the orbits traversed by the 
 planets, and the relation between the size of such orbit and the 
 time required by the planet to traverse it. Newton was able to 
 show by geometrical reasoning that if one body revolved round 
 another attracted towards it by a force decreasing as the square 
 of the distance increases, it would necessarily describe an orbit 
 of which Kepler's laws would be true, and which would there- 
 fore exactly resemble the orbits of the planets. Here was a 
 partial verification of his theory by appeal to the results of ex- 
 perience. But several other philosophers had gone so far in the 
 investigation of the subject. It is Newton's chief claim to 
 honor, that he carried on his deductions and verifications until he 
 attained complete demonstration. To do this it was necessary 
 first of all to show that the moon actually does fall towards th* 
 earth just as rapidly as a stone would if it were in the same cir- 
 cumstances. Using the best information then attainable as to the 
 distance of the moon, Newton calculated that the moon falls 
 through the space of 13 feet in one minute, but that a stone, if 
 elevated so high, would fall through 15 feet. Most men would 
 have considered this approach to coincidence as a proof of hie
 
 254 METHOD. 
 
 theory, but Newton's love of certain truth rendered him different 
 even from most philosophers, and the discrepancy caused him to 
 lay " aside at that time any further thoughts of this matter." 
 
 It was not till many years afterwards (probably 15 or 16) that 
 Newton, hearing of some more exact data from which he could 
 calculate the distance of the moon, was able to explain the dis- 
 crepancy. His theory of gravitation was then verified so far as the 
 moon was concerned ; but this was to him only the beginning of a 
 long course of deductive calculations, each ending in a verification, 
 If the earth and moon attract each other, and also the sun and the 
 earth, similarly there is no reason why the sun and moon should 
 not attract each other. Newton followed out the consequences 
 of this inference, and showed that the moon would not move as 
 if attracted by the earth only, but sometimes faster and some- 
 times slower. CJomparisons with Flamsteed's observations of the 
 moon showed that such was the case. Newton argued again, 
 that as the waters of the ocean are not rigidly attached to the 
 earth, they might attract the moon, and be attracted in return, 
 independently of the rest of the earth. Certain daily motiona 
 would then be caused thereby exactly resembling the tides, and 
 there were the tides to verily the fact. It was the almost super- 
 human power with which he traced out geometrically the conse- 
 quences of his theory, and submitted them to repeated compari- 
 son with experience, which constitutes his pre-eminence over all 
 philosophers. 
 
 3. The Nature of E^xplanation. 
 
 Explanation is literally the making plain or clear, so 
 that there shall be nothing uneven or obscure to inter- 
 rupt our view. Scientific explanation consists in har- 
 monizing fact with fact, or fact witli law, or law with 
 law, 80 that we may see them both to be cases of one 
 uniform law of causation. If we hear of a great earth- 
 quake in some part of the world, and subsequently hear 
 that a neighboring volcano has broken out, we say that 
 the earthquake is thus partially explained. The erup-
 
 OOMPLBTE METHOD. 255 
 
 tion shows that there were great forces operating be- 
 neath the earth's surface, and the earthquake is obvi- 
 ously an effect of such causes. The scratches which 
 may be plainly seen upon the surface of rocks in cer- 
 tain parts of Wales and Cumberland, are explained by 
 the former existence of glaciers in those mountains; 
 the scratches exactly harmonize with the effects of 
 glaciers now existing in Switzerland, Greenland, and 
 elsewhere. These may be considered explanations of 
 Tact by fact. 
 
 A fact may also be explained by a general law of 
 nature, that is, the cause and mode of its production 
 may be pointed out and shown to be the same as oper- 
 ates in many apparently different cases. Thus the 
 cracking of glass by heat may be explained as one result 
 of the universal law that heat increases the dimensions 
 of solid bodies. The trade-winds are explained as one 
 case of the general tendency of warm air to rise and be 
 displaced by cold and dense air. The very same simple 
 laws of heat and mechanics which cause a draught to flow 
 up a chimney when there is a fire below, cause winds 
 to blow from each hemisphere towards the equator. 
 At the same time the easterly direction from which the 
 winds come is explained by the simplest laws of motion ; 
 for as the earth rotates from west to east, and moves 
 much more rapidly at the equator than nearer the 
 poles, the air tends to preserve its slower rate of motion, 
 and the earth near the equator moving under it occa- 
 sions an apparent motion of the wind from east to 
 west. 
 
 There are, according to Mr. Mill, three distinct ways in which
 
 256 METHOD. 
 
 one law may be explained by other laws, or brought Into hat 
 mony witli them. 
 
 The first is the case where there are really two or more separate 
 causes in action, the results of which are combined or added to- 
 gether, homogeneously. As was before explained, homogeneous 
 Intermixture of effects means that the joint effect is simply the 
 sum of the separate effects, and is of the same kind with them. 
 Oar last example of the trade- winds really comes under this case, 
 for we find that there is one law or tendency which causes winds 
 to blow from the arctic regions towards the equator, and a second 
 tendency which causes them to blow from east to west. These 
 tendencies are combined together, and cause the trade-winds to 
 blow from the north-east in the northern hemisphere, and from 
 the south-east in the southern hemisphere The law according 
 to which the temperature of the air is governed in any part of the 
 earth is a very complicated one, depending partly on the law by 
 which the sun's heating power is governed, partly on the power 
 of the earth to radiate the heat away into space, but even more 
 perhaps on the effect of currents of air or water in bringing 
 warmth or carryinpf it away. The path of a cannon ball or other 
 projectile is determined by the joint action of several laws; first, 
 the simple law of motion, by which any moving body tends to 
 move onward at a uniform rate in a straight line ; secondly, the 
 law of gravity, which continually deflects the body towards the 
 earth's surface ; thirdly, the resistance of the air, which tends to 
 diminish its velocity. 
 
 In the second case of explanation an effect is shown to be due, 
 not to the supposed cause directly, but to an Intermediate effect 
 of that cause. Instead of A being the cause of 0, it is found 
 that A is the cause of B, and B the cau8(' of C, so that B consti- 
 tutes an intermediate link. This explanation may seem to in- 
 crease the complexity of the matter, but it really simplifies it; 
 for the connection of A with B may be a case of a familiar and 
 simple law, and so may that of B with C; wliereas the law that 
 A produces Cmay be purely empirical and apparently out of har- 
 mony with everything else. Thus in lightning it seems as il 
 electricity had the |>ower of creating a loud ox])losion ; but in 
 reality electricity only produces heal, and it is the heat, which
 
 COMPLETE METHOD. 857 
 
 occasions soand by suddenly expanding the air. Thus thundet 
 comes iuto harmony with the sound of artillery, which is al8 
 occasioned by the sudden expansion of the heated gases emitted 
 by the powder. When chlorine was discovered it was soon found 
 to have a strong power of bleaching, and at the present day 
 almost all bleaching is done by chlorine instead of the sun as 
 formerly. Inquiry showed, however, that it was not really the 
 chlorine which destroyed color, but that oxygen is the inter- 
 mediate and active agent. Chlorine decomposes water, and tak- 
 ing the hydrogen leaves the oxygen in a state of great acti%ity 
 and ready to destroy the organic coloring matter. Thus a num- 
 ber of facts are harmonized ; we learn why dry chlorine does not 
 bleach, and why there are several other substances which re- 
 semble chlorine in its bleaching power, for instance, ozone, 
 peroxide of hydrogen, sulphurous acid, and a peculiar oxide of 
 vanadium, lately discovered by Dr. Roscoe. It would be impos- 
 sible to understand the eflFect at all unless we knew that it ia 
 probably due to active oxygen or ozone in all the cases, even in 
 the old method of bleaching by ex^wsure to the sun. 
 
 The third and much more important case of explanation is 
 where one law is shown to be a case of a more general law. 
 As was explained in Section I, we naturally discover the less 
 general first, and gradually penetrate to the more simple but pro- 
 found secrets of nature. It has often been found that scientific 
 men were in possession of several well-known laws without peK 
 ceiving the bond which connected them together. Men, for 
 instance, had long known that all heavy bodies tended to faU 
 towards the earth, and before the time of Newton it was known 
 to Hooke, Huyghens, and others, that some force probably con- 
 nected the earth with the sun and moon. It was Newton, 
 however, who clearly brought these and many other facts under 
 one general law, so that each fact or less general law throws 
 light upon every other. 
 
 4. Pascal on Method. 
 
 As no treatment of the subject of Method would be 
 complete without a reference to Pascal's rules, we here
 
 268 METHOD. 
 
 add them as prepared by him for the Port Roydi 
 Logic: 
 
 1. To admit no terms in the least obscure or equivo- 
 cal without defining them. 
 
 2. To employ in the definitions only terms perfectly 
 known or already explained. 
 
 3. To demand as axioms only truths perfectly evi- 
 dent. 
 
 4. To prove all propositions which are at all obscure, 
 by employing in their proof only the definitions which 
 have preceded, or the axioms which have been accorded, 
 or the propositions which have been already demon- 
 strated, or the construction of the thing itself which is 
 in dispute, when there may be any operation to per- 
 form. 
 
 5. Never to abuse the equivocation of terms by fail- 
 ing to substitute for them, mentally, the definitions 
 which restrict and explain them. 
 
 It may be doubted whether any man ever possessed a more 
 acute and perfect intellect than that of Blaise Pascal. He waa 
 bom in 1633, at Clermont in Auvergne, and from his earliest 
 years displayed signs of a remarkable character. His father 
 attempted at first to prevent his studying geometry, but such was 
 Pascal's genius and love of this science, that, by the age of 
 twelve, he had found out many of the propositions of Euclid's 
 first book without the aid of any person or treatise. It is difficult 
 to say whether he is most to be admired for his mathematical 
 discoveries, his invention of the first calculating machine, his 
 wonderful Provincial Letters written against the Jesuits, or for 
 hifl profound Pensees or Thoughts, a collection of his reflections 
 OQ scientific and religious topics. 
 
 Among these Thoughts is to be found a remarkable fragment 
 apoD Log:ical method, the Babstanc of which is also given in tho
 
 COMPLETE METHOD. 259 
 
 Port Royal Logic. It forms the second article of the Pentie* 
 and is entitled Reflexions sur la Gcometrie en general. As I know 
 no composition in which perfection of truth and clearness of ex 
 pression are more nearly attained, I propose to give in this Section 
 a free translation o* the more important parts of this fragment, 
 appending to it rules of method from the Port Royal Logic, and 
 from Descartes' celebrated Essay on Method. The words of Pascal 
 are nearly as follows : 
 
 " The true method, which would furnish demonstrations of thfl 
 highest excellence, if it were possible to employ the method 
 fully, consists in observing two principal, rules. The first rule is 
 not to employ any term of which we have not clearly explained 
 the meaning ; the second rule is never to put forward any prop- 
 osition which we cannot demonstrate by truths already known ; 
 that is to say, in a word, to define all the terma, and to prove all 
 the propositions. But, in order that I may observe the rules ol 
 the method which I am explaining, it is necessary that I declare 
 what is to be understood by Definition. 
 
 " We recognize in Geometry only those definitions which 
 logicians call Nominal Definitions, that is to say, only those 
 definitions which impose a name ujxjn things clearly designated 
 in terms perfectly known ; and I speak only of those definitions." 
 
 Their value and use is to clear and abbreviate discourse by ex- 
 pressing in the single name which we impose what could not 
 be otherwise expressed but in several words: provided, neverthe- 
 less, that the name imposed remain divested of any other mean 
 ing which it might possess, so as to bear that alone for which we 
 intend it to stand. 
 
 " For example, if we need to distinguish among numbers those 
 which are divisible into two equal parts, from those which are 
 not so divisible, in order to avoid the frequent repetition of thift 
 distinction, we give a name to it in this manner : we call everj 
 number divisible Into two equal parts an Even Number. 
 
 " This is a geometrical definition, because after having clear!} 
 designated a thing, namely any number divisible into two equal 
 parts, we give it a name divested of every other meaning which 
 it might have, in order to bestow upon it the meaning de- 
 signated.
 
 260 METHOD. 
 
 " Hence it appears that definitioDS are very free, and that thej> 
 tan never be subject to contradiction, for there is nothing more 
 ullowable, than to give any name we wish to a thing which we 
 have clearly pointed out. It is only necessary to take care ibat 
 we do not abuse tliis liberty of imposing names, by giving the 
 same name to two different things. Even that would be allow- 
 able, provided that we did not confuse the results, and extend 
 them from one to the other. But if we fall into this vice, we 
 have a very sure and infallible remedy : it is, to substitute men- 
 tally the definition in place of the thing defined, and to hold the 
 definition always so present in the mind, that every time we 
 speak, for instance, of an even number, we may understand pre- 
 cisely that it is a number divisible into two equal parts, and so 
 that these two things should be so combined and inseparable in 
 thought, that as often as one is expressed in discourse, the mind 
 may direct itself immediately to the other. 
 
 " For geometers and all who proceed methodically only impose 
 names upon things in order to abbreviate discourse, and not to 
 lessen or change the ideas of the things concerning which they 
 discourse. They pretend that the mind always supplies the 
 entire definition of the brief terms which they employ simply to 
 avoid the confusion produced by a multitude of words. 
 
 " Nothing prevents more promptly and effectively the insidious 
 fallacies of the sophists than this method, which we should always 
 employ, and which alone suflBces to banish all sorts of difficulties 
 and equivocations. 
 
 " These things being well understood, I return to my explana- 
 tion of the true mothod, which consists, as I said, in defining 
 everything and proving everything. 
 
 " Certainly this method would be an excellent one, were it not 
 absolutely impossible. It is evident that the first terms we 
 wished to define would require previous terms to serve for their 
 explanation, and similarly the first propositions we wished to 
 prove, would presuppose other propositions preceding them in our 
 knowledge ; and thus it is clear that we should never arrive at 
 the first terms or first propositions. 
 
 'Accordingly in pushing our researches further and further, we 
 urive necessarily at primitive words which we cannot define
 
 COMPLETE METHOD. 261 
 
 and at principles so clear, that we cannot find any principles 
 more clear to prove them by. Thus it appears that men are 
 naturally and inevitably incapable of treating any science what 
 ever in a perfect method ; but it does not thence follow that we 
 ought to abandon every kind of method .... The most perfect 
 method available to men consists not in defining everything and 
 demonstrating everything, nor in defining nothing and demon- 
 etratinor nothing, but in pursuing the middle course of not 
 defining things which are clear and understood by all persons, 
 but of defining all others ; and of not proving truths known to 
 all persons, but of proving all others. From this method they 
 equally err who undertake to define and prove everything, and 
 they who neglect to do it in things which are not self-evident." 
 
 It is made plain in this admirable passage that we can never 
 by using words avoid an ultimate appeal to things, because each 
 definition of a word must reqvure one or more other words, which 
 also will require definition, and so on, ad infinitum. Nor must 
 we ever return back upon the words already defined ; for if we 
 define A by B, and B by C, and G by D, and then D by ^, we 
 commit what may be called a cireulua in definiendo; a most 
 serious fallacy, which might lead us to suppose that we know 
 the nature of A, B, G, and D, when we really know nothing 
 about them. 
 
 5. Descartes on Method. 
 
 We also add here the rules of the celebrated Des- 
 cartes for guiding the reason in the attainment of 
 truth. They are as follows : 
 
 lo Never to accept anything as true, which we do 
 not clearly know to be so ; that is to say, carefully to 
 avoid haste or prejudice, and to comprise nothing more 
 in our judgments than what presents itself so clearly 
 and distinctly to the mind that we cannot have any 
 room to doubt it. 
 
 2. To divide each difficulty we examine into aa
 
 263 METHOD. 
 
 many parts as possible, or as may be required for re- 
 solving it. 
 
 3. To conduct our thoughts in an orderly manner, 
 commencing with the most simple and easily known 
 objects, in order to ascend by degrees to the knowledge 
 of the most complex. 
 
 4. To make in every case enumerations so complete, 
 and reviews so wide, that we may be sure of omitting 
 nothing. 
 
 These rules were first stated by Descartes in his admirable 
 Discourse on Method, in which he gives his reflections on the 
 right mode of conducting the reason, and searching for truth in 
 any of the sciences. This little treatise is easily to be obtained 
 in the original French, and has also been translated into English 
 by Mr. Veitch.* Tbe learner can be strongly advised to study 
 it. Always to observe the rules of Descartes and Pascal, or to 
 know whether we in every case observe them properly, is im 
 possible, but it must nevertheless be valuable to know at what 
 we ought to aim. 
 
 Read Locke's brief Esmy on the Cond^ict of the Understanding 
 which contains admirable remarks on the acquirement ol 
 exact and logical habits of thought ; and Mr. Spencer Baynes' 
 Translation of the Port Royal Logic, p. 317 et seq. 
 
 In this Section, on ** Complete Method,** we have 
 considered z 
 
 1. Empirical and Rational Knowledge. 
 
 2. The Elements of Complete Method. 
 
 3. Tlie Nature of Explanation. 
 4c. Pascal on Method. 
 
 5. Descartes on Method, 
 
 Published at Rdinbnigh in ISOfr
 
 CHAPTEB VH. 
 
 RECENT LOGICAL VIEWS. 
 
 The principal part of the preceding chapters is but a 
 restatement of what has been taught as constituting the 
 science of Logic ever since the days of Aristotle. Some 
 additions have, indeed, been made, and they have been 
 incorporated with the older doctrines as accepted re- 
 sults of thought in this department of knowledge. 
 There are, however, certain other views which have not 
 been generally adopted as rightly claiming a place in 
 the science of Logic, but which, nevertheless, are suffi- 
 ciently important to deserve some attention from the 
 student of this subject. These new views may be pre- 
 sented in outline here in two sections : (1) The 
 Quantification of the Predicate; and (2) 
 Boole's System of Logic. 
 
 SEOTION ! 
 
 THE QUANTIFICATION OF THE PREDICATE. 
 
 1. Meaning of the Expression. 
 
 To quantify the predicate is simply to state whether 
 the whole or the part only of the predicate agrees with 
 OP differs from the subject. In this proposition, 
 "All metals are elements,"
 
 264 EECENT LOGICAL VIEWS. 
 
 the subject is quantified, but the predicate is not; we 
 know that all metals are elements, but the proposition 
 does not distinctly assert whether metals make the 
 whole of the elements or not. In the quantified propo- 
 sition 
 
 **A11 metals are some elements," 
 
 the little word some expresses clearly that in reality 
 the metals form only a part of the elements. Aristotle 
 avoided the use of any mark of quantity by assuming, 
 as we have seen, that all affirmative propositions have 
 a particular predicate, like the example just given ; and 
 that only negative propositions have a distributed or 
 universal predicate. The fact, however, is that he was 
 entirely in error, and thus excluded from his system an 
 infinite number of affirmative propositions which are 
 universal in both terms. It is true that 
 
 "All equilateral triangles are all equiangular triangles," 
 
 but this proposition could not have appeared in hi? 
 system except in the mutilated form 
 
 "All equilateral triangles are equiangular/* 
 Such a proposition as 
 
 ** London is the capital of England," 
 or ** Iron is the cheapest metal," 
 
 had no proper place whatever in his syllogism, sinct 
 both terms are singular and identical with each other 
 and both are accordingly universal. 
 
 2. Conversion with a Quantified Predicate. 
 
 As soon as we allow the quantity of the predicate to 
 be stated the forms of reasoning become much simpli*
 
 QUANTIFICATION OP THE PBBDICATE. 266 
 
 fied. We may first consider the process of conversion. 
 In our treatment of the subject it was necessary to 
 dirtinguish between conversion by limitation and simple 
 conversion. But now one single process of simple con- 
 veifsion is sufficient for all kinds of propositions. Thus 
 fhe quantified proposition of the form A, 
 
 "All metals are some elements," 
 is tjimply converted into 
 
 * ' Some elements are all metals. " 
 Tho particular affirmative proposition 
 
 " Some metals are some brittle substances ** 
 becomes by mere transposition of terms 
 
 " Some brittle substances are some metals." 
 The particular negative proposition 
 
 ''Some men are not (any) trustworthy persons'' 
 is also converted into 
 
 "Not any trustworthy persons are some men," 
 though the result may appear less satisfactory in this 
 form than in the affirmative form, as follows, 
 
 "Some men are some not-trustworthy persons," 
 converted simply into 
 
 "Some not-trustworthy persons are some men." 
 The universal negative proposition E is converted 
 simply as before, and finally we have a new affirmative 
 proposition universal botli in subject and predicate ; 
 as in 
 
 "All equilateral triangles are all equiangular triangles," 
 which may obviously be converted simi)ly into 
 "All equiangular triangles are all equilateral triangles. *^ 
 13
 
 266 EEOBlffT LOGICAL VIEWS. 
 
 This doubly universal affirmative proposition is of 
 most frequent occurrence ; as in the case of all defi- 
 nitions and singular propositions ; I may give as in- 
 stances " Honesty is the best policy," " The greatest 
 truths are the simplest truths," " Virtue alone is hap- 
 piness helow," ** Self-exaltation \i. the fool's paradise." 
 
 3. The Rule for Conversion. 
 
 When affirmative propositions are expressed in the 
 quantified form all immediate inferences can be readily 
 drawn from them by this one rule, that whatever 
 we do with one term toe should do ivith the other 
 term. Thus from the doubly universal proposition, 
 ''Honesty is the best policy," we infer that "what is 
 not the best policy is not honesty," and also " what is 
 not honesty is not the best policy." From this propo- 
 sition in fact we can draw two contrapositives ; but the 
 learner will carefully remember that from the ordinary 
 unquantified proposition A we can only draw one con- 
 trapositive (see p. 90). Thus if "metals are elements" 
 we must not say that "what are not metals are not 
 elements." But if we quantify the predicate thus, "All 
 metals are some elements," we may infer that " what 
 are not metals are not some elements." Immediate 
 inference by added determinant and complex concep- 
 tion can also be applied in either direction to quanti- 
 fied propositions without fear of the errors noticed in 
 pp. 91, 92. 
 
 4. Number of Propositions with Quantified 
 Predicate. 
 
 It is clear that in admitting the mark of quantity
 
 QUANTIFICATION Qf THE PREDICATE. 267 
 
 before the predicate we shall double the number of 
 propositions which must be admitted into the syllogism, 
 because the predicate of each of the four propositions 
 A, E, I, may be either universal or particular. Thus 
 we arrive at a list of eight conceivable kinds of propo- 
 sitions, which are stated in the following table : 
 
 U AllXisalir. j 
 
 I Some X is some K ( Affirmative 
 
 A All X is some Y. ( propositions. 
 
 Y Some X is all r. ) 
 
 E NoXis (any) Y, \ 
 
 o> Some X is not some Y. ( Negative 
 
 71 No X is some Y. ( propositions. 
 
 Some X is no Y. ) 
 
 The letters X and l^are used to stand for any sub- 
 ject and predicate respectively, and the learner by sub- 
 stituting various terms can easily make propositions of 
 each kind. The symbolic letters on the left-hand side 
 were proposed by Archbishop Thomson as a convenient 
 mode of referring to each of the eight propositions, 
 and are very suitably chosen. The doubly universal 
 affirmative proposition is called U ; the simple con- 
 verse of A is called Y; the Greek letter ri {Eta, e) is 
 applied to the proposition obtained by changing the 
 universal predicate of E into a particular predicate ; and 
 the Greek at {Omega, o) is applied to the proposition 
 similarly determined from O. All these eight proposi- 
 tions are employed by Sir W. Hamilton, but Archbishop 
 Thomson considers that two of them, ri and o), are 
 never really used. It is remarkable that a complete 
 table of the above eight propositions was given by Mr. 
 George Bentham in a work called Outline of a Neu
 
 368 RECENT LOGiPAL VIEWS. 
 
 System of Logic, published in 1827, several years pre 
 vious to the earliest of the logical publications of Sir 
 W. Hamilton. But Mr. Bentham considered that some 
 of the propositions are hardly to be distinguished from 
 others ; as Y from A, of which it is the simple con- 
 verse ; or ri from 0. 
 
 5. Xuniber of Syllogrisnis with Quantified 
 Predicate. 
 
 The employment even of the additional two proposi- 
 tions U and Y introduced by Thomson much extends 
 the list of possible syllogisms, making them altogether 
 62 in number, without counting the fourth figure, 
 which is not employed by Hamilton and Thomson. 
 When the whole eight propositions are admitted into 
 use we are obliged to extend the list of possible syllo^ 
 gisms so as to contain 12 affirmative and 24 negative 
 moods in each of the first three figures. The whole of 
 these moods are conveniently stated in the table on 
 the next page, given by Archbishop Thomson at p. 188 
 of his Laics of Thought. 
 
 6. Hamilton's Notation. 
 
 Sir W. Hamilton also devised a curious system of 
 notation for exhibiting all the moods of the syllogism 
 in a clear manner. He always employed the letter M 
 to denote the middle term of the syllogism, and th 
 two letters C and r (the Greek capital letter Gamma) 
 for the two terms appearing in the conclusion.
 
 QDANTIFICATIONT OF THE PREDICATE. 
 
 269 
 
 Table of Moods of the Syllogism. 
 
 
 FiBST FlOUBS. 1 
 
 Skoohs 
 
 PlOUBE. 
 
 Thibd 
 
 F^OUBB. 
 
 
 Affirm. 
 
 Neg. 
 
 Affirm. 
 
 Neg. 
 
 Affirm. 
 
 Neg. 
 
 1 
 
 uu u 
 
 EUE 
 UEE 
 
 UUU 
 
 EUE 
 UEE 
 
 UUU 
 
 EU E 
 UEE 
 
 11 
 
 ATI 
 
 vYu 
 AO w 
 
 YYI 
 
 OYw 
 YOu 
 
 A AI 
 
 77 A u 
 
 A T) u 
 
 m 
 
 AAA 
 
 V A.71 
 
 YAA 
 
 Aj7 
 
 Yvv 
 
 AYA 
 
 vYv 
 AOti 
 
 iv 
 
 TYY 
 
 OYO 
 YOO 
 
 AYY 
 
 ?Y0 
 AOO 
 
 YA Y 
 
 AO 
 YEO 
 
 V 
 
 AI I 
 
 nicj 
 
 A u u 
 
 YII 
 
 OIu 
 
 Y (J w 
 
 All 
 
 1)1 u 
 
 A u u 
 
 vi 
 
 lYI 
 
 o Y w 
 lOco 
 
 lYI 
 
 W Y G> 
 
 lOu 
 
 I AI 
 
 <j A u 
 I j; u 
 
 vii 
 
 UYY 
 
 EYO 
 UOO 
 
 UYY 
 
 EYO 
 UOO 
 
 U AY 
 
 E AO 
 
 U70 
 
 viii 
 
 AUA 
 
 ;?U7 
 AE7 
 
 YUA 
 
 0U7 
 
 YEt? 
 
 AUA 
 
 A E77 
 
 ix 
 
 U AA 
 
 E AE 
 
 { U AA 
 
 1 
 
 E AE 
 
 U7777 
 
 UYA 
 
 EYE 
 
 V On 
 
 X 
 
 YUY 
 
 ouo 
 
 YEE 
 
 i AUY 
 
 ;?U0 
 A EE 
 
 YUY 
 
 OUO 
 YEE 
 
 xi 
 
 U II 
 
 EIO 
 
 U w w 
 
 : UII 
 
 EIO 
 
 U w w 
 
 UII 
 
 EIO 
 
 xu 
 
 I UI 
 
 (J U w 
 
 IE77 
 
 lUI 
 
 w U w 
 lEri 
 
 lUI 
 
 (J U w 
 
 IE7 
 
 The copula of the proposition was indicated by a line thickened 
 towards the subject : thus Cf^^^^ Jf means that " C is 
 
 M." To indicate the quantity of the terms Hamilton inserted a 
 colon (:) between the term and the copula when the quantity is 
 universal, and a comma (,) when the quantity is particular. Thug 
 we readily express the following affirmative propositions. 
 
 C:i 
 C:i 
 ,i 
 
 M All (7's are some Jf's (A) 
 
 M All (7's are all M's (U) 
 
 , M Some C's are some i/'*s (I) 
 
 imd BO on Any aflSrmative proposition can be converted intt
 
 270 RECENT LOGICAL VIEWS, 
 
 the corresponding negative proposition by drawing a strobe 
 through the line denoting the copula, as in the following 
 
 : m I : M No (7 is any M (E) 
 
 C . ^ I : if Some C is not any M (0) 
 
 C , ^"^"""~" , M Some C is not some M (w) 
 
 Any syllogism can be represented by placing M the middlt 
 term in the centre and connecting it on each side with the othei 
 terms. The copula representing the conclusion can then b 
 placed below ; Barbara is expressed as foUows 
 
 C . M : M, : r 
 
 The negative mood Celarent is similarly 
 
 O: 1 :M, 
 
 J- 
 
 Cesare in the second figure is thus represented 
 
 : M : I : r 
 
 I 
 
 7. Hamilton's Canon of the Syllogrlsm. 
 
 Sir W. Hamilton also proposed a new law or supreme 
 canon of the syllogism by which the validity of all 
 forms of the syllogism might be tested. This was 
 stated in the following words : " What worse relation 
 of subject and predicate subsists between either of two 
 terms and a common third term, with which both are 
 related, and one at least positively so that relation 
 subsists between these two terms themselves." 
 
 By a worse relation, Sir William means that a nejfative rela- 
 tion is worse than an aflBrmative, and a particular than a universal. 
 This canon thus expresses the rules that if tliere be a negative 
 premise the conclusion must be negative, and if there be a par
 
 ^UANTIFICATIOlf OF THE PREDICATE. 271 
 
 tiealar premise the conclusion must be particular. Special canons 
 were also developed for each of the three figures, but in thus 
 rendering the system complex the advantages of the quantified 
 form of proposition seem to be lost. 
 
 Prof. De Morgan also discovered the advantages of the quanti 
 fied predicate, and invented a system differing greatly from that 
 of Sir W. Hamilton. It is fully explained in his Formal Logic, 
 The Syllabus of a new System of Logic, and various important 
 memoirs on the Syllogism in the Transactions of the Cambridge 
 Philosophical Society. In these works is also given a complete 
 explanation of the "Numerically Definite Syllogism." Mr. De 
 Morgan pointed out that two particular premises may often give 
 a valid conclusion provided that the actual quantities of the two 
 terms are stated, and when added together exceed the quantity of 
 the middle term. Thus if the majority of a public meeting vote 
 for the first resolution, and a majority also vote for the second, 
 it follows necessarily that some who voted for the first voted also 
 for the second. The two majorities added together exceed the 
 whole number of the meeting, so that they could not consist of 
 entirely different people They may indeed consist of exactly 
 the same people ; but all that we can deduce from the premises 
 is that the excess of the two majorities added together over the 
 number of the meeting must have voted in favor of each resolu- 
 tion. This kind of inference has by Sir VV. Hamilton been said 
 to depend on ultra-total distribution ; and the name of Plurative 
 Propositions has been proposed for all those which give a dis- 
 tinct idea of the fraction or number of the subject involved in the 
 assertion. 
 
 T. Spencer Baynes, Essay on the new Analytic of Logical 
 
 Forms ; Edinburgh, 1850. 
 Prof. Bowen's Treatise on Logic or tlie Laws of Pure Thought, 
 
 Cambridge, Mass., 1866, gives a full and excellent account cf 
 
 Hamilton's Logic. 
 Bee also Hamilton's Lectures on Logic, New York, 185&
 
 272 RBCElfT LOGICAL VIEWS. 
 
 In this Section^ on "The Quantitication of the 
 Predicate," we liave considered : 
 
 1. Metnuug of the Expression. 
 
 2. Convefsion with <i Quantified Predicate, 
 
 3. Tlie Rale for Conversion. 
 
 4. Number of Propositions with Quantified Pred- 
 
 icate. 
 
 5. Number of Syllogisms with Quantified Pred- 
 
 icate. 
 
 6. Hatnilton's Notation. 
 
 7. Hatnilton's Canon of the Syllogism, 
 
 SECTION U. 
 BOOLE'S SYSTEM OF LOGIC. 
 
 1. The Difficulty of Dr. Boole's Statement. 
 
 It would not be possible to give in an elementary work 
 a notion of the system of indirect inference first dis- 
 covered by the late Dr. Boole, the Professor of Mathe- 
 matics at the Queen's College, Cork. This system was 
 founded upon the Quantification of the Predicate, but 
 Dr. Boole regarded Logic as a branch of Mathematics, 
 and believed that he could arrive at every possible 
 inference by the principles of algebra. The proc* ss as 
 actually employed by him i very obscure and difficult; 
 and hardly any attempt to introduce it into elementary 
 text-books of Logic has yet been made. 
 
 I have been able to arrive at exactly the same results 
 as Dr. Boole without the use of any mathematics; and 
 though the very simple process which I am going to 
 describe can hardly be said to be strictly Dr. Boole'a
 
 BOOLE'S SYSTEM OF LOGIC. 27b 
 
 logic, it is yet very similar to it and can prove every- 
 thing that Dr. Boole proved. This Method of Indirect 
 Inference is founded upon the three primary Laws of 
 Thought, and the learner who may have thought them 
 mere useless truisms will perhaps be surprised to find 
 how extensive and elegant a system of deduction may 
 be derived from them. 
 
 2. Application of the Law of Excluded Middle. 
 
 The Law of Excluded Middle enables us to assert 
 that anything must either have a given quality or must 
 have it not. Thus if iron be the thing, and co^nbusti- 
 bility the quality, any one must see that 
 
 "Iron is either combustible or incombustible." 
 
 This division of alternatives may be repeated as often 
 as we like. Thus let book be the class of things to be 
 divided, and English and Scientific two (jualities. Then 
 any book must be either English or not English ; again 
 an English book must be either Scientific or not Scien- 
 tific, and the same may be said of books which arc not 
 English. Thus we can at once divide books into four 
 classes 
 
 Books, English and Scientific. 
 Books, English and not-Scientific. 
 Books, not-English and Scientific. 
 Books, not-English and not-Scientific. 
 
 This is what we may call an exhaustive division of 
 <.he class hooks; for there is no possible book which 
 iocs not fall into one division or other of these four, 
 for the simple reason, that if it does not fall into any oi 
 ihe first three it must fall into the last The process
 
 274 EECEKT LOGICAL VIEWS. 
 
 can be repeated without end, as long as any new ci^ 
 cumstance can be suggested as the ground of division. 
 Thus we might divide each class again according as the 
 books are octavo or not octavo, bound or unbound, 
 published in London or elsewhere, and so on. We 
 shall call this process of twofold division, which is 
 really the process of Dichotomy, the development of a 
 tepm, because it enables us always to develop the utmost 
 number of alternatives whicli need be considered. 
 
 3. Application of the Law of Coutradiction, 
 
 As a general rule it is not likely that all the alterna- 
 tives thus unfolded or developed can exist, and the next 
 point is to ascertain how many do or may exist. The 
 Law of Contradiction asserts that nothing can combine 
 contradictory attributes or qualities, and if we meet 
 with any term which is thus self-contradictory we are 
 authorized at once to strike it out of the list. Now 
 consider our old example of a syllogism : 
 
 Iron is a metal ; 
 
 All metals are elements ; 
 
 Therefore iron is an element. 
 
 We can readily prove this conclusion by the indirect 
 method. For if we develop the term iron, we have foul 
 alternatives ; thus 
 
 Iron, metal, element. 
 
 Iron, metal, not-element. 
 
 Iron, not-metal, element 
 
 Iron, not-metal, not-element. 
 
 But if we compare each of these alternatives with the 
 premises of the syllogism, it will be apparent that
 
 BOOLES' SYSTEM OF LOGIC. 275 
 
 several of them are incapable of existing. Iron, we are 
 informed, is a metal. Hence no class of things ** iron, 
 not-metal " can exist. Thus we are enabled by the 6rst 
 premise to strike out both of the last two alternatives 
 which combine iron and not-metal. The second alter- 
 native, again, combines metal and not-element; but as 
 the second premise informs us that *'all metals are 
 elements," it must be struck out. There remains, then, 
 only one alternative which is capable of existing if the 
 premises be true, and as there cannot conceivably be 
 more alternatives than those considered, it follows dem- 
 onstratively that iron occurs only in combination with 
 the qualities of metal and element, or, in brief, that it 
 is an element. 
 
 4. Universality of the Method. 
 
 We can, however, prove not only the ordinary syllo- 
 gistic conclusion, but any other conclusion which can 
 be drawn from the same premises ; the syllogistic con- 
 clusion is in fact only one out of many which can 
 usually be obtained from given premises. Suppose, for 
 instance, that we wish to know what is the nature of 
 the term or class not-element, so far as we can learn 
 it from the premises just considered. We can develop 
 the alternatives of this term, just as we did those of 
 iron, and get the following 
 
 Not-element, iron, metal. 
 Not-element, iron, not-metal. 
 Not-element, not-iron, metal. 
 Not-element, not-iron, not-metal. 
 
 Compare these combinations as before with the prera-
 
 276 EECENT LOGICAL VIEWS. 
 
 ises. The drst it is easily seen cannot exist, because 
 all metals are elements ; for the same reason the third 
 cannot exist ; the second is likewise excluded, because 
 iron is a metal and cannot exist in combination with 
 the qualities of not-metal. Hence there remains onlj 
 one combination to represent the class desired namely, 
 Not-element, not-iron, not-metal. 
 Thus we learn from the premises that every not- 
 element is not a metal and is not iron. 
 
 As another example of this kind of deductive process 
 I will take a case of the Disjunctive Syllogism, in the 
 negative mood, as follows: 
 
 A fungus is either plant or animal, 
 A fungus is not an animal ; 
 Therefore it is a plant. 
 
 Now if we develop all the possible ways in which 
 fungus, plant and animal can be combined together, 
 we obtain for the term fungus 
 
 (1) Fungus, plant, animal. 
 
 (2) Fungus, plant, not-animal. 
 
 (3) Fungus, not^j)lant, animal. 
 
 (4) Fungus, not-plant, not-animal 
 
 Of these, however, the 4th cannot exist because by 
 the premise a fungus must be a plant, or if not a plant 
 an animal. The first and 3d again cannot exist because 
 the minor premise informs us that a fungus is not an 
 animal. There remains then only the second combi- 
 nation, 
 
 Fungus, plant, not^animal, 
 from which we learn the syllogistic conclusion that "a 
 fungus is a plant''
 
 BOOLE'S SYSTEM OF LOGIC. 277 
 
 5. Comparative Excellence of the System. 
 
 The chief excellence of this mode of deduction con- 
 gists in the fact that it is not restricted to any definite 
 series of forms like the syllogism, but is applicable, 
 without any additional rules, to all kinds of proposi- 
 tions or problems which can be conceived and stated. 
 There may be any number of premises, and they 
 may contain any number of terms ; all we have to do 
 to obtain any possible inference is to develop the term 
 required into all its alternatives, and then to examine 
 how many of these agree with the premises. What 
 remain after this examination necessarily form the 
 description of the term. The only inconvenience of 
 the method is that, as the number of terms increases, 
 the number of alternatives to be examined increases 
 very rapidly, and it soon becomes tedious to write them 
 all out. This work may be abbreviated if we substitute 
 single letters to stand for the terms, somewhat as in 
 algebra; thus we may take A, B, C, D, etc., to stand 
 for the affirmative terms, and a, J, c, d, etc., for the 
 corresponding negative ones. 
 
 Let us take as a first example the premises 
 Organic substance is either vegetable or animal. 
 Vegetable substance consists mainly of carbon, hydrogen, and 
 
 nitrogen. 
 Ajiimal substance consists mainly of carbon, hydrogen, and 
 nitrogen. 
 
 It would take a long time to write out all the combinations of 
 ihe four terms occurring in the above ; but if we substitute letters- 
 rs follows 
 
 ..4 = organic substance, 
 B = vegetable substance, 
 = animal substance, 
 2) = consisting mainly of carbon, hydrogen, and nitrogen.
 
 278 EECENT LOGICAL VIEWS. 
 
 we can readily represent all the combinations which can belonf 
 to the term A. 
 
 
 (1) 
 (2) 
 
 (8) 
 
 (4) 
 
 ABCD 
 ABCd 
 ABcD 
 ABcd 
 
 AbCD 
 AbCd 
 AbcD 
 Abed 
 
 (5) 
 
 (6) 
 (7) 
 (8) 
 
 Now the 
 
 premises amount to the statemente 
 
 i,that 
 
 
 
 A must be either B or 0, 
 B must be D, 
 C must he D. 
 
 
 The combinations (7) and (8) are inconsistent with the firs* 
 premise; the combinations (2) and (4) witli the second premise; 
 and (6) is inconsistent with the third premise. There remain 
 jnly, 
 
 ABCD 
 ABcD 
 AbCD. 
 
 Whence we learn at once that " organic substance (A) always 
 consists mainly of carbon, hydrogen and nitrogen," because it 
 always occurs in connection with D. The reader may perhaps 
 notice that the' term ABCD implies that organic substance may 
 be both vegetable (B) and animal (C). If the first premise be 
 interpreted as meaning that this is not possible, of course this 
 combination should also be struck out. It is an unsettled pomt 
 whether the alternatives of a disjunctive proposition can co-exist 
 or not i^see p. 157), but I much prefer the opinion that they can ; 
 and as a matter of fact it is quite likely that there exist very 
 simple kinds of living beings, which cannot be distinctly asserted 
 to be vegetable only or animal only, but partake of the nature of 
 each. 
 
 Asa more complicated problem to show the powers of this 
 system, let us consider the premises which were treated by Dr. 
 Boole in his Laws of Thought, p. 125, as follows : 
 
 " Similar figures consist of all whose corresponding angles are 
 equal, and whose corresponding sides are proportional. 
 
 Triangles whose corresponding angles are equAl bftTW *4ei7 
 corresponding siden proportional ; and ^64 vertd.
 
 BOOLE'S SYSTEM OF LOGIC. 279 
 
 Triangles whose corresponding sides are proportional havif 
 their corresponding angles equal." 
 Now if we take our symbol letters as follows : 
 A = similar figure, 
 B = triangle, 
 
 G= having corresponding angles equal, 
 2>= having corresponding sides proportional, 
 
 the premises will be seen to amount to the statements that 
 
 A is identical with CD, 
 and that 
 
 BO ia identical with BD; 
 
 in other words, all ^'s ought to be CD'b, 0D' ought to be ^.'s, 
 all BG'a ought to be BD' and all BD's ought to be BC's. 
 
 The possible combinations in which the letters may be united 
 are 16 in number and are shown in the following table: 
 
 ABGD 
 
 aBGD 
 
 ABGd 
 
 aBGd 
 
 ABcD 
 
 aBcD 
 
 ABcd 
 
 aAcD 
 
 AbGD 
 
 abGD 
 
 AhGd 
 
 abGd 
 
 AhoD 
 
 abcD 
 
 Abed 
 
 abed 
 
 CJomparing each of these combinations with the "premise, we see 
 that ABGd, ABcD, ABcd, and others, are to be struck out be- 
 cause every A is also to be GD. The combinations cBCD and 
 abGD are struck out because every GD should also be A. Again, 
 aBGd is inconsistent with the condition that every BG is also to 
 be BD ; and if the learner carefully follows out the same process 
 of examination, there will remain only six combinations, whicl. 
 agree with all the premises, thus 
 
 ABGD aBcd 
 
 AbOD abGd 
 
 abeD 
 abed 
 
 From these combinations we can draw any description we like ol
 
 380 RECENT LOGICAL VLEW8. 
 
 the classes of thiags agreeing with the premises. The class A oi 
 similar figures is represented by only two combinations or alter- 
 natives ; the negative class a or dissimilar figures, by four com- 
 binations, whence we may draw the following conclusion: " Dis- 
 similar figures consist of all trianj^les which have not their 
 corresponding angles equal, and sides proportional (aBcd), and of 
 all figures, not being triangles, which have either their angles 
 equal and sides not proportional (abCd), or their corresponding 
 sides proportional and angles not equal (abcD), or neither their 
 corresponding angles equal nor corresponding sides proportional 
 (abed)." 
 
 6. The Logical Abacus and the Logrical Machine. 
 
 In performing this method of inference it is soon 
 seen to proceed in a very simple mechanical manner, 
 and the only inconvenience is the large number of 
 alternatives or combinations to be examined. I have, 
 therefore, devised several modes by which the labor can 
 be decreased ; the simplest of these consists in engrav- 
 ing the series of 16 comt)inations on the opposite page, 
 which occur over and over again in problems, with 
 larger and smaller sets, upon a common writing slate, 
 so that the ejccluded ones may be readily struck out 
 with a common slate pencil, and yet the series may be 
 employed again for any future logical question. A 
 second device, which I have called the " Logical aba- 
 cus," is constructed by printing the letters upon slips 
 of wood furnished with pins, contrived so that any part 
 or class of the combinations can be picked out mechani- 
 cally with very little trouble ; and a logical problem is 
 thus solved by the hand, rather than by the head. 
 More recently, however, I have reduced the system to 
 a completely mechanical form, and have thus embodied 
 the whole of the indirect process of inference in what
 
 BOOLE'S SYSTEM OF LOGIC. 281 
 
 may be called a Logical Machine. In the front of the 
 machine are seen certain movable wooden rods carry- 
 ing the set of 16 combinations of letters which are 
 seen on page 279. At the foot are 21 keys like 
 those of a piano; eight keys towards the left hand 
 are marked with tho letters A, a, B, b, C, c, D, d, and 
 are intended to represent these terms when occurring 
 in the subject of a proposition. Eight other keys 
 towards the right hand represent the same letters or 
 terms when occurring in the predicate. The copula of 
 a proposition is represented by a key in the middle of 
 the series ; the full stop by one to the extreme right, 
 while there are two other keys which serve for the dis- 
 junctive conjunction or, according as it occurs in sub- 
 ject or predicate. Now if the letters be taken to stand 
 for the terms of a syllogism or any other logical argu- 
 ment, and the keys of the instrument be pressed 
 exactly in the order corresponding to the words of the 
 premises, the 16 combinations will be so selected and 
 arranged thereby that at the end only the possible com- 
 binations will remain in view. Any question can then 
 be asked of the machine, and an infallible answer will 
 be obtained from the combinations remaining. The 
 internal construction of the machine is such, therefore, 
 as actually to perform the work of inference which, in 
 Dr. Boole's system, was performed by a very compli- 
 cated mathematical calculation. It should be added, 
 that there is one remaining key to the extreme left 
 which has the effect of obliterating all previous opera- 
 tions and restoring all the combinations to their original 
 place, so that the machine -is then ready for the per- 
 formance of any new problem.
 
 282 RECENT LOGICAL VIEWS. 
 
 An account of this logical machine may be foand in the Pro- 
 ceedings of the Royal Society for Jan. 20tli, 1870, the machine 
 having on that day been exhibited in action to the Fellows of the 
 Society. The principles of the method of inference here described 
 are more completely stated in The Substitution of Similars* and 
 the Pure Logie,\ which I published in the years 1869 and 1864. 
 I may add, that the first-named of these works contains certain 
 views as to the real nature of the process of inference which I do 
 not think it desirable to introduce into an elementary work like 
 the present, on account of their speculative character. The pro- 
 cess of inference, on the other hand, which I have derived from 
 Boole's system, is ol so self-evident a character, and is so clearly 
 proved to be true by its reduction to a mechanical form, that I do 
 not hesitate to bring it to the learner's notice. 
 
 George Boole, Mathematical Analysis of Logic, 1847. 
 An Investigation of the Laws of ThougM. Londor, Walton & 
 Maberly. 1854. 
 
 In this section, on "Boole's System of Logic,'* 
 we have considered : 
 
 1. Tlie Difficulty of Dr. Boole* a Sfatetnent. 
 
 2. Application of the Law of Excluded Middle, 
 
 3. Application of the Law of Coiifradictioti. 
 
 4. Universality of the MetJwd 
 
 5. Comparative Excellence of the System. 
 
 O. The Loyic,al Abacus and the Logical Machine. 
 
 * Tht 9ubtUuUon of Similars th trve Principle qf Reasoning, derived from 
 a modification of ArislotW 8 Dictum. Macmillaa & Co., 1869. 
 
 t Pvre Logic, or the Logic of (Quality apart from ^uantU)/, tte. Edwan 
 Stanford, Charing Ctoea.
 
 Ifes^isft, 
 
 AHQ 0UEST!OHS. 
 
 INTRODUCTION. 
 
 1. What is the definition of Lo^c ? 
 
 2. What are the meanings of a Law of Nature, and a Law ol 
 
 Thought? 
 8. Explain the distinction between the Form of Thought, a.'^d 
 the Matter of Thouglit. 
 
 4. In what sense may Logic be called the Science of Sciences? 
 
 5. How does a Science differ from an Art, and why is Logic more 
 
 in the form of a Science than an Art ? 
 
 6. Can we say that Logic is a necessary aid in correct reasoning, 
 
 when persons who have never studied logic reason cor- 
 rectly ? 
 
 7. Name the parts of which a syllogism is composed. 
 
 8. How far is it correct to say that Logic is concerned with 
 
 language ? 
 
 9. What are the three acts of mind considered in Logic? Which 
 
 of them is more especially the subject of the Science? 
 
 10. Can you state exactly what is meant by a general notion, 
 idea, or conception ? 
 
 1. How do the Nominalists, Realists, and Conceptualists diflfej 
 in their opinions as to the nature of a general notion ?
 
 1284 liLKEECliSES AND QUEtJTIONS. 
 
 CHAPTER I. 
 TERMS. 
 
 SECTION 1. 
 THE VARIOUS KINDS OF TERMS 
 
 1. Define a name or term. 
 
 2. What is a categoreinatic term ? 
 
 8. Explain tlie distinction between a collective jttid a general 
 
 term. 
 4. Distinguish the collective and distributive use of the word aH 
 
 In the following : 
 
 (1) Non omnia moriar (i. e. I shall not all die). 
 
 (2) "All men find their own in ull men's good. 
 
 And all men join in noble brotherhood." 
 
 Tennyson, 
 
 (8) Non omnia possumus omnes (i. e. we cannot all do all 
 
 things). 
 
 6. Which of the following are al)8tract terms? 
 
 Act, ingratitude, home, houriy, homeliness, introduction, 
 individuality, truth, true, trueness, yellow, yellowness, 
 childhood, book, blue, intention, reason, rationality, reason- 
 ableness. 
 
 6. Define a negative term, and mention the mark by which you 
 
 may recognize it. 
 
 7. Distinguish a privative from a negative term, and find some 
 
 instances of privative terms 
 
 8. Descrilx* the logical characters of the following terms, with 
 
 the precautions given at p. 28 :
 
 TERMS. 
 
 285 
 
 Metropolis 
 
 Book 
 
 Library 
 
 Great Britain 
 
 Caesar 
 
 Void 
 
 Gold 
 
 Prime Minister 
 
 Indigeslibility 
 
 Mancliester 
 
 Recollection 
 
 Insignificant 
 
 Brilliant 
 
 Independence 
 
 Heaviness 
 
 Illustration 
 
 Section 
 
 Whiteuesa 
 
 Consciousness 
 
 Lord Chancellor 
 
 Vegetable Kingdom 
 
 Brilliance 
 
 Weight 
 
 Sensation 
 
 Ceesar 
 
 Csesarism 
 
 Application 
 
 Individual 
 
 Volume 
 
 Language 
 
 Adornment 
 
 Agreement 
 
 Obliquity 
 
 Motionless 
 
 Henry VIII. 
 
 Formal Logic 
 
 Sect 
 
 Nation 
 
 Institution 
 
 Light 
 
 Observation 
 
 Tongue 
 
 Air 
 
 Mentor 
 
 Anarchy 
 
 Retribution 
 
 Solemnity 
 
 Understanding 
 
 Geology 
 
 Demeanor 
 
 Resemblance 
 
 Departure 
 
 Nestor 
 
 Alexander 
 
 SECTION II, 
 
 THE AMBIGUITY OF TERMS 
 
 1. Define uni vocal terms, and suggest some terms which are per 
 
 fectly uni vocal. 
 
 2. What are the other names by which equivocal terms are often 
 
 called? 
 
 3. Distinguish the three kinds of ambiguous terms, and find 
 
 instances of each. 
 
 4. Distinguish the three causes by which the third and most im 
 
 portant class of ambiguous terms have been produced. 
 
 5. Explain the ambiguity of any of the following terras, referring 
 
 each to its proper cause, and tracing out as far as possible 
 the derivation of each separate meaning from the original 
 vaeamng.
 
 286 
 
 EXERCISES AND QUESTIONS. 
 
 BUI 
 
 Minister 
 
 Subject 
 
 Letter 
 
 Table 
 
 Clerk 
 
 Object 
 
 Star 
 
 Term 
 
 Order 
 
 Earth 
 
 Pole 
 
 School 
 
 Wood 
 
 Law 
 
 Reason 
 
 Air 
 
 Bull 
 
 Sensatiou 
 
 Bed 
 
 Glaas 
 
 Volume 
 
 Art 
 
 Bowl 
 
 Peer 
 
 Scale 
 
 Interest 
 
 End 
 
 Sense 
 
 Feeling 
 
 Paper 
 
 Division 
 
 Ball 
 
 Kind 
 
 Bolt 
 
 Class 
 
 SECTION III, 
 
 EXTENSION AND INTENSION. 
 
 L Distinguish very carefully the meanings in extension and in 
 tension of the terms 
 Quadruped, railway, human being, engine, mountain, Mem- 
 ber of Parliament. 
 
 2. E^numerate the synonyms or other names used instead of ex> 
 tension and intension. 
 
 8. According to what law is the quantity of extension connected 
 with the quantity of intension ? Show that the law holds 
 true of the following series of terms 
 
 (1) Iron, metal, element, matter, substance. 
 
 (2) Matter, organized matter, animal, man. 
 
 (8) Ship, steamship, screw steamship, iron screw-steamship, 
 
 British iron screw-steamship. 
 (4) Book, printed book, dictionary, Latin dictionary, 
 4. Distinguish between the connotation and denotation of a term. 
 6. Select from the list of terms under Section I., Question 8 
 (p. 285), sucli terms as are non-connotative according to Mr. 
 Mill's views. 
 I Arrange the following terms in series as in Question 8, placing 
 each term of greater extension before a term of less exten- 
 sion. Point out which are the terms of greatest and least 
 intension in each series.
 
 TEBM8. 
 
 287 
 
 Emperor 
 
 Teacher 
 
 Baptist 
 
 Timber 
 
 Person 
 
 Horse 
 
 Heavenly body 
 
 Christian 
 
 Animal 
 
 Dissenter 
 
 Individual 
 
 Jupiter 
 
 Ruler 
 
 Organized substance 
 
 Lawyer 
 
 Alexander 
 
 Planet 
 
 Mammalian 
 
 Matter 
 
 Solicitor 
 
 Quadruped 
 
 Being 
 
 Napoleon III. 
 
 Episcopalian 
 
 SECTION IV. 
 
 THE GROWTH OF LANGUAGE. 
 
 1. Trace out the generalization or specialization which has taken 
 place in any of the following words : 
 Kind, genus, class, species, order, rank, Augustus, president, 
 speaker, Utopia, rock, Commons, doctor. 
 8. Point out metaphors derived from the notions of weight, 
 
 straightness, rock, wind. 
 8. Distinguish as accurately as possible the meanings of the fol- 
 lowing synonyms : 
 Sickness, malady; mud, mire; confutation, refutation; 
 boundary, imit ; mind, intellect ; recollection, reminis- 
 cence; procrastination, dilatoriness; converse, reverse, 
 obverse, inverse. 
 4. Form lists of all the words derived from any of the foUovdng 
 roots: 
 
 (1) Tendere, to stretch, as in intention, attention. 
 
 (2) Pouere, to place, as in position, supposition. 
 
 (3) Gentis, tribe or kind, as in genus, generation. 
 
 (4) Munus, gift, as in remuneration, common (Latin, Com 
 
 munis). 
 
 (5) Modus, shape or fashion, as in mood, moderate. 
 
 (6) Scribere, to write, as in scribe, inscription, describe. 
 
 (7) Capere to take, as in deception, incipient.
 
 388 EXERCISES AND QUESTIONS. 
 
 SECTION V, 
 
 THE PERFECT AND THE IMPERFECT KNOWLEDGE OF 
 TERMS. 
 
 1. What are the characters of perfect knowledge ? 
 9. Describe the character of the knowledge which we have of th* 
 following notions or objects : 
 
 A syllogism. 
 
 Electricity. 
 
 Motion. 
 
 A triangle. 
 
 Eternity. 
 
 The weight of the earth (5852 trillions of tons). 
 
 The color of the sKy. 
 
 8. EiXplain exactly what you mean by intuitive knowiadge. 
 
 CHAPTER II. 
 PROPOSITIONS. 
 
 SECTION I. 
 
 THE KINDS OF PROPOSITIONS. 
 
 1. Define a proposition, and name the parts of which ^t is com- 
 
 posed. 
 
 2. How are propositions classified ? 
 
 8. Name the four kinds of categorical propositions, and their 
 
 symbols. 
 4. Under which classes arc Hlngular and indefinite propositions 
 
 placed? 
 i. Enumerate the most asaal signs of the quantity of a i roDogi 
 
 tkm.
 
 PROPOSITIONS. ^9 
 
 0. What are modal propositions according to early logicians, and 
 
 according to Thomson ? 
 7. How far do logicians consider propositions witli regard to their 
 
 truth or falsity? 
 
 SECTION II. 
 
 OPPOSITION OF PROPOSITIONS. 
 
 1. State >he quantity of the subject and predicate in each of th 
 
 propositions A, E, I, 0. 
 
 2. Select out of the following propositions, pairs of contrary, 
 
 contradictory, subaltern, and subcontrary propositions 
 
 (1) Some elements are known. 
 
 (2) No elements are known. 
 
 (3) All elements are known. 
 
 (4) Not all elements are known. 
 
 (5) Some elements are not knowa 
 
 (6) All elements are not known. 
 
 8. What propositions are true, false, or doubtful, 
 
 (1) when A is false, (3) when I is false, 
 
 (2) wlien E is false, (4) when is false ? 
 
 4. Prove by means of the contradictory propositions that subcon- 
 
 trary propositions cannot both be false. 
 
 5. Show by means of the subcontrary pro[)ositions that contrary 
 
 propositions may both be false. 
 
 9. What quantity would you assign to each of the following 
 
 propositions ? 
 
 (1) Knowledge is power. 
 
 (2) Nebulae are material bodies. 
 
 (3) Light is the vibration of an ether. 
 
 (4) Men are more to be trusted than we think. 
 
 (5) The Chinese are industrious. 
 
 ^ Why is it desirable in controversy to refute a statement by its 
 contradictory and not by its contrary?
 
 W EXEBCISE8 AND QUESTIONS. 
 
 SECTION III. 
 
 CONVERSION AND IMMEDIATE INFERENCE. 
 
 1. Define inference and conversion. 
 
 2. What are converse and convertend propositions? 
 8. State tlie rules of valid conversion. 
 
 4- Name all the kinds of conversion. 
 
 5. By what process do we pass fix)m each of the following prop- 
 
 ositions to the next? 
 
 (1) No knowledge is useless. 
 
 (2) No useless thing is knowledge. 
 (8) All knowledge is not useless. 
 
 (4) All knowledge is useful. 
 
 (5) What is not useful is not knowledge. 
 
 (6) What is useless is not knowledge. 
 
 (7) No knowledge is useless. 
 
 6. Give the logical opposites of the following proposition, and 
 
 the converse of its contradictory : 
 
 " He cannot become rich who will not labor." 
 
 7. Apply negative conception to the proposition "All men are 
 
 fallible ;" then convert and show that the result is the con- 
 trapositive of the original. 
 
 8. Classify the propositions subjoined into the four following 
 
 groups : 
 
 a. Those which can be inferred from (1). 
 
 b. Those from which (1) can be inferred. 
 
 c. Those which do not contradict (1), but cannot be inferred 
 
 from it. 
 
 d. Those which contradict (1). 
 
 (1) All just acts are expedient acta. 
 
 (2) No expedient acts are unjust. 
 
 (8) No just acts are inexpedient 
 (4) All inexpedient acts are unjust. 
 ^5) Some unjust ac*s are inexpedient. 
 
 (6) No expedient acts are just 
 
 (7) Some inexpedient acts are ui\}uat
 
 PROPOSITIONS. S91 
 
 (8) All expedient acts are just. 
 
 (9) No inexpedient acts are just. 
 
 (10) All unjust acts are inexpedient. 
 
 (11) Some inexpedient acts are just acts. 
 (13) Some expedient acts are just. 
 
 (13) Some just acts are expedient. 
 
 (14) Some unjust acts are expedient. 
 
 SECTION IV. 
 
 THE LOGICAL ANALYSIS OF SENTENCES. 
 
 1. How does the grammatical predicate differ from the k>g^cal 
 
 predicate ? 
 3. Distinguish between a compound and a complex sentence ; and 
 
 between co-ordinate and subordinate propositions. 
 
 3. Enumerate the grammatical expressions which may form 
 
 (1) A subject. (4) An object. 
 
 (3) An attribute. (5) An adverbial. 
 
 (3) A predicate. 
 
 4. Examine the following sentences, ascertain which are com- 
 
 pound or complex, and point out the co-ordinate or subordi- 
 nate propositions: 
 (1) Happy is the man that findeth wisdom, and the man that 
 
 getteth understanding. 
 (8) Heat, being motion, can be converted into mechanicai 
 force. 
 
 (3) Ceres, Pallas, Juno, and Vesta are minor planets, oi 
 
 asteroids. 
 
 (4) Knowledge comes, but wisdom lingers. 
 
 (5) Fortune often sells to the hasty what she gives to thoM 
 
 who wait. 
 
 (6) Thousands at His bidding speed. 
 And post o'er land and ocean without rest ; 
 They also serve who only stand and wait. 
 
 (7) Pride that dines on vanity, sups on contempt
 
 293 EXEBGISES AND QUESTIONS. 
 
 (8) Nobody can be healthful without exercise, neither natural 
 
 body, nor politic. 
 
 (9) Nature is often hidden, somet^imes overcome, seldom ex- 
 
 tinguished. 
 
 (10) It is impossible to love and be wise. 
 
 (11) Though gods they were, as men they died. 
 
 (12) He that is not industrious envieth him that is. 
 
 (13) Ye are my frieuds, if ye do whatsoever 1 command you. 
 
 John XV. 14. 
 
 (14) The wisdom that is from above is first pure, then peace- 
 
 able, gentle, and easy to be intreated, full of mercy, and 
 good fruits, without partiality, and without hyj)Ocrisy. 
 James iii. 17. 
 5. Analyze in the form of a scheme or diagram any of the follow- 
 ing sentences : 
 
 (1) The first aphorism of Bacon's Novum Organum, on p. 202. 
 
 (2) Some judgments are merely explanatory of their subject, 
 
 having for their predicate, a conception which it fairly 
 implies, to all who know and can define its nature. 
 
 (3) There be none of the affections which have been noted to 
 
 fascinate or bewitch, but love and envy ; they both have 
 vehement wishes ; they frame themselves readily into 
 imaginations and sui^gestiuns ; and they come easily into 
 the eye, e8i)ecially upon the presence of the objects, which 
 are the points that conduce to fascination, if any such 
 there be. 
 
 GENERAL EXERCISES ON PROPOSITIONS. 
 
 The learner is desired to ascertain the logical character of each 
 of the following propositions ; he is to state of each whether it is 
 affirmative or negative, universal, particular, singular or in- 
 definite, pure or modal, exclusive or exceptive, etc. ; when 
 irregularly stated he is to reduce the proj)osition to the simple 
 logical order; he is then to convert the proposition, and to draw 
 immediate inferences from it by any process which may be 
 applicable. 
 
 (1) All birds are feathered. 
 
 (2) No reptiles are feathered.
 
 PROPOSITIONS. XVS 
 
 (8) Fixed stars are Belf-hiininous. 
 
 (4) Perfect happiness is impossible. 
 
 (5) Life every man holds dear. 
 
 (6) Every mistake is not a proof of ignorance. 
 
 (7) Some of the most valuable books are seldom read 
 
 (8) He jests at scars who never felt a wound. 
 
 (9) Heated metals are softened. 
 
 (10) Not one of the Greeks at Thermopylae escaped. 
 
 (11) Few are acquainted with themselves. 
 
 (12) Whoso loveth instruction loveth knowledge. 
 
 (13) Nothing is harmless that is mistaken for a virtaa 
 
 (14) Some of our muscles act without volition. 
 
 (15) Metals are all good conductors of heat. 
 
 (16) Fame is no plant that grows on mortal soil. 
 
 (17) Only the brave deserve the fair. 
 
 (18) No one is free who doth not command himself. 
 
 (19) Nothing is beautiful except truth. 
 
 (20) The wicked shall fall by his own wickedness. 
 f21) Unsafe are all things unbecoming. 
 
 (22) There is no excellent beauty that hath not some strange 
 
 ness in the proportion. 
 
 (23) It is a poor centre of a man's actions, himself. 
 (34) Mercy but murders, pardoning those that kilL 
 
 (25) I shall not all die. (Non ojnnis moiiar.) 
 
 (26) A regiment consists of two battalions. 
 
 (27) 'Tis cruelty to load a falling man. 
 
 (28) Every mistake is not culpable. 
 (89) Quadrupeds are vertebrate animals. 
 
 (30) Not many of the metals are brittle. 
 
 (31) Many are the deserving men who are unfortunate. 
 
 (32) Amalgams are alloys of mercury. 
 
 (33) One kind of metal at least is liquid. 
 
 (34) Talents are often misused. 
 
 (35) Some parallelograms have their adjoining sides equal 
 
 (36) Britain is an island. 
 
 (37) Romulus and Remus were twins. 
 
 (38) A man's a man. 
 (89) Heaven is all mercy.
 
 294 EXERCISES AND QUESTIONS. 
 
 (40) Every one is a good judge of liis own interests. 
 
 (41) All parallelograms have their opposite angles eqoaL 
 
 (42) Familiarity breeds contempt. 
 
 (43) No one is al ways happy. 
 
 (44) Every little makes a mickle. 
 
 CHAPTER in* 
 SYLLOGISMS. 
 
 SECTION I. 
 
 THE LAWS OF THOUGHT 
 
 1. State the three Fundamental Laws of Thought, aud apply tbexn 
 
 to the following notions : 
 
 (1) Matter, organic, inorganic. 
 
 (2) Undulations, polarized, nonpolarized. 
 (8) Figure, rectilinear, curvilinear. 
 
 2. Is it wrong to assert that an animal cannot both be vertebrate 
 
 and invertebrate, seeing that some animals are vertebrate 
 
 and some are not ? 
 8. Select from the foIlo\ving such terms as are negatives of the 
 
 others, and such ai are opposites: Light, plenum, gain, 
 
 heat, decrease, loss, darkness, cold, increase, vacuum. 
 4. How is Aristotle's dictum applicable to the following argfu- 
 
 mentsV 
 
 (1) Silver is a good conductor of electricity ; for such are all 
 
 the metals. 
 
 (2) Comets cannot be without weight ; for they are composed 
 
 of matter, which is not without weight
 
 8YLL0GISMB. 295 
 
 SECTION II. 
 
 THE RULES OF THE SYLLOGISM. 
 
 I Distinguish mediate and immediate inference. 
 
 8. Define syllogism, and state with what it is synonTmoos. 
 
 8. What are the six principal and two sabordinate rules of th 
 syllogism ? 
 
 4. In the following syllogisms point out in succession the con- 
 clusion, the middle term, the major term, the minor term, 
 the major premise and the minor premise, observing this 
 precise order. 
 
 (1) All men are fallible ; 
 All kings are men ; 
 
 Therefore all kings are fallible. 
 
 (2) Platinum is a metal ; 
 
 All metals combine with oxygen ; 
 Therefore Platinum combines with oxygen. 
 (3) Hottentots are capable of education ; for Hottentots are 
 men, and all men are capable of education. 
 6. Explain carefully what is meant by non-distribution of the 
 middle term. 
 
 SECTION III. 
 
 THE MOODS AND FIGURES OF THE SYLLOGISM. 
 
 1. Name the rules of the syllogism which are broken by any ol 
 
 the following moods, no regard being paid to figure : 
 AIA, EEI, lEA, lOI, IIA, AEI, 
 
 2. Write out all the 64 moods of the syllogism and strike out th< 
 
 53 invalid ones. 
 
 8. Show in what figures the following premises give a valid con- 
 clusion : AA, AT, EA, OA. 
 
 4 In what figures are lEO and EI valid?
 
 296 EXERCISES AXD QUESTIONS. 
 
 B. To what moods do the following valid Byllogisms belongl 
 Arrange thetii in conect logical order. 
 (1) Some Y's are Z's. (2) All Z's are Y'a 
 
 No X's are Y's. No Y's are X's. 
 
 Some Z's are not X's No Z's are X'a 
 
 (8) No fish suckles its young ; 
 The whale suckles its young ; 
 Therefore the whale is no fish. 
 
 6. Deduce conclusions from the following premises ; and state to 
 
 what tnood the syllogism belongs. 
 
 (1) Some amphibious animals are mammalian. 
 All mammalian animals are vertebrate. 
 
 (2) All planets are heavenly bodies. 
 No planets are self-luminous. 
 
 (3) Mammalian animals are quadrupeds. 
 No birds are quadrupeds 
 
 (4) Ruminant animals are not predaceous. 
 The lion is predaceous. 
 
 7. Invent examples to sliow that false premises may give true 
 
 conclusions. 
 
 8. Supply premises to the following conclusions. 
 
 (1) Some logicians are not good reasoners. 
 
 (2) The rings of Saturn are material bodies. 
 
 (3) Party government exists in every democracy. 
 
 (4) All fixed stars obey the law of gravitation. 
 
 SECTION IV. 
 THF REDUCTION OF SYLLOGISMS. 
 
 1. State and wxplain the mnemonic lines Barbara, Celarent, etc. 
 
 8. Construct syllogisms in each of the following moods, taking 
 X, Y, Z, for the major, middle, and minor temis resjH'Ctively 
 and show how to reduce them to the first figure: 
 Cesare, Festino, Darapti, Datisi, Fi'rison, Camenes, Fesapo. 
 
 8. What is the use of Reduction? 
 
 1 Prove that the following premises cannot give a universa' 
 oonclusion 1, lA, OA, IE.
 
 SYLLOGISMS. 297 
 
 5. Prove that the third figure must have an affirmative minoi 
 
 premise, and a particular coiiclusion. 
 
 6. Reduce the moods Cesare and Camenes by the Indirect method, 
 
 or Reductio ad Impossibile. 
 
 SECTION V. 
 IRREGULAR AND COMPOUND SYLLOGISMS. 
 
 1, Describe the meaning of each of the terms Enthymeme 
 
 Prosyllogism, Episjllogism, Epicheirema, Sorites. 
 
 2. Make an example of a syllogism in which there are two pro- 
 
 syllogisms. 
 8. Construct a sorites of foar premises and resolve it into distinct 
 syllogisms. 
 
 4. Wliat are the rules to which a sorites must conform ? 
 
 5. The learner is requested to analyze the following arguments, 
 
 to detect those which are false, and to ascertain tlie rules a. 
 the syllojjism which tliey break ; if the argument appears 
 valid he is to ascertain the figure and mood to which it 
 belongs, to state it in correct logical form, and then if it be 
 in an imperfect figure to prove it by reduction to the first 
 figure. The first six of the examples should be arranged 
 both in the extensive and intensive orders 
 ^1) None but mortals are men. 
 Monarchs are men- 
 Therefore monarchs are mortsils. 
 
 (2) Personal deformity is an affliction of naturt 
 Disgrace is not an affliction of nature. 
 Therefore personal deformity is not disgrace. 
 
 (3) Some statesmen are also authors ; for such are Mr. Glad 
 
 stone. Lord Derby, Lord Russell, and Sir G. C. Lewis 
 
 (4) This explosion must have been occasioned by gunpowder 
 
 for nothing else would have possessed sufficient force. 
 
 (5) Every man should be moderate ; for excess will cause di* 
 
 ease 
 ;G) Blessed are the meiciful ; for they shall obtain mercy
 
 298 EXERCISES AN"D QUESTIONS. 
 
 (7) As almost all the organs of the body have a known om 
 
 the spleen must have some use. 
 
 (8) Cogito, ergo sum. (I think, therefore I exist.) 
 
 (9) Some speculative men are unworthy of trust ; for they an 
 
 unwise, and no unwise man can be trusted. 
 
 (10) No idle person can be a successful writer of history 
 therefore Hume, Macaulay, Hallam and Qrote must have 
 been industrious. 
 
 fll) Who spareth the rod, hateth his child ; the parent who 
 loveth his child therefore spareth not the rod. 
 
 (12) Comets must consist of heavy matter ; for otherwise they 
 would not obey the law of gravitation. 
 
 (18) Lithium is an element ; for it is an alkali-producing sab- 
 stance, which is a metal, which is an element. 
 
 (14) Rational beings are accountable for their actions ; brutea 
 not being rational, are therefore exempt from responsi- 
 bility. 
 
 (16) A singular proposition is a universal one ; for it applies to 
 
 the whole of its subject, 
 |16) Whatever tends to withdraw the mind from pursuits ot 
 a low nature deserves to be promoted ; classical learning 
 does this, since it gives us a taste for intellectual enjoy* 
 ments ; therefore it deserves to be promoted. 
 
 (17) Bacon was a great lawyer and statesman ; and as he was 
 
 also a philosopher, we may infer that any philosopher may 
 be a great lawyer and statesman. 
 
 (18) Immoral companions should be avoided ; but some im- 
 
 moral companions arc intelligent persons, so that some 
 
 intelligent persons should be avoided. 
 (10) Mathematical study undoubtedly improves the reasoning 
 
 powers ; but, as the study of logic is not mathematical 
 
 study, we may infer that it does not improve the reasoning 
 
 powers. 
 (20) Every candid man acknowledges merit in a rival ; every 
 
 learned man does not do so ; therefore every learned man 
 
 ia not candid.
 
 SYLLOGISMS. 29S 
 
 SECTION VI. 
 
 CONDITIONAL ARGUMENTS. 
 
 t What are the kiads of conditional propositions, and by whftt 
 signs can you recognize them ? 
 
 2. What are the rules of the hypothetical syllogism? 
 
 8. To what categorical fallacies do breaches of these rules cor- 
 respond ? 
 
 i. Select from the following such as are valid arguments, and 
 reduce them to the categorical form ; explain the fallacious 
 reasoning in the others : 
 
 (1) Rain has fallen if the ground is wet; but the ground is 
 
 not wet ; therefore rain has not fallen. 
 (8) If rain has fallen, the ground is wet; but rain has not 
 
 fallen ; therefore the ground is not wet. 
 (8) The ground is wet, if rain has fallen ; the ground is wet ; 
 
 therefore rain has fallen. 
 (4) If the ground is wet, rain has fallen ; but rain has fallen ; 
 
 therefore the ground is wet. 
 N. B. In these as in other logical examples the student must 
 argue only from the premises, and not from any other knowledge 
 of the subject-matter. 
 
 5. Show that the canons of syllogism (pp. 108, 109) may be 
 
 stated indifferently in the hypothetical or categorical form. 
 1 State the following in the form of a Disjunctive or Dilemmatio 
 argument, and name the kind to which it belongs. 
 If pain is severe it will be brief; and if it last long it will b* 
 slight ; therefore it is to be patiently borne.
 
 300 RXEECISES AND QUESTIONS 
 
 CHAPTBH lY. 
 
 FALLACIES. 
 
 L Classify fallacies. 
 
 3. Explain the following expressions : 
 
 A dicto secundum quid ad dictum simpliciter ; ignoratio elencbl ; 
 
 argumentum ad hominem ; argumentum ad populum ; 
 
 petitio principii; circulus in probando; non sequitur; post 
 
 hoc ergo propter hoc. 
 
 8. What is arguing in a circle ; and what is a question-begging 
 
 epithet ? 
 
 4. What dlflFerences of meaning may be produced in the follow- 
 
 ing sentence by varying the accent ? 
 " Newton's discovery of gravitation is not generally believed 
 to have been at all anticipated by several philosophers in 
 England and Holland." 
 
 5. Point out the misinterpretations to which the following sen- 
 
 tences might be liable. 
 
 (1) He went to London and then to Brighton by the expresa 
 
 train. 
 
 (2) Did you make a long speech at the meeting? 
 
 (3) How much is five times seven and nine? 
 
 8. The following examples consist partly of true and partly of 
 false arguments. The learner is requested to treat them a 
 follows : 
 
 (1) If the example is not in a simple and complete logical form 
 
 to complete it in the form which ap[)ear8 most appropriate. 
 
 (2) To ascertain whether it is a valid or fallacious argument. 
 (8) To assign the exact name of the argument or fallacy as the 
 
 case may be. 
 
 (4) If a categorical syllogism, to reduce it to the first figure. 
 
 (5) If a hypothetical syllogism, to state it in the categorical 
 
 form.
 
 FALLACIES. 301 
 
 EXAMPLES OF ARGUMENTS. 
 
 .. Elementary substances alone are metals. Iron is a metal 
 
 therefore it is an elementary substance. 
 2. No Athenians could liave been Helots ; for all the Helots wer 
 
 slaves, and all Athenians were free men. 
 8. Aristotle must have been a man of extraordinary industry; 
 
 for only such a man could have produced his works. 
 1 Nothing is better than wisdom ; dry bread is better than 
 
 nothing ; therefore dry bread is better than wisdom. 
 6. Pitt was not a great and useful minister ; for though ue would 
 
 have been so had he carried out Adam Smith's doctrines of 
 
 Free Trade, he did not carry out those doctrines. 
 
 6. Only the virtuous are truly noble ; some who are called noble 
 
 are not virtuous; therefore some who are called noble are 
 not truly noble. 
 
 7. Ireland is idle and therefore starves ; she starves, and there. 
 
 fore rebels. 
 
 8. No designing person ought to be trusted : engravers are by 
 
 profession designers ; therefore they ought not to hi trusted. 
 0. Logic as it was cultivated by the schoolmen proved a fruitless 
 study ; therefore Logic as it is cultivated at the present day 
 must be a fruitless study likewise, 
 
 10. Is a stone a body? Yes. Then is not an animal a body? 
 Yes. Are you an animal ? I think so. Ergo, you are a 
 stone, being a body. Lucia n, 
 
 11. If ye were Abraham's children, ye would do the works oi 
 
 Abraham. John viii. 39. 
 
 12. He that is of God heareth God's words : ye therefore hear 
 them not, because ye are not of God. John viii. 47. 
 
 13. Mahomet was a wise lawgiver ; for he studied the character 
 of his people. 
 
 14. Every one desires virtue, because every one desires happi- 
 ness. 
 
 15. His imbecility of character might have been inferred from 
 his proneness to favorites ; for all weak princes have thli 
 failing. De Morgan. 
 
 t6 He is brave who conquers his passions ; he who resists temp
 
 SOS EXERCISES AND QUESTIONS. 
 
 tation conquers his passions ; so that he who resists temp 
 tation is brave. 
 
 17. Suicide is not always to be condemned ; for it is but volun- 
 tary death, and this has been gladly embraced by many ol 
 the greatest heroes of antiquity. 
 
 J8. Since all metals are elements, the most rare of all the metalr 
 must be the most rare of all the elements. 
 
 19. The express train alone does not stop at this station ; and aa 
 the last train did not stop it must have been the express 
 train. 
 
 80. Peel's remission of taxes was beneficial ; the taxes remitted 
 by Peel were indirect ; therefore the remission of indirect 
 taxes is beneficial. 
 
 31. Books are a source both of instruction and amusement ; k 
 table of logarithms is a book ; therefore it is a source both of 
 instruction and amusement. 
 
 23. All desires are not blameable ; all desires are liable to ex- 
 cess ; therefore some things liable to excess are not blameable. 
 
 23. Whosoever intentionally kills another should suflFer death ; a 
 soldier, therefore, who kills his enemy should sufier death. 
 
 84. Projectors are xmfit to be trusted ; this man has formed a 
 project ; therefore he is unfit to be trusted. 
 
 25. Few towns in the United Kingdom have more than 800,000 
 inhabitants ; and as all such towns ought to be represented 
 by three members in Parliament, it is evident that few 
 towns ought to have three representatives. 
 
 80. All the works of Shakspeare cannot be read in a day ; there- 
 fore the play of Hamlet, being one of the works of Shak 
 speare, cannot be read in a day 
 
 S7. In moral matters we cannot stand still ; therefore he who 
 does not go forward is sure to fall behind. 
 
 28. The people of the country are suffering from famine ; and a* 
 you are one of the people of the country you must he suffer- 
 ing from famine. 
 
 28. Those substances which are lighter than water can float upoa 
 it; those metals which can float upon it are potassium, 
 sodium, lithium, etc.; therefore potassium, sodium, lithium 
 titc.. are lishter than water.
 
 FALLACIES. 808 
 
 30. The laws of nature must be ascertained by Deduction, Tm- 
 
 duction or Induction ; but the former two are insufficient for 
 the purpose ; therefore the laws of nature must be ascertained 
 by Induction. 
 
 31. A successful author must be either very industrious or very 
 
 talenterl ; Gibbon was very industrious, therefore he waa 
 not very talented. 
 33. You are not what I am ; I am a man ; therefore you are not a 
 man. 
 
 33. The liolder of some shares in a lottery is sure to gain a 
 
 prize ; and as I am the holder of some shares in a lottery I 
 am sure to gain a prize. 
 
 34. Gold and silver are wealth ; and therefore the diminution of 
 
 the gold and silver in the country by exportation is the 
 diminution of the wealth of the country. 
 
 85. Over-credulous persons ought never to be believed ; and as 
 
 the Ancient Historians were in many instances over-credu 
 lous they ought never to be believed. 
 
 86. Some mineral compounds are not decomposed by heat ; all 
 
 organic substai^ces are decomposed by heat; therefore no 
 organic substances are mineral compounds. 
 
 87. Whatever schools exclude religion are irreligious ; Non- 
 
 sectarian schools do not allow the teaching of religious 
 creeds ; therefore they are irreligious. 
 
 88. Night must be the cause of day ; for it invariably precedes it. 
 
 39. The ancient Greeks produced the greatest master-pieces of 
 
 eloquence and philosophy ; the Lacedaemonians were ancient 
 Greeks ; therefore they produced the greatest master-pieces 
 of eloquence and philosophy. 
 
 40. All presuming men are contemptible; this man, therefore, is 
 
 'Contemptible ; for he presumes to believe his opinions are 
 correct. 
 
 41. If a substance is solid it possesses elasticity, and so also it does 
 
 if it be liquid or gaseous ; but all substances are either solid, 
 liquid or gaseous ; therefore all substances possess elasticity. 
 2 If Parr's life pills are of any value those who take them will 
 improve in health ; now my friend who has been taking 
 them has improved in health ; therefore they are of valu.
 
 304 EXERCISES AND QUESTIONS. 
 
 43. He who calls yoa a man speaks truly ; he who calls you e 
 
 fool calls you a man ; therefore he who calls you a fool 
 speaks truly. 
 
 44. Who is most hungry eats most ; who eats least is most 
 
 hungry ; therefore who eats least eats most. 
 
 45. What produces intoxication should be prohibited; the use of 
 
 spirituous liquors causes intoxication ; therefore the use ol 
 spirituous liquors should be prohibited. 
 
 46. What we eat grew in the fields ; loaves of bread are what we 
 
 eat ; therefore loaves of bread grew in the fields. 
 
 47. If light consisted of material {larticles it would possess mo- 
 
 mentum ; it cannot therefore consist of material particles, 
 for it does not i)08sess momentum. 
 
 48. Everything is allowed by law which is morally right ; in- 
 
 dulgence in pleasures is allowed by law ; therefore indul 
 gence in pleasures is morally right. 
 
 49. All the trees in the park make a thick shade ; this isrone of 
 
 them, therefore this tree makes a thick shade. 
 
 60. All visible bodies shine by their own or by reflected light. 
 
 The moon does not shine by its own, therefore it shines by 
 reflected light ; but the sun shines by its own light, there- 
 fore it cannot shine by reflected liglit. 
 
 61. Honesty deserves reward ; and a negro is a fellow -creature ; 
 
 therefore, an honest negro is a fellow-creature deserving ol 
 reward. 
 52. Nearly all the satellites revolve round their planets from 
 west to east; the moon is a satellite; therefore it revolves 
 round its planet from west to east. 
 
 63. Italy is a Catholic country and abounds in beggars; France 
 
 is also a Catholic country, and therefore abounds in beg- 
 gars. 
 
 64. Every law is either useless or it occasions hurt to some per- 
 
 son ; now a law that is useless ought to be abolished ; and 
 
 so ought every law that occasions hurt ; therefore every 
 
 law ought to be alx>li8hed. 
 56. The end of a thing is its perfection ; death is the end of life 
 
 therefore death is the perfection of life. 
 66. When we hear that all the righteous people are happy, it it
 
 FALLACIES. SOfi 
 
 hard to avoid exclaiming, Wliat i are all the unhappy per- 
 sons we see to be thought unrighteous ? 
 
 57. I am oflFered a sum of money to fcSc.st this person in gaining 
 the oflBce he desires ; to assist a person is to do him good, 
 and no rule of morality forbids the doing of good ; therefore 
 no rule of morality fori)ids me to receive the sum of money 
 for assisting the pei-son. 
 
 68. Ruminant animals are those which have cloven feet, and 
 they usually have horns ; the extinct animal which left this 
 foot-print had a cloven foot ; tlierefore it was a ruminant 
 animal and had horns. Again, as no beasts of prey are 
 ruminant animals it cannot have been a beast of prey. 
 
 59. We must either gratify our vicious propensities, or resist 
 
 them ; the former course will involve us in sin and misery ; 
 the latter requires self-denial; tlierefore we must either fall 
 into sin and misery or practise self-deniaL 
 
 60. The stonemasons are benefited by the masons' union ; the 
 
 bricklayers by the bricklayers' miion ; the hatmakers by the 
 hatmakers' union ; in short, every trade by its own union : 
 therefore it is evident that if all workmen had unions all 
 workmen would be benefited thereby. 
 
 61. Every moral aim requires the rational means of attaining it ; 
 
 these means are the establishment of laws ; and as happiness 
 is the moral aim of man it follows that the attainment of 
 happiness requires the establishment of laws. 
 
 62. He that can swim needs not despair to fly; for to swim is to 
 
 fly in a grosser fluid, and to fly is to swim in a subtler. 
 
 63. The Helvetii, if they went thrr>ugh the country of the 
 
 Sequani, were sure to meet with yarious difficulties ; and if 
 they went through the Roman p.-ovince, they were exjKJsed 
 to the danger of opposition from Ca?sar ; but they were 
 obliged to go one way or the other ; therefore they were 
 either sure of meeting with various diflBculties, or of being 
 exposed to the danger of opposition from Caesar. De Belle 
 GnUico, lib. i. 6. 
 
 64. Riches are for spending, and spending for honor and good 
 
 actions; therefore extraordinary expense must oe limited 
 by the worth of the occasion. Bacon.
 
 306 BXERCrSES AKD QUBSTIONB. 
 
 65. If liglit is not refracted near the surface of the tnoon, ther 
 cannot be any twilight ; but if the moon has no atmosphere 
 light is not refracted near its surface ; therefore.if the moon 
 has no atmosphere there cannot be any twilight. 
 
 33. The preservation of society requires exchange ; whatever re- 
 quires exchange requires equitable valuation of property; 
 this requires the adoption of a common measure ; hence the 
 preservation of society requires the adoption of a common 
 measure. 
 
 67 The Several species of brutes beinjr created to prey upon one 
 another proves that the human species were intended to 
 prey upon them. 
 
 68. The more correct the logic, the more certainly the conclusion 
 
 will be wrong if the premises are false. Therefore where 
 the premises are wholly uncertain, the best logician is the 
 least safe guide. 
 
 69. If our rulers could be trusted always to look to the best 
 
 interests of their subject-s, monarchy would be the best form 
 of government ; but they cannot be trusted ; therefore 
 monarchy is not the best form of government. 
 
 70. If men were prudent, they would act morally for their own 
 
 good ; if benevolent, for the good of others. But many men 
 will not act morally, either for tlieir own good, or that ot 
 others ; such men, therefore, are not prudent or benevolent. 
 
 71. He who bears arms at the command of the magistrate does 
 
 what is lawful for a Christian ; the Swiss in the French ser- 
 vice, and the British in the American service, bore arms at 
 the command of the magistrate ; therefore they did what 
 was lawful for a Christian. Whately. 
 
 72. A man that hath no virtue in himself ever envieth virtue in 
 
 others ; for men's minds will either feed upon their own 
 good or upon others' evil ; and who wanteth the one will 
 prey upon the other. B<icon. 
 
 ?3. The object of war is durable peace ; therefore soldiers are the 
 best peace-makers. 
 
 74 Confidence in promises is essential to the intercourse of 
 human life ; for without it the greatest part of our coodud 
 would proceed upon chance. But there could be no confi
 
 FALLACIES. 80? 
 
 deoce in promises, if men were not obliged to perform them 
 the obligation, therefore, to perform promises is essential to 
 the same ends and in the same degree. 
 76, If the majority of those who use public-houses are prepared 
 to close them, legislation is unnecessary ; but if they are not 
 prepared for such a measure, then to force it on them by out- 
 side pressure is both dangerous and unjust. 
 
 76. He who believes himself to be always in the right in hia 
 
 opinion, lays claim to infallibility ; you always believe your, 
 self to be in the right in your opinion ; therefore you lay 
 daim to infallibility. Wliately. 
 
 77. If we never find skins except as the teguments of animals, we 
 
 may safely conclude that animals cannot exist without skina 
 If color cannot exist by itself, it follows that neither can any 
 thing that is colored exist without color. So, if language 
 without thought is unreal, thought without language must 
 also be so. 
 
 78. No soldiers should be brought into the field who are not well 
 
 qualified to perform their part ; none but veterans are well 
 qualified to perform their part ; therefore none but veterans 
 should be brought into the field, Whately. 
 
 79. The minimum visibile is the least magnitude which can be 
 
 seen ; no part of it alone is visible, and yet all parts of it 
 must aflfect the mind in order that it may be visible; there- 
 fore, every part of it must affect the mind without being 
 visible. 
 
 80. The scarlet poppy belongs to the genus Papaver, of the 
 
 natural order Papaveraceae ; which again is part of the sub- 
 class Thalamiflorae, belonging to the great class of Dicotyle- 
 dons. Hence the scarlet poppy is one of the Dicotyledons. 
 81 Improbable events happen almost every day; but wha< 
 happens almost every day is a very probable event ; there. 
 fore improbable events are very probable events. WTiateij,
 
 808 EXEBCISES ASD QUESTI01I& 
 
 CHAPTSK Y. 
 INDUCTION. 
 
 SECTION I. 
 
 THE INDUCTIVE SYLLOGISM. 
 
 1. How do Induction and Deduction diflfer? 
 
 2. Find an instance of reasoning in Traduction. 
 8. Distinguish Perfi^ct and Imjxjrfect Induction. 
 
 4. How does Mr. Mill define Induction, and what is his opinion 
 
 of Imperfect Induction? 
 6. What is the use of Perfect Induction ? 
 6. Construct some instances of the inductive syllogism, and 
 
 show that they may be thrown into a disjunctive form. 
 
 SECTION II. 
 THE FORMS OF INDUCTION. 
 
 L Prom what circumstance arise the certainty and generality of 
 reasoning in geometry ? 
 
 i. Rnd other instances of certain and general reasoning concern- 
 ing the properties of numbers. 
 
 3. Why are inductive conclusions concerning prime numbers im- 
 certain and not general ? 
 
 4 Why is a single instance sometimes sufficient to warrant a 
 universal conclusion, while in other cases the greatest pos- 
 sible number of concurring instances, without any exception, 
 is not sufficient to warrant such n conclusion? 
 
 fi. What are the strict and ordinary meanings of the ynx6 
 analogy?
 
 METHOD. 809 
 
 CHAPTER YI. 
 
 METHOD. 
 
 SECTION I. 
 
 INDUCTIVE METHOD. 
 
 1. What Is th false method of Sdence against which Bacon pro 
 
 tested ? 
 
 2. Explain tue exact meaning of Bacon's assertions, that man ia 
 
 the Servant and Interpreter of Nature, and that Knowledge 
 is Power. 
 
 3. How does experiment differ from observation? 
 
 4. Classify the sciences according as they employ passive obser- 
 
 vation, experiment, or both. 
 
 5. Name the chief points in which experiment is superior to 
 
 mere observation. 
 
 6. What is the principal precaution needful in observation ? 
 
 7. Explain how it is |xssible to anticipate nature and yet 
 
 establish all conclusions upon the results of experience, 
 
 8. Define exactly what is meant by a cause of an event, and 
 
 distinguish cause, occasion, antecedent. 
 
 9. Point out all the causes concerned in the following ph<v 
 
 nomena : 
 (1) The burning of a fire. 
 (3) The ordinary growth of vegetables. 
 (3) The cracking of a glass by hot water. 
 
 10. State and explain in your own words Mr. Mill's first threa 
 
 Canons of Inductive Method. 
 
 11. Point out exactly how the Joint Method differs from th* 
 
 simple Method of Difference. 
 
 12. Give some instances of simple experiments fulfilling com 
 
 pletely the conditions of the Method of Difference.
 
 310 EXERCISES AND QUESTIONS. 
 
 18. \Vhat can jou infer from the following instances? 
 Antecedents. Consequents. 
 
 ABBE stqp 
 
 BOB qar 
 
 BFQ vqu 
 
 ABE. tp 
 
 EK. xqw 
 
 ABFG ,pqu9 
 
 ABK i pqt. 
 
 SECTION 11 = 
 DEDUCTIVE METHOD. 
 
 1. Define each of Jne five predicables. 
 
 2. In what sense may we saj that the genus is part of the 
 
 species, and in what sense that the species is part of th 
 gtnus? 
 
 8. Select from the terms in the sixth question of Chapter I, 
 Section III, p. 287, such as are genera, species, highest 
 genera, or lowest species of other terms. 
 
 4. Explain the expressions sui generis, homogeneous, hetero- 
 geneous, summum genus, infima species, tree of Porphyry. 
 
 6. Name a property and accident of each of the following 
 
 classes ; Circle, Planet, Bird, Member of Parliament, Ru- 
 minant Animal. 
 8. Wliat are the rules of correct logical division? 
 
 7. The first name in each of the following series of terms is that 
 
 of a class which you are to divide and subdivide so as to 
 include all the subjoined minor classes in accordance with 
 the laws of division. 
 
 (1) People. (2) Triangle. (8) Remoning. 
 
 Laity EJquiangular Induction (Imperfect; 
 
 Aliens Isosceles Deduction 
 
 Naturalized Subjects Right angled Mediate Inference
 
 METHOD. 
 
 811 
 
 (I) People. 
 
 Peers 
 
 Natural-bora Subjects 
 
 Clergy 
 
 Baronets 
 
 Commous 
 
 (2) Tnangle. 
 
 Scalene 
 
 Obtuse-angled 
 
 (3) Reasoning. 
 Induction 
 
 Hypothetical Syllogism 
 Disjunctive Syllogism 
 
 8 Divide any of the following classes : Governments, Sciences 
 
 Logical terms, Propositions. 
 
 9 Of what does a logical definition consist? 
 10. What are the rules of correct definition ? 
 
 U. What rules do the following definitions break ? 
 
 (1) Life is the sum of the vital functions. 
 
 (2) Genus is the material part of the species. 
 
 (3) Illative conversion is that in which the truth of the con 
 
 verse can be inferred from that of the convertend. 
 
 (4) Mineral substances are those which have not been pro- 
 
 duced by the powers of vegetable or animal life. 
 
 (5) An equilateral triangle is a triangle whose sides and angles 
 
 are respectively equal. 
 
 (6) An acute-angled triangle is one which has an acute angle. 
 
 12. Define classification, and give the derivation of the word. 
 
 13. What do you mean by important characters in classification? 
 
 14. State the requisites of a good classification. 
 
 15. What are the three purposes for which we use language? 
 
 16. What are the essentials of language as an instrument ol 
 
 scientific record ? 
 
 SECTION III. 
 COMPLETE METHOD. 
 
 1. Define Empirical Law, and find a few additional instances of 
 such laws. 
 
 2. What are the three steps of the Complete Method ? 
 
 8. Trace some of the successive steps in the progress of the
 
 312 EXERCISES AND QUESTIONS. 
 
 iheorj of gravitation, showing that it was estahlished bj 
 this method. 
 4 Wliat do you mean by the explanation of a fact? 
 
 6. State the three ways in which a law of nature may be ex- 
 
 plained, and suggest some additional instances of each case. 
 8. State the five rules of metliod given in the Port Royal Logic 
 
 7. Explain Descartes' rules for the attainment of truth. 
 
 CHAPTBE YII* 
 RECENT LOGICAL VIEWS. 
 
 SECTION I. 
 
 THE QUANTIFICATION OF THE PREDICATE. 
 
 1. What does the quantification of the predicate mean ? 
 8. Assign to each of the following propositions its proper sym 
 bol, and the symbol of its converse : 
 
 (1) Knowledge is power. 
 
 (2) Some rectangles are all squares. 
 
 (8) Only the honest u timately prosper. 
 (4) Princes have but their titles for their glories. 
 (6) In man there is nothing? great but mind. 
 (6) The end of philosophy is the detection of unity. 
 8. Draw all the contrapositive propositions and immediate infer 
 ences you can from the following propositions: 
 
 (1) London is a great city. 
 
 (2) London is the capital of England. 
 
 (3) All ruminant animals are all cloven-footed animals. 
 
 (4) Some meml^ers of parliament are all the ministers. 
 
 i. Write out in Hamilton's notation the moods Baroko, Darapti, 
 Feiapton, Bokarda
 
 SECEirr LOGICAL VIEWS. 818 
 
 SECTION II. 
 
 BOOLE'S SYSTEM OF LOGIC. 
 
 1. Apply tliis Bystem of inference to prove the syllogisms on 
 
 p. 130, in Cesare, and Camestres. 
 
 2. Show that if all A'& are not B's, then no B'n are ^'s ; and 
 
 that if all -4*8 are all B'b, then all not A'b are aU not B'b. 
 8. Develop the term substance, as regards the terms vegetable, 
 
 animal, organic ; then select the combinations which agree 
 
 with these premises : 
 
 ' What is vegetable is not animal but is organic ; what 
 is animal is organic." 
 4. Test the validity of this argument : " Good always triumphs, 
 
 and vice always fails ; therefore the victor cannot be wrong, 
 
 nor the vanquished right.' 
 6. It is known of a certain class of things that 
 
 (1) Where the quality A is, B is not. 
 
 (2) Where B is, and only where B is, C and Z> are. 
 
 What can we infer from these premises of the class of 
 things in which A is not present but G is present ? 
 . If all A'b are B'b ; all B'b are C's ; all G'b are B'b\ show that 
 all A!fs are B'b, and that all not Ifb are not .4*8.
 
 AND GLOSSARY. 
 
 Note. In this Index and Glossary, besides references to all 
 the important topics treatftd of in the volume, may be found brief 
 definitions of all the logical and philosophical terms employed, 
 and short sketches of the lives of the principal writers men- 
 tioned. 
 
 Abacus, the logical, 285. 
 
 Abscissio Infiniti (the cutting 
 off of the infinite or negative 
 part), the process by wliich 
 we determine the position of 
 an object in a system of 
 classes, by successive com- 
 parison and rejection of those 
 classes to which it does not 
 belong. 
 
 Absolute terms, i.e., non-rela- 
 tive terms, 27 ; sometimes 
 used as name of non-conno- 
 tative terms, 4.5. 
 
 Abstract terms, 22, 45. 
 
 Accent, fallacy of, t67. 
 
 Accident, fallacy of, 169 ; the 
 predicable, 232. 
 
 Accidental definition is a defi- 
 nition which assigns the pro- 
 perties of a species, or the 
 
 accidents of an individual ; it 
 
 is more commonly called a 
 
 Description. 
 Added determinants, inference 
 
 by, 91. 
 Adequate knowledge, 59. 
 A dicto secundum quid, etc., 
 
 fallacy of, 169. 
 Adjectives, 38. 
 Adverbials, 99. 
 Affirmative propositions, 67. 
 Algebraic reasoning, 61, 190. 
 Ambiguity of all, 22 ; of some, 
 
 84 ; of many old terms, 34. 
 Ambiguous middle term, 118, 
 
 163. 
 Amphibology, fallacy of, 164 
 Ampliative propositions, 73. 
 Analogue, a thing analogous 
 
 to some other thing. 
 Analysis, method of, 199.
 
 INDEX AND GLOSSARY. 
 
 81ft 
 
 Analogy, the cause of ambi- 
 guity, 38 ; reas^^ning by, 167, 
 168. 
 
 Analytics (rd 'XvaTivrtKu), the 
 title given in the second cen- 
 tury to portions of the Orga- 
 non, or Logical Treatises of 
 Aristotle ; they were distin- 
 guished as the Prior and Pos- 
 terior Analytics. 
 
 Analytic syllogism, a syllo- 
 gism in which the conclusion 
 is placed first, the premises 
 following as the reasons. See 
 Synthetic Syllogism ; the dis- 
 tinction is unimportant. 
 
 Antecedent, of a hypothetical 
 proposition, 150 ; of an event, 
 214. 
 
 Anticipation of nature, 202. 
 
 Antinomy (uvtI, against ; vourf, 
 law), the opposition of one 
 law or rule to another. Kant. 
 
 A posteriori knowledge, 200. 
 
 A priori knowledge, 200. 
 
 Arbor Porphyriana, see Tree 
 of Porphyry. 
 
 Argument, (Latin, argus, from 
 apydf, clear, manifest,) the 
 process of reasoning, the 
 showing or proving that 
 which is doubtful by that 
 which is known. See Infer- 
 ence. The middle term of a 
 syllogism is sometimes called 
 specially the argument. 
 
 Argumentum a fortiori, an 
 argument in which we prove 
 
 that the case in question ia 
 more strong or probable than 
 one already conceded to be 
 suflBciently so. 
 
 Argumentum ad hominem 
 172. 
 
 Argumentum ad judicium, an 
 appeal to the common sense 
 of mankind. 
 
 Argumentum ad ignorantiam, 
 an argument founded on the 
 ignorance of adversaries. 
 
 Argumentum ad populum, 172. 
 
 Argumentum ad verecundiam, 
 an appeal to our respect for 
 some great authority. 
 
 Argumentum ex concesso, a 
 proof derived from a proposi- 
 tion already conceded. 
 
 Aristotle, one of the greatest 
 philosophers of antiquity (B.C. 
 384-322), a pupil of Plato, and 
 preceptor of Alexander the 
 Great. Aristotle wrote fam- 
 ous works on Metaphysics, 
 Physics, Logic and Psychol- 
 ogy. His Logic has furnished 
 the foundations of the science 
 treated under that name since 
 his day, and he may justly be 
 regarded as the father of that 
 science. His doctrines were 
 accepted by the schoolmen of 
 the European Universities 
 and, though strangely mis- 
 understood by them, were re- 
 garded as having an almost 
 divine authority.
 
 816 
 
 IKDEX AND GLOSSABT. 
 
 Aristotle's Dicta, 111. 
 
 Assertion, {ad, to ; sero, to 
 join,) a statement or proposi- 
 tion, afQrmative or negative. 
 
 Association of ideas, {associo, 
 to accompany ; aociug, a com- 
 panion,) the natural connec- 
 tion existing in the mind be- 
 tween impressions whicli liave 
 previously coexisted, or wliich 
 are similar. Any idea tends 
 to bring into the mind its 
 associated ideas, in accordance 
 with the two g^eat laws of 
 association, the Law of Con- 
 tiguity, and the Law of 
 Similarity. 
 
 Assumption, {assumo, to take 
 for granted,) any proposition 
 taken as the basis of argu- 
 ment ; in a special sense, the 
 minor premise of a categori- 
 cal siyllogism. 
 
 Attribute, (attrtbuo, to give or 
 ascribe to,) a quality or cir- 
 cumstance which may be 
 affirmed (or denied) of a 
 thing ; opposed to Substance, 
 which see. 
 
 Attribute in grammar, 98. 
 
 Attributive term, i.e., Connota- 
 tive term. 43. 
 
 Axiom, definition of, 110. 
 
 Baconian method, 251. 
 Barbara, Celarent, etc., 134. 
 Begging the Question, 173. 
 Belief, assent to a proposition. 
 
 admitting of any degree of 
 strength, from the slightest 
 probabi lity to the fullest cer- 
 tainty ; see Prubainlity. 
 
 Bentham, George, new system 
 of Logic, 268. 
 
 Boole, George, his system of 
 Logic, 272. 
 
 Canons of syllogism, 108, 9; 
 Hamilton's supreme Canon. 
 
 Canons of Mill's Inductive 
 Methods, 215. 
 
 Categorematic words, 19. 
 
 Categorical propositions, 67. 
 
 Categories, the aumma genera, 
 or most extensive classes into 
 which things can be distrib- 
 uted ; they are ten in num. 
 ber, as follows : 
 
 Ovnin, Substance; Iloff^v, 
 Quantity ; Hohw, Quality 
 ripoi' Ti, Relation; V\oLlv, 
 Action; Yldaxeiv, Passion, or 
 suffering ; Hoi, Place ; YIote, 
 Time ; KelnOai, Position ; 
 'E^f/i', Habit or condition. 
 
 Everything which can be 
 affirmed must come under 
 one or other of these highest 
 predicates, wliich were de- 
 scribed in the first treatise of 
 Aristotle's Oiganon, called 
 the Categories. 
 
 Cause, meaning of, 213. 
 
 Aristotle distinguished foul 
 kinds of causes for the exist 
 ence of a thing 1. The Ms
 
 DTDEX AND QLOSSABY. 
 
 817 
 
 terial Cause, the substance or 
 matter composing it ; 2. The 
 Formal Cause, the pattern, 
 type or design, according to 
 which it is shaped ; 3. The 
 Efficient Cause, the force em- 
 ployed in shaping it ; 4. The 
 Final Cause, the end, motive 
 or purpose of the work. 
 
 Chance, ignorance of the causes 
 which are in action ; see 
 Prdbability. 
 
 Character, derivation of the 
 word, 48. 
 
 Circulus in definiendo, 239. 
 
 Circulus in probando, 173. 
 
 Clearness of knowledge, 57. 
 
 Cognition, (cognoseo, to know,) 
 knowledge, or the action of 
 mind in acquiring knowledge. 
 
 Colligation of Facts, Dr. Whe- 
 well's expression for the men- 
 tal union of facts by some 
 suitable conception. 
 
 Collective terms, 21. 
 
 Combined or complete method 
 of investigation, 249. 
 
 Comparison, {com, together ; 
 par, equal or like,) the action 
 of mind by which we judge 
 whether two objects of 
 thought are the same or 
 different in certain points. 
 See Judgment. 
 
 Compatible terms are those 
 which, though distiuct, are 
 not contradictory, and can 
 therefore be affirmed of the 
 
 same subject ; as "large " and 
 " heavy ;" " bright-colored " 
 and " nauseous." 
 
 Complex conception, infer 
 ence by, 92. 
 
 Complex sentence, 98 ; syllo- 
 gism, 141. 
 
 Composition of Causes, the 
 principle which is exemplified 
 in all cases in which the joint 
 effect of several causes is 
 identical \vith the sum of their 
 separate effects. J. S. Mill. 
 
 Composition, fallacy of, 165. 
 
 Compound sentence, 94, 95. 
 
 Comprehension of terms, see 
 Intension. 
 
 Concept, that which is con- 
 ceived, the result of the act 
 of conception ; nearly synony- 
 mous with general notion, 
 idea, thought. 
 
 Conception (con, together ; 
 capio, to take). An ambigu- 
 ous term, meaning properly 
 the action of mind in which 
 it takes several things to- 
 gether, so as to form a general 
 notion ; or, again, in which it 
 forms " a mental image of the 
 several attributes given in 
 any word or combination of 
 words." Mansel. 
 
 Conceptualists, 14. 
 
 Concrete terms, 22. 
 
 Conditional propositions, 149. 
 
 Confusion of words, ambiguity 
 from. 33.
 
 318 
 
 nn>BX AND GLOSSABT. 
 
 Conjugate words, those which 
 come from the same root or 
 stock, as known, knowing, 
 knowingly, knowledge. 
 
 Connotation of terms, 43 ; 
 ought to be exactly fixed, 247. 
 
 Consciousness, the immediate 
 knowledge which the mind 
 has of its sensations and 
 thoughts, and, in general, of 
 all its present operations. 
 Beid. 
 
 Consectary=Corollary. 
 
 Consequence, the connection 
 between antecedent and con- 
 sequent ; but often used am- 
 biguously for tbe latter. 
 
 Consequent of a hypothetical 
 proposition, 150. 
 
 Consequent or effect of a cause, 
 214. 
 
 Consequent, fallacy of the, 175. 
 
 Consilience of inductions, the 
 agreement of inductions de- 
 rived from different and inde- 
 pendent series of facts, as 
 when we learn the motion of 
 the earth by entirely different 
 modes of observation and 
 reasoning. Whewdl. 
 
 Consistency of propositions, 
 83. 
 
 Consistent terras, see compat- 
 ible terms. 
 
 Contingent, (contingo, to touch.) 
 that which may or may not 
 happen ; opposed to the neeea- 
 mry and imposnble. 
 
 Contingent matter, 85. 
 
 Continuity, L&vf of, the prin- 
 ciple that nothing can pass 
 from one extreme to another 
 without passing through all 
 the intermediate degrees ; 
 motion, for instance, cannot 
 be instantaneously produced 
 or destroyed. 
 
 Contradiction, Law of, 105. 
 
 Contradictory terras, 26 : prop- 
 ositions, 83. 
 
 Contraposition, conversion by, 
 89. 
 
 Converse fallacy of accident, 
 169. 
 
 Conversion of propositions, 
 86 ; with quantified predicate. 
 266. 
 
 Convertend, 87, 
 
 Co-ordinate propositions, 96. 
 
 Copula, 65. 
 
 Corollary, a proposition which 
 follows immediately from an- 
 other which has been proved. 
 
 Correlative terms, 27. 
 
 Criterion {Kpirripinv, from Kplvu, 
 to judge), any fact, rule, 
 knowledge, or means requi- 
 site to the formation of a 
 judgment which shall decide 
 a doubtful question. 
 
 Cross division, 235. 
 
 Data, (plural of datum, that 
 wliich is given,) the facts or 
 assertions from which an in- 
 ference is to be drawn.
 
 INDEX AND GL0S8ABT. 
 
 819 
 
 Deduction and Induction, 178. 
 
 Deductive method, 237. 
 
 De facto, what actually or 
 really happens; opposed to 
 dejure, what ought to happen 
 by law or right. 
 
 Definition, the logical process, 
 238 ; of logic, 1. 
 
 Degree, terms expressing, 26 ; 
 questions of, 107. 
 
 Demonstration, {demonstro, to 
 point out,) strictly the point- 
 ing out the connection be- 
 tween premises and conclu- 
 sion. The term is more 
 generally used for any argu- 
 ment or reasoning regarded 
 as proving an asserted con- 
 clusion. A demonstration is 
 either Direct or Indirect. In 
 ihe latter case we prove the 
 conclusion by disproving its 
 contradictory, or showing 
 that the conclusion cannot be 
 supposed untrue. 
 
 Demonstrative Induction, 182. 
 
 Descartes, Rene, a French 
 philosopher and mathema- 
 tician of the most distin- 
 guished originality (1596- 
 1650) ; author of La Dis- 
 cours de la Method, Les Prin- 
 eipes, Les Meditations, and 
 other works. Descartes has 
 been called "the Father of 
 Modem Psychology, " His 
 criterion of truth was the 
 tieamess of ideas. His first 
 
 principle of knowledge, which 
 he declared was left certain 
 when everything else was 
 denied, is expressed in hig 
 now famous maxim : Cogito, 
 ergo sum. Descartes' method 
 was largely suggested by 
 mathematical method. He 
 believed that the mind ought 
 to be studied by the examina- 
 tion of consciousness, or by 
 what has now come to be 
 known as the introspective 
 method. 
 
 Descartes on Method, 261. 
 
 De Morgan's logical disoov 
 eries and writings, 271. 
 
 Denotation of terms, 41. 
 
 Depth of a notion, see Inten- 
 sion. 
 
 Derivatives from the root spec, 
 sight, 55. 
 
 Description, see Ac/;idental 
 Defin ition. 
 
 Destructive dilemma, 159. 
 
 Desynonymization of terms, 
 51. 
 
 Determination, the distin- 
 guishing of parts of a genua 
 by reunion of the genus and 
 difference. See Division. 
 
 Development of a term, 274 
 
 Diagrams, of sentences. 99, 
 103 ; of syllogisms, 120, 131 ; 
 of propositions, 88. 
 
 Dialectic (JmPte^rtK^ TeKvri the 
 art of discourse, from Stale- 
 yeadai, to discourse), Tb
 
 820 
 
 htdex and glossaet. 
 
 ori^nal name of Logic, per- 
 haps invented by Plato ; also 
 used to denote the Logic of 
 Probable Matter (Aristotle), 
 the right use of Reason and 
 Langaage, the Science of Be- 
 ing ; it is thus a highly am- 
 biguous term. 
 
 Dichotomy, division by, 107, 
 286. 
 
 Dicta de omni et nullo, 111. 
 
 Difference, the predicable, 228. 
 
 Differentiation of terms, 51. 
 
 Dilemma, 158. 
 
 Disbelief, the state of mind in 
 which we are fully persuaded 
 that some opinion is not true. 
 J. B. Mill. It is equivalent 
 to belief in the contradictory 
 opinion or assertion, and is 
 not to be confused with 
 Dovbt, which see. 
 
 Discourse, or reasoning, 16. 
 
 Discovery, method of, 199. 
 
 Disjunctive, propositions, 150; 
 syllogism, 156. 
 
 Distinct knowledge, 65. 
 
 Distribution of terms, 79. 
 
 Division, logical, 234; meta- 
 physical, 288 ; fallacy of, 
 166. 
 
 Doubt, {dubito, to go two 
 ways,) the state of mind in 
 which we hesitate between 
 two or more inconsistent 
 opinions. See Disbelief. 
 
 Drift of a proposition, the vary- 
 ing meaning which may be 
 
 attributed to the same sen 
 tence according to accentua 
 tion. See Fallacy of accent, 
 167. 
 
 Empiricism {ifineif}ia, experi- 
 ence), the doctrine of those 
 who consider that all knowl- 
 edge is derived merely from 
 experience. 
 
 Empirical Law, 249. 
 
 Enthymeme, 142. 
 
 Epicheirema, 145. , 
 
 Episyllogism, 144. 
 
 Equivocal terms, 81. 
 
 Equivocation, causes of, 88 , 
 fallacy of, 163. 
 
 Essence, {essentia, from esse, to 
 be,) " the very being of any. 
 thing, whereby it is what it 
 is." Locke. It is an ancient 
 scholastic word, which cannot 
 be really defined, and should 
 be banished from use. 
 
 Essential propositions, 72. 
 
 Euler's diagrams, 120, 121. 
 
 Evidence, (e, and videre, to 
 see,) literally the seeing of 
 anything. The word now 
 means any facts apprehended 
 by the mind and made the 
 grounds of knowledge and 
 belief. 
 
 Examples, use of, 175. 
 
 Exceptive propositions, 72. 
 
 Excluded middle, law of 
 166. 
 
 Exclusive propositions, 72. 
 
 Exhaustive division, 107. 236
 
 HTDEX AND GLOSSARY. 
 
 831 
 
 Ezperimentum cnicis, an ex- 
 periment which decides be- 
 tween two rival theories, and 
 Bhows which is to be adopted, 
 as a finger-post shows which 
 of two roads is to be taken. 
 
 Explanation, of facts, 255 ; of 
 laws, 256. 
 
 Explicative propositions, 72. 
 
 Exposita, a proposition given 
 to be treated by some logical 
 process. 
 
 Extension and intension, 39. 
 
 Extensive Syllogism, 149. 
 
 Extremes of a proposition, are 
 its ends or terms, the subject 
 and predicate. 
 
 Fact, 212. 
 
 Fallacy, purely logical, 162 ; 
 semi-logical, 162; material, 
 169 ; in hypothetical syllo- 
 gism, 155 ; in dilemma, 158. 
 
 False cause, fallacy of, 175. 
 
 False propositions, 74. 
 
 Figure of speech, fallacy of, 
 168. 
 
 Figures of the syllogism, 137 ; 
 their uses, 130. 
 
 Form and matter of thought, 
 5. 
 
 Fundamentum divisionis, 234. 
 
 Fundamentum relationis, the 
 ground of relation, i.e., the 
 series of events or circum- 
 stances which establish a re- 
 lation between two correlative 
 terms. 
 
 Fundamental principles of syl 
 logism, 108. 
 
 Galenian, or fourth figure o 
 
 the syllogism, 131. 
 General notions, 14; terma^ 
 
 20. 
 Generalization of names, 47. 
 Generic property, 232. 
 Genus, 238 ; generalissimum, 
 
 230. 
 Geometiical reasoning, 61, 
 
 187 ; Pascal on, 258. 
 Grammatical predicate, 98 i 
 
 sentence, 68. 
 Gravitation, theory of, 252. 
 
 Hamilton, Sir William, a 
 Scotch philosopher (1788- 
 1856); professor at the Uni 
 versity of Edinburgh (1836- 
 1856) ; author of Discussions 
 in Philosophy and Literature, 
 largely reprinted from his 
 essays in the Edinburgh Be- 
 view, Lectw'es on Metaphysics, 
 and Lectures on Logic. Hamil- 
 ton wae the most erudite 
 philosopher of his time in 
 Great Britain. 
 
 Hamilton, Sir W., Method of 
 Notation. 368. 
 
 Heterogeneous, 230 ; intermix- 
 ture of effects, 224. 
 
 Homogeneous, 268 ; intermix 
 ture of effects, 324. 
 
 Homologue,'whatever is A(?nioi 
 ogous.
 
 322 
 
 INDEX AND GLOSSABT. 
 
 Homology, a special term for 
 the analogy existing between 
 parts of different plants and 
 animals, as between the wing 
 of a bird and the tore leg of a 
 quadruped, or between the 
 scales of a fish and the 
 feathers of a bird. 
 
 Homonymous terms, 32. 
 
 Hypothesis, 208. 
 
 Hypothetical propositions, 66 ; 
 syllogism, 15. 
 
 Idea (l()ea, eldo^, image), a term 
 used ambiguously, but gener- 
 ally equivalent to thought, 
 notion, concept. Defined by 
 Locke as " Phantasm, notion, 
 species, or whatever it is 
 which the mind can be em- 
 ployed about in thinking." 
 To have an idea of a thing is 
 to think of that thing. 
 
 Identity, law of, 104. 
 
 Idol (n(^(j}.ov, ftfJor, image), 
 Bacon's figurative name for 
 the sources of error ; he enu- 
 merated four kinds , Idols of 
 the Tribe, whicli affect nil 
 people; Idols of the Cave, 
 which are peculiar to an in- 
 dividual ; of the Forum, 
 which arisi' in the intercourse 
 of men ; of the Theatre, 
 which proceed from the sys 
 terns of phil(opher8. 
 
 Ignoratio Elenchi, 172. 
 
 Illation (iUntum, past participle 
 
 of infero, to bring in). S 
 Inference. 
 
 Illative, that which can be in- 
 ferred. 
 
 Illicit process, of the minor 
 term, 119 ; of the major term, 
 128. 
 
 Immediate inference, 86. 
 
 Imperfect figures of the syllo- 
 gism, 145. 
 
 Imperfect Induction, 181. 
 
 Impossible matter, 85. 
 
 Inconsistent terms imply qual- 
 ities which cannot coexist in 
 the same thing. See compat- 
 ible terms. 
 
 Inconsistent propositions, 83. 
 
 Indefinite proijositions, 68. 
 
 Indefinite or infinite term, is 
 a negative term which only 
 marks un object by exclusion 
 from a class. 
 
 Indesignate propositions. See 
 Indefinite propositions. 
 
 Indirect demonstration. See 
 Demonstration. 
 
 Indirect inference, method of, 
 138. 
 
 Indirect reduction of the syl- 
 logism, 137. 
 
 Individual, what cannot be 
 divided without losing its 
 name and distinctive quali- 
 ties, although generally capa- 
 ble of physical division oi 
 partition, which see. 
 
 Induction, 178. 
 
 Inductive syllogism, 183, 184.
 
 INDEX AD GLOSS ABT. 
 
 833 
 
 Inference, defined, 86 ; imme- 
 diate, 87 ; mediate, 113. 
 
 Infima species, 230. 
 
 Innate ideas, see a priori 
 truths. 
 
 Inseparable accident, 232. 
 
 Intension and extension of 
 terms. 39 ; law of relation, 
 42. 
 
 Intensive syllogism, 149. 
 
 Intention, first and second, a 
 distinctioa between terms 
 thus defined by Hobbes : " Of 
 the first intention are the 
 names of things, a man, 
 stone, &c. ; of the second 
 are the names of names, and 
 speeches, as universal, par- 
 ticular, genus, species, syllo 
 gism, and the like." A term 
 of the second intention ex- 
 presses the mode in which 
 the mind regards or classi- 
 fies those of the first inten- 
 tion. 
 
 Intermediate link, explanation 
 by, 256. 
 
 Intuitive knowledge, 57. 
 
 Irrelevant conclusion, fallacy 
 of, 171. 
 
 Judgment, 13. 
 
 Language, the subject of logic, 
 
 10. 
 Language, three purposes of, 
 
 245. 
 Lav7s of thought, 2, 104 
 
 Leibnitz (146-1716), the great 
 est of the earlier German 
 philosophers and celebrated 
 as a matliematician and uni 
 versal genius ; author ol 
 Nouveaux Essais siir I' Eju 
 tendement Hunain, and La 
 Theodicee Leibnitz invented 
 the infinitesimal calculus at 
 the same time as Newton. 
 Although lie advocated some 
 strange doctrines, Leibnitz 
 must be regarded as one of 
 the greatest intellects which 
 the world has known. He 
 criticised the foundations of 
 human knowledge as they 
 were set forth by Locke, and 
 maintained that there is an. 
 other source of knowledge 
 than experience, the intui- 
 tions of the mind. 
 
 Leibnitz on knowledge, 56. 
 
 Lemma (Xa/i[3uvij, to take or 
 assume), a proposition, a pre- 
 mise granted ; in geometry, 
 a preliminary proposition. 
 
 Limitation, conversion by, 87. 
 
 Locke, John, an English phy- 
 sician and philosoplier (1632- 
 1704); influential also as a 
 writer on government and 
 religious toleration ; author of 
 the celebrated work Essay 
 Concerning Human Under- 
 standing, an epoch-making 
 production in which human 
 knowledge is referred entirelj
 
 324 
 
 INDEX AND GLOSSARY. 
 
 to experience, to* the exclu- 
 sion of any innate element. 
 Locke may justly be regarded 
 as the founder of the Eng- 
 lish school of psychology. 
 His influence in France was 
 also great. In Germany 
 Locke was less followed and 
 has been severely reviewed 
 by Leibnitz and otiiers. It is 
 likely that lie did not see all 
 the ultimate bearings of his 
 doctrines. He advocated the 
 doctrine of representative 
 ideas, which prepared the 
 way for the doctrines of 
 Hume and of Berkeley, and 
 has been ably reviewed by 
 Thomas Reid and Sir W. 
 Hamilton. 
 
 Logic, derivation of name, 1, 
 
 Logical abacus, slate and ma- 
 chine. 280. 
 
 Logomachy, a war of words. 
 
 Lowest species, 230. 
 
 Machine, the logical, 280. 
 
 Major, term, 116 ; premise, 
 116. 
 
 Many questions, fallacy of, 
 176. 
 
 Material fallacies, 169. 
 
 Mathematical induction, 187. 
 
 Matter of thought, 5; of pro- 
 positions, 85. 
 
 Matter is defined by J. S. Mill 
 as " the external cause to 
 which we ascribe our sensa- 
 
 tions," or as Permanent Pos- 
 sibility of Sensation. 
 
 Mediate inference, 118. 
 
 Membra dividentia, the parts 
 into which a class is divided ; 
 the constituent species of a 
 genus. 
 
 Metaphor, 52. 
 
 Metaphysical division, 238. 
 
 Metaphysics (ru /uerd ru ^vai- 
 K'l), the works of Aristotle 
 which followed or were 
 studied after his Physics. 
 First Philosophy, or the so- 
 called science of things in 
 their own nature; ontology 
 or the science of Being. 
 
 Method ((itdodoc, fxera and 6f>6i, 
 way), mode, way or instru- 
 ment of accomplishing an 
 end. 
 
 Method, 201 ; Pascal on, 257 ; 
 Descartes' Discourse on, 263. 
 
 Methods of Induction, Agree- 
 ment, 215 ; DiflFerence, 216 ; 
 of Experiment, 218; Joint 
 Method, 219; Residues, 224; 
 Concomitant Variations, 221. 
 
 Metonymy (//era, and bvofia, 
 name), grammatical name for 
 the transfer of meaning of a 
 word to a closely connected 
 thing, as when we speak of 
 the church, meaninf/ the 
 people in it. See Transfer 
 of meaning. 
 
 Middle Term, 114. 
 
 Mill, John Stuart, an English
 
 INDEX AND GLOSSARY. 
 
 325 
 
 philosopher and economist 
 (1806-1873) ; son of James 
 Mill, whose doctrines with 
 some modifications he taught; 
 autlior of A System of Logic, 
 (in which the syllogism is 
 severely criticised and much 
 is made of induction,) numer- 
 ous political and sociological 
 works, and An Examination 
 of the Philosophy of Sir W. 
 Hamilton. Mill was an em- 
 piricist in philosophy and a 
 utilitarian in morals. His 
 writings have been severely 
 criticised by Professor Jevons 
 in a series of articles in the 
 Contemporary and other re- 
 views. 
 
 Mill, J. S., on Connotative 
 terms, 43 ; on Induction, 182, 
 215 ; on Observation, 206. 
 
 Minor term, 116 ; premise, 118. 
 
 Mnemonic verses, Barbara, 
 etc., 133. 
 
 Modal proposition, 73. 
 
 Modus, ponens, 151 ,- toUens, 
 151. 
 
 Modus, ponendo toUens, 156 ; 
 tollendo ponens, 157. 
 
 Moods of the syllogism, 124; 
 according to Hamilton, 268. 
 
 MuUer, F. Max, a German 
 philologist of note (born in 
 1823), still (1883) and for a 
 long time a resident in Eng- 
 land and professor at Ox- 
 ford University. Professor 
 
 Muller is a fascinating and 
 informing writer, but his 
 theories of language have 
 been severely criticised by 
 Professor W. D. Whitney, 
 an American philologist and 
 professor in Yale College. 
 
 Name, or term, 17. 
 
 Necessary matter, 85. 
 
 Necessity (ne, not; and cesso, 
 to cease), that which always 
 is and cannot but be. 
 
 Negation, conversion by, 88. 
 
 Negative, terms, 24; proposi- 
 tions, 24; premises, fallacy 
 of, 102. 
 
 Newton's experiments, 253. 
 
 Nominal definitions, 259. 
 
 Nominalists, 14. 
 
 Non causa, pro causa, 175. 
 
 Non sequitur, 175. 
 
 Notion {nosco, to know), the 
 action of apprehending or 
 taking note of the various 
 qualities of an object ; or 
 more commonly the result of 
 that action. See Idea, Con- 
 cept. 
 
 Notiora naturae, 199. 
 
 Novum Organum, first apho- 
 risms of, 202. 
 
 Numerically definite syllogism, 
 184. 
 
 Object of verb, 98. 
 Objective, that which belongs 
 to the object of thought, the
 
 326 
 
 INDEX AND GLOSSARY. 
 
 non-ego; opposed to Sub- 
 
 jective, which see. 
 
 Obscure knowledge, 57. 
 
 Observation, 206. 
 
 Occasion of an event, the proxi- 
 mate cause, or last condiiion 
 which is requisite to bring 
 other causes into action, 213. 
 
 Opposite terms, 24. 
 
 Opposition of propositions, 83. 
 
 Organon {opyavov, Latin Or- 
 ganum, Instrument), a name 
 for Aristotle's logical trea- 
 tises, first generally used in 
 the 15th century, implying 
 that they may be regarded as 
 an instrument to assist the 
 mind. The name was adopted 
 by Bacon for his Novum Or- 
 ganum. 
 
 Paradox (Trapti, 6d^a, contrary to 
 opinion), an assertion con- 
 trary to common opinion, and 
 which may or may not prove 
 true ; often wrongly used to 
 mean what is self-contradic- 
 tory and absurd. 
 
 Paralogism {napaloyil^oixai, to 
 reason wrongly), a purely 
 logical fallacy, or breach of 
 the rules of deductive logic. 
 
 Parity of reasoning, an expres- 
 sion used to denote that when 
 one case has been demon- 
 strated, other similar cases 
 can be demonstrated by a like 
 course of reasoning. 
 
 Paronymous words, see Conju- 
 gate words. 
 
 Particular propositions, 67. 
 
 Particular premises, fallacy 
 of, 162. 
 
 Partition or physical divi- 
 sion, 238. 
 
 Pascal, Blaise, a French thinker 
 of wonderful genius and not 
 less distinguished piety (1623- 
 1662), who excelled in geom- 
 etry and other branches of 
 mathematics ; author of the 
 famous Provincial Letters, in 
 which he powerfully de- 
 nounces the Jesuits, and the 
 still more celebrated Thoughts, 
 designed to humble the rea- 
 son of man in the presence 
 of the great mysteries of be- 
 ing and lead to a devout 
 Christian faith. His works 
 are characterized by remark- 
 able insight, dialectic skill 
 and eloquence. 
 
 Per accidens, conversion, 87. 
 
 Perfect Figure of the Syllo- 
 gism, 134. 
 
 Perfect knowledge, characters 
 of, 56. 
 
 Periodic changes, 228. 
 
 Peripatetic Philosophy {nepi- 
 nareu, to walk about), the 
 name usually given to the 
 doctrines of Aristotle and his 
 followers, who are said to 
 have carried on their studies 
 and discussions while walking
 
 INDEX AND GLOSSARY. 
 
 837 
 
 about the halls and prome- 
 nades of the Lyceum. 
 
 Petitio Principii, 173. 
 
 Phenomenon, 213. 
 
 Physical definition assigns the 
 parts into which a thing may 
 be separated by partition or 
 physical division. 
 
 Polylemma, an argument of 
 the same form as a dilemma, 
 but in which there are more 
 than two alternatives. 
 
 Porphyry, tree of, 233. 
 
 Port Royal Logic, 259. 
 
 Positive terms, 24. 
 
 Post hoc, ergo propter hoc, 
 175. 
 
 Postulate ( postulatum, a thing 
 demanded), a proposition 
 which is necessarily demanded 
 as a basis of argument ; in 
 geometry, the postulates de- 
 fine the practical conditions 
 required. 
 
 Predicables, 227. 
 
 Predicaments ( proedicamenta, 
 what can be predicated), see 
 Categories. 
 
 Predicate, 66, 80, 98, 263. 
 
 Premise, or Premiss, 113. 
 
 Primary Laws of Thought, 104, 
 
 Principle {principium, begin- 
 ning), the first source of any- 
 thing ; sometimes specially 
 used to mean the major 
 premise of a syllogism. 
 
 Privative conception, infer- 
 ence by. 91. 
 
 Privative tenns, 26. 
 
 Probability, quuntity or de 
 gree of belief, or more truly 
 quantity of information con- 
 cerning an uncertain event, 
 measured by the ratio of the 
 number of cases favorable to 
 the event to the total number 
 of cases which are possil)le. 
 
 Probability, of propositions, 
 74 ; of inductions, 181. 
 
 Problem (Trpo/i/.jy/za.that which, 
 is thrown down), an assertion 
 put forward for proof or dis 
 proof. 
 
 Proof, the assigning a reason 
 or argument for the support 
 of a given proposition. 
 
 Proper names, 29, 32, 44. 
 
 Propositions, see the cTuip- 
 ter on, pp. 64, 99, and the 
 particular references in this 
 Index. 
 
 Prosyllogism, 144. 
 
 Proximate genns, 237. 
 
 Quantification of predicate, 
 
 263 
 Quantity of propositions, 67; 
 
 questions of quantity, 68. 
 Quaternio terminorum, 162. 
 
 Ramean tree, see Tree of Por- 
 phyry. 
 
 Ratiocination, a name equiva- 
 let to Syllogism or Deduo 
 tion, adopted by J. S. MilL 
 
 Realism, 14.
 
 328 
 
 INDEX AND GLOSSARY. 
 
 Reason {ratio from reor, to 
 think), a term of wide and 
 ambiguous meaniiif? ; it has 
 sometimes been special ly used 
 to denote the minor premise 
 of a syllogism. 
 
 Reasoning, or discourse, 15. 
 
 Record, language as instru- 
 ment of, 245. 
 
 Reductio ad absurdum or ad 
 impombile, an indirect dem- 
 onstration founded upon the 
 impossibility of a contradic 
 tory sup jKisi lion. 
 
 Reduction of the syllogistic 
 figures, 135 ; of hypothetical 
 to categorical syllogisms, 153. 
 
 Relation {relatum, past parti- 
 ciple of refero, to bear back), 
 any connection in thought or 
 fact between two things. 
 
 Relative terms, 27. 
 
 Residual phenomena. 226. 
 
 Residues, method of, 225. 
 
 Rules of the syllogism, 113. 
 
 Scholastic Philosophy, a gen- 
 eral name for the systems of 
 philosophy taught during the 
 middle ages from the 9th to 
 the 16th century, flourishing 
 chiefly in the 13th and 14th 
 centuries. The subject was 
 chiefly the logic of Aristotle, 
 varied with theology, meta- 
 physics, grammar, or rhetoric. 
 
 Second Intention, see Inten- 
 tion. 
 
 Secundi adjao-iit'.s, of the 
 second adjacent, an expres- 
 sion in incorrect Latin, ap 
 plied to a grammatical sen- 
 tence or proposition contain- 
 ing only two parts, the sub 
 ject and verb, without a dis- 
 tinct copula. 
 
 Self-contradictory terms, 26. 
 
 Semilogical fallacies, 162. 
 
 Sentence, grammatical, 65. 
 
 Separable accident, 232. 
 
 Significates of a term are 
 things denoted or signified by 
 it. 
 
 Similars, substitution of, 282. 
 
 Simple, apprehension, 12 ; con- 
 version, 88, 266. 
 
 Singular, terms, 20 ; proposi- 
 tions, 69. 
 
 Sophism (aoipiafia, from ao(pia, 
 wisdom), a false argument ; 
 the name often implies that a 
 false argument is consciously 
 used for deception. 
 
 Sorites, 145. 
 
 Specialization of names, 60. 
 
 Species, in logic, 228; in 
 natural history, 231. 
 
 Spencer, Herbert, a contempo- 
 rary English thinker and 
 writer of great ability and 
 influence (1820); author of 
 many miscellaneous works, 
 but most celebrated as the 
 writer of the Synthetic Phil 
 osophy, an undertaking o\ 
 great magnitude not yet
 
 INDEX AND GLOSSARY. 
 
 329 
 
 (1888) completed. Spencer 
 has covered nearly the whole 
 range of speculative thought, 
 and his aim is to apply the 
 doctrine of evolution to every 
 department of knowledge. 
 He is a clear and instructive, 
 but sometimes a misleading, 
 writer, as any one is likely to 
 be who undertakes to culti- 
 vate so wide a field in the 
 service of a theory already 
 formed rather than derived 
 from a minute study of the 
 facts in the different depart- 
 ments of knowledge. 
 
 Subaltern, propositions, 82 ; 
 genera and species, 233. 
 
 Subalternans, subalternates, 
 82. 
 
 Subcontrary Propositions, 82. 
 
 Subject of a proposition, 66. 
 
 Subjective, that which belongs 
 to the thinking subject, the 
 ego, or mind engaged in 
 thought ; opposed to objective, 
 which see. 
 
 Subordinate propositions, 97. 
 
 Substance {sub, under ; stana 
 from stare, to stand), that 
 which underlies and bears 
 phenomena - or attributes ; 
 strictly speaking it is either 
 mind or matter, but it is 
 more commonly used in the 
 material sense. 
 
 Substitution of similars, see 
 mnUart. 
 
 Subsumption {nub, under; sumo, 
 to take or put), a name used 
 by Sir W. Hamilton for the 
 minor premise of a syllo- 
 gism, because it brings or 
 subsumes a special case under 
 the rule expressed in vhe 
 major premise or sumption. 
 
 Subsumption of a law is Mr. 
 Mill's expression for the third 
 mode of explaining a law by 
 showing it to be a particu- 
 lar case of a more general 
 law 
 
 Sufficient Reason, Principle or 
 Law of, 112. 
 
 Sui generis, 230. 
 
 Summum genus, 230. 
 
 Sumption (sumo, to take), Sir 
 W. Hamilton's name for the 
 major premise of a syllo- 
 gism. 
 
 Syllogism, 10, 113; inductive, 
 178. 
 
 Symbolical knowledge, 60. 
 
 Syncategorematic words, 18. 
 
 Synthesis, 200. 
 
 Synthetic syllogism, a syllo- 
 gism in which the conclu- 
 sion stands last ; see Analytit 
 syllogism. 
 
 System, (avarrjfia, from crvvi<7' 
 TTjut, to put together), a con. 
 nected body of knowledge. 
 
 Tacit premise, 143. 
 Tautologous propositions, 73. 
 Tendency, 213.
 
 330 
 
 INDEX AND GLOSSARY. 
 
 Terms, see chapter an, pp. 17, 
 62. 
 
 Tertii adjacentis, of the third 
 adjacent, an expression in in- 
 correct Latin, applied to a 
 grammatical sentence or prop- 
 osition in which the subject, 
 copula and predicate, are all 
 distinctly stated. 
 
 Theory {tttupla, contemplation), 
 knowledge of principles, as 
 opposed to practice ; ambigu- 
 ously used, see p. 210. 
 
 Thesis {fieai',, from ridjjfit, to 
 place), an assertion or propo- 
 sition which is put forth to be 
 proved or supported, by argu 
 ments. 
 
 Thoughts or things, the object 
 of logic, 11. 
 
 Totum divisum, a class or 
 notion which is divided into 
 parts by a difference. 
 
 Traduction, 179. 
 
 Transfer of meaning of terms, 
 35. 
 
 Tree of Porphyry, 232. 
 
 Trilemma, an argument resem- 
 bling a dilemma, but in which 
 there are three alternatives. 
 
 Truth, conformity of our 
 knowledge with the things 
 known. 
 
 Ultra-total distribution, 266. 
 Uniformity of nature, 185. 
 Universal propositions, 6? 
 
 70 ; affirmative, 68 ; negative 
 
 67. 
 Univocal terms, 31. 
 
 Variations, method of, 221. 
 Verb, 94 
 
 Watts, Isaac, an English 
 clergyman, hymn-writer and 
 theologian (1674-1748) ; author 
 of a useful practical work on 
 logic which was very popular 
 in its lime, but which is nowi 
 little known. 
 
 Weakened conclusion, 129. 
 
 Whately, Richard, Archbishop 
 of Dublin, an English eccle- 
 siastic and writer on logic, 
 political economy and rhetoric 
 (1787-1863); r. shrewd and 
 ingenious writer, but lacking 
 in profound erudition as a 
 logician. Whately's works 
 on logic and rhetoric have 
 been until recently very pop. 
 ular, especially in America 
 as text-books on these sub- 
 
 jects. 
 Worse relation (Hamilton) 
 
 270.
 
 
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